arXiv:0909.3092v1 [astro-ph.GA] 16 Sep 2009 Accepted to ApJ on 2009 Sep 15 Preprint typeset using L A T E X style emulateapj v. 08/22/09 MULTI-ELEMENT ABUNDANCE MEASUREMENTS FROM MEDIUM-RESOLUTION SPECTRA. I. THE SCULPTOR DWARF SPHEROIDAL GALAXY Evan N. Kirby, Puragra Guhathakurta, Michael Bolte University of California Observatories/Lick Observatory, Department of Astronomy & Astrophysics, University of California, Santa Cruz, CA 95064 Christopher Sneden McDonald Observatory, University of Texas, Austin, TX 78712 and Marla C. Geha Astronomy Department, Yale University, New Haven, CT 06520 Accepted to ApJ on 2009 Sep 15 ABSTRACT We present measurements of Fe, Mg, Si, Ca, and Ti abundances for 388 radial velocity member stars in the Sculptor dwarf spheroidal galaxy (dSph), a satellite of the Milky Way. This is the largest sample of individual α element (Mg, Si, Ca, Ti) abundance measurements in any single dSph. The measurements are made from Keck/DEIMOS medium-resolution spectra (6400–9000 ˚ A, R ∼ 6500). Based on comparisons to published high-resolution (R 20000) spectroscopic measurements, our measurements have uncertainties of σ[Fe/H] = 0.14 and σ[α/Fe] = 0.13. The Sculptor [Fe/H] distribution has a mean 〈[Fe/H]〉 = −1.58 and is asymmetric with a long, metal-poor tail, indicative of a history of extended star formation. Sculptor has a larger fraction of stars with [Fe/H] < −2 than the Milky Way halo. We have discoveredone star with [Fe/H] = −3.80 ±0.28, which is the most metal- poor star known anywhere except the Milky Way halo, but high-resolution spectroscopy is needed to measure this star’s detailed abundances. As has been previously reported based on high-resolution spectroscopy, [α/Fe] in Sculptor falls as [Fe/H] increases. The metal-rich stars ([Fe/H] ∼−1.5) have lower [α/Fe] than Galactic halo field stars of comparable metallicity. This indicates that star formation proceeded more gradually in Sculptor than in the Galactic halo. We also observe radial abundance gradients of −0.030 ± 0.003 dex per arcmin in [Fe/H] and +0.013 ± 0.003 dex per arcmin in [α/Fe] out to 11 arcmin (275 pc). Together, these measurements cast Sculptor and possibly other surviving dSphs as representative of the dwarf galaxies from which the metal-poor tail of the Galactic halo formed. Subject headings: galaxies: individual (Sculptor dwarf) — galaxies: dwarf — galaxies: abundances — Galaxy: evolution — Local Group 1. INTRODUCTION The dwarf spheroidal galaxy (dSph) companions of the Milky Way (MW) are excellent laboratories for investi- gating the chemical evolution and star formation histo- ries of dwarf galaxies. These galaxies have undergone at most a few star formation episodes (Holtzman et al. 2006) and are dynamically simple (Walker et al. 2007). The dSphs of the MW provide an opportunity to ex- amine closely the processes that establish the galaxy luminosity-metallicity relation (e.g., Salvadori & Ferrara 2009). The MW dSphs are also considered to be strong candi- dates of a population of dwarf galaxies that were tidally stripped by the young Galaxy and eventually incorpo- rated into the Galactic halo. This scenario has be- come central to our picture of how large galaxies form (Searle & Zinn 1978; Robertson et al. 2005). Impor- tant tests of this scenario are to compare the details of 1 Data herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA. The Observatory was made possible by the generous financial sup- port of the W. M. Keck Foundation. the metallicity distribution function of the collection of dSphs to that of the Galactic halo stars and to compare abundance ratio patterns seen in dSphs to those mea- sured for the halo (e.g., Venn et al. 2004). To date, each of these areas has been hampered by the small sample of dSph stars for which high-quality measurements of [Fe/H] and abundance ratios for other elements have been available. Lanfranchi & Matteucci (2004) compared their models of dSphs less massive than Sagittarius to six or fewer stars per galaxy. The usual approach for high-quality detailed abundance determina- tions is to use high-resolution spectroscopy (HRS, R> 20000) of individual stars. Because of the large distances to even the nearest dSphs, these are time-consuming ob- servations even using the largest telescopes. Our approach is to derive abundances from medium- resolution spectroscopy (MRS, R ∼ 6500) using the Deep Imaging Multi-Object Spectrometer (DEIMOS, Faber et al. 2003) on the Keck II telescope. As demon- strated by Kirby et al. (2008a,b), accurate measurements can be made for Fe and some α elements (Mg, Si, Ca, and Ti) with these individual stellar spectra. Shetrone et al. (2009) demonstrated similarly precise results using the
Transcript
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9Accepted to ApJ on 2009 Sep 15Preprint typeset using LATEX style emulateapj v 082209
MULTI-ELEMENT ABUNDANCE MEASUREMENTS FROM MEDIUM-RESOLUTION SPECTRAI THE SCULPTOR DWARF SPHEROIDAL GALAXY
Evan N Kirby Puragra Guhathakurta Michael BolteUniversity of California ObservatoriesLick Observatory Department of Astronomy amp Astrophysics
University of California Santa Cruz CA 95064
Christopher SnedenMcDonald Observatory University of Texas Austin TX 78712
and
Marla C GehaAstronomy Department Yale University New Haven CT 06520
Accepted to ApJ on 2009 Sep 15
ABSTRACT
We present measurements of Fe Mg Si Ca and Ti abundances for 388 radial velocity memberstars in the Sculptor dwarf spheroidal galaxy (dSph) a satellite of the Milky Way This is thelargest sample of individual α element (Mg Si Ca Ti) abundance measurements in any single dSphThe measurements are made from KeckDEIMOS medium-resolution spectra (6400ndash9000 A R sim6500) Based on comparisons to published high-resolution (R amp 20000) spectroscopic measurementsour measurements have uncertainties of σ[FeH] = 014 and σ[αFe] = 013 The Sculptor [FeH]distribution has a mean 〈[FeH]〉 = minus158 and is asymmetric with a long metal-poor tail indicativeof a history of extended star formation Sculptor has a larger fraction of stars with [FeH] lt minus2 thanthe Milky Way halo We have discovered one star with [FeH] = minus380plusmn028 which is the most metal-poor star known anywhere except the Milky Way halo but high-resolution spectroscopy is needed tomeasure this starrsquos detailed abundances As has been previously reported based on high-resolutionspectroscopy [αFe] in Sculptor falls as [FeH] increases The metal-rich stars ([FeH] sim minus15) havelower [αFe] than Galactic halo field stars of comparable metallicity This indicates that star formationproceeded more gradually in Sculptor than in the Galactic halo We also observe radial abundancegradients of minus0030 plusmn 0003 dex per arcmin in [FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]out to 11 arcmin (275 pc) Together these measurements cast Sculptor and possibly other survivingdSphs as representative of the dwarf galaxies from which the metal-poor tail of the Galactic haloformedSubject headings galaxies individual (Sculptor dwarf) mdash galaxies dwarf mdash galaxies abundances mdash
Galaxy evolution mdash Local Group
1 INTRODUCTION
The dwarf spheroidal galaxy (dSph) companions of theMilky Way (MW) are excellent laboratories for investi-gating the chemical evolution and star formation histo-ries of dwarf galaxies These galaxies have undergoneat most a few star formation episodes (Holtzman et al2006) and are dynamically simple (Walker et al 2007)The dSphs of the MW provide an opportunity to ex-amine closely the processes that establish the galaxyluminosity-metallicity relation (eg Salvadori amp Ferrara2009)
The MW dSphs are also considered to be strong candi-dates of a population of dwarf galaxies that were tidallystripped by the young Galaxy and eventually incorpo-rated into the Galactic halo This scenario has be-come central to our picture of how large galaxies form(Searle amp Zinn 1978 Robertson et al 2005) Impor-tant tests of this scenario are to compare the details of
1 Data herein were obtained at the W M Keck Observatorywhich is operated as a scientific partnership among the CaliforniaInstitute of Technology the University of California and NASAThe Observatory was made possible by the generous financial sup-port of the W M Keck Foundation
the metallicity distribution function of the collection ofdSphs to that of the Galactic halo stars and to compareabundance ratio patterns seen in dSphs to those mea-sured for the halo (eg Venn et al 2004)
To date each of these areas has been hampered bythe small sample of dSph stars for which high-qualitymeasurements of [FeH] and abundance ratios for otherelements have been available Lanfranchi amp Matteucci(2004) compared their models of dSphs less massive thanSagittarius to six or fewer stars per galaxy The usualapproach for high-quality detailed abundance determina-tions is to use high-resolution spectroscopy (HRS R gt20000) of individual stars Because of the large distancesto even the nearest dSphs these are time-consuming ob-servations even using the largest telescopes
Our approach is to derive abundances from medium-resolution spectroscopy (MRS R sim 6500) using theDeep Imaging Multi-Object Spectrometer (DEIMOSFaber et al 2003) on the Keck II telescope As demon-strated by Kirby et al (2008ab) accurate measurementscan be made for Fe and some α elements (Mg Si Ca andTi) with these individual stellar spectra Shetrone et al(2009) demonstrated similarly precise results using the
2 Kirby et al
Keck I LRIS spectrometer on a sample of individual starsin the Leo II dSph In a typical dSph the DEIMOS fieldof view allows between 80 and 150 red giant stars tobe targeted per multi-object mask Samples of severalhundred giants can be observed in a given dSph TheDwarf Abundances and Radial Velocities team (DARTTolstoy et al 2004 hereafter T04) has been collecting acombination of MRS and HRS in dSphs to exploit theadvantages of both techniques
This paper is the first in a series that explores themulti-element abundances of stellar systems measuredwith MRS The particular focus of this series is to char-acterize the distributions of [FeH] and [αFe] in MWdSphs These measurements will provide insight into therole of dSphs in building the Galactic stellar halo (ieSearle amp Zinn 1978 White amp Rees 1978)
Our first target is the Sculptor dSph (α = 1h00mδ = minus3343prime MV = minus111 Mateo 1998) Sculptor hasbeen a favored HRS and MRS target for the past tenyears Of all the dSphs it appears most often in expla-nations of dSph chemical evolution and galaxy formation(eg T04 Shetrone et al 2003 Geisler et al 2007) T04discovered that Sculptor is actually ldquotwo galaxiesrdquo in onewith two stellar populations that are kinematically andcompositionally distinct Battaglia et al (2006) latershowed that Fornax also displays multiple stellar pop-ulations with different kinematics spatial extents andmetallicities But Sculptor is also unique in that it isthe only MW dSph known to rotate (Battaglia et al2008a) Recently Walker et al (2009) published radialvelocities for 1365 Sculptor members and Venn amp Hill(2005 2008) presented high-resolution abundance mea-surements of Mg Ca Ti and Fe for 91 stars in SculptorThey also measured Y Ba and Eu for some of thosestars
This paper consists of six sections and an ap-pendix Section 2 introduces the spectroscopic tar-get selection and observations and Sec 3 explainshow the spectra are prepared for abundance mea-surements Section 4 describes the technique to ex-tract abundances which builds on the method de-scribed by Kirby Guhathakurta amp Sneden (2008a here-after KGS08) In Sec 5 we present the metallicity dis-tribution and multi-element abundance trends of Sculp-tor In Sec 6 we summarize our findings in the con-text of dSph chemical evolution and the formation of theGalaxy Finally we devote the appendix to quantifyingthe uncertainties in our MRS measurements includingcomparisons to independent HRS of the same stars
2 OBSERVATIONS
21 Target Selection
We selected targets from the Sculptor photometric cat-alog of Westfall et al (2006) The catalog includes pho-tometry in three filters M and T2 in the Washing-ton system and the intermediate-width DDO51 filter(henceforth called D) centered at 5150 A This bandprobes the flux from a spectral region susceptible to ab-sorption by the surface gravity-sensitive Mg I and MgHlines Majewski et al (2000) and Westfall et al (2006)outlined the procedure for distinguishing between distantred giant stars and foreground Galactic dwarf stars usingthese three filters We followed the same procedure to se-
10 5 0 -5 -10∆α (arcmin)
-10
-5
0
5
10
15
∆δ (
arcm
in)
-300 -200 -100 0 100 200 300
∆x (pc)
-200
0
200
400
∆y (
pc)
scl1scl1
scl2scl2
scl3scl3
scl5scl5scl6
scl6N
W
singly targeted starsdoubly targeted starsuntargeted starsstars with previous high-resolution abundances
singly targeted starsdoubly targeted starsuntargeted starsstars with previous high-resolution abundances
Fig 1mdash DEIMOS slitmask footprints laid over a map of sourcesfrom the photometric catalog Targets selected for spectroscopyare shown in red Targets observed in more than one mask areshown in green Blue diamonds enclose stars with previous HRSabundance measurements The left and bottom axis scales showthe angular displacement in arcmin from the center of the galaxy(α0 = 1h00m09s δ0 = minus3342prime30primeprime Mateo 1998) and the rightand top axis scales show the physical displacement for an assumeddistance of 859 kpc (Pietrzynski et al 2008)
lect a sample of red giant candidates from the SculptorMT2D catalog
Nine stars listed in Table 1 have previously pub-lished HRS abundance measurements (Shetrone et al2003 Geisler et al 2005) These stars were observedand provide the basis for demonstrating the accuracyof the MRS abundance measurements described in theappendix
22 Slitmask Design
We designed the DEIMOS slitmasks with the IRAFsoftware module dsimulator2 Each slitmask subtendedapproximately 16prime times 4prime In order to adequately subtractnight sky emission lines we required a minimum slitlength of 4primeprime The minimum space between slits was0primeprime35 When these constraints forced the selection ofone among multiple possible red giant candidates thebrightest object was selected The slits were designedto be at the approximate parallactic angle at the antici-pated time of observation (minus25) This choice minimizedthe small light losses due to differential atmospheric re-fraction This configuration was especially important forSculptor which was visible from Keck Observatory onlyat a low elevation The slitmasksrsquo sky position angle (PA)was minus35 The 10 offset between the slit PA and theslitmask PA tilted the night sky emission lines relative tothe CCD pixel grid to increase the subpixel wavelengthsampling and improve sky subtraction
TABLE 1Targets with Previous High-Resolution Abundances
name reference RA Dec M T2
H482 Shetrone et al (2003) 00h59m58s2 minus3341prime08primeprime 17967 plusmn 0030 16324 plusmn 0020H459 Shetrone et al (2003) 01h00m12s5 minus3343prime01primeprime 18465 plusmn 0032 16924 plusmn 0031H479 Shetrone et al (2003) 01h00m12s7 minus3341prime15primeprime 17562 plusmn 0023 15860 plusmn 0030H400 Shetrone et al (2003) 01h00m17s0 minus3345prime13primeprime 18413 plusmn 0030 17140 plusmn 0027H461 Shetrone et al (2003) 01h00m18s2 minus3342prime12primeprime 17806 plusmn 0028 16166 plusmn 00271446 Geisler et al (2005) 00h59m46s4 minus3341prime23primeprime 17618 plusmn 0023 15695 plusmn 0022195 Geisler et al (2005) 00h59m55s6 minus3346prime39primeprime 17515 plusmn 0022 15845 plusmn 0018982 Geisler et al (2005) 01h00m16s2 minus3342prime37primeprime 17433 plusmn 0025 15552 plusmn 0028770 Geisler et al (2005) 01h00m23s8 minus3342prime17primeprime 17623 plusmn 0025 15857 plusmn 0026
TABLE 2DEIMOS Observations
Slitmask Targets UT Date Exposures Seeing
scl1 86 2008 Aug 3 3 times 1200 s 0primeprime8scl2 106 2008 Aug 3 2 times 900 s 0primeprime8scl3 87 2008 Aug 4 1 times 462 s 0primeprime9
2008 Aug 31 1 times 1000 s 0primeprime82008 Aug 31 1 times 834 s 0primeprime8
scl5 95 2008 Sep 1 3 times 720 s 0primeprime8scl6 91 2008 Sep 1 3 times 720 s 1primeprime2
Note mdash The scl4 slitmask was not observed
Figure 1 shows the coordinates of all the objects inthe catalog regardless of their probability of membershipin Sculptor Five DEIMOS slitmask footprints enclosethe spectroscopic targets scl1 scl2 scl3 scl5 and scl6(see Tab 2) The scl5 slitmask included 24 targets alsoincluded on other masks These duplicate observationsprovide estimates of uncertainty in radial velocity andabundance measurements (Sec 33 and Sec A1) Thespectral coverage of each slit is not the same The min-imum and maximum wavelengths of spectra of targetsnear the long straight edge of the DEIMOS footprint canbe up to 400 A lower than for targets near the irregularlyshaped edge of the footprint (upper left and lower rightof the slitmask footprints in Fig 1 respectively) Fur-thermore spectra of targets near either extreme of thelong axis of the slitmask suffered from vignetting whichreduced the spectral range It is important to keep thesedifferences of spectral range in mind when interpretingthe differences of measurements derived from duplicateobservations
Figure 2 shows the color-magnitude diagram (CMD)of the targets within the right ascension and declinationranges of the axes in Fig 1 The MT2D membershipcriteria caused the selected red giants to form a tight se-quence This selection may have imposed a metallicitybias on the spectroscopic sample Although only a tinyfraction of stars lay outside the main locus of the redgiant branch some may have been spectroscopically un-targeted members of Sculptor For example if Sculptorcontained any old stars with [FeH] amp minus05 they wouldhave been too red to be included in the spectroscopicsample Any such metallicity bias should have excludedat most a few stars
23 Spectroscopic Configuration and Exposures
00 05 10 15 20 25 30(M minus T2)0
20
19
18
17
16
15
(T2)
0 =
(IC) 0
00 05 10 15 20
(VC minus IC)0
Fig 2mdash Color-magnitude diagram in the Washington andCousins systems for the sources within the right ascension anddeclination ranges shown in Fig 1 The symbols have the samemeanings as in Fig 1 The transformation from the Washingtonsystem (M and T2) to the Cousins system (VC and IC) is IC = T2
and VC minus IC = 0800(M minus T2) minus 0006 (Majewski et al 2000)
Our observing strategy was nearly identical to that ofSimon amp Geha (2007) and Kirby et al (2008a) In sum-mary we used with the 1200 lines mmminus1 grating at acentral wavelength of 7800 A The slit widths were 0primeprime7yielding a spectral resolution of sim 13 A FWHM (resolv-ing power R sim 6500 at 8500 A) The OG550 filter blockeddiffraction orders higher than m = 1 The spectral rangewas about 6400ndash9000 A with variation depending on theslitrsquos location along the dispersion axis Exposures ofKr Ne Ar and Xe arc lamps provided wavelength cal-ibration and exposures of a quartz lamp provided flatfielding Table 2 lists the number of targets for each slit-mask the dates of observations the exposure times andthe approximate seeing
Fig 3mdash Examples of small regions of DEIMOS spectra of fourdifferent stars The continuum in each spectrum has been normal-ized to unity The IC magnitude measured effective temperatureand measured [FeH] is given for each star The top two panelsshow two stars with very different [FeH] and the bottom two pan-els show two stars with nearly the same temperature and [FeH]but different SNR The colors show the regions used to measureeach of the Fe Mg Si Ca and Ti abundances (see Fig 5)
We reduced the raw frames using version 114 ofthe DEIMOS data reduction pipeline developed by theDEEP Galaxy Redshift Survey3 Guhathakurta et al(2006) give the details of the data reduction We alsomade use of the optimizations to the code described bySimon amp Geha (2007 Sec 22 of their article) Thesemodifications provided better extraction of unresolvedstellar sources
In summary the pipeline traced the edges of slits in theflat field to determine the CCD location of each slit Thewavelength solution was given by a polynomial fit to theCCD pixel locations of arc lamp lines Each exposureof stellar targets was rectified and then sky-subtractedbased on a B-spline model of the night sky emission linesNext the exposures were combined with cosmic ray rejec-tion into one two-dimensional spectrum for each slit Fi-nally the one-dimensional stellar spectrum was extractedfrom a small spatial window encompassing the light of thestar in the two-dimensional spectrum The product ofthe pipeline was a wavelength-calibrated sky-subtractedcosmic ray-cleaned one-dimensional spectrum for eachtarget
Some of the spectra suffered from unrecoverable de-fects such as a failure to find an acceptable polynomialfit to the wavelength solution There were 53 such spec-tra An additional 2 spectra had such poor signal-to-noise ratios (SNR) that abundance measurements wereimpossible leaving 410 useful spectra comprising 393unique targets and 17 duplicate measurements
Figure 3 shows four example spectra at a variety ofIC magnitudes effective temperatures and [FeH] The
3 httpastroberkeleyedu$^sim$cooperdeepspec2d
two upper panels show stars in the top 10 of the SNRdistribution The two lower panels show stars from themiddle and bottom 10 of the distribution
The one-dimensional DEIMOS spectra needed to beprepared for abundance measurements The preparationincluded velocity measurement removal of telluric ab-sorption and continuum division KGS08 (their Sec 3)described these preparations in detail We followed thesame process with some notable exceptions describedbelow
32 Telluric Absorption Correction
We removed the absorption introduced into the stellarspectra by the earthrsquos atmosphere in the same manneras KGS08 division by a hot star template spectrumHowever the high airmass of the Sculptor observationscaused much stronger absorption than KGS08 observedin globular cluster (GC) spectra Even after scaling thehot star template spectrum by the airmass large resid-uals in the Sculptor stellar spectra remained Conse-quently we masked spectral regions of heavy telluric ab-sorption before measuring abundances These regions are6864ndash6932 A 7162ndash7320 A 7591ndash7703 A 8128ndash8351 Aand 8938ndash10000 A (see Fig 5)
33 Radial Velocities and Spectroscopic MembershipDetermination
Our primary interest in this paper is chemical abun-dances and we measured radial velocities only to deter-mine membership and to shift the spectra into the restframe
Following KGS08 we measured stellar radial velocitiesby cross-correlation with a template spectrum HoweverKGS08 cross-correlated the observed spectra against syn-thetic spectra whereas we cross-correlated the observedspectra against high SNR template spectra of stars ob-served with DEIMOS Templates observed with the sameinstrument should provide more accurate radial velocitymeasurements than synthetic templates Simon amp Geha(2007) provided their template spectra to us For therest of the analysis the spectra are shifted to the restframe
Although the MT2D selection eliminated almost all ofthe foreground MW contaminants from the spectroscopicsample we checked the membership of each target by ra-dial velocity selection Figure 4 shows the distribution ofradial velocities in this spectroscopic data set along withthe best-fit Gaussian We consider the radial velocitylimits of Sculptor membership to be 848 km sminus1 lt vr lt1383 km sminus1 We chose these limits because beyondthem the expected number of Sculptor members per2 km sminus1 bin (the approximate maximum velocity res-olution of DEIMOS Simon amp Geha 2007) is fewer than05 This selection eliminated just 5 out of 393 uniquetargets
As a check on our procedure we compared some de-rived quantities from the velocity distribution to previ-ous measurements The mean velocity of our sampleis 〈vhelio〉 = 1116 plusmn 05 km sminus1 with a dispersion ofσv = 80 plusmn 07 km sminus1 The velocity dispersion is theper-measurement velocity error subtracted in quadraturefrom the 1σ width of the velocity distribution The per-measurement error is 39 km sminus1 which is the standard
Abundances in the Sculptor dSph 5
80 100 120 140vhelio (km sminus1)
0
10
20
30
40
N
langvhelioranglangvheliorang = 1116 plusmn 05 km sminus1
σv σv = 80 plusmn 07 km sminus1
Fig 4mdash Distribution of measured radial velocities for targetsin the Sculptor field along with the best-fit Gaussian The topleft label gives the mean and standard deviation of this Gaussianfit The five stars outside of the dashed lines are not consideredSculptor members The velocity range of this plot includes all starsfor which a velocity measurement was possible
deviations of the differences in measured velocities forthe 17 duplicate spectra In comparison Westfall et al(2006) found 〈vhelio〉 = 1104 plusmn 08 km sminus1 (difference of+12σ) and σv = 88plusmn 06 km sminus1 (difference of minus09σ)The comparison of the velocity dispersions depends onthe assumed binary fraction (Queloz et al 1995) andmdashgiven the presence of multiple kinematically and spa-tially distinct populations in Sculptor (T04)mdashthe regionof spectroscopic selection Furthermore Walker et al(2007 2009) reported velocity dispersion gradients andBattaglia et al (2008a) reported mean velocity gradientsalong the major axis indicating rotation We choose notto address the kinematic complexity of this system inthis paper
34 Continuum Determination
In the abundance analysis described in Sec 4 it isnecessary to normalize each stellar spectrum by dividingby the slowly varying stellar continuum KGS08 deter-mined the continuum by smoothing the regions of thestellar spectrum free from strong absorption lines In-stead of smoothing we fit a B-spline with a breakpointspacing of 150 A to the same ldquocontinuum regionsrdquo de-fined by KGS08 Each pixel was weighted by its inversevariance in the fit Furthermore the fit was performediteratively such that pixels that deviated from the fit bymore than 5σ were removed from the next iteration ofthe fit
The spline fit results in a smoother continuum determi-nation than smoothing Whereas the smoothed contin-uum value may be influenced heavily by one or a few pix-els within a relatively small smoothing kernel the splinefit is a global fit It is more likely to be representative ofthe true stellar continuum than a smoothed spectrum
Shetrone et al (2009) pointed out the importance ofdetermining the continuum accurately when measur-ing weak lines in medium-resolution spectra They re-fined their continuum determinations by iteratively fit-
TABLE 3New Grid of ATLAS9 Model Atmospheres
Parameter Minimum Value Maximum Value Step
Teff (K) 3500 5600 1005600 8000 200
log g (cm sminus2) 00 (Teff lt 7000 K) 50 0505 (Teff ge 7000 K) 50 05
[AH] minus40 00 05[αFe] minus08 +12 01
ting a high-order spline to the quotient of the observedspectrum and the best-fitting synthetic spectrum Weadopted this procedure as well As part of the iterativeprocess described in Sec 47 we fit a B-spline with abreakpoint spacing of 50 A to the observed spectrum di-vided by the best-fitting synthetic spectrum We dividedthe observed spectrum by this spline before the next it-eration of abundance measurement
4 ABUNDANCE MEASUREMENTS
The following section details some improvements onthe abundance measurement techniques of KGS08 As-pects of the technique not mentioned here were un-changed from the technique of KGS08 In summaryeach observed spectrum was compared to a large gridof synthetic spectra The atmospheric abundances wereadopted from the synthetic spectrum with the lowest χ2
A major improvement was our measurement of fourindividual elemental abundances in addition to Fe MgSi Ca and Ti We chose these elements because they areimportant in characterizing the star formation history ofa stellar population and because a significant numberof lines represent each of them in the DEIMOS spectralrange
41 Model Atmospheres
Like KGS08 we built synthetic spectra based on AT-LAS9 model atmospheres (Kurucz 1993) with no con-vective overshooting (Castelli et al 1997) KGS08 choseto allow the atmospheres to have [αFe] = +04 or[αFe] = 00 This choice allowed them to use the largegrid of ATLAS9 model atmospheres computed with newopacity distribution functions (Castelli amp Kurucz 2004)However we found that best-fitting model spectra com-puted by KGS08 tended to cluster around [αFe] = +02due to the discontinuity in χ2 caused by the abruptswitch between alpha-enhanced and solar-scaled models
To avoid this discontinuity we recomputed ATLAS9model atmospheres on the grid summarized in Table 3The new grid required recomputing new opacity distri-bution functions (ODFs) for which we used the DF-SYNTHE code (Castelli 2005) Unlike the grid ofCastelli amp Kurucz (2004) we adopted the solar compo-sition of Anders amp Grevesse (1989) except for Fe forwhich we followed Sneden et al (1992 see the note in Ta-ble 4) One opacity distribution function was computedfor each of the 189 combinations of [AH] and [αFe]specified in Table 3 The abundances of all the elementsexcept H and He were augmented by [AH] Addition-ally the abundances of O Ne Mg Si Ar Ca and Tiwere augmented by [αFe] These ODFs were used tocompute one ATLAS9 model atmosphere for each grid
6 Kirby et al
point in Table 3 and for two values of microturbulentvelocity for a total of 139104 model atmospheres
42 Microturbulent Velocity
In order to reduce the number of parameters requiredto determine a stellar abundance KGS08 assumed thatthe microturbulent velocity (ξ) of the stellar atmospherewas tied to the surface gravity (log g) They chose to fita line to the spectroscopically measured ξ and log g ofthe giant stars in Fulbrightrsquos (2000) sample
ξ (km sminus1) = 270 minus 051 log g (1)
We also adopted a relation between ξ and log g but were-determined this relation from the GC red giant sampleof KGS08 combined with Kirbyrsquos (2009) compilation ofhigh-resolution spectroscopic measurements from the lit-erature (Frebel et al 2009 Geisler et al 2005 Johnson2002 Lai et al 2007 Shetrone et al 2001 2003 and ref-erences from KGS08) The best-fit line between the spec-troscopically measured ξ and log g is
corresponding roughly to a 00ndash05 km sminus1 decrease inξ depending on log g In the generation of the grid ofsynthetic stellar spectra described in Sec 44 ξ was nota free parameter but was fixed to log g via Eq 2
In general a decrease in ξ increases the measurementof [FeH] Therefore this change tended to increase thederived values of [FeH] A typical change in [FeH] was +005 dex This change would be more severe in anHRS analysis based on equivalent widths (EWs) In ourχ2 minimization the abundance measurement was mostsensitive to lines with large d(EW)d[FeH] Such linesare the weak unsaturated transitions whose strengthdoes not depend on ξ The DEIMOS spectra containenough of these weak lines that ξ did not play a largerole in the abundance determination
43 Line List
We compared the Fe I oscillator strengths (log gf) inthe KGS08 line list to values measured in the labora-tory (Fuhr amp Wiese 2006) Most of the KGS08 oscilla-tor strengths were stronger than the laboratory measure-ments The average offset was 013 dex Because KGS08calibrated their line list to the solar spectrum we in-terpreted this offset as a systematic error in the solarmodel atmosphere solar spectral synthesis andor solarcomposition Accepting the laboratory-measured valuesas more accurate than the solar calibration we replacedFe I oscillator strengths with Fuhr amp Wiese where avail-able and we subtracted 013 dex from log gf for all otherFe I transitions in the KGS08 line list All other data re-mained unchanged
Decreasing the oscillator strengths requires a larger[FeH] to match the observed spectrum The amount ofchange in [FeH] depends on the atmospheric parametersas well as the saturation of the measured Fe lines Fromcomparison of results with the old and new line lists weestimate a typical change in [FeH] to be sim +01 dex
44 Generation of Synthetic Spectra
TABLE 4Adopted Solar Composition
Element 12 + log ǫ Element 12 + log ǫ
Mg 758 Ti 499Ca 636 Fe 752Si 755
Note mdash This composition is adopted fromAnders amp Grevesse (1989) except for Fe Forjustification of the adopted Fe solar abun-dance see Sneden et al (1992) The abun-dance of an element X is defined as its numberdensity relative to hydrogen 12 + log ǫX =12 + log(nX) minus log(nH)
The spectra were synthesized as described in KGS08Specifically the current version of the local thermody-namic equilibrium (LTE) spectrum synthesis softwareMOOG (Sneden 1973) generated one spectrum for eachpoint on the grid The spectral grid was more finelyspaced in [FeH] than the model atmosphere grid Thespacing is 01 dex for each of [FeH] and [αFe] yieldinga total of 316848 synthetic spectra
The solar composition used in the generation of thesynthetic spectra was identical to the solar compositionused in the computation of the model atmospheres Ta-ble 4 lists the adopted solar abundances for the five el-ements for which we measure abundances in Sculptorstars
45 Effective Temperatures and Surface Gravities
Different spectroscopic studies of chemical abundancesrely on different sources of information for determin-ing the effective temperature (Teff) and surface grav-ity (log g) of the stellar atmosphere KGS08 con-sulted Yonsei-Yale model isochrones (Demarque et al2004) to determine the temperature and gravity thatcorrespond to a dereddened color and an extinction-corrected absolute magnitude They also consideredVictoria-Regina (VandenBerg et al 2006) and Padova(Girardi et al 2002) model isochrones as well as an em-pirical color-temperature relation (Ramırez amp Melendez2005)
The Fe lines accessible in DEIMOS spectra span a largerange of excitation potential Together these differentlines provide a constraint on Teff KGS08 (their Sec 51)showed thatmdashwithout any photometric informationmdashthe synthesis analysis of medium-resolution spectra ofGC stars yielded values of Teff very close to values previ-ously measured from HRS Therefore we chose to mea-sure Teff from photometry and spectroscopy simultane-ously
To begin we converted extinction-corrected(Schlegel et al 1998) Washington M and T2 magnitudesto Cousins VC and IC magnitudes (Majewski et al2000) With these magnitudes we computed Teff fromthe Yonsei-Yale Victoria-Regina and Padova modelisochrones as well as the Ramırez amp Melendez (2005)empirical color-based Teff For each measurement we es-timated the effect of photometric error by measuring thestandard deviation of Teff determined from 1000 MonteCarlo realizations of VC and IC In each realization VC
and IC were chosen from a normal distribution with amean of the measured extinction-corrected magnitude
Abundances in the Sculptor dSph 7
and a standard deviation of the photometric error Wecall this error δTeffi where i represents each of the fourphotometric methods of determining Teff In order toarrive at a single photometric Teff we averaged the fourTeffi together with appropriate error weighting We alsoestimated the random and systematic components oferror In summary
Teff =
sum
i TeffiδTminus2effi
sum
i δTminus2effi
(3)
δrandTeff =
sum
i δTminus1effi
sum
i δTminus2effi
(4)
δsysTeff =
radic
radic
radic
radic
radic
sum
i δTminus2effi
sum
i δTminus2effi
(
Teffi minus Teff
)2
1 minus(
sum
i δTminus2effi
)2sum
i δTminus4effi
(5)
δtotalTeff =radic
(δrandTeff)2 + (δsysTeff)2 (6)
For the stars in this data set the median randomsystematic and total errors on Teff were 98 K 58 Kand 117 K respectively The somewhat large errors onthe photometric temperatures indicated that the spec-tra may help constrain Teff Therefore Eq 3 does notshow the final temperature used in the abundance deter-mination Section 47 describes the iterative process fordetermining Teff and elemental abundances from spec-troscopy
We followed a similar procedure for determining log gphotometrically except that we used only the threemodel isochrones and not any empirical calibrationThe error on the true distance modulus (1967 plusmn 012Pietrzynski et al 2008) was included in the Monte Carlodetermination of the error on log g The median ran-dom systematic and total errors on log g were 006 001and 006 These errors are very small and the medium-resolution red spectra have little power to help constrainlog g because there are so few ionized lines visible There-fore we assumed the photometric value of log g for theabundance analysis
46 Wavelength Masks
The procedure described in the next section consistedof separately measuring the abundances of five elementsMg Si Ca Ti and Fe The procedure relied on findingthe synthetic spectrum that best matched an observedspectrum In order to make this matching most sensitiveto a particular element we masked all spectral regionsthat were not significantly affected by abundance changesof that element
To make the wavelength masks we began with a basespectrum that represented the solar composition in whichthe abundances of all the metals were scaled down by15 dex ([AH] = minus15) The temperature and gravityof the synthetic star were Teff = 4000 K and log g = 10Then we created two pairs of spectra for each of thefive elements In one spectrum the abundance of theelement was enhanced by 03 dex and in the other de-pleted by 03 dex Spectral regions where the flux differ-ence between these two spectra exceeds 05 were usedin the abundance determination of that element This
Fig 5mdash A coaddition of all Sculptor stars with the continuumnormalized to unity The high SNR provided by the coadditionmakes stellar absorption lines readily apparent The colored re-gions show the wavelength masks used in the determination of theabundance of each element Regions susceptible to telluric absorp-tion are labeled with blue text Because large residuals from thetelluric absorption correction remain we eliminate these regionsfrom the abundance analysis Some stellar features excluded fromthe abundances measurement are also labeled
small threshold assured that weak lines which experi-ence large fractional changes in EW as [FeH] changeswere included in the analysis We repeated this proce-dure for spectra with Teff = 5000 K 6000 K 7000 K and8000 K Additional spectral regions that passed the 05flux difference criterion were also included in the abun-dance determination of that element All other wave-lengths were masked
The result was one wavelength mask for each of MgSi Ca Ti and Fe shown in Fig 5 We also createdone ldquoαrdquo mask as the intersection of the Mg Si Ca andTi masks The α element regions do not overlap witheach other but the α element regions do overlap withthe Fe regions The most severe case is the Ca maskwhere sim 35 of the pixels are shared with the Fe maskHowever the overlap did not introduce interdependencein the abundance measurements The α element abun-dances were held fixed while [FeH] was measured andthe Fe abundance was held fixed while [αFe] was mea-sured The measurements of [FeH] and [αFe] were per-formed iteratively (see the next subsection) We testedthe independence of the measurements by removing alloverlapping pixels from consideration Abundance mea-surements changed on average by only 001 dex
47 Measuring Atmospheric Parameters and ElementalAbundances
A Levenberg-Marquardt algorithm (the IDL routineMPFIT written by Markwardt 2009) found the best-fitting synthetic spectrum in ten iterative steps In eachstep the χ2 was computed between an observed spec-trum and a synthetic spectrum degraded to match theresolution of the observed spectrum First we interpo-
8 Kirby et al
lated the synthetic spectrum onto the same wavelengtharray as the observed spectrum Then we smoothedthe synthetic spectrum through a Gaussian filter whosewidth was the observed spectrumrsquos measured resolutionas a function of wavelength
1 Teff and [FeH] first pass An observed spectrumwas compared to a synthetic spectrum with Teff
and log g determined as described in Sec 45 and[FeH] determined from Yonsei-Yale isochronesFor this iteration [αFe] was fixed at 00 (solar)and only spectral regions most susceptible to Fe ab-sorption (Sec 46) were considered The two quan-tities Teff and [FeH] were varied and the algo-rithm found the best-fitting synthetic spectrum byminimizing χ2 We sampled the parameter spacebetween grid points by linearly interpolating thesynthetic spectra at the neighboring grid pointsTeff was also loosely constrained by photometry Asthe spectrum caused Teff to stray from the photo-metric values χ2 increased and it increased moresharply for smaller photometric errors (as calcu-lated in Eq 6) Therefore both photometry andspectroscopy determined Teff Photometry alonedetermined log g
2 [αFe] first pass For this iteration Teff log g and[FeH] were fixed Only [αFe] was allowed to varyIn the model stellar atmosphere the abundances ofthe α elements with respect to Fe varied togetherOnly the spectral regions susceptible to absorptionby Mg Si Ca or Ti were considered
3 Continuum refinement The continuum-dividedobserved spectrum was divided by the syntheticspectrum with the parameters determined in steps1 and 2 The result approximated a flat noise spec-trum To better determine the continuum we fita B-spline with a breakpoint spacing of 50 A tothe residual spectrum We divided the observedspectrum by the spline fit
4 [FeH] second pass We repeated step 1 with therevised spectrum but Teff was held fixed at thepreviously determined value
5 [MgFe] We repeated step 2 However only Mgspectral lines were considered in the abundancemeasurement
6 [SiFe] We repeated step 5 for Si instead of Mg
7 [CaFe] We repeated step 5 for Ca instead of Mg
8 [TiFe] We repeated step 5 for Ti instead of Mg
9 [αFe] second pass We repeated step 2 for allof the α elements instead of just Mg This stepwas simply a different way to average the α el-ement abundances than combining the individualmeasurements of [MgFe] [SiFe] [CaFe] and[TiFe]
10 [FeH] third pass The value of [αFe] affected themeasurement of [FeH] because [αFe] can affect
the structure of the stellar atmosphere Specif-ically the greater availability of electron donorswith an increased [αFe] ratio allows for a higherdensity of Hminus ions The subsequent increase in con-tinuous opacity decreases the strength of Fe andother non-α element lines With [αFe] fixed atthe value determined in step 9 we re-measured[FeH] Typically [FeH] changed from the valuedetermined in step 1 by much less than 01 dex
48 Correction to [FeH]
In comparing our MRS measurements of [FeH] to HRSmeasurements of the same stars (see the appendix) wenoticed that our measurements of metal-poor stars wereconsistently sim 015 dex lower The same pattern is alsovisible in the Kirby et al (2008a) GC measurements (seetheir Figs 6 7 10 and 11)
We have thoroughly examined possible sources of thisdifference of scale The changes to the microturbulentvelocity relation (Sec 42) and the line list (Sec 43)were intended to yield a more accurate and standardizedestimation of [FeH] but the offset still remained Re-stricting the analysis to narrow spectral regions did notreveal any systematic trend of [FeH] with wavelength
A possible explanation for this offset is overionization(Thevenin amp Idiart 1999) Ultraviolet radiation in stellaratmospheres can ionize Fe more than would be expectedin LTE Therefore the abundance of Fe I would seem tobe lower than the abundance of Fe II in an LTE analysisFe II does not suffer from this effect However the effectis smaller at higher [FeH] and we do not observe a trendwith metallicity for the offset of our values relative toHRS studies
In order to standardize our measurements with previ-ous HRS studies we added 015 dex to all of our mea-surements of [FeH] This offset and the microturbu-lent velocity-surface gravity relation are the only ways inwhich previous HRS studies inform our measurementsFurthermore this offset is not intended to change thestandardization of our abundances All of the abundancein this article including those from other studies aregiven relative to the solar abundances quoted in Table 4
49 Error Estimation
We repeated the error estimation procedure describedby KGS08 (their Sec 6) by repeating their abundanceanalysis on GC stars with the above modifications Weno longer found a convincing trend of δ[FeH] with[FeH] Instead we estimate the total error on [FeH] byadding a systematic error in quadrature with the SNR-dependent uncertainty of the synthetic spectral fit Themagnitude of δsys[FeH] = 0136 was the value requiredto force HRS and MRS [FeH] estimates of the same GCstars to agree at the 1σ level We also estimated sys-tematic errors for each of [MgFe] [SiFe] [CaFe] and
Abundances in the Sculptor dSph 9
minus4 minus3 minus2 minus1 0[FeH]
0
10
20
30
40
50N
([F
eH
])
0
100
200
300
400
500
dN
d[F
eH
]
SculptorSimple ModelInfall Model
Fig 6mdash The metallicity distribution in Sculptor The red curveis the maximum likelihood fit to a galactic chemical evolutionmodel with pre-enrichment (Eq 7) and the green curve is the max-imum likelihood fit to a model of star formation in the presence ofinfalling zero-metallicity gas (Eq 11) The long metal-poor tailis typical for systems with non-instantaneous star formation
[TiFe] in the same manner as for [FeH] These are listedin Table 5
5 RESULTS
In this section we discuss the interpretation of theabundance measurements in Sculptor all of which arepresented in Table 6 on the last page of this manuscript
51 Metallicity Distribution
The metallicity distribution function (MDF) of a dwarfgalaxy can reveal much about its star formation his-tory In chemical evolution models of dwarf galax-ies (eg Lanfranchi amp Matteucci 2004 Marcolini et al2006 2008) the duration of star formation affects theshape of the MDF The MDF also has implications forthe formation of the MW If the MW halo was built fromdSphs (Searle amp Zinn 1978 White amp Rees 1978) then itis important to find dSph counterparts to halo field starsat all metallicities as pointed out by Helmi et al (2006hereafter H06)
Figure 6 shows the MDF of Sculptor The shape of theMDF is highly asymmetric with a long metal-poor tail(as predicted by Salvadori amp Ferrara 2009) The inverse-variance weighted mean is 〈[FeH]〉 = minus158 with a stan-dard deviation of 041 The median is minus158 with a me-dian absolute deviation of 033 and an interquartile rangeof 067
The MDF boasts an exceptionally metal-poor starS1020549 The metallicity is [FeH] = minus380 plusmn 028Figure 7 shows how weak the Fe absorption lines are inthis star Frebel Kirby amp Simon (in preparation) haveconfirmed this extremely low metallicity with a high-resolution spectrum
Sculptor is now the most luminous dSph in whichan extremely metal-poor (EMP [FeH] lt minus3) starhas been detected [Kirby et al (2008b) discovered 15EMP stars across eight ultra-faint dwarf galaxies andCohen amp Huang (2009) discovered one EMP star in theDraco dSph] Stars more metal-poor than S1020549 areknown to exist only in the field of the Milky Way fieldThis discovery hints that dSph galaxies like Sculptor mayhave contributed to the formation of the metal-poor com-
Fig 7mdash Regions of the DEIMOS spectrum of the extremelymetal-poor star S1020549 which has [FeH] = minus380 plusmn 028 Thespectrum appears particularly noisy because the y-axis range issmall Some Fe absorption lines are barely detectable but all to-gether they contain enough signal to make a quantitative mea-surement of [FeH] The shading corresponds to the same spectralregion shown in Fig 5 Frebel Kirby amp Simon (in preparation)will present a high-resolution spectrum of this star which confirmsthe extremely low metallicity
ponent of the halo We discuss Sculptorrsquos link to the halofurther in Sec 513
The MT2D photometric selection of spectroscopic tar-gets may have introduced a tiny [FeH] bias Figure 2shows that the RGB is sharply defined in Sculptor Be-cause the number density of stars redward and bluewardof the RGB is much lower than the number density on theRGB the number of very young or very metal-poor stars(blueward) or very metal-rich stars (redward) missed byphotometric pre-selection must be negligible Further-more the hard color cut (as opposed to one that dependson M minus D color) was 06 lt (M minus T2)0 lt 22 The CMDgives no reason to suspect Sculptor RGB members out-side of these limits but it is possible that some extremelyblue Sculptor members have been excluded
511 Possible Explanation of the Discrepancy withPrevious Results
Our measured MDF and our detection of EMP stars inSculptor are at odds with the findings of H06 Whereasour MDF peaks at [FeH] sim minus13 theirs peaks at[FeH] sim minus18 Furthermore our observed MDF is muchmore asymmetric than that of H06 which may even beslightly asymmetric in the opposite sense (a longer metal-rich tail) The greater symmetry would indicate a lessextended star formation history or early infall of a largeamount of gas (Prantzos 2003)
Battaglia et al (2008b hereafter B08b) observed asubset of the H06 stars at high resolution The MDFsfrom the two studies have noticeably different shapesFigure 8 shows that the HRS MDF peaks at [FeH] simminus13 which is also the peak that we observe The meanand standard deviation of their MDF are minus156 and 038
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
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Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
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Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
2 Kirby et al
Keck I LRIS spectrometer on a sample of individual starsin the Leo II dSph In a typical dSph the DEIMOS fieldof view allows between 80 and 150 red giant stars tobe targeted per multi-object mask Samples of severalhundred giants can be observed in a given dSph TheDwarf Abundances and Radial Velocities team (DARTTolstoy et al 2004 hereafter T04) has been collecting acombination of MRS and HRS in dSphs to exploit theadvantages of both techniques
This paper is the first in a series that explores themulti-element abundances of stellar systems measuredwith MRS The particular focus of this series is to char-acterize the distributions of [FeH] and [αFe] in MWdSphs These measurements will provide insight into therole of dSphs in building the Galactic stellar halo (ieSearle amp Zinn 1978 White amp Rees 1978)
Our first target is the Sculptor dSph (α = 1h00mδ = minus3343prime MV = minus111 Mateo 1998) Sculptor hasbeen a favored HRS and MRS target for the past tenyears Of all the dSphs it appears most often in expla-nations of dSph chemical evolution and galaxy formation(eg T04 Shetrone et al 2003 Geisler et al 2007) T04discovered that Sculptor is actually ldquotwo galaxiesrdquo in onewith two stellar populations that are kinematically andcompositionally distinct Battaglia et al (2006) latershowed that Fornax also displays multiple stellar pop-ulations with different kinematics spatial extents andmetallicities But Sculptor is also unique in that it isthe only MW dSph known to rotate (Battaglia et al2008a) Recently Walker et al (2009) published radialvelocities for 1365 Sculptor members and Venn amp Hill(2005 2008) presented high-resolution abundance mea-surements of Mg Ca Ti and Fe for 91 stars in SculptorThey also measured Y Ba and Eu for some of thosestars
This paper consists of six sections and an ap-pendix Section 2 introduces the spectroscopic tar-get selection and observations and Sec 3 explainshow the spectra are prepared for abundance mea-surements Section 4 describes the technique to ex-tract abundances which builds on the method de-scribed by Kirby Guhathakurta amp Sneden (2008a here-after KGS08) In Sec 5 we present the metallicity dis-tribution and multi-element abundance trends of Sculp-tor In Sec 6 we summarize our findings in the con-text of dSph chemical evolution and the formation of theGalaxy Finally we devote the appendix to quantifyingthe uncertainties in our MRS measurements includingcomparisons to independent HRS of the same stars
2 OBSERVATIONS
21 Target Selection
We selected targets from the Sculptor photometric cat-alog of Westfall et al (2006) The catalog includes pho-tometry in three filters M and T2 in the Washing-ton system and the intermediate-width DDO51 filter(henceforth called D) centered at 5150 A This bandprobes the flux from a spectral region susceptible to ab-sorption by the surface gravity-sensitive Mg I and MgHlines Majewski et al (2000) and Westfall et al (2006)outlined the procedure for distinguishing between distantred giant stars and foreground Galactic dwarf stars usingthese three filters We followed the same procedure to se-
10 5 0 -5 -10∆α (arcmin)
-10
-5
0
5
10
15
∆δ (
arcm
in)
-300 -200 -100 0 100 200 300
∆x (pc)
-200
0
200
400
∆y (
pc)
scl1scl1
scl2scl2
scl3scl3
scl5scl5scl6
scl6N
W
singly targeted starsdoubly targeted starsuntargeted starsstars with previous high-resolution abundances
singly targeted starsdoubly targeted starsuntargeted starsstars with previous high-resolution abundances
Fig 1mdash DEIMOS slitmask footprints laid over a map of sourcesfrom the photometric catalog Targets selected for spectroscopyare shown in red Targets observed in more than one mask areshown in green Blue diamonds enclose stars with previous HRSabundance measurements The left and bottom axis scales showthe angular displacement in arcmin from the center of the galaxy(α0 = 1h00m09s δ0 = minus3342prime30primeprime Mateo 1998) and the rightand top axis scales show the physical displacement for an assumeddistance of 859 kpc (Pietrzynski et al 2008)
lect a sample of red giant candidates from the SculptorMT2D catalog
Nine stars listed in Table 1 have previously pub-lished HRS abundance measurements (Shetrone et al2003 Geisler et al 2005) These stars were observedand provide the basis for demonstrating the accuracyof the MRS abundance measurements described in theappendix
22 Slitmask Design
We designed the DEIMOS slitmasks with the IRAFsoftware module dsimulator2 Each slitmask subtendedapproximately 16prime times 4prime In order to adequately subtractnight sky emission lines we required a minimum slitlength of 4primeprime The minimum space between slits was0primeprime35 When these constraints forced the selection ofone among multiple possible red giant candidates thebrightest object was selected The slits were designedto be at the approximate parallactic angle at the antici-pated time of observation (minus25) This choice minimizedthe small light losses due to differential atmospheric re-fraction This configuration was especially important forSculptor which was visible from Keck Observatory onlyat a low elevation The slitmasksrsquo sky position angle (PA)was minus35 The 10 offset between the slit PA and theslitmask PA tilted the night sky emission lines relative tothe CCD pixel grid to increase the subpixel wavelengthsampling and improve sky subtraction
TABLE 1Targets with Previous High-Resolution Abundances
name reference RA Dec M T2
H482 Shetrone et al (2003) 00h59m58s2 minus3341prime08primeprime 17967 plusmn 0030 16324 plusmn 0020H459 Shetrone et al (2003) 01h00m12s5 minus3343prime01primeprime 18465 plusmn 0032 16924 plusmn 0031H479 Shetrone et al (2003) 01h00m12s7 minus3341prime15primeprime 17562 plusmn 0023 15860 plusmn 0030H400 Shetrone et al (2003) 01h00m17s0 minus3345prime13primeprime 18413 plusmn 0030 17140 plusmn 0027H461 Shetrone et al (2003) 01h00m18s2 minus3342prime12primeprime 17806 plusmn 0028 16166 plusmn 00271446 Geisler et al (2005) 00h59m46s4 minus3341prime23primeprime 17618 plusmn 0023 15695 plusmn 0022195 Geisler et al (2005) 00h59m55s6 minus3346prime39primeprime 17515 plusmn 0022 15845 plusmn 0018982 Geisler et al (2005) 01h00m16s2 minus3342prime37primeprime 17433 plusmn 0025 15552 plusmn 0028770 Geisler et al (2005) 01h00m23s8 minus3342prime17primeprime 17623 plusmn 0025 15857 plusmn 0026
TABLE 2DEIMOS Observations
Slitmask Targets UT Date Exposures Seeing
scl1 86 2008 Aug 3 3 times 1200 s 0primeprime8scl2 106 2008 Aug 3 2 times 900 s 0primeprime8scl3 87 2008 Aug 4 1 times 462 s 0primeprime9
2008 Aug 31 1 times 1000 s 0primeprime82008 Aug 31 1 times 834 s 0primeprime8
scl5 95 2008 Sep 1 3 times 720 s 0primeprime8scl6 91 2008 Sep 1 3 times 720 s 1primeprime2
Note mdash The scl4 slitmask was not observed
Figure 1 shows the coordinates of all the objects inthe catalog regardless of their probability of membershipin Sculptor Five DEIMOS slitmask footprints enclosethe spectroscopic targets scl1 scl2 scl3 scl5 and scl6(see Tab 2) The scl5 slitmask included 24 targets alsoincluded on other masks These duplicate observationsprovide estimates of uncertainty in radial velocity andabundance measurements (Sec 33 and Sec A1) Thespectral coverage of each slit is not the same The min-imum and maximum wavelengths of spectra of targetsnear the long straight edge of the DEIMOS footprint canbe up to 400 A lower than for targets near the irregularlyshaped edge of the footprint (upper left and lower rightof the slitmask footprints in Fig 1 respectively) Fur-thermore spectra of targets near either extreme of thelong axis of the slitmask suffered from vignetting whichreduced the spectral range It is important to keep thesedifferences of spectral range in mind when interpretingthe differences of measurements derived from duplicateobservations
Figure 2 shows the color-magnitude diagram (CMD)of the targets within the right ascension and declinationranges of the axes in Fig 1 The MT2D membershipcriteria caused the selected red giants to form a tight se-quence This selection may have imposed a metallicitybias on the spectroscopic sample Although only a tinyfraction of stars lay outside the main locus of the redgiant branch some may have been spectroscopically un-targeted members of Sculptor For example if Sculptorcontained any old stars with [FeH] amp minus05 they wouldhave been too red to be included in the spectroscopicsample Any such metallicity bias should have excludedat most a few stars
23 Spectroscopic Configuration and Exposures
00 05 10 15 20 25 30(M minus T2)0
20
19
18
17
16
15
(T2)
0 =
(IC) 0
00 05 10 15 20
(VC minus IC)0
Fig 2mdash Color-magnitude diagram in the Washington andCousins systems for the sources within the right ascension anddeclination ranges shown in Fig 1 The symbols have the samemeanings as in Fig 1 The transformation from the Washingtonsystem (M and T2) to the Cousins system (VC and IC) is IC = T2
and VC minus IC = 0800(M minus T2) minus 0006 (Majewski et al 2000)
Our observing strategy was nearly identical to that ofSimon amp Geha (2007) and Kirby et al (2008a) In sum-mary we used with the 1200 lines mmminus1 grating at acentral wavelength of 7800 A The slit widths were 0primeprime7yielding a spectral resolution of sim 13 A FWHM (resolv-ing power R sim 6500 at 8500 A) The OG550 filter blockeddiffraction orders higher than m = 1 The spectral rangewas about 6400ndash9000 A with variation depending on theslitrsquos location along the dispersion axis Exposures ofKr Ne Ar and Xe arc lamps provided wavelength cal-ibration and exposures of a quartz lamp provided flatfielding Table 2 lists the number of targets for each slit-mask the dates of observations the exposure times andthe approximate seeing
Fig 3mdash Examples of small regions of DEIMOS spectra of fourdifferent stars The continuum in each spectrum has been normal-ized to unity The IC magnitude measured effective temperatureand measured [FeH] is given for each star The top two panelsshow two stars with very different [FeH] and the bottom two pan-els show two stars with nearly the same temperature and [FeH]but different SNR The colors show the regions used to measureeach of the Fe Mg Si Ca and Ti abundances (see Fig 5)
We reduced the raw frames using version 114 ofthe DEIMOS data reduction pipeline developed by theDEEP Galaxy Redshift Survey3 Guhathakurta et al(2006) give the details of the data reduction We alsomade use of the optimizations to the code described bySimon amp Geha (2007 Sec 22 of their article) Thesemodifications provided better extraction of unresolvedstellar sources
In summary the pipeline traced the edges of slits in theflat field to determine the CCD location of each slit Thewavelength solution was given by a polynomial fit to theCCD pixel locations of arc lamp lines Each exposureof stellar targets was rectified and then sky-subtractedbased on a B-spline model of the night sky emission linesNext the exposures were combined with cosmic ray rejec-tion into one two-dimensional spectrum for each slit Fi-nally the one-dimensional stellar spectrum was extractedfrom a small spatial window encompassing the light of thestar in the two-dimensional spectrum The product ofthe pipeline was a wavelength-calibrated sky-subtractedcosmic ray-cleaned one-dimensional spectrum for eachtarget
Some of the spectra suffered from unrecoverable de-fects such as a failure to find an acceptable polynomialfit to the wavelength solution There were 53 such spec-tra An additional 2 spectra had such poor signal-to-noise ratios (SNR) that abundance measurements wereimpossible leaving 410 useful spectra comprising 393unique targets and 17 duplicate measurements
Figure 3 shows four example spectra at a variety ofIC magnitudes effective temperatures and [FeH] The
3 httpastroberkeleyedu$^sim$cooperdeepspec2d
two upper panels show stars in the top 10 of the SNRdistribution The two lower panels show stars from themiddle and bottom 10 of the distribution
The one-dimensional DEIMOS spectra needed to beprepared for abundance measurements The preparationincluded velocity measurement removal of telluric ab-sorption and continuum division KGS08 (their Sec 3)described these preparations in detail We followed thesame process with some notable exceptions describedbelow
32 Telluric Absorption Correction
We removed the absorption introduced into the stellarspectra by the earthrsquos atmosphere in the same manneras KGS08 division by a hot star template spectrumHowever the high airmass of the Sculptor observationscaused much stronger absorption than KGS08 observedin globular cluster (GC) spectra Even after scaling thehot star template spectrum by the airmass large resid-uals in the Sculptor stellar spectra remained Conse-quently we masked spectral regions of heavy telluric ab-sorption before measuring abundances These regions are6864ndash6932 A 7162ndash7320 A 7591ndash7703 A 8128ndash8351 Aand 8938ndash10000 A (see Fig 5)
33 Radial Velocities and Spectroscopic MembershipDetermination
Our primary interest in this paper is chemical abun-dances and we measured radial velocities only to deter-mine membership and to shift the spectra into the restframe
Following KGS08 we measured stellar radial velocitiesby cross-correlation with a template spectrum HoweverKGS08 cross-correlated the observed spectra against syn-thetic spectra whereas we cross-correlated the observedspectra against high SNR template spectra of stars ob-served with DEIMOS Templates observed with the sameinstrument should provide more accurate radial velocitymeasurements than synthetic templates Simon amp Geha(2007) provided their template spectra to us For therest of the analysis the spectra are shifted to the restframe
Although the MT2D selection eliminated almost all ofthe foreground MW contaminants from the spectroscopicsample we checked the membership of each target by ra-dial velocity selection Figure 4 shows the distribution ofradial velocities in this spectroscopic data set along withthe best-fit Gaussian We consider the radial velocitylimits of Sculptor membership to be 848 km sminus1 lt vr lt1383 km sminus1 We chose these limits because beyondthem the expected number of Sculptor members per2 km sminus1 bin (the approximate maximum velocity res-olution of DEIMOS Simon amp Geha 2007) is fewer than05 This selection eliminated just 5 out of 393 uniquetargets
As a check on our procedure we compared some de-rived quantities from the velocity distribution to previ-ous measurements The mean velocity of our sampleis 〈vhelio〉 = 1116 plusmn 05 km sminus1 with a dispersion ofσv = 80 plusmn 07 km sminus1 The velocity dispersion is theper-measurement velocity error subtracted in quadraturefrom the 1σ width of the velocity distribution The per-measurement error is 39 km sminus1 which is the standard
Abundances in the Sculptor dSph 5
80 100 120 140vhelio (km sminus1)
0
10
20
30
40
N
langvhelioranglangvheliorang = 1116 plusmn 05 km sminus1
σv σv = 80 plusmn 07 km sminus1
Fig 4mdash Distribution of measured radial velocities for targetsin the Sculptor field along with the best-fit Gaussian The topleft label gives the mean and standard deviation of this Gaussianfit The five stars outside of the dashed lines are not consideredSculptor members The velocity range of this plot includes all starsfor which a velocity measurement was possible
deviations of the differences in measured velocities forthe 17 duplicate spectra In comparison Westfall et al(2006) found 〈vhelio〉 = 1104 plusmn 08 km sminus1 (difference of+12σ) and σv = 88plusmn 06 km sminus1 (difference of minus09σ)The comparison of the velocity dispersions depends onthe assumed binary fraction (Queloz et al 1995) andmdashgiven the presence of multiple kinematically and spa-tially distinct populations in Sculptor (T04)mdashthe regionof spectroscopic selection Furthermore Walker et al(2007 2009) reported velocity dispersion gradients andBattaglia et al (2008a) reported mean velocity gradientsalong the major axis indicating rotation We choose notto address the kinematic complexity of this system inthis paper
34 Continuum Determination
In the abundance analysis described in Sec 4 it isnecessary to normalize each stellar spectrum by dividingby the slowly varying stellar continuum KGS08 deter-mined the continuum by smoothing the regions of thestellar spectrum free from strong absorption lines In-stead of smoothing we fit a B-spline with a breakpointspacing of 150 A to the same ldquocontinuum regionsrdquo de-fined by KGS08 Each pixel was weighted by its inversevariance in the fit Furthermore the fit was performediteratively such that pixels that deviated from the fit bymore than 5σ were removed from the next iteration ofthe fit
The spline fit results in a smoother continuum determi-nation than smoothing Whereas the smoothed contin-uum value may be influenced heavily by one or a few pix-els within a relatively small smoothing kernel the splinefit is a global fit It is more likely to be representative ofthe true stellar continuum than a smoothed spectrum
Shetrone et al (2009) pointed out the importance ofdetermining the continuum accurately when measur-ing weak lines in medium-resolution spectra They re-fined their continuum determinations by iteratively fit-
TABLE 3New Grid of ATLAS9 Model Atmospheres
Parameter Minimum Value Maximum Value Step
Teff (K) 3500 5600 1005600 8000 200
log g (cm sminus2) 00 (Teff lt 7000 K) 50 0505 (Teff ge 7000 K) 50 05
[AH] minus40 00 05[αFe] minus08 +12 01
ting a high-order spline to the quotient of the observedspectrum and the best-fitting synthetic spectrum Weadopted this procedure as well As part of the iterativeprocess described in Sec 47 we fit a B-spline with abreakpoint spacing of 50 A to the observed spectrum di-vided by the best-fitting synthetic spectrum We dividedthe observed spectrum by this spline before the next it-eration of abundance measurement
4 ABUNDANCE MEASUREMENTS
The following section details some improvements onthe abundance measurement techniques of KGS08 As-pects of the technique not mentioned here were un-changed from the technique of KGS08 In summaryeach observed spectrum was compared to a large gridof synthetic spectra The atmospheric abundances wereadopted from the synthetic spectrum with the lowest χ2
A major improvement was our measurement of fourindividual elemental abundances in addition to Fe MgSi Ca and Ti We chose these elements because they areimportant in characterizing the star formation history ofa stellar population and because a significant numberof lines represent each of them in the DEIMOS spectralrange
41 Model Atmospheres
Like KGS08 we built synthetic spectra based on AT-LAS9 model atmospheres (Kurucz 1993) with no con-vective overshooting (Castelli et al 1997) KGS08 choseto allow the atmospheres to have [αFe] = +04 or[αFe] = 00 This choice allowed them to use the largegrid of ATLAS9 model atmospheres computed with newopacity distribution functions (Castelli amp Kurucz 2004)However we found that best-fitting model spectra com-puted by KGS08 tended to cluster around [αFe] = +02due to the discontinuity in χ2 caused by the abruptswitch between alpha-enhanced and solar-scaled models
To avoid this discontinuity we recomputed ATLAS9model atmospheres on the grid summarized in Table 3The new grid required recomputing new opacity distri-bution functions (ODFs) for which we used the DF-SYNTHE code (Castelli 2005) Unlike the grid ofCastelli amp Kurucz (2004) we adopted the solar compo-sition of Anders amp Grevesse (1989) except for Fe forwhich we followed Sneden et al (1992 see the note in Ta-ble 4) One opacity distribution function was computedfor each of the 189 combinations of [AH] and [αFe]specified in Table 3 The abundances of all the elementsexcept H and He were augmented by [AH] Addition-ally the abundances of O Ne Mg Si Ar Ca and Tiwere augmented by [αFe] These ODFs were used tocompute one ATLAS9 model atmosphere for each grid
6 Kirby et al
point in Table 3 and for two values of microturbulentvelocity for a total of 139104 model atmospheres
42 Microturbulent Velocity
In order to reduce the number of parameters requiredto determine a stellar abundance KGS08 assumed thatthe microturbulent velocity (ξ) of the stellar atmospherewas tied to the surface gravity (log g) They chose to fita line to the spectroscopically measured ξ and log g ofthe giant stars in Fulbrightrsquos (2000) sample
ξ (km sminus1) = 270 minus 051 log g (1)
We also adopted a relation between ξ and log g but were-determined this relation from the GC red giant sampleof KGS08 combined with Kirbyrsquos (2009) compilation ofhigh-resolution spectroscopic measurements from the lit-erature (Frebel et al 2009 Geisler et al 2005 Johnson2002 Lai et al 2007 Shetrone et al 2001 2003 and ref-erences from KGS08) The best-fit line between the spec-troscopically measured ξ and log g is
corresponding roughly to a 00ndash05 km sminus1 decrease inξ depending on log g In the generation of the grid ofsynthetic stellar spectra described in Sec 44 ξ was nota free parameter but was fixed to log g via Eq 2
In general a decrease in ξ increases the measurementof [FeH] Therefore this change tended to increase thederived values of [FeH] A typical change in [FeH] was +005 dex This change would be more severe in anHRS analysis based on equivalent widths (EWs) In ourχ2 minimization the abundance measurement was mostsensitive to lines with large d(EW)d[FeH] Such linesare the weak unsaturated transitions whose strengthdoes not depend on ξ The DEIMOS spectra containenough of these weak lines that ξ did not play a largerole in the abundance determination
43 Line List
We compared the Fe I oscillator strengths (log gf) inthe KGS08 line list to values measured in the labora-tory (Fuhr amp Wiese 2006) Most of the KGS08 oscilla-tor strengths were stronger than the laboratory measure-ments The average offset was 013 dex Because KGS08calibrated their line list to the solar spectrum we in-terpreted this offset as a systematic error in the solarmodel atmosphere solar spectral synthesis andor solarcomposition Accepting the laboratory-measured valuesas more accurate than the solar calibration we replacedFe I oscillator strengths with Fuhr amp Wiese where avail-able and we subtracted 013 dex from log gf for all otherFe I transitions in the KGS08 line list All other data re-mained unchanged
Decreasing the oscillator strengths requires a larger[FeH] to match the observed spectrum The amount ofchange in [FeH] depends on the atmospheric parametersas well as the saturation of the measured Fe lines Fromcomparison of results with the old and new line lists weestimate a typical change in [FeH] to be sim +01 dex
44 Generation of Synthetic Spectra
TABLE 4Adopted Solar Composition
Element 12 + log ǫ Element 12 + log ǫ
Mg 758 Ti 499Ca 636 Fe 752Si 755
Note mdash This composition is adopted fromAnders amp Grevesse (1989) except for Fe Forjustification of the adopted Fe solar abun-dance see Sneden et al (1992) The abun-dance of an element X is defined as its numberdensity relative to hydrogen 12 + log ǫX =12 + log(nX) minus log(nH)
The spectra were synthesized as described in KGS08Specifically the current version of the local thermody-namic equilibrium (LTE) spectrum synthesis softwareMOOG (Sneden 1973) generated one spectrum for eachpoint on the grid The spectral grid was more finelyspaced in [FeH] than the model atmosphere grid Thespacing is 01 dex for each of [FeH] and [αFe] yieldinga total of 316848 synthetic spectra
The solar composition used in the generation of thesynthetic spectra was identical to the solar compositionused in the computation of the model atmospheres Ta-ble 4 lists the adopted solar abundances for the five el-ements for which we measure abundances in Sculptorstars
45 Effective Temperatures and Surface Gravities
Different spectroscopic studies of chemical abundancesrely on different sources of information for determin-ing the effective temperature (Teff) and surface grav-ity (log g) of the stellar atmosphere KGS08 con-sulted Yonsei-Yale model isochrones (Demarque et al2004) to determine the temperature and gravity thatcorrespond to a dereddened color and an extinction-corrected absolute magnitude They also consideredVictoria-Regina (VandenBerg et al 2006) and Padova(Girardi et al 2002) model isochrones as well as an em-pirical color-temperature relation (Ramırez amp Melendez2005)
The Fe lines accessible in DEIMOS spectra span a largerange of excitation potential Together these differentlines provide a constraint on Teff KGS08 (their Sec 51)showed thatmdashwithout any photometric informationmdashthe synthesis analysis of medium-resolution spectra ofGC stars yielded values of Teff very close to values previ-ously measured from HRS Therefore we chose to mea-sure Teff from photometry and spectroscopy simultane-ously
To begin we converted extinction-corrected(Schlegel et al 1998) Washington M and T2 magnitudesto Cousins VC and IC magnitudes (Majewski et al2000) With these magnitudes we computed Teff fromthe Yonsei-Yale Victoria-Regina and Padova modelisochrones as well as the Ramırez amp Melendez (2005)empirical color-based Teff For each measurement we es-timated the effect of photometric error by measuring thestandard deviation of Teff determined from 1000 MonteCarlo realizations of VC and IC In each realization VC
and IC were chosen from a normal distribution with amean of the measured extinction-corrected magnitude
Abundances in the Sculptor dSph 7
and a standard deviation of the photometric error Wecall this error δTeffi where i represents each of the fourphotometric methods of determining Teff In order toarrive at a single photometric Teff we averaged the fourTeffi together with appropriate error weighting We alsoestimated the random and systematic components oferror In summary
Teff =
sum
i TeffiδTminus2effi
sum
i δTminus2effi
(3)
δrandTeff =
sum
i δTminus1effi
sum
i δTminus2effi
(4)
δsysTeff =
radic
radic
radic
radic
radic
sum
i δTminus2effi
sum
i δTminus2effi
(
Teffi minus Teff
)2
1 minus(
sum
i δTminus2effi
)2sum
i δTminus4effi
(5)
δtotalTeff =radic
(δrandTeff)2 + (δsysTeff)2 (6)
For the stars in this data set the median randomsystematic and total errors on Teff were 98 K 58 Kand 117 K respectively The somewhat large errors onthe photometric temperatures indicated that the spec-tra may help constrain Teff Therefore Eq 3 does notshow the final temperature used in the abundance deter-mination Section 47 describes the iterative process fordetermining Teff and elemental abundances from spec-troscopy
We followed a similar procedure for determining log gphotometrically except that we used only the threemodel isochrones and not any empirical calibrationThe error on the true distance modulus (1967 plusmn 012Pietrzynski et al 2008) was included in the Monte Carlodetermination of the error on log g The median ran-dom systematic and total errors on log g were 006 001and 006 These errors are very small and the medium-resolution red spectra have little power to help constrainlog g because there are so few ionized lines visible There-fore we assumed the photometric value of log g for theabundance analysis
46 Wavelength Masks
The procedure described in the next section consistedof separately measuring the abundances of five elementsMg Si Ca Ti and Fe The procedure relied on findingthe synthetic spectrum that best matched an observedspectrum In order to make this matching most sensitiveto a particular element we masked all spectral regionsthat were not significantly affected by abundance changesof that element
To make the wavelength masks we began with a basespectrum that represented the solar composition in whichthe abundances of all the metals were scaled down by15 dex ([AH] = minus15) The temperature and gravityof the synthetic star were Teff = 4000 K and log g = 10Then we created two pairs of spectra for each of thefive elements In one spectrum the abundance of theelement was enhanced by 03 dex and in the other de-pleted by 03 dex Spectral regions where the flux differ-ence between these two spectra exceeds 05 were usedin the abundance determination of that element This
Fig 5mdash A coaddition of all Sculptor stars with the continuumnormalized to unity The high SNR provided by the coadditionmakes stellar absorption lines readily apparent The colored re-gions show the wavelength masks used in the determination of theabundance of each element Regions susceptible to telluric absorp-tion are labeled with blue text Because large residuals from thetelluric absorption correction remain we eliminate these regionsfrom the abundance analysis Some stellar features excluded fromthe abundances measurement are also labeled
small threshold assured that weak lines which experi-ence large fractional changes in EW as [FeH] changeswere included in the analysis We repeated this proce-dure for spectra with Teff = 5000 K 6000 K 7000 K and8000 K Additional spectral regions that passed the 05flux difference criterion were also included in the abun-dance determination of that element All other wave-lengths were masked
The result was one wavelength mask for each of MgSi Ca Ti and Fe shown in Fig 5 We also createdone ldquoαrdquo mask as the intersection of the Mg Si Ca andTi masks The α element regions do not overlap witheach other but the α element regions do overlap withthe Fe regions The most severe case is the Ca maskwhere sim 35 of the pixels are shared with the Fe maskHowever the overlap did not introduce interdependencein the abundance measurements The α element abun-dances were held fixed while [FeH] was measured andthe Fe abundance was held fixed while [αFe] was mea-sured The measurements of [FeH] and [αFe] were per-formed iteratively (see the next subsection) We testedthe independence of the measurements by removing alloverlapping pixels from consideration Abundance mea-surements changed on average by only 001 dex
47 Measuring Atmospheric Parameters and ElementalAbundances
A Levenberg-Marquardt algorithm (the IDL routineMPFIT written by Markwardt 2009) found the best-fitting synthetic spectrum in ten iterative steps In eachstep the χ2 was computed between an observed spec-trum and a synthetic spectrum degraded to match theresolution of the observed spectrum First we interpo-
8 Kirby et al
lated the synthetic spectrum onto the same wavelengtharray as the observed spectrum Then we smoothedthe synthetic spectrum through a Gaussian filter whosewidth was the observed spectrumrsquos measured resolutionas a function of wavelength
1 Teff and [FeH] first pass An observed spectrumwas compared to a synthetic spectrum with Teff
and log g determined as described in Sec 45 and[FeH] determined from Yonsei-Yale isochronesFor this iteration [αFe] was fixed at 00 (solar)and only spectral regions most susceptible to Fe ab-sorption (Sec 46) were considered The two quan-tities Teff and [FeH] were varied and the algo-rithm found the best-fitting synthetic spectrum byminimizing χ2 We sampled the parameter spacebetween grid points by linearly interpolating thesynthetic spectra at the neighboring grid pointsTeff was also loosely constrained by photometry Asthe spectrum caused Teff to stray from the photo-metric values χ2 increased and it increased moresharply for smaller photometric errors (as calcu-lated in Eq 6) Therefore both photometry andspectroscopy determined Teff Photometry alonedetermined log g
2 [αFe] first pass For this iteration Teff log g and[FeH] were fixed Only [αFe] was allowed to varyIn the model stellar atmosphere the abundances ofthe α elements with respect to Fe varied togetherOnly the spectral regions susceptible to absorptionby Mg Si Ca or Ti were considered
3 Continuum refinement The continuum-dividedobserved spectrum was divided by the syntheticspectrum with the parameters determined in steps1 and 2 The result approximated a flat noise spec-trum To better determine the continuum we fita B-spline with a breakpoint spacing of 50 A tothe residual spectrum We divided the observedspectrum by the spline fit
4 [FeH] second pass We repeated step 1 with therevised spectrum but Teff was held fixed at thepreviously determined value
5 [MgFe] We repeated step 2 However only Mgspectral lines were considered in the abundancemeasurement
6 [SiFe] We repeated step 5 for Si instead of Mg
7 [CaFe] We repeated step 5 for Ca instead of Mg
8 [TiFe] We repeated step 5 for Ti instead of Mg
9 [αFe] second pass We repeated step 2 for allof the α elements instead of just Mg This stepwas simply a different way to average the α el-ement abundances than combining the individualmeasurements of [MgFe] [SiFe] [CaFe] and[TiFe]
10 [FeH] third pass The value of [αFe] affected themeasurement of [FeH] because [αFe] can affect
the structure of the stellar atmosphere Specif-ically the greater availability of electron donorswith an increased [αFe] ratio allows for a higherdensity of Hminus ions The subsequent increase in con-tinuous opacity decreases the strength of Fe andother non-α element lines With [αFe] fixed atthe value determined in step 9 we re-measured[FeH] Typically [FeH] changed from the valuedetermined in step 1 by much less than 01 dex
48 Correction to [FeH]
In comparing our MRS measurements of [FeH] to HRSmeasurements of the same stars (see the appendix) wenoticed that our measurements of metal-poor stars wereconsistently sim 015 dex lower The same pattern is alsovisible in the Kirby et al (2008a) GC measurements (seetheir Figs 6 7 10 and 11)
We have thoroughly examined possible sources of thisdifference of scale The changes to the microturbulentvelocity relation (Sec 42) and the line list (Sec 43)were intended to yield a more accurate and standardizedestimation of [FeH] but the offset still remained Re-stricting the analysis to narrow spectral regions did notreveal any systematic trend of [FeH] with wavelength
A possible explanation for this offset is overionization(Thevenin amp Idiart 1999) Ultraviolet radiation in stellaratmospheres can ionize Fe more than would be expectedin LTE Therefore the abundance of Fe I would seem tobe lower than the abundance of Fe II in an LTE analysisFe II does not suffer from this effect However the effectis smaller at higher [FeH] and we do not observe a trendwith metallicity for the offset of our values relative toHRS studies
In order to standardize our measurements with previ-ous HRS studies we added 015 dex to all of our mea-surements of [FeH] This offset and the microturbu-lent velocity-surface gravity relation are the only ways inwhich previous HRS studies inform our measurementsFurthermore this offset is not intended to change thestandardization of our abundances All of the abundancein this article including those from other studies aregiven relative to the solar abundances quoted in Table 4
49 Error Estimation
We repeated the error estimation procedure describedby KGS08 (their Sec 6) by repeating their abundanceanalysis on GC stars with the above modifications Weno longer found a convincing trend of δ[FeH] with[FeH] Instead we estimate the total error on [FeH] byadding a systematic error in quadrature with the SNR-dependent uncertainty of the synthetic spectral fit Themagnitude of δsys[FeH] = 0136 was the value requiredto force HRS and MRS [FeH] estimates of the same GCstars to agree at the 1σ level We also estimated sys-tematic errors for each of [MgFe] [SiFe] [CaFe] and
Abundances in the Sculptor dSph 9
minus4 minus3 minus2 minus1 0[FeH]
0
10
20
30
40
50N
([F
eH
])
0
100
200
300
400
500
dN
d[F
eH
]
SculptorSimple ModelInfall Model
Fig 6mdash The metallicity distribution in Sculptor The red curveis the maximum likelihood fit to a galactic chemical evolutionmodel with pre-enrichment (Eq 7) and the green curve is the max-imum likelihood fit to a model of star formation in the presence ofinfalling zero-metallicity gas (Eq 11) The long metal-poor tailis typical for systems with non-instantaneous star formation
[TiFe] in the same manner as for [FeH] These are listedin Table 5
5 RESULTS
In this section we discuss the interpretation of theabundance measurements in Sculptor all of which arepresented in Table 6 on the last page of this manuscript
51 Metallicity Distribution
The metallicity distribution function (MDF) of a dwarfgalaxy can reveal much about its star formation his-tory In chemical evolution models of dwarf galax-ies (eg Lanfranchi amp Matteucci 2004 Marcolini et al2006 2008) the duration of star formation affects theshape of the MDF The MDF also has implications forthe formation of the MW If the MW halo was built fromdSphs (Searle amp Zinn 1978 White amp Rees 1978) then itis important to find dSph counterparts to halo field starsat all metallicities as pointed out by Helmi et al (2006hereafter H06)
Figure 6 shows the MDF of Sculptor The shape of theMDF is highly asymmetric with a long metal-poor tail(as predicted by Salvadori amp Ferrara 2009) The inverse-variance weighted mean is 〈[FeH]〉 = minus158 with a stan-dard deviation of 041 The median is minus158 with a me-dian absolute deviation of 033 and an interquartile rangeof 067
The MDF boasts an exceptionally metal-poor starS1020549 The metallicity is [FeH] = minus380 plusmn 028Figure 7 shows how weak the Fe absorption lines are inthis star Frebel Kirby amp Simon (in preparation) haveconfirmed this extremely low metallicity with a high-resolution spectrum
Sculptor is now the most luminous dSph in whichan extremely metal-poor (EMP [FeH] lt minus3) starhas been detected [Kirby et al (2008b) discovered 15EMP stars across eight ultra-faint dwarf galaxies andCohen amp Huang (2009) discovered one EMP star in theDraco dSph] Stars more metal-poor than S1020549 areknown to exist only in the field of the Milky Way fieldThis discovery hints that dSph galaxies like Sculptor mayhave contributed to the formation of the metal-poor com-
Fig 7mdash Regions of the DEIMOS spectrum of the extremelymetal-poor star S1020549 which has [FeH] = minus380 plusmn 028 Thespectrum appears particularly noisy because the y-axis range issmall Some Fe absorption lines are barely detectable but all to-gether they contain enough signal to make a quantitative mea-surement of [FeH] The shading corresponds to the same spectralregion shown in Fig 5 Frebel Kirby amp Simon (in preparation)will present a high-resolution spectrum of this star which confirmsthe extremely low metallicity
ponent of the halo We discuss Sculptorrsquos link to the halofurther in Sec 513
The MT2D photometric selection of spectroscopic tar-gets may have introduced a tiny [FeH] bias Figure 2shows that the RGB is sharply defined in Sculptor Be-cause the number density of stars redward and bluewardof the RGB is much lower than the number density on theRGB the number of very young or very metal-poor stars(blueward) or very metal-rich stars (redward) missed byphotometric pre-selection must be negligible Further-more the hard color cut (as opposed to one that dependson M minus D color) was 06 lt (M minus T2)0 lt 22 The CMDgives no reason to suspect Sculptor RGB members out-side of these limits but it is possible that some extremelyblue Sculptor members have been excluded
511 Possible Explanation of the Discrepancy withPrevious Results
Our measured MDF and our detection of EMP stars inSculptor are at odds with the findings of H06 Whereasour MDF peaks at [FeH] sim minus13 theirs peaks at[FeH] sim minus18 Furthermore our observed MDF is muchmore asymmetric than that of H06 which may even beslightly asymmetric in the opposite sense (a longer metal-rich tail) The greater symmetry would indicate a lessextended star formation history or early infall of a largeamount of gas (Prantzos 2003)
Battaglia et al (2008b hereafter B08b) observed asubset of the H06 stars at high resolution The MDFsfrom the two studies have noticeably different shapesFigure 8 shows that the HRS MDF peaks at [FeH] simminus13 which is also the peak that we observe The meanand standard deviation of their MDF are minus156 and 038
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 3
TABLE 1Targets with Previous High-Resolution Abundances
name reference RA Dec M T2
H482 Shetrone et al (2003) 00h59m58s2 minus3341prime08primeprime 17967 plusmn 0030 16324 plusmn 0020H459 Shetrone et al (2003) 01h00m12s5 minus3343prime01primeprime 18465 plusmn 0032 16924 plusmn 0031H479 Shetrone et al (2003) 01h00m12s7 minus3341prime15primeprime 17562 plusmn 0023 15860 plusmn 0030H400 Shetrone et al (2003) 01h00m17s0 minus3345prime13primeprime 18413 plusmn 0030 17140 plusmn 0027H461 Shetrone et al (2003) 01h00m18s2 minus3342prime12primeprime 17806 plusmn 0028 16166 plusmn 00271446 Geisler et al (2005) 00h59m46s4 minus3341prime23primeprime 17618 plusmn 0023 15695 plusmn 0022195 Geisler et al (2005) 00h59m55s6 minus3346prime39primeprime 17515 plusmn 0022 15845 plusmn 0018982 Geisler et al (2005) 01h00m16s2 minus3342prime37primeprime 17433 plusmn 0025 15552 plusmn 0028770 Geisler et al (2005) 01h00m23s8 minus3342prime17primeprime 17623 plusmn 0025 15857 plusmn 0026
TABLE 2DEIMOS Observations
Slitmask Targets UT Date Exposures Seeing
scl1 86 2008 Aug 3 3 times 1200 s 0primeprime8scl2 106 2008 Aug 3 2 times 900 s 0primeprime8scl3 87 2008 Aug 4 1 times 462 s 0primeprime9
2008 Aug 31 1 times 1000 s 0primeprime82008 Aug 31 1 times 834 s 0primeprime8
scl5 95 2008 Sep 1 3 times 720 s 0primeprime8scl6 91 2008 Sep 1 3 times 720 s 1primeprime2
Note mdash The scl4 slitmask was not observed
Figure 1 shows the coordinates of all the objects inthe catalog regardless of their probability of membershipin Sculptor Five DEIMOS slitmask footprints enclosethe spectroscopic targets scl1 scl2 scl3 scl5 and scl6(see Tab 2) The scl5 slitmask included 24 targets alsoincluded on other masks These duplicate observationsprovide estimates of uncertainty in radial velocity andabundance measurements (Sec 33 and Sec A1) Thespectral coverage of each slit is not the same The min-imum and maximum wavelengths of spectra of targetsnear the long straight edge of the DEIMOS footprint canbe up to 400 A lower than for targets near the irregularlyshaped edge of the footprint (upper left and lower rightof the slitmask footprints in Fig 1 respectively) Fur-thermore spectra of targets near either extreme of thelong axis of the slitmask suffered from vignetting whichreduced the spectral range It is important to keep thesedifferences of spectral range in mind when interpretingthe differences of measurements derived from duplicateobservations
Figure 2 shows the color-magnitude diagram (CMD)of the targets within the right ascension and declinationranges of the axes in Fig 1 The MT2D membershipcriteria caused the selected red giants to form a tight se-quence This selection may have imposed a metallicitybias on the spectroscopic sample Although only a tinyfraction of stars lay outside the main locus of the redgiant branch some may have been spectroscopically un-targeted members of Sculptor For example if Sculptorcontained any old stars with [FeH] amp minus05 they wouldhave been too red to be included in the spectroscopicsample Any such metallicity bias should have excludedat most a few stars
23 Spectroscopic Configuration and Exposures
00 05 10 15 20 25 30(M minus T2)0
20
19
18
17
16
15
(T2)
0 =
(IC) 0
00 05 10 15 20
(VC minus IC)0
Fig 2mdash Color-magnitude diagram in the Washington andCousins systems for the sources within the right ascension anddeclination ranges shown in Fig 1 The symbols have the samemeanings as in Fig 1 The transformation from the Washingtonsystem (M and T2) to the Cousins system (VC and IC) is IC = T2
and VC minus IC = 0800(M minus T2) minus 0006 (Majewski et al 2000)
Our observing strategy was nearly identical to that ofSimon amp Geha (2007) and Kirby et al (2008a) In sum-mary we used with the 1200 lines mmminus1 grating at acentral wavelength of 7800 A The slit widths were 0primeprime7yielding a spectral resolution of sim 13 A FWHM (resolv-ing power R sim 6500 at 8500 A) The OG550 filter blockeddiffraction orders higher than m = 1 The spectral rangewas about 6400ndash9000 A with variation depending on theslitrsquos location along the dispersion axis Exposures ofKr Ne Ar and Xe arc lamps provided wavelength cal-ibration and exposures of a quartz lamp provided flatfielding Table 2 lists the number of targets for each slit-mask the dates of observations the exposure times andthe approximate seeing
Fig 3mdash Examples of small regions of DEIMOS spectra of fourdifferent stars The continuum in each spectrum has been normal-ized to unity The IC magnitude measured effective temperatureand measured [FeH] is given for each star The top two panelsshow two stars with very different [FeH] and the bottom two pan-els show two stars with nearly the same temperature and [FeH]but different SNR The colors show the regions used to measureeach of the Fe Mg Si Ca and Ti abundances (see Fig 5)
We reduced the raw frames using version 114 ofthe DEIMOS data reduction pipeline developed by theDEEP Galaxy Redshift Survey3 Guhathakurta et al(2006) give the details of the data reduction We alsomade use of the optimizations to the code described bySimon amp Geha (2007 Sec 22 of their article) Thesemodifications provided better extraction of unresolvedstellar sources
In summary the pipeline traced the edges of slits in theflat field to determine the CCD location of each slit Thewavelength solution was given by a polynomial fit to theCCD pixel locations of arc lamp lines Each exposureof stellar targets was rectified and then sky-subtractedbased on a B-spline model of the night sky emission linesNext the exposures were combined with cosmic ray rejec-tion into one two-dimensional spectrum for each slit Fi-nally the one-dimensional stellar spectrum was extractedfrom a small spatial window encompassing the light of thestar in the two-dimensional spectrum The product ofthe pipeline was a wavelength-calibrated sky-subtractedcosmic ray-cleaned one-dimensional spectrum for eachtarget
Some of the spectra suffered from unrecoverable de-fects such as a failure to find an acceptable polynomialfit to the wavelength solution There were 53 such spec-tra An additional 2 spectra had such poor signal-to-noise ratios (SNR) that abundance measurements wereimpossible leaving 410 useful spectra comprising 393unique targets and 17 duplicate measurements
Figure 3 shows four example spectra at a variety ofIC magnitudes effective temperatures and [FeH] The
3 httpastroberkeleyedu$^sim$cooperdeepspec2d
two upper panels show stars in the top 10 of the SNRdistribution The two lower panels show stars from themiddle and bottom 10 of the distribution
The one-dimensional DEIMOS spectra needed to beprepared for abundance measurements The preparationincluded velocity measurement removal of telluric ab-sorption and continuum division KGS08 (their Sec 3)described these preparations in detail We followed thesame process with some notable exceptions describedbelow
32 Telluric Absorption Correction
We removed the absorption introduced into the stellarspectra by the earthrsquos atmosphere in the same manneras KGS08 division by a hot star template spectrumHowever the high airmass of the Sculptor observationscaused much stronger absorption than KGS08 observedin globular cluster (GC) spectra Even after scaling thehot star template spectrum by the airmass large resid-uals in the Sculptor stellar spectra remained Conse-quently we masked spectral regions of heavy telluric ab-sorption before measuring abundances These regions are6864ndash6932 A 7162ndash7320 A 7591ndash7703 A 8128ndash8351 Aand 8938ndash10000 A (see Fig 5)
33 Radial Velocities and Spectroscopic MembershipDetermination
Our primary interest in this paper is chemical abun-dances and we measured radial velocities only to deter-mine membership and to shift the spectra into the restframe
Following KGS08 we measured stellar radial velocitiesby cross-correlation with a template spectrum HoweverKGS08 cross-correlated the observed spectra against syn-thetic spectra whereas we cross-correlated the observedspectra against high SNR template spectra of stars ob-served with DEIMOS Templates observed with the sameinstrument should provide more accurate radial velocitymeasurements than synthetic templates Simon amp Geha(2007) provided their template spectra to us For therest of the analysis the spectra are shifted to the restframe
Although the MT2D selection eliminated almost all ofthe foreground MW contaminants from the spectroscopicsample we checked the membership of each target by ra-dial velocity selection Figure 4 shows the distribution ofradial velocities in this spectroscopic data set along withthe best-fit Gaussian We consider the radial velocitylimits of Sculptor membership to be 848 km sminus1 lt vr lt1383 km sminus1 We chose these limits because beyondthem the expected number of Sculptor members per2 km sminus1 bin (the approximate maximum velocity res-olution of DEIMOS Simon amp Geha 2007) is fewer than05 This selection eliminated just 5 out of 393 uniquetargets
As a check on our procedure we compared some de-rived quantities from the velocity distribution to previ-ous measurements The mean velocity of our sampleis 〈vhelio〉 = 1116 plusmn 05 km sminus1 with a dispersion ofσv = 80 plusmn 07 km sminus1 The velocity dispersion is theper-measurement velocity error subtracted in quadraturefrom the 1σ width of the velocity distribution The per-measurement error is 39 km sminus1 which is the standard
Abundances in the Sculptor dSph 5
80 100 120 140vhelio (km sminus1)
0
10
20
30
40
N
langvhelioranglangvheliorang = 1116 plusmn 05 km sminus1
σv σv = 80 plusmn 07 km sminus1
Fig 4mdash Distribution of measured radial velocities for targetsin the Sculptor field along with the best-fit Gaussian The topleft label gives the mean and standard deviation of this Gaussianfit The five stars outside of the dashed lines are not consideredSculptor members The velocity range of this plot includes all starsfor which a velocity measurement was possible
deviations of the differences in measured velocities forthe 17 duplicate spectra In comparison Westfall et al(2006) found 〈vhelio〉 = 1104 plusmn 08 km sminus1 (difference of+12σ) and σv = 88plusmn 06 km sminus1 (difference of minus09σ)The comparison of the velocity dispersions depends onthe assumed binary fraction (Queloz et al 1995) andmdashgiven the presence of multiple kinematically and spa-tially distinct populations in Sculptor (T04)mdashthe regionof spectroscopic selection Furthermore Walker et al(2007 2009) reported velocity dispersion gradients andBattaglia et al (2008a) reported mean velocity gradientsalong the major axis indicating rotation We choose notto address the kinematic complexity of this system inthis paper
34 Continuum Determination
In the abundance analysis described in Sec 4 it isnecessary to normalize each stellar spectrum by dividingby the slowly varying stellar continuum KGS08 deter-mined the continuum by smoothing the regions of thestellar spectrum free from strong absorption lines In-stead of smoothing we fit a B-spline with a breakpointspacing of 150 A to the same ldquocontinuum regionsrdquo de-fined by KGS08 Each pixel was weighted by its inversevariance in the fit Furthermore the fit was performediteratively such that pixels that deviated from the fit bymore than 5σ were removed from the next iteration ofthe fit
The spline fit results in a smoother continuum determi-nation than smoothing Whereas the smoothed contin-uum value may be influenced heavily by one or a few pix-els within a relatively small smoothing kernel the splinefit is a global fit It is more likely to be representative ofthe true stellar continuum than a smoothed spectrum
Shetrone et al (2009) pointed out the importance ofdetermining the continuum accurately when measur-ing weak lines in medium-resolution spectra They re-fined their continuum determinations by iteratively fit-
TABLE 3New Grid of ATLAS9 Model Atmospheres
Parameter Minimum Value Maximum Value Step
Teff (K) 3500 5600 1005600 8000 200
log g (cm sminus2) 00 (Teff lt 7000 K) 50 0505 (Teff ge 7000 K) 50 05
[AH] minus40 00 05[αFe] minus08 +12 01
ting a high-order spline to the quotient of the observedspectrum and the best-fitting synthetic spectrum Weadopted this procedure as well As part of the iterativeprocess described in Sec 47 we fit a B-spline with abreakpoint spacing of 50 A to the observed spectrum di-vided by the best-fitting synthetic spectrum We dividedthe observed spectrum by this spline before the next it-eration of abundance measurement
4 ABUNDANCE MEASUREMENTS
The following section details some improvements onthe abundance measurement techniques of KGS08 As-pects of the technique not mentioned here were un-changed from the technique of KGS08 In summaryeach observed spectrum was compared to a large gridof synthetic spectra The atmospheric abundances wereadopted from the synthetic spectrum with the lowest χ2
A major improvement was our measurement of fourindividual elemental abundances in addition to Fe MgSi Ca and Ti We chose these elements because they areimportant in characterizing the star formation history ofa stellar population and because a significant numberof lines represent each of them in the DEIMOS spectralrange
41 Model Atmospheres
Like KGS08 we built synthetic spectra based on AT-LAS9 model atmospheres (Kurucz 1993) with no con-vective overshooting (Castelli et al 1997) KGS08 choseto allow the atmospheres to have [αFe] = +04 or[αFe] = 00 This choice allowed them to use the largegrid of ATLAS9 model atmospheres computed with newopacity distribution functions (Castelli amp Kurucz 2004)However we found that best-fitting model spectra com-puted by KGS08 tended to cluster around [αFe] = +02due to the discontinuity in χ2 caused by the abruptswitch between alpha-enhanced and solar-scaled models
To avoid this discontinuity we recomputed ATLAS9model atmospheres on the grid summarized in Table 3The new grid required recomputing new opacity distri-bution functions (ODFs) for which we used the DF-SYNTHE code (Castelli 2005) Unlike the grid ofCastelli amp Kurucz (2004) we adopted the solar compo-sition of Anders amp Grevesse (1989) except for Fe forwhich we followed Sneden et al (1992 see the note in Ta-ble 4) One opacity distribution function was computedfor each of the 189 combinations of [AH] and [αFe]specified in Table 3 The abundances of all the elementsexcept H and He were augmented by [AH] Addition-ally the abundances of O Ne Mg Si Ar Ca and Tiwere augmented by [αFe] These ODFs were used tocompute one ATLAS9 model atmosphere for each grid
6 Kirby et al
point in Table 3 and for two values of microturbulentvelocity for a total of 139104 model atmospheres
42 Microturbulent Velocity
In order to reduce the number of parameters requiredto determine a stellar abundance KGS08 assumed thatthe microturbulent velocity (ξ) of the stellar atmospherewas tied to the surface gravity (log g) They chose to fita line to the spectroscopically measured ξ and log g ofthe giant stars in Fulbrightrsquos (2000) sample
ξ (km sminus1) = 270 minus 051 log g (1)
We also adopted a relation between ξ and log g but were-determined this relation from the GC red giant sampleof KGS08 combined with Kirbyrsquos (2009) compilation ofhigh-resolution spectroscopic measurements from the lit-erature (Frebel et al 2009 Geisler et al 2005 Johnson2002 Lai et al 2007 Shetrone et al 2001 2003 and ref-erences from KGS08) The best-fit line between the spec-troscopically measured ξ and log g is
corresponding roughly to a 00ndash05 km sminus1 decrease inξ depending on log g In the generation of the grid ofsynthetic stellar spectra described in Sec 44 ξ was nota free parameter but was fixed to log g via Eq 2
In general a decrease in ξ increases the measurementof [FeH] Therefore this change tended to increase thederived values of [FeH] A typical change in [FeH] was +005 dex This change would be more severe in anHRS analysis based on equivalent widths (EWs) In ourχ2 minimization the abundance measurement was mostsensitive to lines with large d(EW)d[FeH] Such linesare the weak unsaturated transitions whose strengthdoes not depend on ξ The DEIMOS spectra containenough of these weak lines that ξ did not play a largerole in the abundance determination
43 Line List
We compared the Fe I oscillator strengths (log gf) inthe KGS08 line list to values measured in the labora-tory (Fuhr amp Wiese 2006) Most of the KGS08 oscilla-tor strengths were stronger than the laboratory measure-ments The average offset was 013 dex Because KGS08calibrated their line list to the solar spectrum we in-terpreted this offset as a systematic error in the solarmodel atmosphere solar spectral synthesis andor solarcomposition Accepting the laboratory-measured valuesas more accurate than the solar calibration we replacedFe I oscillator strengths with Fuhr amp Wiese where avail-able and we subtracted 013 dex from log gf for all otherFe I transitions in the KGS08 line list All other data re-mained unchanged
Decreasing the oscillator strengths requires a larger[FeH] to match the observed spectrum The amount ofchange in [FeH] depends on the atmospheric parametersas well as the saturation of the measured Fe lines Fromcomparison of results with the old and new line lists weestimate a typical change in [FeH] to be sim +01 dex
44 Generation of Synthetic Spectra
TABLE 4Adopted Solar Composition
Element 12 + log ǫ Element 12 + log ǫ
Mg 758 Ti 499Ca 636 Fe 752Si 755
Note mdash This composition is adopted fromAnders amp Grevesse (1989) except for Fe Forjustification of the adopted Fe solar abun-dance see Sneden et al (1992) The abun-dance of an element X is defined as its numberdensity relative to hydrogen 12 + log ǫX =12 + log(nX) minus log(nH)
The spectra were synthesized as described in KGS08Specifically the current version of the local thermody-namic equilibrium (LTE) spectrum synthesis softwareMOOG (Sneden 1973) generated one spectrum for eachpoint on the grid The spectral grid was more finelyspaced in [FeH] than the model atmosphere grid Thespacing is 01 dex for each of [FeH] and [αFe] yieldinga total of 316848 synthetic spectra
The solar composition used in the generation of thesynthetic spectra was identical to the solar compositionused in the computation of the model atmospheres Ta-ble 4 lists the adopted solar abundances for the five el-ements for which we measure abundances in Sculptorstars
45 Effective Temperatures and Surface Gravities
Different spectroscopic studies of chemical abundancesrely on different sources of information for determin-ing the effective temperature (Teff) and surface grav-ity (log g) of the stellar atmosphere KGS08 con-sulted Yonsei-Yale model isochrones (Demarque et al2004) to determine the temperature and gravity thatcorrespond to a dereddened color and an extinction-corrected absolute magnitude They also consideredVictoria-Regina (VandenBerg et al 2006) and Padova(Girardi et al 2002) model isochrones as well as an em-pirical color-temperature relation (Ramırez amp Melendez2005)
The Fe lines accessible in DEIMOS spectra span a largerange of excitation potential Together these differentlines provide a constraint on Teff KGS08 (their Sec 51)showed thatmdashwithout any photometric informationmdashthe synthesis analysis of medium-resolution spectra ofGC stars yielded values of Teff very close to values previ-ously measured from HRS Therefore we chose to mea-sure Teff from photometry and spectroscopy simultane-ously
To begin we converted extinction-corrected(Schlegel et al 1998) Washington M and T2 magnitudesto Cousins VC and IC magnitudes (Majewski et al2000) With these magnitudes we computed Teff fromthe Yonsei-Yale Victoria-Regina and Padova modelisochrones as well as the Ramırez amp Melendez (2005)empirical color-based Teff For each measurement we es-timated the effect of photometric error by measuring thestandard deviation of Teff determined from 1000 MonteCarlo realizations of VC and IC In each realization VC
and IC were chosen from a normal distribution with amean of the measured extinction-corrected magnitude
Abundances in the Sculptor dSph 7
and a standard deviation of the photometric error Wecall this error δTeffi where i represents each of the fourphotometric methods of determining Teff In order toarrive at a single photometric Teff we averaged the fourTeffi together with appropriate error weighting We alsoestimated the random and systematic components oferror In summary
Teff =
sum
i TeffiδTminus2effi
sum
i δTminus2effi
(3)
δrandTeff =
sum
i δTminus1effi
sum
i δTminus2effi
(4)
δsysTeff =
radic
radic
radic
radic
radic
sum
i δTminus2effi
sum
i δTminus2effi
(
Teffi minus Teff
)2
1 minus(
sum
i δTminus2effi
)2sum
i δTminus4effi
(5)
δtotalTeff =radic
(δrandTeff)2 + (δsysTeff)2 (6)
For the stars in this data set the median randomsystematic and total errors on Teff were 98 K 58 Kand 117 K respectively The somewhat large errors onthe photometric temperatures indicated that the spec-tra may help constrain Teff Therefore Eq 3 does notshow the final temperature used in the abundance deter-mination Section 47 describes the iterative process fordetermining Teff and elemental abundances from spec-troscopy
We followed a similar procedure for determining log gphotometrically except that we used only the threemodel isochrones and not any empirical calibrationThe error on the true distance modulus (1967 plusmn 012Pietrzynski et al 2008) was included in the Monte Carlodetermination of the error on log g The median ran-dom systematic and total errors on log g were 006 001and 006 These errors are very small and the medium-resolution red spectra have little power to help constrainlog g because there are so few ionized lines visible There-fore we assumed the photometric value of log g for theabundance analysis
46 Wavelength Masks
The procedure described in the next section consistedof separately measuring the abundances of five elementsMg Si Ca Ti and Fe The procedure relied on findingthe synthetic spectrum that best matched an observedspectrum In order to make this matching most sensitiveto a particular element we masked all spectral regionsthat were not significantly affected by abundance changesof that element
To make the wavelength masks we began with a basespectrum that represented the solar composition in whichthe abundances of all the metals were scaled down by15 dex ([AH] = minus15) The temperature and gravityof the synthetic star were Teff = 4000 K and log g = 10Then we created two pairs of spectra for each of thefive elements In one spectrum the abundance of theelement was enhanced by 03 dex and in the other de-pleted by 03 dex Spectral regions where the flux differ-ence between these two spectra exceeds 05 were usedin the abundance determination of that element This
Fig 5mdash A coaddition of all Sculptor stars with the continuumnormalized to unity The high SNR provided by the coadditionmakes stellar absorption lines readily apparent The colored re-gions show the wavelength masks used in the determination of theabundance of each element Regions susceptible to telluric absorp-tion are labeled with blue text Because large residuals from thetelluric absorption correction remain we eliminate these regionsfrom the abundance analysis Some stellar features excluded fromthe abundances measurement are also labeled
small threshold assured that weak lines which experi-ence large fractional changes in EW as [FeH] changeswere included in the analysis We repeated this proce-dure for spectra with Teff = 5000 K 6000 K 7000 K and8000 K Additional spectral regions that passed the 05flux difference criterion were also included in the abun-dance determination of that element All other wave-lengths were masked
The result was one wavelength mask for each of MgSi Ca Ti and Fe shown in Fig 5 We also createdone ldquoαrdquo mask as the intersection of the Mg Si Ca andTi masks The α element regions do not overlap witheach other but the α element regions do overlap withthe Fe regions The most severe case is the Ca maskwhere sim 35 of the pixels are shared with the Fe maskHowever the overlap did not introduce interdependencein the abundance measurements The α element abun-dances were held fixed while [FeH] was measured andthe Fe abundance was held fixed while [αFe] was mea-sured The measurements of [FeH] and [αFe] were per-formed iteratively (see the next subsection) We testedthe independence of the measurements by removing alloverlapping pixels from consideration Abundance mea-surements changed on average by only 001 dex
47 Measuring Atmospheric Parameters and ElementalAbundances
A Levenberg-Marquardt algorithm (the IDL routineMPFIT written by Markwardt 2009) found the best-fitting synthetic spectrum in ten iterative steps In eachstep the χ2 was computed between an observed spec-trum and a synthetic spectrum degraded to match theresolution of the observed spectrum First we interpo-
8 Kirby et al
lated the synthetic spectrum onto the same wavelengtharray as the observed spectrum Then we smoothedthe synthetic spectrum through a Gaussian filter whosewidth was the observed spectrumrsquos measured resolutionas a function of wavelength
1 Teff and [FeH] first pass An observed spectrumwas compared to a synthetic spectrum with Teff
and log g determined as described in Sec 45 and[FeH] determined from Yonsei-Yale isochronesFor this iteration [αFe] was fixed at 00 (solar)and only spectral regions most susceptible to Fe ab-sorption (Sec 46) were considered The two quan-tities Teff and [FeH] were varied and the algo-rithm found the best-fitting synthetic spectrum byminimizing χ2 We sampled the parameter spacebetween grid points by linearly interpolating thesynthetic spectra at the neighboring grid pointsTeff was also loosely constrained by photometry Asthe spectrum caused Teff to stray from the photo-metric values χ2 increased and it increased moresharply for smaller photometric errors (as calcu-lated in Eq 6) Therefore both photometry andspectroscopy determined Teff Photometry alonedetermined log g
2 [αFe] first pass For this iteration Teff log g and[FeH] were fixed Only [αFe] was allowed to varyIn the model stellar atmosphere the abundances ofthe α elements with respect to Fe varied togetherOnly the spectral regions susceptible to absorptionby Mg Si Ca or Ti were considered
3 Continuum refinement The continuum-dividedobserved spectrum was divided by the syntheticspectrum with the parameters determined in steps1 and 2 The result approximated a flat noise spec-trum To better determine the continuum we fita B-spline with a breakpoint spacing of 50 A tothe residual spectrum We divided the observedspectrum by the spline fit
4 [FeH] second pass We repeated step 1 with therevised spectrum but Teff was held fixed at thepreviously determined value
5 [MgFe] We repeated step 2 However only Mgspectral lines were considered in the abundancemeasurement
6 [SiFe] We repeated step 5 for Si instead of Mg
7 [CaFe] We repeated step 5 for Ca instead of Mg
8 [TiFe] We repeated step 5 for Ti instead of Mg
9 [αFe] second pass We repeated step 2 for allof the α elements instead of just Mg This stepwas simply a different way to average the α el-ement abundances than combining the individualmeasurements of [MgFe] [SiFe] [CaFe] and[TiFe]
10 [FeH] third pass The value of [αFe] affected themeasurement of [FeH] because [αFe] can affect
the structure of the stellar atmosphere Specif-ically the greater availability of electron donorswith an increased [αFe] ratio allows for a higherdensity of Hminus ions The subsequent increase in con-tinuous opacity decreases the strength of Fe andother non-α element lines With [αFe] fixed atthe value determined in step 9 we re-measured[FeH] Typically [FeH] changed from the valuedetermined in step 1 by much less than 01 dex
48 Correction to [FeH]
In comparing our MRS measurements of [FeH] to HRSmeasurements of the same stars (see the appendix) wenoticed that our measurements of metal-poor stars wereconsistently sim 015 dex lower The same pattern is alsovisible in the Kirby et al (2008a) GC measurements (seetheir Figs 6 7 10 and 11)
We have thoroughly examined possible sources of thisdifference of scale The changes to the microturbulentvelocity relation (Sec 42) and the line list (Sec 43)were intended to yield a more accurate and standardizedestimation of [FeH] but the offset still remained Re-stricting the analysis to narrow spectral regions did notreveal any systematic trend of [FeH] with wavelength
A possible explanation for this offset is overionization(Thevenin amp Idiart 1999) Ultraviolet radiation in stellaratmospheres can ionize Fe more than would be expectedin LTE Therefore the abundance of Fe I would seem tobe lower than the abundance of Fe II in an LTE analysisFe II does not suffer from this effect However the effectis smaller at higher [FeH] and we do not observe a trendwith metallicity for the offset of our values relative toHRS studies
In order to standardize our measurements with previ-ous HRS studies we added 015 dex to all of our mea-surements of [FeH] This offset and the microturbu-lent velocity-surface gravity relation are the only ways inwhich previous HRS studies inform our measurementsFurthermore this offset is not intended to change thestandardization of our abundances All of the abundancein this article including those from other studies aregiven relative to the solar abundances quoted in Table 4
49 Error Estimation
We repeated the error estimation procedure describedby KGS08 (their Sec 6) by repeating their abundanceanalysis on GC stars with the above modifications Weno longer found a convincing trend of δ[FeH] with[FeH] Instead we estimate the total error on [FeH] byadding a systematic error in quadrature with the SNR-dependent uncertainty of the synthetic spectral fit Themagnitude of δsys[FeH] = 0136 was the value requiredto force HRS and MRS [FeH] estimates of the same GCstars to agree at the 1σ level We also estimated sys-tematic errors for each of [MgFe] [SiFe] [CaFe] and
Abundances in the Sculptor dSph 9
minus4 minus3 minus2 minus1 0[FeH]
0
10
20
30
40
50N
([F
eH
])
0
100
200
300
400
500
dN
d[F
eH
]
SculptorSimple ModelInfall Model
Fig 6mdash The metallicity distribution in Sculptor The red curveis the maximum likelihood fit to a galactic chemical evolutionmodel with pre-enrichment (Eq 7) and the green curve is the max-imum likelihood fit to a model of star formation in the presence ofinfalling zero-metallicity gas (Eq 11) The long metal-poor tailis typical for systems with non-instantaneous star formation
[TiFe] in the same manner as for [FeH] These are listedin Table 5
5 RESULTS
In this section we discuss the interpretation of theabundance measurements in Sculptor all of which arepresented in Table 6 on the last page of this manuscript
51 Metallicity Distribution
The metallicity distribution function (MDF) of a dwarfgalaxy can reveal much about its star formation his-tory In chemical evolution models of dwarf galax-ies (eg Lanfranchi amp Matteucci 2004 Marcolini et al2006 2008) the duration of star formation affects theshape of the MDF The MDF also has implications forthe formation of the MW If the MW halo was built fromdSphs (Searle amp Zinn 1978 White amp Rees 1978) then itis important to find dSph counterparts to halo field starsat all metallicities as pointed out by Helmi et al (2006hereafter H06)
Figure 6 shows the MDF of Sculptor The shape of theMDF is highly asymmetric with a long metal-poor tail(as predicted by Salvadori amp Ferrara 2009) The inverse-variance weighted mean is 〈[FeH]〉 = minus158 with a stan-dard deviation of 041 The median is minus158 with a me-dian absolute deviation of 033 and an interquartile rangeof 067
The MDF boasts an exceptionally metal-poor starS1020549 The metallicity is [FeH] = minus380 plusmn 028Figure 7 shows how weak the Fe absorption lines are inthis star Frebel Kirby amp Simon (in preparation) haveconfirmed this extremely low metallicity with a high-resolution spectrum
Sculptor is now the most luminous dSph in whichan extremely metal-poor (EMP [FeH] lt minus3) starhas been detected [Kirby et al (2008b) discovered 15EMP stars across eight ultra-faint dwarf galaxies andCohen amp Huang (2009) discovered one EMP star in theDraco dSph] Stars more metal-poor than S1020549 areknown to exist only in the field of the Milky Way fieldThis discovery hints that dSph galaxies like Sculptor mayhave contributed to the formation of the metal-poor com-
Fig 7mdash Regions of the DEIMOS spectrum of the extremelymetal-poor star S1020549 which has [FeH] = minus380 plusmn 028 Thespectrum appears particularly noisy because the y-axis range issmall Some Fe absorption lines are barely detectable but all to-gether they contain enough signal to make a quantitative mea-surement of [FeH] The shading corresponds to the same spectralregion shown in Fig 5 Frebel Kirby amp Simon (in preparation)will present a high-resolution spectrum of this star which confirmsthe extremely low metallicity
ponent of the halo We discuss Sculptorrsquos link to the halofurther in Sec 513
The MT2D photometric selection of spectroscopic tar-gets may have introduced a tiny [FeH] bias Figure 2shows that the RGB is sharply defined in Sculptor Be-cause the number density of stars redward and bluewardof the RGB is much lower than the number density on theRGB the number of very young or very metal-poor stars(blueward) or very metal-rich stars (redward) missed byphotometric pre-selection must be negligible Further-more the hard color cut (as opposed to one that dependson M minus D color) was 06 lt (M minus T2)0 lt 22 The CMDgives no reason to suspect Sculptor RGB members out-side of these limits but it is possible that some extremelyblue Sculptor members have been excluded
511 Possible Explanation of the Discrepancy withPrevious Results
Our measured MDF and our detection of EMP stars inSculptor are at odds with the findings of H06 Whereasour MDF peaks at [FeH] sim minus13 theirs peaks at[FeH] sim minus18 Furthermore our observed MDF is muchmore asymmetric than that of H06 which may even beslightly asymmetric in the opposite sense (a longer metal-rich tail) The greater symmetry would indicate a lessextended star formation history or early infall of a largeamount of gas (Prantzos 2003)
Battaglia et al (2008b hereafter B08b) observed asubset of the H06 stars at high resolution The MDFsfrom the two studies have noticeably different shapesFigure 8 shows that the HRS MDF peaks at [FeH] simminus13 which is also the peak that we observe The meanand standard deviation of their MDF are minus156 and 038
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Fig 3mdash Examples of small regions of DEIMOS spectra of fourdifferent stars The continuum in each spectrum has been normal-ized to unity The IC magnitude measured effective temperatureand measured [FeH] is given for each star The top two panelsshow two stars with very different [FeH] and the bottom two pan-els show two stars with nearly the same temperature and [FeH]but different SNR The colors show the regions used to measureeach of the Fe Mg Si Ca and Ti abundances (see Fig 5)
We reduced the raw frames using version 114 ofthe DEIMOS data reduction pipeline developed by theDEEP Galaxy Redshift Survey3 Guhathakurta et al(2006) give the details of the data reduction We alsomade use of the optimizations to the code described bySimon amp Geha (2007 Sec 22 of their article) Thesemodifications provided better extraction of unresolvedstellar sources
In summary the pipeline traced the edges of slits in theflat field to determine the CCD location of each slit Thewavelength solution was given by a polynomial fit to theCCD pixel locations of arc lamp lines Each exposureof stellar targets was rectified and then sky-subtractedbased on a B-spline model of the night sky emission linesNext the exposures were combined with cosmic ray rejec-tion into one two-dimensional spectrum for each slit Fi-nally the one-dimensional stellar spectrum was extractedfrom a small spatial window encompassing the light of thestar in the two-dimensional spectrum The product ofthe pipeline was a wavelength-calibrated sky-subtractedcosmic ray-cleaned one-dimensional spectrum for eachtarget
Some of the spectra suffered from unrecoverable de-fects such as a failure to find an acceptable polynomialfit to the wavelength solution There were 53 such spec-tra An additional 2 spectra had such poor signal-to-noise ratios (SNR) that abundance measurements wereimpossible leaving 410 useful spectra comprising 393unique targets and 17 duplicate measurements
Figure 3 shows four example spectra at a variety ofIC magnitudes effective temperatures and [FeH] The
3 httpastroberkeleyedu$^sim$cooperdeepspec2d
two upper panels show stars in the top 10 of the SNRdistribution The two lower panels show stars from themiddle and bottom 10 of the distribution
The one-dimensional DEIMOS spectra needed to beprepared for abundance measurements The preparationincluded velocity measurement removal of telluric ab-sorption and continuum division KGS08 (their Sec 3)described these preparations in detail We followed thesame process with some notable exceptions describedbelow
32 Telluric Absorption Correction
We removed the absorption introduced into the stellarspectra by the earthrsquos atmosphere in the same manneras KGS08 division by a hot star template spectrumHowever the high airmass of the Sculptor observationscaused much stronger absorption than KGS08 observedin globular cluster (GC) spectra Even after scaling thehot star template spectrum by the airmass large resid-uals in the Sculptor stellar spectra remained Conse-quently we masked spectral regions of heavy telluric ab-sorption before measuring abundances These regions are6864ndash6932 A 7162ndash7320 A 7591ndash7703 A 8128ndash8351 Aand 8938ndash10000 A (see Fig 5)
33 Radial Velocities and Spectroscopic MembershipDetermination
Our primary interest in this paper is chemical abun-dances and we measured radial velocities only to deter-mine membership and to shift the spectra into the restframe
Following KGS08 we measured stellar radial velocitiesby cross-correlation with a template spectrum HoweverKGS08 cross-correlated the observed spectra against syn-thetic spectra whereas we cross-correlated the observedspectra against high SNR template spectra of stars ob-served with DEIMOS Templates observed with the sameinstrument should provide more accurate radial velocitymeasurements than synthetic templates Simon amp Geha(2007) provided their template spectra to us For therest of the analysis the spectra are shifted to the restframe
Although the MT2D selection eliminated almost all ofthe foreground MW contaminants from the spectroscopicsample we checked the membership of each target by ra-dial velocity selection Figure 4 shows the distribution ofradial velocities in this spectroscopic data set along withthe best-fit Gaussian We consider the radial velocitylimits of Sculptor membership to be 848 km sminus1 lt vr lt1383 km sminus1 We chose these limits because beyondthem the expected number of Sculptor members per2 km sminus1 bin (the approximate maximum velocity res-olution of DEIMOS Simon amp Geha 2007) is fewer than05 This selection eliminated just 5 out of 393 uniquetargets
As a check on our procedure we compared some de-rived quantities from the velocity distribution to previ-ous measurements The mean velocity of our sampleis 〈vhelio〉 = 1116 plusmn 05 km sminus1 with a dispersion ofσv = 80 plusmn 07 km sminus1 The velocity dispersion is theper-measurement velocity error subtracted in quadraturefrom the 1σ width of the velocity distribution The per-measurement error is 39 km sminus1 which is the standard
Abundances in the Sculptor dSph 5
80 100 120 140vhelio (km sminus1)
0
10
20
30
40
N
langvhelioranglangvheliorang = 1116 plusmn 05 km sminus1
σv σv = 80 plusmn 07 km sminus1
Fig 4mdash Distribution of measured radial velocities for targetsin the Sculptor field along with the best-fit Gaussian The topleft label gives the mean and standard deviation of this Gaussianfit The five stars outside of the dashed lines are not consideredSculptor members The velocity range of this plot includes all starsfor which a velocity measurement was possible
deviations of the differences in measured velocities forthe 17 duplicate spectra In comparison Westfall et al(2006) found 〈vhelio〉 = 1104 plusmn 08 km sminus1 (difference of+12σ) and σv = 88plusmn 06 km sminus1 (difference of minus09σ)The comparison of the velocity dispersions depends onthe assumed binary fraction (Queloz et al 1995) andmdashgiven the presence of multiple kinematically and spa-tially distinct populations in Sculptor (T04)mdashthe regionof spectroscopic selection Furthermore Walker et al(2007 2009) reported velocity dispersion gradients andBattaglia et al (2008a) reported mean velocity gradientsalong the major axis indicating rotation We choose notto address the kinematic complexity of this system inthis paper
34 Continuum Determination
In the abundance analysis described in Sec 4 it isnecessary to normalize each stellar spectrum by dividingby the slowly varying stellar continuum KGS08 deter-mined the continuum by smoothing the regions of thestellar spectrum free from strong absorption lines In-stead of smoothing we fit a B-spline with a breakpointspacing of 150 A to the same ldquocontinuum regionsrdquo de-fined by KGS08 Each pixel was weighted by its inversevariance in the fit Furthermore the fit was performediteratively such that pixels that deviated from the fit bymore than 5σ were removed from the next iteration ofthe fit
The spline fit results in a smoother continuum determi-nation than smoothing Whereas the smoothed contin-uum value may be influenced heavily by one or a few pix-els within a relatively small smoothing kernel the splinefit is a global fit It is more likely to be representative ofthe true stellar continuum than a smoothed spectrum
Shetrone et al (2009) pointed out the importance ofdetermining the continuum accurately when measur-ing weak lines in medium-resolution spectra They re-fined their continuum determinations by iteratively fit-
TABLE 3New Grid of ATLAS9 Model Atmospheres
Parameter Minimum Value Maximum Value Step
Teff (K) 3500 5600 1005600 8000 200
log g (cm sminus2) 00 (Teff lt 7000 K) 50 0505 (Teff ge 7000 K) 50 05
[AH] minus40 00 05[αFe] minus08 +12 01
ting a high-order spline to the quotient of the observedspectrum and the best-fitting synthetic spectrum Weadopted this procedure as well As part of the iterativeprocess described in Sec 47 we fit a B-spline with abreakpoint spacing of 50 A to the observed spectrum di-vided by the best-fitting synthetic spectrum We dividedthe observed spectrum by this spline before the next it-eration of abundance measurement
4 ABUNDANCE MEASUREMENTS
The following section details some improvements onthe abundance measurement techniques of KGS08 As-pects of the technique not mentioned here were un-changed from the technique of KGS08 In summaryeach observed spectrum was compared to a large gridof synthetic spectra The atmospheric abundances wereadopted from the synthetic spectrum with the lowest χ2
A major improvement was our measurement of fourindividual elemental abundances in addition to Fe MgSi Ca and Ti We chose these elements because they areimportant in characterizing the star formation history ofa stellar population and because a significant numberof lines represent each of them in the DEIMOS spectralrange
41 Model Atmospheres
Like KGS08 we built synthetic spectra based on AT-LAS9 model atmospheres (Kurucz 1993) with no con-vective overshooting (Castelli et al 1997) KGS08 choseto allow the atmospheres to have [αFe] = +04 or[αFe] = 00 This choice allowed them to use the largegrid of ATLAS9 model atmospheres computed with newopacity distribution functions (Castelli amp Kurucz 2004)However we found that best-fitting model spectra com-puted by KGS08 tended to cluster around [αFe] = +02due to the discontinuity in χ2 caused by the abruptswitch between alpha-enhanced and solar-scaled models
To avoid this discontinuity we recomputed ATLAS9model atmospheres on the grid summarized in Table 3The new grid required recomputing new opacity distri-bution functions (ODFs) for which we used the DF-SYNTHE code (Castelli 2005) Unlike the grid ofCastelli amp Kurucz (2004) we adopted the solar compo-sition of Anders amp Grevesse (1989) except for Fe forwhich we followed Sneden et al (1992 see the note in Ta-ble 4) One opacity distribution function was computedfor each of the 189 combinations of [AH] and [αFe]specified in Table 3 The abundances of all the elementsexcept H and He were augmented by [AH] Addition-ally the abundances of O Ne Mg Si Ar Ca and Tiwere augmented by [αFe] These ODFs were used tocompute one ATLAS9 model atmosphere for each grid
6 Kirby et al
point in Table 3 and for two values of microturbulentvelocity for a total of 139104 model atmospheres
42 Microturbulent Velocity
In order to reduce the number of parameters requiredto determine a stellar abundance KGS08 assumed thatthe microturbulent velocity (ξ) of the stellar atmospherewas tied to the surface gravity (log g) They chose to fita line to the spectroscopically measured ξ and log g ofthe giant stars in Fulbrightrsquos (2000) sample
ξ (km sminus1) = 270 minus 051 log g (1)
We also adopted a relation between ξ and log g but were-determined this relation from the GC red giant sampleof KGS08 combined with Kirbyrsquos (2009) compilation ofhigh-resolution spectroscopic measurements from the lit-erature (Frebel et al 2009 Geisler et al 2005 Johnson2002 Lai et al 2007 Shetrone et al 2001 2003 and ref-erences from KGS08) The best-fit line between the spec-troscopically measured ξ and log g is
corresponding roughly to a 00ndash05 km sminus1 decrease inξ depending on log g In the generation of the grid ofsynthetic stellar spectra described in Sec 44 ξ was nota free parameter but was fixed to log g via Eq 2
In general a decrease in ξ increases the measurementof [FeH] Therefore this change tended to increase thederived values of [FeH] A typical change in [FeH] was +005 dex This change would be more severe in anHRS analysis based on equivalent widths (EWs) In ourχ2 minimization the abundance measurement was mostsensitive to lines with large d(EW)d[FeH] Such linesare the weak unsaturated transitions whose strengthdoes not depend on ξ The DEIMOS spectra containenough of these weak lines that ξ did not play a largerole in the abundance determination
43 Line List
We compared the Fe I oscillator strengths (log gf) inthe KGS08 line list to values measured in the labora-tory (Fuhr amp Wiese 2006) Most of the KGS08 oscilla-tor strengths were stronger than the laboratory measure-ments The average offset was 013 dex Because KGS08calibrated their line list to the solar spectrum we in-terpreted this offset as a systematic error in the solarmodel atmosphere solar spectral synthesis andor solarcomposition Accepting the laboratory-measured valuesas more accurate than the solar calibration we replacedFe I oscillator strengths with Fuhr amp Wiese where avail-able and we subtracted 013 dex from log gf for all otherFe I transitions in the KGS08 line list All other data re-mained unchanged
Decreasing the oscillator strengths requires a larger[FeH] to match the observed spectrum The amount ofchange in [FeH] depends on the atmospheric parametersas well as the saturation of the measured Fe lines Fromcomparison of results with the old and new line lists weestimate a typical change in [FeH] to be sim +01 dex
44 Generation of Synthetic Spectra
TABLE 4Adopted Solar Composition
Element 12 + log ǫ Element 12 + log ǫ
Mg 758 Ti 499Ca 636 Fe 752Si 755
Note mdash This composition is adopted fromAnders amp Grevesse (1989) except for Fe Forjustification of the adopted Fe solar abun-dance see Sneden et al (1992) The abun-dance of an element X is defined as its numberdensity relative to hydrogen 12 + log ǫX =12 + log(nX) minus log(nH)
The spectra were synthesized as described in KGS08Specifically the current version of the local thermody-namic equilibrium (LTE) spectrum synthesis softwareMOOG (Sneden 1973) generated one spectrum for eachpoint on the grid The spectral grid was more finelyspaced in [FeH] than the model atmosphere grid Thespacing is 01 dex for each of [FeH] and [αFe] yieldinga total of 316848 synthetic spectra
The solar composition used in the generation of thesynthetic spectra was identical to the solar compositionused in the computation of the model atmospheres Ta-ble 4 lists the adopted solar abundances for the five el-ements for which we measure abundances in Sculptorstars
45 Effective Temperatures and Surface Gravities
Different spectroscopic studies of chemical abundancesrely on different sources of information for determin-ing the effective temperature (Teff) and surface grav-ity (log g) of the stellar atmosphere KGS08 con-sulted Yonsei-Yale model isochrones (Demarque et al2004) to determine the temperature and gravity thatcorrespond to a dereddened color and an extinction-corrected absolute magnitude They also consideredVictoria-Regina (VandenBerg et al 2006) and Padova(Girardi et al 2002) model isochrones as well as an em-pirical color-temperature relation (Ramırez amp Melendez2005)
The Fe lines accessible in DEIMOS spectra span a largerange of excitation potential Together these differentlines provide a constraint on Teff KGS08 (their Sec 51)showed thatmdashwithout any photometric informationmdashthe synthesis analysis of medium-resolution spectra ofGC stars yielded values of Teff very close to values previ-ously measured from HRS Therefore we chose to mea-sure Teff from photometry and spectroscopy simultane-ously
To begin we converted extinction-corrected(Schlegel et al 1998) Washington M and T2 magnitudesto Cousins VC and IC magnitudes (Majewski et al2000) With these magnitudes we computed Teff fromthe Yonsei-Yale Victoria-Regina and Padova modelisochrones as well as the Ramırez amp Melendez (2005)empirical color-based Teff For each measurement we es-timated the effect of photometric error by measuring thestandard deviation of Teff determined from 1000 MonteCarlo realizations of VC and IC In each realization VC
and IC were chosen from a normal distribution with amean of the measured extinction-corrected magnitude
Abundances in the Sculptor dSph 7
and a standard deviation of the photometric error Wecall this error δTeffi where i represents each of the fourphotometric methods of determining Teff In order toarrive at a single photometric Teff we averaged the fourTeffi together with appropriate error weighting We alsoestimated the random and systematic components oferror In summary
Teff =
sum
i TeffiδTminus2effi
sum
i δTminus2effi
(3)
δrandTeff =
sum
i δTminus1effi
sum
i δTminus2effi
(4)
δsysTeff =
radic
radic
radic
radic
radic
sum
i δTminus2effi
sum
i δTminus2effi
(
Teffi minus Teff
)2
1 minus(
sum
i δTminus2effi
)2sum
i δTminus4effi
(5)
δtotalTeff =radic
(δrandTeff)2 + (δsysTeff)2 (6)
For the stars in this data set the median randomsystematic and total errors on Teff were 98 K 58 Kand 117 K respectively The somewhat large errors onthe photometric temperatures indicated that the spec-tra may help constrain Teff Therefore Eq 3 does notshow the final temperature used in the abundance deter-mination Section 47 describes the iterative process fordetermining Teff and elemental abundances from spec-troscopy
We followed a similar procedure for determining log gphotometrically except that we used only the threemodel isochrones and not any empirical calibrationThe error on the true distance modulus (1967 plusmn 012Pietrzynski et al 2008) was included in the Monte Carlodetermination of the error on log g The median ran-dom systematic and total errors on log g were 006 001and 006 These errors are very small and the medium-resolution red spectra have little power to help constrainlog g because there are so few ionized lines visible There-fore we assumed the photometric value of log g for theabundance analysis
46 Wavelength Masks
The procedure described in the next section consistedof separately measuring the abundances of five elementsMg Si Ca Ti and Fe The procedure relied on findingthe synthetic spectrum that best matched an observedspectrum In order to make this matching most sensitiveto a particular element we masked all spectral regionsthat were not significantly affected by abundance changesof that element
To make the wavelength masks we began with a basespectrum that represented the solar composition in whichthe abundances of all the metals were scaled down by15 dex ([AH] = minus15) The temperature and gravityof the synthetic star were Teff = 4000 K and log g = 10Then we created two pairs of spectra for each of thefive elements In one spectrum the abundance of theelement was enhanced by 03 dex and in the other de-pleted by 03 dex Spectral regions where the flux differ-ence between these two spectra exceeds 05 were usedin the abundance determination of that element This
Fig 5mdash A coaddition of all Sculptor stars with the continuumnormalized to unity The high SNR provided by the coadditionmakes stellar absorption lines readily apparent The colored re-gions show the wavelength masks used in the determination of theabundance of each element Regions susceptible to telluric absorp-tion are labeled with blue text Because large residuals from thetelluric absorption correction remain we eliminate these regionsfrom the abundance analysis Some stellar features excluded fromthe abundances measurement are also labeled
small threshold assured that weak lines which experi-ence large fractional changes in EW as [FeH] changeswere included in the analysis We repeated this proce-dure for spectra with Teff = 5000 K 6000 K 7000 K and8000 K Additional spectral regions that passed the 05flux difference criterion were also included in the abun-dance determination of that element All other wave-lengths were masked
The result was one wavelength mask for each of MgSi Ca Ti and Fe shown in Fig 5 We also createdone ldquoαrdquo mask as the intersection of the Mg Si Ca andTi masks The α element regions do not overlap witheach other but the α element regions do overlap withthe Fe regions The most severe case is the Ca maskwhere sim 35 of the pixels are shared with the Fe maskHowever the overlap did not introduce interdependencein the abundance measurements The α element abun-dances were held fixed while [FeH] was measured andthe Fe abundance was held fixed while [αFe] was mea-sured The measurements of [FeH] and [αFe] were per-formed iteratively (see the next subsection) We testedthe independence of the measurements by removing alloverlapping pixels from consideration Abundance mea-surements changed on average by only 001 dex
47 Measuring Atmospheric Parameters and ElementalAbundances
A Levenberg-Marquardt algorithm (the IDL routineMPFIT written by Markwardt 2009) found the best-fitting synthetic spectrum in ten iterative steps In eachstep the χ2 was computed between an observed spec-trum and a synthetic spectrum degraded to match theresolution of the observed spectrum First we interpo-
8 Kirby et al
lated the synthetic spectrum onto the same wavelengtharray as the observed spectrum Then we smoothedthe synthetic spectrum through a Gaussian filter whosewidth was the observed spectrumrsquos measured resolutionas a function of wavelength
1 Teff and [FeH] first pass An observed spectrumwas compared to a synthetic spectrum with Teff
and log g determined as described in Sec 45 and[FeH] determined from Yonsei-Yale isochronesFor this iteration [αFe] was fixed at 00 (solar)and only spectral regions most susceptible to Fe ab-sorption (Sec 46) were considered The two quan-tities Teff and [FeH] were varied and the algo-rithm found the best-fitting synthetic spectrum byminimizing χ2 We sampled the parameter spacebetween grid points by linearly interpolating thesynthetic spectra at the neighboring grid pointsTeff was also loosely constrained by photometry Asthe spectrum caused Teff to stray from the photo-metric values χ2 increased and it increased moresharply for smaller photometric errors (as calcu-lated in Eq 6) Therefore both photometry andspectroscopy determined Teff Photometry alonedetermined log g
2 [αFe] first pass For this iteration Teff log g and[FeH] were fixed Only [αFe] was allowed to varyIn the model stellar atmosphere the abundances ofthe α elements with respect to Fe varied togetherOnly the spectral regions susceptible to absorptionby Mg Si Ca or Ti were considered
3 Continuum refinement The continuum-dividedobserved spectrum was divided by the syntheticspectrum with the parameters determined in steps1 and 2 The result approximated a flat noise spec-trum To better determine the continuum we fita B-spline with a breakpoint spacing of 50 A tothe residual spectrum We divided the observedspectrum by the spline fit
4 [FeH] second pass We repeated step 1 with therevised spectrum but Teff was held fixed at thepreviously determined value
5 [MgFe] We repeated step 2 However only Mgspectral lines were considered in the abundancemeasurement
6 [SiFe] We repeated step 5 for Si instead of Mg
7 [CaFe] We repeated step 5 for Ca instead of Mg
8 [TiFe] We repeated step 5 for Ti instead of Mg
9 [αFe] second pass We repeated step 2 for allof the α elements instead of just Mg This stepwas simply a different way to average the α el-ement abundances than combining the individualmeasurements of [MgFe] [SiFe] [CaFe] and[TiFe]
10 [FeH] third pass The value of [αFe] affected themeasurement of [FeH] because [αFe] can affect
the structure of the stellar atmosphere Specif-ically the greater availability of electron donorswith an increased [αFe] ratio allows for a higherdensity of Hminus ions The subsequent increase in con-tinuous opacity decreases the strength of Fe andother non-α element lines With [αFe] fixed atthe value determined in step 9 we re-measured[FeH] Typically [FeH] changed from the valuedetermined in step 1 by much less than 01 dex
48 Correction to [FeH]
In comparing our MRS measurements of [FeH] to HRSmeasurements of the same stars (see the appendix) wenoticed that our measurements of metal-poor stars wereconsistently sim 015 dex lower The same pattern is alsovisible in the Kirby et al (2008a) GC measurements (seetheir Figs 6 7 10 and 11)
We have thoroughly examined possible sources of thisdifference of scale The changes to the microturbulentvelocity relation (Sec 42) and the line list (Sec 43)were intended to yield a more accurate and standardizedestimation of [FeH] but the offset still remained Re-stricting the analysis to narrow spectral regions did notreveal any systematic trend of [FeH] with wavelength
A possible explanation for this offset is overionization(Thevenin amp Idiart 1999) Ultraviolet radiation in stellaratmospheres can ionize Fe more than would be expectedin LTE Therefore the abundance of Fe I would seem tobe lower than the abundance of Fe II in an LTE analysisFe II does not suffer from this effect However the effectis smaller at higher [FeH] and we do not observe a trendwith metallicity for the offset of our values relative toHRS studies
In order to standardize our measurements with previ-ous HRS studies we added 015 dex to all of our mea-surements of [FeH] This offset and the microturbu-lent velocity-surface gravity relation are the only ways inwhich previous HRS studies inform our measurementsFurthermore this offset is not intended to change thestandardization of our abundances All of the abundancein this article including those from other studies aregiven relative to the solar abundances quoted in Table 4
49 Error Estimation
We repeated the error estimation procedure describedby KGS08 (their Sec 6) by repeating their abundanceanalysis on GC stars with the above modifications Weno longer found a convincing trend of δ[FeH] with[FeH] Instead we estimate the total error on [FeH] byadding a systematic error in quadrature with the SNR-dependent uncertainty of the synthetic spectral fit Themagnitude of δsys[FeH] = 0136 was the value requiredto force HRS and MRS [FeH] estimates of the same GCstars to agree at the 1σ level We also estimated sys-tematic errors for each of [MgFe] [SiFe] [CaFe] and
Abundances in the Sculptor dSph 9
minus4 minus3 minus2 minus1 0[FeH]
0
10
20
30
40
50N
([F
eH
])
0
100
200
300
400
500
dN
d[F
eH
]
SculptorSimple ModelInfall Model
Fig 6mdash The metallicity distribution in Sculptor The red curveis the maximum likelihood fit to a galactic chemical evolutionmodel with pre-enrichment (Eq 7) and the green curve is the max-imum likelihood fit to a model of star formation in the presence ofinfalling zero-metallicity gas (Eq 11) The long metal-poor tailis typical for systems with non-instantaneous star formation
[TiFe] in the same manner as for [FeH] These are listedin Table 5
5 RESULTS
In this section we discuss the interpretation of theabundance measurements in Sculptor all of which arepresented in Table 6 on the last page of this manuscript
51 Metallicity Distribution
The metallicity distribution function (MDF) of a dwarfgalaxy can reveal much about its star formation his-tory In chemical evolution models of dwarf galax-ies (eg Lanfranchi amp Matteucci 2004 Marcolini et al2006 2008) the duration of star formation affects theshape of the MDF The MDF also has implications forthe formation of the MW If the MW halo was built fromdSphs (Searle amp Zinn 1978 White amp Rees 1978) then itis important to find dSph counterparts to halo field starsat all metallicities as pointed out by Helmi et al (2006hereafter H06)
Figure 6 shows the MDF of Sculptor The shape of theMDF is highly asymmetric with a long metal-poor tail(as predicted by Salvadori amp Ferrara 2009) The inverse-variance weighted mean is 〈[FeH]〉 = minus158 with a stan-dard deviation of 041 The median is minus158 with a me-dian absolute deviation of 033 and an interquartile rangeof 067
The MDF boasts an exceptionally metal-poor starS1020549 The metallicity is [FeH] = minus380 plusmn 028Figure 7 shows how weak the Fe absorption lines are inthis star Frebel Kirby amp Simon (in preparation) haveconfirmed this extremely low metallicity with a high-resolution spectrum
Sculptor is now the most luminous dSph in whichan extremely metal-poor (EMP [FeH] lt minus3) starhas been detected [Kirby et al (2008b) discovered 15EMP stars across eight ultra-faint dwarf galaxies andCohen amp Huang (2009) discovered one EMP star in theDraco dSph] Stars more metal-poor than S1020549 areknown to exist only in the field of the Milky Way fieldThis discovery hints that dSph galaxies like Sculptor mayhave contributed to the formation of the metal-poor com-
Fig 7mdash Regions of the DEIMOS spectrum of the extremelymetal-poor star S1020549 which has [FeH] = minus380 plusmn 028 Thespectrum appears particularly noisy because the y-axis range issmall Some Fe absorption lines are barely detectable but all to-gether they contain enough signal to make a quantitative mea-surement of [FeH] The shading corresponds to the same spectralregion shown in Fig 5 Frebel Kirby amp Simon (in preparation)will present a high-resolution spectrum of this star which confirmsthe extremely low metallicity
ponent of the halo We discuss Sculptorrsquos link to the halofurther in Sec 513
The MT2D photometric selection of spectroscopic tar-gets may have introduced a tiny [FeH] bias Figure 2shows that the RGB is sharply defined in Sculptor Be-cause the number density of stars redward and bluewardof the RGB is much lower than the number density on theRGB the number of very young or very metal-poor stars(blueward) or very metal-rich stars (redward) missed byphotometric pre-selection must be negligible Further-more the hard color cut (as opposed to one that dependson M minus D color) was 06 lt (M minus T2)0 lt 22 The CMDgives no reason to suspect Sculptor RGB members out-side of these limits but it is possible that some extremelyblue Sculptor members have been excluded
511 Possible Explanation of the Discrepancy withPrevious Results
Our measured MDF and our detection of EMP stars inSculptor are at odds with the findings of H06 Whereasour MDF peaks at [FeH] sim minus13 theirs peaks at[FeH] sim minus18 Furthermore our observed MDF is muchmore asymmetric than that of H06 which may even beslightly asymmetric in the opposite sense (a longer metal-rich tail) The greater symmetry would indicate a lessextended star formation history or early infall of a largeamount of gas (Prantzos 2003)
Battaglia et al (2008b hereafter B08b) observed asubset of the H06 stars at high resolution The MDFsfrom the two studies have noticeably different shapesFigure 8 shows that the HRS MDF peaks at [FeH] simminus13 which is also the peak that we observe The meanand standard deviation of their MDF are minus156 and 038
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 5
80 100 120 140vhelio (km sminus1)
0
10
20
30
40
N
langvhelioranglangvheliorang = 1116 plusmn 05 km sminus1
σv σv = 80 plusmn 07 km sminus1
Fig 4mdash Distribution of measured radial velocities for targetsin the Sculptor field along with the best-fit Gaussian The topleft label gives the mean and standard deviation of this Gaussianfit The five stars outside of the dashed lines are not consideredSculptor members The velocity range of this plot includes all starsfor which a velocity measurement was possible
deviations of the differences in measured velocities forthe 17 duplicate spectra In comparison Westfall et al(2006) found 〈vhelio〉 = 1104 plusmn 08 km sminus1 (difference of+12σ) and σv = 88plusmn 06 km sminus1 (difference of minus09σ)The comparison of the velocity dispersions depends onthe assumed binary fraction (Queloz et al 1995) andmdashgiven the presence of multiple kinematically and spa-tially distinct populations in Sculptor (T04)mdashthe regionof spectroscopic selection Furthermore Walker et al(2007 2009) reported velocity dispersion gradients andBattaglia et al (2008a) reported mean velocity gradientsalong the major axis indicating rotation We choose notto address the kinematic complexity of this system inthis paper
34 Continuum Determination
In the abundance analysis described in Sec 4 it isnecessary to normalize each stellar spectrum by dividingby the slowly varying stellar continuum KGS08 deter-mined the continuum by smoothing the regions of thestellar spectrum free from strong absorption lines In-stead of smoothing we fit a B-spline with a breakpointspacing of 150 A to the same ldquocontinuum regionsrdquo de-fined by KGS08 Each pixel was weighted by its inversevariance in the fit Furthermore the fit was performediteratively such that pixels that deviated from the fit bymore than 5σ were removed from the next iteration ofthe fit
The spline fit results in a smoother continuum determi-nation than smoothing Whereas the smoothed contin-uum value may be influenced heavily by one or a few pix-els within a relatively small smoothing kernel the splinefit is a global fit It is more likely to be representative ofthe true stellar continuum than a smoothed spectrum
Shetrone et al (2009) pointed out the importance ofdetermining the continuum accurately when measur-ing weak lines in medium-resolution spectra They re-fined their continuum determinations by iteratively fit-
TABLE 3New Grid of ATLAS9 Model Atmospheres
Parameter Minimum Value Maximum Value Step
Teff (K) 3500 5600 1005600 8000 200
log g (cm sminus2) 00 (Teff lt 7000 K) 50 0505 (Teff ge 7000 K) 50 05
[AH] minus40 00 05[αFe] minus08 +12 01
ting a high-order spline to the quotient of the observedspectrum and the best-fitting synthetic spectrum Weadopted this procedure as well As part of the iterativeprocess described in Sec 47 we fit a B-spline with abreakpoint spacing of 50 A to the observed spectrum di-vided by the best-fitting synthetic spectrum We dividedthe observed spectrum by this spline before the next it-eration of abundance measurement
4 ABUNDANCE MEASUREMENTS
The following section details some improvements onthe abundance measurement techniques of KGS08 As-pects of the technique not mentioned here were un-changed from the technique of KGS08 In summaryeach observed spectrum was compared to a large gridof synthetic spectra The atmospheric abundances wereadopted from the synthetic spectrum with the lowest χ2
A major improvement was our measurement of fourindividual elemental abundances in addition to Fe MgSi Ca and Ti We chose these elements because they areimportant in characterizing the star formation history ofa stellar population and because a significant numberof lines represent each of them in the DEIMOS spectralrange
41 Model Atmospheres
Like KGS08 we built synthetic spectra based on AT-LAS9 model atmospheres (Kurucz 1993) with no con-vective overshooting (Castelli et al 1997) KGS08 choseto allow the atmospheres to have [αFe] = +04 or[αFe] = 00 This choice allowed them to use the largegrid of ATLAS9 model atmospheres computed with newopacity distribution functions (Castelli amp Kurucz 2004)However we found that best-fitting model spectra com-puted by KGS08 tended to cluster around [αFe] = +02due to the discontinuity in χ2 caused by the abruptswitch between alpha-enhanced and solar-scaled models
To avoid this discontinuity we recomputed ATLAS9model atmospheres on the grid summarized in Table 3The new grid required recomputing new opacity distri-bution functions (ODFs) for which we used the DF-SYNTHE code (Castelli 2005) Unlike the grid ofCastelli amp Kurucz (2004) we adopted the solar compo-sition of Anders amp Grevesse (1989) except for Fe forwhich we followed Sneden et al (1992 see the note in Ta-ble 4) One opacity distribution function was computedfor each of the 189 combinations of [AH] and [αFe]specified in Table 3 The abundances of all the elementsexcept H and He were augmented by [AH] Addition-ally the abundances of O Ne Mg Si Ar Ca and Tiwere augmented by [αFe] These ODFs were used tocompute one ATLAS9 model atmosphere for each grid
6 Kirby et al
point in Table 3 and for two values of microturbulentvelocity for a total of 139104 model atmospheres
42 Microturbulent Velocity
In order to reduce the number of parameters requiredto determine a stellar abundance KGS08 assumed thatthe microturbulent velocity (ξ) of the stellar atmospherewas tied to the surface gravity (log g) They chose to fita line to the spectroscopically measured ξ and log g ofthe giant stars in Fulbrightrsquos (2000) sample
ξ (km sminus1) = 270 minus 051 log g (1)
We also adopted a relation between ξ and log g but were-determined this relation from the GC red giant sampleof KGS08 combined with Kirbyrsquos (2009) compilation ofhigh-resolution spectroscopic measurements from the lit-erature (Frebel et al 2009 Geisler et al 2005 Johnson2002 Lai et al 2007 Shetrone et al 2001 2003 and ref-erences from KGS08) The best-fit line between the spec-troscopically measured ξ and log g is
corresponding roughly to a 00ndash05 km sminus1 decrease inξ depending on log g In the generation of the grid ofsynthetic stellar spectra described in Sec 44 ξ was nota free parameter but was fixed to log g via Eq 2
In general a decrease in ξ increases the measurementof [FeH] Therefore this change tended to increase thederived values of [FeH] A typical change in [FeH] was +005 dex This change would be more severe in anHRS analysis based on equivalent widths (EWs) In ourχ2 minimization the abundance measurement was mostsensitive to lines with large d(EW)d[FeH] Such linesare the weak unsaturated transitions whose strengthdoes not depend on ξ The DEIMOS spectra containenough of these weak lines that ξ did not play a largerole in the abundance determination
43 Line List
We compared the Fe I oscillator strengths (log gf) inthe KGS08 line list to values measured in the labora-tory (Fuhr amp Wiese 2006) Most of the KGS08 oscilla-tor strengths were stronger than the laboratory measure-ments The average offset was 013 dex Because KGS08calibrated their line list to the solar spectrum we in-terpreted this offset as a systematic error in the solarmodel atmosphere solar spectral synthesis andor solarcomposition Accepting the laboratory-measured valuesas more accurate than the solar calibration we replacedFe I oscillator strengths with Fuhr amp Wiese where avail-able and we subtracted 013 dex from log gf for all otherFe I transitions in the KGS08 line list All other data re-mained unchanged
Decreasing the oscillator strengths requires a larger[FeH] to match the observed spectrum The amount ofchange in [FeH] depends on the atmospheric parametersas well as the saturation of the measured Fe lines Fromcomparison of results with the old and new line lists weestimate a typical change in [FeH] to be sim +01 dex
44 Generation of Synthetic Spectra
TABLE 4Adopted Solar Composition
Element 12 + log ǫ Element 12 + log ǫ
Mg 758 Ti 499Ca 636 Fe 752Si 755
Note mdash This composition is adopted fromAnders amp Grevesse (1989) except for Fe Forjustification of the adopted Fe solar abun-dance see Sneden et al (1992) The abun-dance of an element X is defined as its numberdensity relative to hydrogen 12 + log ǫX =12 + log(nX) minus log(nH)
The spectra were synthesized as described in KGS08Specifically the current version of the local thermody-namic equilibrium (LTE) spectrum synthesis softwareMOOG (Sneden 1973) generated one spectrum for eachpoint on the grid The spectral grid was more finelyspaced in [FeH] than the model atmosphere grid Thespacing is 01 dex for each of [FeH] and [αFe] yieldinga total of 316848 synthetic spectra
The solar composition used in the generation of thesynthetic spectra was identical to the solar compositionused in the computation of the model atmospheres Ta-ble 4 lists the adopted solar abundances for the five el-ements for which we measure abundances in Sculptorstars
45 Effective Temperatures and Surface Gravities
Different spectroscopic studies of chemical abundancesrely on different sources of information for determin-ing the effective temperature (Teff) and surface grav-ity (log g) of the stellar atmosphere KGS08 con-sulted Yonsei-Yale model isochrones (Demarque et al2004) to determine the temperature and gravity thatcorrespond to a dereddened color and an extinction-corrected absolute magnitude They also consideredVictoria-Regina (VandenBerg et al 2006) and Padova(Girardi et al 2002) model isochrones as well as an em-pirical color-temperature relation (Ramırez amp Melendez2005)
The Fe lines accessible in DEIMOS spectra span a largerange of excitation potential Together these differentlines provide a constraint on Teff KGS08 (their Sec 51)showed thatmdashwithout any photometric informationmdashthe synthesis analysis of medium-resolution spectra ofGC stars yielded values of Teff very close to values previ-ously measured from HRS Therefore we chose to mea-sure Teff from photometry and spectroscopy simultane-ously
To begin we converted extinction-corrected(Schlegel et al 1998) Washington M and T2 magnitudesto Cousins VC and IC magnitudes (Majewski et al2000) With these magnitudes we computed Teff fromthe Yonsei-Yale Victoria-Regina and Padova modelisochrones as well as the Ramırez amp Melendez (2005)empirical color-based Teff For each measurement we es-timated the effect of photometric error by measuring thestandard deviation of Teff determined from 1000 MonteCarlo realizations of VC and IC In each realization VC
and IC were chosen from a normal distribution with amean of the measured extinction-corrected magnitude
Abundances in the Sculptor dSph 7
and a standard deviation of the photometric error Wecall this error δTeffi where i represents each of the fourphotometric methods of determining Teff In order toarrive at a single photometric Teff we averaged the fourTeffi together with appropriate error weighting We alsoestimated the random and systematic components oferror In summary
Teff =
sum
i TeffiδTminus2effi
sum
i δTminus2effi
(3)
δrandTeff =
sum
i δTminus1effi
sum
i δTminus2effi
(4)
δsysTeff =
radic
radic
radic
radic
radic
sum
i δTminus2effi
sum
i δTminus2effi
(
Teffi minus Teff
)2
1 minus(
sum
i δTminus2effi
)2sum
i δTminus4effi
(5)
δtotalTeff =radic
(δrandTeff)2 + (δsysTeff)2 (6)
For the stars in this data set the median randomsystematic and total errors on Teff were 98 K 58 Kand 117 K respectively The somewhat large errors onthe photometric temperatures indicated that the spec-tra may help constrain Teff Therefore Eq 3 does notshow the final temperature used in the abundance deter-mination Section 47 describes the iterative process fordetermining Teff and elemental abundances from spec-troscopy
We followed a similar procedure for determining log gphotometrically except that we used only the threemodel isochrones and not any empirical calibrationThe error on the true distance modulus (1967 plusmn 012Pietrzynski et al 2008) was included in the Monte Carlodetermination of the error on log g The median ran-dom systematic and total errors on log g were 006 001and 006 These errors are very small and the medium-resolution red spectra have little power to help constrainlog g because there are so few ionized lines visible There-fore we assumed the photometric value of log g for theabundance analysis
46 Wavelength Masks
The procedure described in the next section consistedof separately measuring the abundances of five elementsMg Si Ca Ti and Fe The procedure relied on findingthe synthetic spectrum that best matched an observedspectrum In order to make this matching most sensitiveto a particular element we masked all spectral regionsthat were not significantly affected by abundance changesof that element
To make the wavelength masks we began with a basespectrum that represented the solar composition in whichthe abundances of all the metals were scaled down by15 dex ([AH] = minus15) The temperature and gravityof the synthetic star were Teff = 4000 K and log g = 10Then we created two pairs of spectra for each of thefive elements In one spectrum the abundance of theelement was enhanced by 03 dex and in the other de-pleted by 03 dex Spectral regions where the flux differ-ence between these two spectra exceeds 05 were usedin the abundance determination of that element This
Fig 5mdash A coaddition of all Sculptor stars with the continuumnormalized to unity The high SNR provided by the coadditionmakes stellar absorption lines readily apparent The colored re-gions show the wavelength masks used in the determination of theabundance of each element Regions susceptible to telluric absorp-tion are labeled with blue text Because large residuals from thetelluric absorption correction remain we eliminate these regionsfrom the abundance analysis Some stellar features excluded fromthe abundances measurement are also labeled
small threshold assured that weak lines which experi-ence large fractional changes in EW as [FeH] changeswere included in the analysis We repeated this proce-dure for spectra with Teff = 5000 K 6000 K 7000 K and8000 K Additional spectral regions that passed the 05flux difference criterion were also included in the abun-dance determination of that element All other wave-lengths were masked
The result was one wavelength mask for each of MgSi Ca Ti and Fe shown in Fig 5 We also createdone ldquoαrdquo mask as the intersection of the Mg Si Ca andTi masks The α element regions do not overlap witheach other but the α element regions do overlap withthe Fe regions The most severe case is the Ca maskwhere sim 35 of the pixels are shared with the Fe maskHowever the overlap did not introduce interdependencein the abundance measurements The α element abun-dances were held fixed while [FeH] was measured andthe Fe abundance was held fixed while [αFe] was mea-sured The measurements of [FeH] and [αFe] were per-formed iteratively (see the next subsection) We testedthe independence of the measurements by removing alloverlapping pixels from consideration Abundance mea-surements changed on average by only 001 dex
47 Measuring Atmospheric Parameters and ElementalAbundances
A Levenberg-Marquardt algorithm (the IDL routineMPFIT written by Markwardt 2009) found the best-fitting synthetic spectrum in ten iterative steps In eachstep the χ2 was computed between an observed spec-trum and a synthetic spectrum degraded to match theresolution of the observed spectrum First we interpo-
8 Kirby et al
lated the synthetic spectrum onto the same wavelengtharray as the observed spectrum Then we smoothedthe synthetic spectrum through a Gaussian filter whosewidth was the observed spectrumrsquos measured resolutionas a function of wavelength
1 Teff and [FeH] first pass An observed spectrumwas compared to a synthetic spectrum with Teff
and log g determined as described in Sec 45 and[FeH] determined from Yonsei-Yale isochronesFor this iteration [αFe] was fixed at 00 (solar)and only spectral regions most susceptible to Fe ab-sorption (Sec 46) were considered The two quan-tities Teff and [FeH] were varied and the algo-rithm found the best-fitting synthetic spectrum byminimizing χ2 We sampled the parameter spacebetween grid points by linearly interpolating thesynthetic spectra at the neighboring grid pointsTeff was also loosely constrained by photometry Asthe spectrum caused Teff to stray from the photo-metric values χ2 increased and it increased moresharply for smaller photometric errors (as calcu-lated in Eq 6) Therefore both photometry andspectroscopy determined Teff Photometry alonedetermined log g
2 [αFe] first pass For this iteration Teff log g and[FeH] were fixed Only [αFe] was allowed to varyIn the model stellar atmosphere the abundances ofthe α elements with respect to Fe varied togetherOnly the spectral regions susceptible to absorptionby Mg Si Ca or Ti were considered
3 Continuum refinement The continuum-dividedobserved spectrum was divided by the syntheticspectrum with the parameters determined in steps1 and 2 The result approximated a flat noise spec-trum To better determine the continuum we fita B-spline with a breakpoint spacing of 50 A tothe residual spectrum We divided the observedspectrum by the spline fit
4 [FeH] second pass We repeated step 1 with therevised spectrum but Teff was held fixed at thepreviously determined value
5 [MgFe] We repeated step 2 However only Mgspectral lines were considered in the abundancemeasurement
6 [SiFe] We repeated step 5 for Si instead of Mg
7 [CaFe] We repeated step 5 for Ca instead of Mg
8 [TiFe] We repeated step 5 for Ti instead of Mg
9 [αFe] second pass We repeated step 2 for allof the α elements instead of just Mg This stepwas simply a different way to average the α el-ement abundances than combining the individualmeasurements of [MgFe] [SiFe] [CaFe] and[TiFe]
10 [FeH] third pass The value of [αFe] affected themeasurement of [FeH] because [αFe] can affect
the structure of the stellar atmosphere Specif-ically the greater availability of electron donorswith an increased [αFe] ratio allows for a higherdensity of Hminus ions The subsequent increase in con-tinuous opacity decreases the strength of Fe andother non-α element lines With [αFe] fixed atthe value determined in step 9 we re-measured[FeH] Typically [FeH] changed from the valuedetermined in step 1 by much less than 01 dex
48 Correction to [FeH]
In comparing our MRS measurements of [FeH] to HRSmeasurements of the same stars (see the appendix) wenoticed that our measurements of metal-poor stars wereconsistently sim 015 dex lower The same pattern is alsovisible in the Kirby et al (2008a) GC measurements (seetheir Figs 6 7 10 and 11)
We have thoroughly examined possible sources of thisdifference of scale The changes to the microturbulentvelocity relation (Sec 42) and the line list (Sec 43)were intended to yield a more accurate and standardizedestimation of [FeH] but the offset still remained Re-stricting the analysis to narrow spectral regions did notreveal any systematic trend of [FeH] with wavelength
A possible explanation for this offset is overionization(Thevenin amp Idiart 1999) Ultraviolet radiation in stellaratmospheres can ionize Fe more than would be expectedin LTE Therefore the abundance of Fe I would seem tobe lower than the abundance of Fe II in an LTE analysisFe II does not suffer from this effect However the effectis smaller at higher [FeH] and we do not observe a trendwith metallicity for the offset of our values relative toHRS studies
In order to standardize our measurements with previ-ous HRS studies we added 015 dex to all of our mea-surements of [FeH] This offset and the microturbu-lent velocity-surface gravity relation are the only ways inwhich previous HRS studies inform our measurementsFurthermore this offset is not intended to change thestandardization of our abundances All of the abundancein this article including those from other studies aregiven relative to the solar abundances quoted in Table 4
49 Error Estimation
We repeated the error estimation procedure describedby KGS08 (their Sec 6) by repeating their abundanceanalysis on GC stars with the above modifications Weno longer found a convincing trend of δ[FeH] with[FeH] Instead we estimate the total error on [FeH] byadding a systematic error in quadrature with the SNR-dependent uncertainty of the synthetic spectral fit Themagnitude of δsys[FeH] = 0136 was the value requiredto force HRS and MRS [FeH] estimates of the same GCstars to agree at the 1σ level We also estimated sys-tematic errors for each of [MgFe] [SiFe] [CaFe] and
Abundances in the Sculptor dSph 9
minus4 minus3 minus2 minus1 0[FeH]
0
10
20
30
40
50N
([F
eH
])
0
100
200
300
400
500
dN
d[F
eH
]
SculptorSimple ModelInfall Model
Fig 6mdash The metallicity distribution in Sculptor The red curveis the maximum likelihood fit to a galactic chemical evolutionmodel with pre-enrichment (Eq 7) and the green curve is the max-imum likelihood fit to a model of star formation in the presence ofinfalling zero-metallicity gas (Eq 11) The long metal-poor tailis typical for systems with non-instantaneous star formation
[TiFe] in the same manner as for [FeH] These are listedin Table 5
5 RESULTS
In this section we discuss the interpretation of theabundance measurements in Sculptor all of which arepresented in Table 6 on the last page of this manuscript
51 Metallicity Distribution
The metallicity distribution function (MDF) of a dwarfgalaxy can reveal much about its star formation his-tory In chemical evolution models of dwarf galax-ies (eg Lanfranchi amp Matteucci 2004 Marcolini et al2006 2008) the duration of star formation affects theshape of the MDF The MDF also has implications forthe formation of the MW If the MW halo was built fromdSphs (Searle amp Zinn 1978 White amp Rees 1978) then itis important to find dSph counterparts to halo field starsat all metallicities as pointed out by Helmi et al (2006hereafter H06)
Figure 6 shows the MDF of Sculptor The shape of theMDF is highly asymmetric with a long metal-poor tail(as predicted by Salvadori amp Ferrara 2009) The inverse-variance weighted mean is 〈[FeH]〉 = minus158 with a stan-dard deviation of 041 The median is minus158 with a me-dian absolute deviation of 033 and an interquartile rangeof 067
The MDF boasts an exceptionally metal-poor starS1020549 The metallicity is [FeH] = minus380 plusmn 028Figure 7 shows how weak the Fe absorption lines are inthis star Frebel Kirby amp Simon (in preparation) haveconfirmed this extremely low metallicity with a high-resolution spectrum
Sculptor is now the most luminous dSph in whichan extremely metal-poor (EMP [FeH] lt minus3) starhas been detected [Kirby et al (2008b) discovered 15EMP stars across eight ultra-faint dwarf galaxies andCohen amp Huang (2009) discovered one EMP star in theDraco dSph] Stars more metal-poor than S1020549 areknown to exist only in the field of the Milky Way fieldThis discovery hints that dSph galaxies like Sculptor mayhave contributed to the formation of the metal-poor com-
Fig 7mdash Regions of the DEIMOS spectrum of the extremelymetal-poor star S1020549 which has [FeH] = minus380 plusmn 028 Thespectrum appears particularly noisy because the y-axis range issmall Some Fe absorption lines are barely detectable but all to-gether they contain enough signal to make a quantitative mea-surement of [FeH] The shading corresponds to the same spectralregion shown in Fig 5 Frebel Kirby amp Simon (in preparation)will present a high-resolution spectrum of this star which confirmsthe extremely low metallicity
ponent of the halo We discuss Sculptorrsquos link to the halofurther in Sec 513
The MT2D photometric selection of spectroscopic tar-gets may have introduced a tiny [FeH] bias Figure 2shows that the RGB is sharply defined in Sculptor Be-cause the number density of stars redward and bluewardof the RGB is much lower than the number density on theRGB the number of very young or very metal-poor stars(blueward) or very metal-rich stars (redward) missed byphotometric pre-selection must be negligible Further-more the hard color cut (as opposed to one that dependson M minus D color) was 06 lt (M minus T2)0 lt 22 The CMDgives no reason to suspect Sculptor RGB members out-side of these limits but it is possible that some extremelyblue Sculptor members have been excluded
511 Possible Explanation of the Discrepancy withPrevious Results
Our measured MDF and our detection of EMP stars inSculptor are at odds with the findings of H06 Whereasour MDF peaks at [FeH] sim minus13 theirs peaks at[FeH] sim minus18 Furthermore our observed MDF is muchmore asymmetric than that of H06 which may even beslightly asymmetric in the opposite sense (a longer metal-rich tail) The greater symmetry would indicate a lessextended star formation history or early infall of a largeamount of gas (Prantzos 2003)
Battaglia et al (2008b hereafter B08b) observed asubset of the H06 stars at high resolution The MDFsfrom the two studies have noticeably different shapesFigure 8 shows that the HRS MDF peaks at [FeH] simminus13 which is also the peak that we observe The meanand standard deviation of their MDF are minus156 and 038
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
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18 Kirby et al
16
18
20
22
24ξ M
RS
(km
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1446
195
H48
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H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
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minus01
00
01
02
03
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m sminus
1 ) minus
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1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
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00
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H] M
RS
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eH
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1446
195
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982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
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Abundances in the Sculptor dSph 19
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minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
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AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
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Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
6 Kirby et al
point in Table 3 and for two values of microturbulentvelocity for a total of 139104 model atmospheres
42 Microturbulent Velocity
In order to reduce the number of parameters requiredto determine a stellar abundance KGS08 assumed thatthe microturbulent velocity (ξ) of the stellar atmospherewas tied to the surface gravity (log g) They chose to fita line to the spectroscopically measured ξ and log g ofthe giant stars in Fulbrightrsquos (2000) sample
ξ (km sminus1) = 270 minus 051 log g (1)
We also adopted a relation between ξ and log g but were-determined this relation from the GC red giant sampleof KGS08 combined with Kirbyrsquos (2009) compilation ofhigh-resolution spectroscopic measurements from the lit-erature (Frebel et al 2009 Geisler et al 2005 Johnson2002 Lai et al 2007 Shetrone et al 2001 2003 and ref-erences from KGS08) The best-fit line between the spec-troscopically measured ξ and log g is
corresponding roughly to a 00ndash05 km sminus1 decrease inξ depending on log g In the generation of the grid ofsynthetic stellar spectra described in Sec 44 ξ was nota free parameter but was fixed to log g via Eq 2
In general a decrease in ξ increases the measurementof [FeH] Therefore this change tended to increase thederived values of [FeH] A typical change in [FeH] was +005 dex This change would be more severe in anHRS analysis based on equivalent widths (EWs) In ourχ2 minimization the abundance measurement was mostsensitive to lines with large d(EW)d[FeH] Such linesare the weak unsaturated transitions whose strengthdoes not depend on ξ The DEIMOS spectra containenough of these weak lines that ξ did not play a largerole in the abundance determination
43 Line List
We compared the Fe I oscillator strengths (log gf) inthe KGS08 line list to values measured in the labora-tory (Fuhr amp Wiese 2006) Most of the KGS08 oscilla-tor strengths were stronger than the laboratory measure-ments The average offset was 013 dex Because KGS08calibrated their line list to the solar spectrum we in-terpreted this offset as a systematic error in the solarmodel atmosphere solar spectral synthesis andor solarcomposition Accepting the laboratory-measured valuesas more accurate than the solar calibration we replacedFe I oscillator strengths with Fuhr amp Wiese where avail-able and we subtracted 013 dex from log gf for all otherFe I transitions in the KGS08 line list All other data re-mained unchanged
Decreasing the oscillator strengths requires a larger[FeH] to match the observed spectrum The amount ofchange in [FeH] depends on the atmospheric parametersas well as the saturation of the measured Fe lines Fromcomparison of results with the old and new line lists weestimate a typical change in [FeH] to be sim +01 dex
44 Generation of Synthetic Spectra
TABLE 4Adopted Solar Composition
Element 12 + log ǫ Element 12 + log ǫ
Mg 758 Ti 499Ca 636 Fe 752Si 755
Note mdash This composition is adopted fromAnders amp Grevesse (1989) except for Fe Forjustification of the adopted Fe solar abun-dance see Sneden et al (1992) The abun-dance of an element X is defined as its numberdensity relative to hydrogen 12 + log ǫX =12 + log(nX) minus log(nH)
The spectra were synthesized as described in KGS08Specifically the current version of the local thermody-namic equilibrium (LTE) spectrum synthesis softwareMOOG (Sneden 1973) generated one spectrum for eachpoint on the grid The spectral grid was more finelyspaced in [FeH] than the model atmosphere grid Thespacing is 01 dex for each of [FeH] and [αFe] yieldinga total of 316848 synthetic spectra
The solar composition used in the generation of thesynthetic spectra was identical to the solar compositionused in the computation of the model atmospheres Ta-ble 4 lists the adopted solar abundances for the five el-ements for which we measure abundances in Sculptorstars
45 Effective Temperatures and Surface Gravities
Different spectroscopic studies of chemical abundancesrely on different sources of information for determin-ing the effective temperature (Teff) and surface grav-ity (log g) of the stellar atmosphere KGS08 con-sulted Yonsei-Yale model isochrones (Demarque et al2004) to determine the temperature and gravity thatcorrespond to a dereddened color and an extinction-corrected absolute magnitude They also consideredVictoria-Regina (VandenBerg et al 2006) and Padova(Girardi et al 2002) model isochrones as well as an em-pirical color-temperature relation (Ramırez amp Melendez2005)
The Fe lines accessible in DEIMOS spectra span a largerange of excitation potential Together these differentlines provide a constraint on Teff KGS08 (their Sec 51)showed thatmdashwithout any photometric informationmdashthe synthesis analysis of medium-resolution spectra ofGC stars yielded values of Teff very close to values previ-ously measured from HRS Therefore we chose to mea-sure Teff from photometry and spectroscopy simultane-ously
To begin we converted extinction-corrected(Schlegel et al 1998) Washington M and T2 magnitudesto Cousins VC and IC magnitudes (Majewski et al2000) With these magnitudes we computed Teff fromthe Yonsei-Yale Victoria-Regina and Padova modelisochrones as well as the Ramırez amp Melendez (2005)empirical color-based Teff For each measurement we es-timated the effect of photometric error by measuring thestandard deviation of Teff determined from 1000 MonteCarlo realizations of VC and IC In each realization VC
and IC were chosen from a normal distribution with amean of the measured extinction-corrected magnitude
Abundances in the Sculptor dSph 7
and a standard deviation of the photometric error Wecall this error δTeffi where i represents each of the fourphotometric methods of determining Teff In order toarrive at a single photometric Teff we averaged the fourTeffi together with appropriate error weighting We alsoestimated the random and systematic components oferror In summary
Teff =
sum
i TeffiδTminus2effi
sum
i δTminus2effi
(3)
δrandTeff =
sum
i δTminus1effi
sum
i δTminus2effi
(4)
δsysTeff =
radic
radic
radic
radic
radic
sum
i δTminus2effi
sum
i δTminus2effi
(
Teffi minus Teff
)2
1 minus(
sum
i δTminus2effi
)2sum
i δTminus4effi
(5)
δtotalTeff =radic
(δrandTeff)2 + (δsysTeff)2 (6)
For the stars in this data set the median randomsystematic and total errors on Teff were 98 K 58 Kand 117 K respectively The somewhat large errors onthe photometric temperatures indicated that the spec-tra may help constrain Teff Therefore Eq 3 does notshow the final temperature used in the abundance deter-mination Section 47 describes the iterative process fordetermining Teff and elemental abundances from spec-troscopy
We followed a similar procedure for determining log gphotometrically except that we used only the threemodel isochrones and not any empirical calibrationThe error on the true distance modulus (1967 plusmn 012Pietrzynski et al 2008) was included in the Monte Carlodetermination of the error on log g The median ran-dom systematic and total errors on log g were 006 001and 006 These errors are very small and the medium-resolution red spectra have little power to help constrainlog g because there are so few ionized lines visible There-fore we assumed the photometric value of log g for theabundance analysis
46 Wavelength Masks
The procedure described in the next section consistedof separately measuring the abundances of five elementsMg Si Ca Ti and Fe The procedure relied on findingthe synthetic spectrum that best matched an observedspectrum In order to make this matching most sensitiveto a particular element we masked all spectral regionsthat were not significantly affected by abundance changesof that element
To make the wavelength masks we began with a basespectrum that represented the solar composition in whichthe abundances of all the metals were scaled down by15 dex ([AH] = minus15) The temperature and gravityof the synthetic star were Teff = 4000 K and log g = 10Then we created two pairs of spectra for each of thefive elements In one spectrum the abundance of theelement was enhanced by 03 dex and in the other de-pleted by 03 dex Spectral regions where the flux differ-ence between these two spectra exceeds 05 were usedin the abundance determination of that element This
Fig 5mdash A coaddition of all Sculptor stars with the continuumnormalized to unity The high SNR provided by the coadditionmakes stellar absorption lines readily apparent The colored re-gions show the wavelength masks used in the determination of theabundance of each element Regions susceptible to telluric absorp-tion are labeled with blue text Because large residuals from thetelluric absorption correction remain we eliminate these regionsfrom the abundance analysis Some stellar features excluded fromthe abundances measurement are also labeled
small threshold assured that weak lines which experi-ence large fractional changes in EW as [FeH] changeswere included in the analysis We repeated this proce-dure for spectra with Teff = 5000 K 6000 K 7000 K and8000 K Additional spectral regions that passed the 05flux difference criterion were also included in the abun-dance determination of that element All other wave-lengths were masked
The result was one wavelength mask for each of MgSi Ca Ti and Fe shown in Fig 5 We also createdone ldquoαrdquo mask as the intersection of the Mg Si Ca andTi masks The α element regions do not overlap witheach other but the α element regions do overlap withthe Fe regions The most severe case is the Ca maskwhere sim 35 of the pixels are shared with the Fe maskHowever the overlap did not introduce interdependencein the abundance measurements The α element abun-dances were held fixed while [FeH] was measured andthe Fe abundance was held fixed while [αFe] was mea-sured The measurements of [FeH] and [αFe] were per-formed iteratively (see the next subsection) We testedthe independence of the measurements by removing alloverlapping pixels from consideration Abundance mea-surements changed on average by only 001 dex
47 Measuring Atmospheric Parameters and ElementalAbundances
A Levenberg-Marquardt algorithm (the IDL routineMPFIT written by Markwardt 2009) found the best-fitting synthetic spectrum in ten iterative steps In eachstep the χ2 was computed between an observed spec-trum and a synthetic spectrum degraded to match theresolution of the observed spectrum First we interpo-
8 Kirby et al
lated the synthetic spectrum onto the same wavelengtharray as the observed spectrum Then we smoothedthe synthetic spectrum through a Gaussian filter whosewidth was the observed spectrumrsquos measured resolutionas a function of wavelength
1 Teff and [FeH] first pass An observed spectrumwas compared to a synthetic spectrum with Teff
and log g determined as described in Sec 45 and[FeH] determined from Yonsei-Yale isochronesFor this iteration [αFe] was fixed at 00 (solar)and only spectral regions most susceptible to Fe ab-sorption (Sec 46) were considered The two quan-tities Teff and [FeH] were varied and the algo-rithm found the best-fitting synthetic spectrum byminimizing χ2 We sampled the parameter spacebetween grid points by linearly interpolating thesynthetic spectra at the neighboring grid pointsTeff was also loosely constrained by photometry Asthe spectrum caused Teff to stray from the photo-metric values χ2 increased and it increased moresharply for smaller photometric errors (as calcu-lated in Eq 6) Therefore both photometry andspectroscopy determined Teff Photometry alonedetermined log g
2 [αFe] first pass For this iteration Teff log g and[FeH] were fixed Only [αFe] was allowed to varyIn the model stellar atmosphere the abundances ofthe α elements with respect to Fe varied togetherOnly the spectral regions susceptible to absorptionby Mg Si Ca or Ti were considered
3 Continuum refinement The continuum-dividedobserved spectrum was divided by the syntheticspectrum with the parameters determined in steps1 and 2 The result approximated a flat noise spec-trum To better determine the continuum we fita B-spline with a breakpoint spacing of 50 A tothe residual spectrum We divided the observedspectrum by the spline fit
4 [FeH] second pass We repeated step 1 with therevised spectrum but Teff was held fixed at thepreviously determined value
5 [MgFe] We repeated step 2 However only Mgspectral lines were considered in the abundancemeasurement
6 [SiFe] We repeated step 5 for Si instead of Mg
7 [CaFe] We repeated step 5 for Ca instead of Mg
8 [TiFe] We repeated step 5 for Ti instead of Mg
9 [αFe] second pass We repeated step 2 for allof the α elements instead of just Mg This stepwas simply a different way to average the α el-ement abundances than combining the individualmeasurements of [MgFe] [SiFe] [CaFe] and[TiFe]
10 [FeH] third pass The value of [αFe] affected themeasurement of [FeH] because [αFe] can affect
the structure of the stellar atmosphere Specif-ically the greater availability of electron donorswith an increased [αFe] ratio allows for a higherdensity of Hminus ions The subsequent increase in con-tinuous opacity decreases the strength of Fe andother non-α element lines With [αFe] fixed atthe value determined in step 9 we re-measured[FeH] Typically [FeH] changed from the valuedetermined in step 1 by much less than 01 dex
48 Correction to [FeH]
In comparing our MRS measurements of [FeH] to HRSmeasurements of the same stars (see the appendix) wenoticed that our measurements of metal-poor stars wereconsistently sim 015 dex lower The same pattern is alsovisible in the Kirby et al (2008a) GC measurements (seetheir Figs 6 7 10 and 11)
We have thoroughly examined possible sources of thisdifference of scale The changes to the microturbulentvelocity relation (Sec 42) and the line list (Sec 43)were intended to yield a more accurate and standardizedestimation of [FeH] but the offset still remained Re-stricting the analysis to narrow spectral regions did notreveal any systematic trend of [FeH] with wavelength
A possible explanation for this offset is overionization(Thevenin amp Idiart 1999) Ultraviolet radiation in stellaratmospheres can ionize Fe more than would be expectedin LTE Therefore the abundance of Fe I would seem tobe lower than the abundance of Fe II in an LTE analysisFe II does not suffer from this effect However the effectis smaller at higher [FeH] and we do not observe a trendwith metallicity for the offset of our values relative toHRS studies
In order to standardize our measurements with previ-ous HRS studies we added 015 dex to all of our mea-surements of [FeH] This offset and the microturbu-lent velocity-surface gravity relation are the only ways inwhich previous HRS studies inform our measurementsFurthermore this offset is not intended to change thestandardization of our abundances All of the abundancein this article including those from other studies aregiven relative to the solar abundances quoted in Table 4
49 Error Estimation
We repeated the error estimation procedure describedby KGS08 (their Sec 6) by repeating their abundanceanalysis on GC stars with the above modifications Weno longer found a convincing trend of δ[FeH] with[FeH] Instead we estimate the total error on [FeH] byadding a systematic error in quadrature with the SNR-dependent uncertainty of the synthetic spectral fit Themagnitude of δsys[FeH] = 0136 was the value requiredto force HRS and MRS [FeH] estimates of the same GCstars to agree at the 1σ level We also estimated sys-tematic errors for each of [MgFe] [SiFe] [CaFe] and
Abundances in the Sculptor dSph 9
minus4 minus3 minus2 minus1 0[FeH]
0
10
20
30
40
50N
([F
eH
])
0
100
200
300
400
500
dN
d[F
eH
]
SculptorSimple ModelInfall Model
Fig 6mdash The metallicity distribution in Sculptor The red curveis the maximum likelihood fit to a galactic chemical evolutionmodel with pre-enrichment (Eq 7) and the green curve is the max-imum likelihood fit to a model of star formation in the presence ofinfalling zero-metallicity gas (Eq 11) The long metal-poor tailis typical for systems with non-instantaneous star formation
[TiFe] in the same manner as for [FeH] These are listedin Table 5
5 RESULTS
In this section we discuss the interpretation of theabundance measurements in Sculptor all of which arepresented in Table 6 on the last page of this manuscript
51 Metallicity Distribution
The metallicity distribution function (MDF) of a dwarfgalaxy can reveal much about its star formation his-tory In chemical evolution models of dwarf galax-ies (eg Lanfranchi amp Matteucci 2004 Marcolini et al2006 2008) the duration of star formation affects theshape of the MDF The MDF also has implications forthe formation of the MW If the MW halo was built fromdSphs (Searle amp Zinn 1978 White amp Rees 1978) then itis important to find dSph counterparts to halo field starsat all metallicities as pointed out by Helmi et al (2006hereafter H06)
Figure 6 shows the MDF of Sculptor The shape of theMDF is highly asymmetric with a long metal-poor tail(as predicted by Salvadori amp Ferrara 2009) The inverse-variance weighted mean is 〈[FeH]〉 = minus158 with a stan-dard deviation of 041 The median is minus158 with a me-dian absolute deviation of 033 and an interquartile rangeof 067
The MDF boasts an exceptionally metal-poor starS1020549 The metallicity is [FeH] = minus380 plusmn 028Figure 7 shows how weak the Fe absorption lines are inthis star Frebel Kirby amp Simon (in preparation) haveconfirmed this extremely low metallicity with a high-resolution spectrum
Sculptor is now the most luminous dSph in whichan extremely metal-poor (EMP [FeH] lt minus3) starhas been detected [Kirby et al (2008b) discovered 15EMP stars across eight ultra-faint dwarf galaxies andCohen amp Huang (2009) discovered one EMP star in theDraco dSph] Stars more metal-poor than S1020549 areknown to exist only in the field of the Milky Way fieldThis discovery hints that dSph galaxies like Sculptor mayhave contributed to the formation of the metal-poor com-
Fig 7mdash Regions of the DEIMOS spectrum of the extremelymetal-poor star S1020549 which has [FeH] = minus380 plusmn 028 Thespectrum appears particularly noisy because the y-axis range issmall Some Fe absorption lines are barely detectable but all to-gether they contain enough signal to make a quantitative mea-surement of [FeH] The shading corresponds to the same spectralregion shown in Fig 5 Frebel Kirby amp Simon (in preparation)will present a high-resolution spectrum of this star which confirmsthe extremely low metallicity
ponent of the halo We discuss Sculptorrsquos link to the halofurther in Sec 513
The MT2D photometric selection of spectroscopic tar-gets may have introduced a tiny [FeH] bias Figure 2shows that the RGB is sharply defined in Sculptor Be-cause the number density of stars redward and bluewardof the RGB is much lower than the number density on theRGB the number of very young or very metal-poor stars(blueward) or very metal-rich stars (redward) missed byphotometric pre-selection must be negligible Further-more the hard color cut (as opposed to one that dependson M minus D color) was 06 lt (M minus T2)0 lt 22 The CMDgives no reason to suspect Sculptor RGB members out-side of these limits but it is possible that some extremelyblue Sculptor members have been excluded
511 Possible Explanation of the Discrepancy withPrevious Results
Our measured MDF and our detection of EMP stars inSculptor are at odds with the findings of H06 Whereasour MDF peaks at [FeH] sim minus13 theirs peaks at[FeH] sim minus18 Furthermore our observed MDF is muchmore asymmetric than that of H06 which may even beslightly asymmetric in the opposite sense (a longer metal-rich tail) The greater symmetry would indicate a lessextended star formation history or early infall of a largeamount of gas (Prantzos 2003)
Battaglia et al (2008b hereafter B08b) observed asubset of the H06 stars at high resolution The MDFsfrom the two studies have noticeably different shapesFigure 8 shows that the HRS MDF peaks at [FeH] simminus13 which is also the peak that we observe The meanand standard deviation of their MDF are minus156 and 038
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
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18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
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m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
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minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
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2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
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161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 7
and a standard deviation of the photometric error Wecall this error δTeffi where i represents each of the fourphotometric methods of determining Teff In order toarrive at a single photometric Teff we averaged the fourTeffi together with appropriate error weighting We alsoestimated the random and systematic components oferror In summary
Teff =
sum
i TeffiδTminus2effi
sum
i δTminus2effi
(3)
δrandTeff =
sum
i δTminus1effi
sum
i δTminus2effi
(4)
δsysTeff =
radic
radic
radic
radic
radic
sum
i δTminus2effi
sum
i δTminus2effi
(
Teffi minus Teff
)2
1 minus(
sum
i δTminus2effi
)2sum
i δTminus4effi
(5)
δtotalTeff =radic
(δrandTeff)2 + (δsysTeff)2 (6)
For the stars in this data set the median randomsystematic and total errors on Teff were 98 K 58 Kand 117 K respectively The somewhat large errors onthe photometric temperatures indicated that the spec-tra may help constrain Teff Therefore Eq 3 does notshow the final temperature used in the abundance deter-mination Section 47 describes the iterative process fordetermining Teff and elemental abundances from spec-troscopy
We followed a similar procedure for determining log gphotometrically except that we used only the threemodel isochrones and not any empirical calibrationThe error on the true distance modulus (1967 plusmn 012Pietrzynski et al 2008) was included in the Monte Carlodetermination of the error on log g The median ran-dom systematic and total errors on log g were 006 001and 006 These errors are very small and the medium-resolution red spectra have little power to help constrainlog g because there are so few ionized lines visible There-fore we assumed the photometric value of log g for theabundance analysis
46 Wavelength Masks
The procedure described in the next section consistedof separately measuring the abundances of five elementsMg Si Ca Ti and Fe The procedure relied on findingthe synthetic spectrum that best matched an observedspectrum In order to make this matching most sensitiveto a particular element we masked all spectral regionsthat were not significantly affected by abundance changesof that element
To make the wavelength masks we began with a basespectrum that represented the solar composition in whichthe abundances of all the metals were scaled down by15 dex ([AH] = minus15) The temperature and gravityof the synthetic star were Teff = 4000 K and log g = 10Then we created two pairs of spectra for each of thefive elements In one spectrum the abundance of theelement was enhanced by 03 dex and in the other de-pleted by 03 dex Spectral regions where the flux differ-ence between these two spectra exceeds 05 were usedin the abundance determination of that element This
Fig 5mdash A coaddition of all Sculptor stars with the continuumnormalized to unity The high SNR provided by the coadditionmakes stellar absorption lines readily apparent The colored re-gions show the wavelength masks used in the determination of theabundance of each element Regions susceptible to telluric absorp-tion are labeled with blue text Because large residuals from thetelluric absorption correction remain we eliminate these regionsfrom the abundance analysis Some stellar features excluded fromthe abundances measurement are also labeled
small threshold assured that weak lines which experi-ence large fractional changes in EW as [FeH] changeswere included in the analysis We repeated this proce-dure for spectra with Teff = 5000 K 6000 K 7000 K and8000 K Additional spectral regions that passed the 05flux difference criterion were also included in the abun-dance determination of that element All other wave-lengths were masked
The result was one wavelength mask for each of MgSi Ca Ti and Fe shown in Fig 5 We also createdone ldquoαrdquo mask as the intersection of the Mg Si Ca andTi masks The α element regions do not overlap witheach other but the α element regions do overlap withthe Fe regions The most severe case is the Ca maskwhere sim 35 of the pixels are shared with the Fe maskHowever the overlap did not introduce interdependencein the abundance measurements The α element abun-dances were held fixed while [FeH] was measured andthe Fe abundance was held fixed while [αFe] was mea-sured The measurements of [FeH] and [αFe] were per-formed iteratively (see the next subsection) We testedthe independence of the measurements by removing alloverlapping pixels from consideration Abundance mea-surements changed on average by only 001 dex
47 Measuring Atmospheric Parameters and ElementalAbundances
A Levenberg-Marquardt algorithm (the IDL routineMPFIT written by Markwardt 2009) found the best-fitting synthetic spectrum in ten iterative steps In eachstep the χ2 was computed between an observed spec-trum and a synthetic spectrum degraded to match theresolution of the observed spectrum First we interpo-
8 Kirby et al
lated the synthetic spectrum onto the same wavelengtharray as the observed spectrum Then we smoothedthe synthetic spectrum through a Gaussian filter whosewidth was the observed spectrumrsquos measured resolutionas a function of wavelength
1 Teff and [FeH] first pass An observed spectrumwas compared to a synthetic spectrum with Teff
and log g determined as described in Sec 45 and[FeH] determined from Yonsei-Yale isochronesFor this iteration [αFe] was fixed at 00 (solar)and only spectral regions most susceptible to Fe ab-sorption (Sec 46) were considered The two quan-tities Teff and [FeH] were varied and the algo-rithm found the best-fitting synthetic spectrum byminimizing χ2 We sampled the parameter spacebetween grid points by linearly interpolating thesynthetic spectra at the neighboring grid pointsTeff was also loosely constrained by photometry Asthe spectrum caused Teff to stray from the photo-metric values χ2 increased and it increased moresharply for smaller photometric errors (as calcu-lated in Eq 6) Therefore both photometry andspectroscopy determined Teff Photometry alonedetermined log g
2 [αFe] first pass For this iteration Teff log g and[FeH] were fixed Only [αFe] was allowed to varyIn the model stellar atmosphere the abundances ofthe α elements with respect to Fe varied togetherOnly the spectral regions susceptible to absorptionby Mg Si Ca or Ti were considered
3 Continuum refinement The continuum-dividedobserved spectrum was divided by the syntheticspectrum with the parameters determined in steps1 and 2 The result approximated a flat noise spec-trum To better determine the continuum we fita B-spline with a breakpoint spacing of 50 A tothe residual spectrum We divided the observedspectrum by the spline fit
4 [FeH] second pass We repeated step 1 with therevised spectrum but Teff was held fixed at thepreviously determined value
5 [MgFe] We repeated step 2 However only Mgspectral lines were considered in the abundancemeasurement
6 [SiFe] We repeated step 5 for Si instead of Mg
7 [CaFe] We repeated step 5 for Ca instead of Mg
8 [TiFe] We repeated step 5 for Ti instead of Mg
9 [αFe] second pass We repeated step 2 for allof the α elements instead of just Mg This stepwas simply a different way to average the α el-ement abundances than combining the individualmeasurements of [MgFe] [SiFe] [CaFe] and[TiFe]
10 [FeH] third pass The value of [αFe] affected themeasurement of [FeH] because [αFe] can affect
the structure of the stellar atmosphere Specif-ically the greater availability of electron donorswith an increased [αFe] ratio allows for a higherdensity of Hminus ions The subsequent increase in con-tinuous opacity decreases the strength of Fe andother non-α element lines With [αFe] fixed atthe value determined in step 9 we re-measured[FeH] Typically [FeH] changed from the valuedetermined in step 1 by much less than 01 dex
48 Correction to [FeH]
In comparing our MRS measurements of [FeH] to HRSmeasurements of the same stars (see the appendix) wenoticed that our measurements of metal-poor stars wereconsistently sim 015 dex lower The same pattern is alsovisible in the Kirby et al (2008a) GC measurements (seetheir Figs 6 7 10 and 11)
We have thoroughly examined possible sources of thisdifference of scale The changes to the microturbulentvelocity relation (Sec 42) and the line list (Sec 43)were intended to yield a more accurate and standardizedestimation of [FeH] but the offset still remained Re-stricting the analysis to narrow spectral regions did notreveal any systematic trend of [FeH] with wavelength
A possible explanation for this offset is overionization(Thevenin amp Idiart 1999) Ultraviolet radiation in stellaratmospheres can ionize Fe more than would be expectedin LTE Therefore the abundance of Fe I would seem tobe lower than the abundance of Fe II in an LTE analysisFe II does not suffer from this effect However the effectis smaller at higher [FeH] and we do not observe a trendwith metallicity for the offset of our values relative toHRS studies
In order to standardize our measurements with previ-ous HRS studies we added 015 dex to all of our mea-surements of [FeH] This offset and the microturbu-lent velocity-surface gravity relation are the only ways inwhich previous HRS studies inform our measurementsFurthermore this offset is not intended to change thestandardization of our abundances All of the abundancein this article including those from other studies aregiven relative to the solar abundances quoted in Table 4
49 Error Estimation
We repeated the error estimation procedure describedby KGS08 (their Sec 6) by repeating their abundanceanalysis on GC stars with the above modifications Weno longer found a convincing trend of δ[FeH] with[FeH] Instead we estimate the total error on [FeH] byadding a systematic error in quadrature with the SNR-dependent uncertainty of the synthetic spectral fit Themagnitude of δsys[FeH] = 0136 was the value requiredto force HRS and MRS [FeH] estimates of the same GCstars to agree at the 1σ level We also estimated sys-tematic errors for each of [MgFe] [SiFe] [CaFe] and
Abundances in the Sculptor dSph 9
minus4 minus3 minus2 minus1 0[FeH]
0
10
20
30
40
50N
([F
eH
])
0
100
200
300
400
500
dN
d[F
eH
]
SculptorSimple ModelInfall Model
Fig 6mdash The metallicity distribution in Sculptor The red curveis the maximum likelihood fit to a galactic chemical evolutionmodel with pre-enrichment (Eq 7) and the green curve is the max-imum likelihood fit to a model of star formation in the presence ofinfalling zero-metallicity gas (Eq 11) The long metal-poor tailis typical for systems with non-instantaneous star formation
[TiFe] in the same manner as for [FeH] These are listedin Table 5
5 RESULTS
In this section we discuss the interpretation of theabundance measurements in Sculptor all of which arepresented in Table 6 on the last page of this manuscript
51 Metallicity Distribution
The metallicity distribution function (MDF) of a dwarfgalaxy can reveal much about its star formation his-tory In chemical evolution models of dwarf galax-ies (eg Lanfranchi amp Matteucci 2004 Marcolini et al2006 2008) the duration of star formation affects theshape of the MDF The MDF also has implications forthe formation of the MW If the MW halo was built fromdSphs (Searle amp Zinn 1978 White amp Rees 1978) then itis important to find dSph counterparts to halo field starsat all metallicities as pointed out by Helmi et al (2006hereafter H06)
Figure 6 shows the MDF of Sculptor The shape of theMDF is highly asymmetric with a long metal-poor tail(as predicted by Salvadori amp Ferrara 2009) The inverse-variance weighted mean is 〈[FeH]〉 = minus158 with a stan-dard deviation of 041 The median is minus158 with a me-dian absolute deviation of 033 and an interquartile rangeof 067
The MDF boasts an exceptionally metal-poor starS1020549 The metallicity is [FeH] = minus380 plusmn 028Figure 7 shows how weak the Fe absorption lines are inthis star Frebel Kirby amp Simon (in preparation) haveconfirmed this extremely low metallicity with a high-resolution spectrum
Sculptor is now the most luminous dSph in whichan extremely metal-poor (EMP [FeH] lt minus3) starhas been detected [Kirby et al (2008b) discovered 15EMP stars across eight ultra-faint dwarf galaxies andCohen amp Huang (2009) discovered one EMP star in theDraco dSph] Stars more metal-poor than S1020549 areknown to exist only in the field of the Milky Way fieldThis discovery hints that dSph galaxies like Sculptor mayhave contributed to the formation of the metal-poor com-
Fig 7mdash Regions of the DEIMOS spectrum of the extremelymetal-poor star S1020549 which has [FeH] = minus380 plusmn 028 Thespectrum appears particularly noisy because the y-axis range issmall Some Fe absorption lines are barely detectable but all to-gether they contain enough signal to make a quantitative mea-surement of [FeH] The shading corresponds to the same spectralregion shown in Fig 5 Frebel Kirby amp Simon (in preparation)will present a high-resolution spectrum of this star which confirmsthe extremely low metallicity
ponent of the halo We discuss Sculptorrsquos link to the halofurther in Sec 513
The MT2D photometric selection of spectroscopic tar-gets may have introduced a tiny [FeH] bias Figure 2shows that the RGB is sharply defined in Sculptor Be-cause the number density of stars redward and bluewardof the RGB is much lower than the number density on theRGB the number of very young or very metal-poor stars(blueward) or very metal-rich stars (redward) missed byphotometric pre-selection must be negligible Further-more the hard color cut (as opposed to one that dependson M minus D color) was 06 lt (M minus T2)0 lt 22 The CMDgives no reason to suspect Sculptor RGB members out-side of these limits but it is possible that some extremelyblue Sculptor members have been excluded
511 Possible Explanation of the Discrepancy withPrevious Results
Our measured MDF and our detection of EMP stars inSculptor are at odds with the findings of H06 Whereasour MDF peaks at [FeH] sim minus13 theirs peaks at[FeH] sim minus18 Furthermore our observed MDF is muchmore asymmetric than that of H06 which may even beslightly asymmetric in the opposite sense (a longer metal-rich tail) The greater symmetry would indicate a lessextended star formation history or early infall of a largeamount of gas (Prantzos 2003)
Battaglia et al (2008b hereafter B08b) observed asubset of the H06 stars at high resolution The MDFsfrom the two studies have noticeably different shapesFigure 8 shows that the HRS MDF peaks at [FeH] simminus13 which is also the peak that we observe The meanand standard deviation of their MDF are minus156 and 038
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
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Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
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18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
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m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
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minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
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Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
8 Kirby et al
lated the synthetic spectrum onto the same wavelengtharray as the observed spectrum Then we smoothedthe synthetic spectrum through a Gaussian filter whosewidth was the observed spectrumrsquos measured resolutionas a function of wavelength
1 Teff and [FeH] first pass An observed spectrumwas compared to a synthetic spectrum with Teff
and log g determined as described in Sec 45 and[FeH] determined from Yonsei-Yale isochronesFor this iteration [αFe] was fixed at 00 (solar)and only spectral regions most susceptible to Fe ab-sorption (Sec 46) were considered The two quan-tities Teff and [FeH] were varied and the algo-rithm found the best-fitting synthetic spectrum byminimizing χ2 We sampled the parameter spacebetween grid points by linearly interpolating thesynthetic spectra at the neighboring grid pointsTeff was also loosely constrained by photometry Asthe spectrum caused Teff to stray from the photo-metric values χ2 increased and it increased moresharply for smaller photometric errors (as calcu-lated in Eq 6) Therefore both photometry andspectroscopy determined Teff Photometry alonedetermined log g
2 [αFe] first pass For this iteration Teff log g and[FeH] were fixed Only [αFe] was allowed to varyIn the model stellar atmosphere the abundances ofthe α elements with respect to Fe varied togetherOnly the spectral regions susceptible to absorptionby Mg Si Ca or Ti were considered
3 Continuum refinement The continuum-dividedobserved spectrum was divided by the syntheticspectrum with the parameters determined in steps1 and 2 The result approximated a flat noise spec-trum To better determine the continuum we fita B-spline with a breakpoint spacing of 50 A tothe residual spectrum We divided the observedspectrum by the spline fit
4 [FeH] second pass We repeated step 1 with therevised spectrum but Teff was held fixed at thepreviously determined value
5 [MgFe] We repeated step 2 However only Mgspectral lines were considered in the abundancemeasurement
6 [SiFe] We repeated step 5 for Si instead of Mg
7 [CaFe] We repeated step 5 for Ca instead of Mg
8 [TiFe] We repeated step 5 for Ti instead of Mg
9 [αFe] second pass We repeated step 2 for allof the α elements instead of just Mg This stepwas simply a different way to average the α el-ement abundances than combining the individualmeasurements of [MgFe] [SiFe] [CaFe] and[TiFe]
10 [FeH] third pass The value of [αFe] affected themeasurement of [FeH] because [αFe] can affect
the structure of the stellar atmosphere Specif-ically the greater availability of electron donorswith an increased [αFe] ratio allows for a higherdensity of Hminus ions The subsequent increase in con-tinuous opacity decreases the strength of Fe andother non-α element lines With [αFe] fixed atthe value determined in step 9 we re-measured[FeH] Typically [FeH] changed from the valuedetermined in step 1 by much less than 01 dex
48 Correction to [FeH]
In comparing our MRS measurements of [FeH] to HRSmeasurements of the same stars (see the appendix) wenoticed that our measurements of metal-poor stars wereconsistently sim 015 dex lower The same pattern is alsovisible in the Kirby et al (2008a) GC measurements (seetheir Figs 6 7 10 and 11)
We have thoroughly examined possible sources of thisdifference of scale The changes to the microturbulentvelocity relation (Sec 42) and the line list (Sec 43)were intended to yield a more accurate and standardizedestimation of [FeH] but the offset still remained Re-stricting the analysis to narrow spectral regions did notreveal any systematic trend of [FeH] with wavelength
A possible explanation for this offset is overionization(Thevenin amp Idiart 1999) Ultraviolet radiation in stellaratmospheres can ionize Fe more than would be expectedin LTE Therefore the abundance of Fe I would seem tobe lower than the abundance of Fe II in an LTE analysisFe II does not suffer from this effect However the effectis smaller at higher [FeH] and we do not observe a trendwith metallicity for the offset of our values relative toHRS studies
In order to standardize our measurements with previ-ous HRS studies we added 015 dex to all of our mea-surements of [FeH] This offset and the microturbu-lent velocity-surface gravity relation are the only ways inwhich previous HRS studies inform our measurementsFurthermore this offset is not intended to change thestandardization of our abundances All of the abundancein this article including those from other studies aregiven relative to the solar abundances quoted in Table 4
49 Error Estimation
We repeated the error estimation procedure describedby KGS08 (their Sec 6) by repeating their abundanceanalysis on GC stars with the above modifications Weno longer found a convincing trend of δ[FeH] with[FeH] Instead we estimate the total error on [FeH] byadding a systematic error in quadrature with the SNR-dependent uncertainty of the synthetic spectral fit Themagnitude of δsys[FeH] = 0136 was the value requiredto force HRS and MRS [FeH] estimates of the same GCstars to agree at the 1σ level We also estimated sys-tematic errors for each of [MgFe] [SiFe] [CaFe] and
Abundances in the Sculptor dSph 9
minus4 minus3 minus2 minus1 0[FeH]
0
10
20
30
40
50N
([F
eH
])
0
100
200
300
400
500
dN
d[F
eH
]
SculptorSimple ModelInfall Model
Fig 6mdash The metallicity distribution in Sculptor The red curveis the maximum likelihood fit to a galactic chemical evolutionmodel with pre-enrichment (Eq 7) and the green curve is the max-imum likelihood fit to a model of star formation in the presence ofinfalling zero-metallicity gas (Eq 11) The long metal-poor tailis typical for systems with non-instantaneous star formation
[TiFe] in the same manner as for [FeH] These are listedin Table 5
5 RESULTS
In this section we discuss the interpretation of theabundance measurements in Sculptor all of which arepresented in Table 6 on the last page of this manuscript
51 Metallicity Distribution
The metallicity distribution function (MDF) of a dwarfgalaxy can reveal much about its star formation his-tory In chemical evolution models of dwarf galax-ies (eg Lanfranchi amp Matteucci 2004 Marcolini et al2006 2008) the duration of star formation affects theshape of the MDF The MDF also has implications forthe formation of the MW If the MW halo was built fromdSphs (Searle amp Zinn 1978 White amp Rees 1978) then itis important to find dSph counterparts to halo field starsat all metallicities as pointed out by Helmi et al (2006hereafter H06)
Figure 6 shows the MDF of Sculptor The shape of theMDF is highly asymmetric with a long metal-poor tail(as predicted by Salvadori amp Ferrara 2009) The inverse-variance weighted mean is 〈[FeH]〉 = minus158 with a stan-dard deviation of 041 The median is minus158 with a me-dian absolute deviation of 033 and an interquartile rangeof 067
The MDF boasts an exceptionally metal-poor starS1020549 The metallicity is [FeH] = minus380 plusmn 028Figure 7 shows how weak the Fe absorption lines are inthis star Frebel Kirby amp Simon (in preparation) haveconfirmed this extremely low metallicity with a high-resolution spectrum
Sculptor is now the most luminous dSph in whichan extremely metal-poor (EMP [FeH] lt minus3) starhas been detected [Kirby et al (2008b) discovered 15EMP stars across eight ultra-faint dwarf galaxies andCohen amp Huang (2009) discovered one EMP star in theDraco dSph] Stars more metal-poor than S1020549 areknown to exist only in the field of the Milky Way fieldThis discovery hints that dSph galaxies like Sculptor mayhave contributed to the formation of the metal-poor com-
Fig 7mdash Regions of the DEIMOS spectrum of the extremelymetal-poor star S1020549 which has [FeH] = minus380 plusmn 028 Thespectrum appears particularly noisy because the y-axis range issmall Some Fe absorption lines are barely detectable but all to-gether they contain enough signal to make a quantitative mea-surement of [FeH] The shading corresponds to the same spectralregion shown in Fig 5 Frebel Kirby amp Simon (in preparation)will present a high-resolution spectrum of this star which confirmsthe extremely low metallicity
ponent of the halo We discuss Sculptorrsquos link to the halofurther in Sec 513
The MT2D photometric selection of spectroscopic tar-gets may have introduced a tiny [FeH] bias Figure 2shows that the RGB is sharply defined in Sculptor Be-cause the number density of stars redward and bluewardof the RGB is much lower than the number density on theRGB the number of very young or very metal-poor stars(blueward) or very metal-rich stars (redward) missed byphotometric pre-selection must be negligible Further-more the hard color cut (as opposed to one that dependson M minus D color) was 06 lt (M minus T2)0 lt 22 The CMDgives no reason to suspect Sculptor RGB members out-side of these limits but it is possible that some extremelyblue Sculptor members have been excluded
511 Possible Explanation of the Discrepancy withPrevious Results
Our measured MDF and our detection of EMP stars inSculptor are at odds with the findings of H06 Whereasour MDF peaks at [FeH] sim minus13 theirs peaks at[FeH] sim minus18 Furthermore our observed MDF is muchmore asymmetric than that of H06 which may even beslightly asymmetric in the opposite sense (a longer metal-rich tail) The greater symmetry would indicate a lessextended star formation history or early infall of a largeamount of gas (Prantzos 2003)
Battaglia et al (2008b hereafter B08b) observed asubset of the H06 stars at high resolution The MDFsfrom the two studies have noticeably different shapesFigure 8 shows that the HRS MDF peaks at [FeH] simminus13 which is also the peak that we observe The meanand standard deviation of their MDF are minus156 and 038
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
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18 Kirby et al
16
18
20
22
24ξ M
RS
(km
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1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
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ξ HR
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1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
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982
H40
0
H46
1
770
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RS
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1446
195
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982
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0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
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Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
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AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
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Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
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Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 9
minus4 minus3 minus2 minus1 0[FeH]
0
10
20
30
40
50N
([F
eH
])
0
100
200
300
400
500
dN
d[F
eH
]
SculptorSimple ModelInfall Model
Fig 6mdash The metallicity distribution in Sculptor The red curveis the maximum likelihood fit to a galactic chemical evolutionmodel with pre-enrichment (Eq 7) and the green curve is the max-imum likelihood fit to a model of star formation in the presence ofinfalling zero-metallicity gas (Eq 11) The long metal-poor tailis typical for systems with non-instantaneous star formation
[TiFe] in the same manner as for [FeH] These are listedin Table 5
5 RESULTS
In this section we discuss the interpretation of theabundance measurements in Sculptor all of which arepresented in Table 6 on the last page of this manuscript
51 Metallicity Distribution
The metallicity distribution function (MDF) of a dwarfgalaxy can reveal much about its star formation his-tory In chemical evolution models of dwarf galax-ies (eg Lanfranchi amp Matteucci 2004 Marcolini et al2006 2008) the duration of star formation affects theshape of the MDF The MDF also has implications forthe formation of the MW If the MW halo was built fromdSphs (Searle amp Zinn 1978 White amp Rees 1978) then itis important to find dSph counterparts to halo field starsat all metallicities as pointed out by Helmi et al (2006hereafter H06)
Figure 6 shows the MDF of Sculptor The shape of theMDF is highly asymmetric with a long metal-poor tail(as predicted by Salvadori amp Ferrara 2009) The inverse-variance weighted mean is 〈[FeH]〉 = minus158 with a stan-dard deviation of 041 The median is minus158 with a me-dian absolute deviation of 033 and an interquartile rangeof 067
The MDF boasts an exceptionally metal-poor starS1020549 The metallicity is [FeH] = minus380 plusmn 028Figure 7 shows how weak the Fe absorption lines are inthis star Frebel Kirby amp Simon (in preparation) haveconfirmed this extremely low metallicity with a high-resolution spectrum
Sculptor is now the most luminous dSph in whichan extremely metal-poor (EMP [FeH] lt minus3) starhas been detected [Kirby et al (2008b) discovered 15EMP stars across eight ultra-faint dwarf galaxies andCohen amp Huang (2009) discovered one EMP star in theDraco dSph] Stars more metal-poor than S1020549 areknown to exist only in the field of the Milky Way fieldThis discovery hints that dSph galaxies like Sculptor mayhave contributed to the formation of the metal-poor com-
Fig 7mdash Regions of the DEIMOS spectrum of the extremelymetal-poor star S1020549 which has [FeH] = minus380 plusmn 028 Thespectrum appears particularly noisy because the y-axis range issmall Some Fe absorption lines are barely detectable but all to-gether they contain enough signal to make a quantitative mea-surement of [FeH] The shading corresponds to the same spectralregion shown in Fig 5 Frebel Kirby amp Simon (in preparation)will present a high-resolution spectrum of this star which confirmsthe extremely low metallicity
ponent of the halo We discuss Sculptorrsquos link to the halofurther in Sec 513
The MT2D photometric selection of spectroscopic tar-gets may have introduced a tiny [FeH] bias Figure 2shows that the RGB is sharply defined in Sculptor Be-cause the number density of stars redward and bluewardof the RGB is much lower than the number density on theRGB the number of very young or very metal-poor stars(blueward) or very metal-rich stars (redward) missed byphotometric pre-selection must be negligible Further-more the hard color cut (as opposed to one that dependson M minus D color) was 06 lt (M minus T2)0 lt 22 The CMDgives no reason to suspect Sculptor RGB members out-side of these limits but it is possible that some extremelyblue Sculptor members have been excluded
511 Possible Explanation of the Discrepancy withPrevious Results
Our measured MDF and our detection of EMP stars inSculptor are at odds with the findings of H06 Whereasour MDF peaks at [FeH] sim minus13 theirs peaks at[FeH] sim minus18 Furthermore our observed MDF is muchmore asymmetric than that of H06 which may even beslightly asymmetric in the opposite sense (a longer metal-rich tail) The greater symmetry would indicate a lessextended star formation history or early infall of a largeamount of gas (Prantzos 2003)
Battaglia et al (2008b hereafter B08b) observed asubset of the H06 stars at high resolution The MDFsfrom the two studies have noticeably different shapesFigure 8 shows that the HRS MDF peaks at [FeH] simminus13 which is also the peak that we observe The meanand standard deviation of their MDF are minus156 and 038
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
MRSHRS (Battaglia et al 2008b)CaT (Helmi et al 2006)
Fig 8mdash Sculptorrsquos metallicity distribution as observed in thisstudy (MRS black) and by B08b (HRS red) which is a subsetof the MDF observed by H06 (Ca triplet green) The CaT-basedMDF is more metal-poor probably because the sample of H06 ismore spatially extended than the other two samples
However the MDF of H06 peaks at [FeH] sim minus18 andthe mean and standard deviation are minus182 and 035The overlapping stars between the samples of B08b andH06 agree very well
The most likely explanation for the different MDFs isthe different spatial sampling of the three studies Sculp-tor has a steep radial metallicity gradient (Tolstoy et al2004 Westfall et al 2006 Walker et al 2009 also seeSec 53) The stars in the center of Sculptor are moremetal-rich than stars far from the center H06 sampledstars out to the tidal radius (rt = 765 arcmin Mateo1998) but we and B08b sampled stars only out to about11 arcmin As a result the mean metallicity of the H06CaT sample is lower than our MRS sample and the B08bHRS sample In the next subsection we address thechemical evolution of Sculptor based on its MDF Ourconclusions are based only on stars within the central11 arcmin
512 Quantifying Chemical Evolution in Sculptor
In chemical evolution models extended star formationproduces a long metal-poor tail Prantzos (2008) de-scribed the shape of the differential metallicity distribu-tion derived from a ldquosimple modelrdquo of galactic chemicalevolution Expressed in terms of [FeH] instead of metalfraction Z the predicted distribution is
dN
d[FeH]= A
(
10[FeH] minus 10[FeH]i
)
exp
(
minus10[FeH]
p
)
(7)where p is the effective yield in units of the solar metalfraction (Z⊙) and [FeH]i is the initial gas metallicityAn initial metallicity is needed to resolve the GalacticG dwarf problem (van den Bergh 1962 Schmidt 1963)A is a normalization that depends on p [FeH]i thefinal metallicity [FeH]f and the number of stars in thesample N
A =(N ln 10)p
exp(
minus 10[FeH]i
p
)
minus exp(
minus 10[FeH]f
p
) (8)
The red curve in Figure 6 is the two-parameter maxi-
mum likelihood fit to Eq 7 The likelihood Li that stari is drawn from the probability distribution defined byEq 7 is the integral of the product of the error distri-bution for the star and the probability distribution Thetotal likelihood L =
prod
i Li The most likely p and [FeH]0are the values that maximize L For display the curvehas been convolved with an error distribution which isa composite of N unit Gaussians N is the total numberof stars in the observed distribution and the width ofthe ith Gaussian is the estimated total [FeH] error onthe ith star This convolution approximates the effectof measurement error on the model curve under the as-sumption that the error on [FeH] does not depend on[FeH] This assumption seems to be valid because ourestimates of δ[FeH] do not show a trend with [FeH]
The most likely yieldmdashlargely determined by the[FeH] at the peak of the MDFmdashis p = 0031Z⊙[From the MDF of H06 Prantzos (2008) calculatedp = 0016Z⊙] We also measure [FeH]0 = minus292H06 also measured [FeH]0 = minus290 plusmn 021 for Sculp-tor even though they included stars out to the tidal ra-dius which are more metal-poor on average than thecentrally concentrated stars in our sample (Instead offinding the maximum likelihood model they performeda least-squares fit to the cumulative metallicity distri-bution without accounting for experimental uncertaintyIn general observational errors exaggerate the extremaof the metallicity distribution and the least-squares fitconverges on a lower [FeH]0 than the maximum likeli-hood fit) One explanation that they proposed for thisnon-zero initial metallicity was pre-enrichment of the in-terstellar gas that formed the first stars Pre-enrichmentcould result from a relatively late epoch of formationfor Sculptor after the supernova (SN) ejecta from othergalaxies enriched the intergalactic medium from whichSculptor formed However our observation of a star at[FeH] = minus380 is inconsistent with pre-enrichment atthe level of [FeH]0 = minus29
Prantzos (2008) instead interpreted the apparentdearth of EMP stars as an indication of early gas in-fall (Prantzos 2003) wherein star formation begins froma small amount of gas while the majority of gas that willeventually form dSph stars is still falling in In order totest this alternative to pre-enrichment we have also fit anInfall Model the ldquoBest Accretion Modelrdquo of Lynden-Bell(1975 also see Pagel 1997) It is one of the models whichaccounts for a time-decaying gas infall that has an ana-lytic solution The model assumes that the gas mass gin units of the initial mass is related quadratically to thestellar mass s in units of the initial mass
g(s) =(
1 minuss
M
) (
1 + s minuss
M
)
(9)
where M is a parameter greater than 1 When M = 1Eq 9 reduces to g = 1 minus s which describes the ClosedBox Model Otherwise M monotonically increases withthe amount of gas infall and with the departure from theSimple Model Following Lynden-Bell (1975) and Pagel(1997) we assume that the initial and infalling gas metal-licity is zero The differential metallicity distribution isdescribed by two equations
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
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18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
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Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
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2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
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Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 11
[FeH](s)= log
p
(
M
1 + s minus sM
)2
times (10)
[
ln1
1 minus sM
minuss
M
(
1 minus1
M
)]
dN
d[FeH]=A
10[FeH]
ptimes (11)
1 + s(
1 minus 1M
)
(
1 minus sM
)minus1minus 2
(
1 minus 1M
)
times 10[FeH]p
Equation 10 is transcendental and it must be solved fors numerically Equation 11 decouples the peak of theMDF from the yield p As M increases the MDF peakdecreases independently of p
The green line in Fig 6 shows the most likely InfallModel convolved with the error distribution as describedabove The Infall Model has M = 176 which is only asmall departure from the Simple Model
Neither the Simple Model nor the Infall Model fitsthe data particularly well Both models fail to repro-duce the sharp peak at [FeH] sim minus13 and the steepmetal-rich tail However the Infall Model does repro-duce the metal-poor tail about as well as the SimpleModel Therefore the Infall Model is a reasonable al-ternative to pre-enrichment and it allows the existenceof the star at [FeH] = minus380 In reality a precise ex-planation of the MDF will likely incorporate the radialmetallicity gradients and multiple superposed popula-tions It is tempting to conclude from Fig 6 that Sculp-tor displays two metallicity populations We have notattempted a two-component fit but that would seem tobe a reasonable approach for future work especially inlight of Tolstoy et alrsquos (2004) report of two distinct stel-lar populations in Sculptor
Searches for the lowest metallicity stars in the MWhalo have revealed some exquisitely metal-poor stars(eg [FeH] = minus596 Frebel et al 2008) Such exoticstars have not yet been discovered in any dSph How-ever if Sculptor was not pre-enriched a large enoughsample of [FeH] measurements in Sculptormdashand possi-bly other dSphsmdashmay reveal stars as metal-poor as thelowest metallicity stars in the MW halo
513 Comparison to the Milky Way Halo MDF
Searle amp Zinn (1978) and White amp Rees (1978)posited that the MW halo formed from the accretionand dissolution of dwarf galaxies The dSphs thatexist today may be the survivors from the cannibalisticconstruction of the Galactic halo Helmi et al (2006)suggested that at least some of the halo field stars couldnot have come from counterparts to the surviving dSphsbecause the halo field contained extremely metal-poorstars whereas the dSphs do not However Schoerck et al(2008) showed that the HamburgESO Surveyrsquos haloMDF after correction for selection bias actually looksremarkably like the MDFs of the dSphs Fornax UrsaMinor and Draco Furthermore Kirby et al (2008b)presented MRS evidence for a large fraction of EMPstars in the ultra-faint dSph sample of Simon amp Geha(2007) suggesting that todayrsquos surviving dSphs contain
minus35 minus30 minus25 minus20[FeH]
00
02
04
06
08
10
N (
lt [F
eH
])
Sculptor (spectral synthesis this work)Sculptor (CaT Helmi et al 2006)Milky Way halo (Schoerck et al 2008)
Fig 9mdash The metal-poor tails of the MDFs in Sculptor (black)and Galactic halo field stars (red Schoerck et al 2008) shown ascumulative distributions all normalized to the number of starswith [FeH] lt minus2 The green line shows the MDF measured bythe DART team (Helmi et al 2006) with a calibration based onthe Ca triplet The calibration may overpredict very low metallic-ities The synthesis-based metallicities (black this work) are validat lower [FeH] than the Ca triplet [FeH] Regardless the halohas a steeper metal-poor tail than Sculptor in both representa-tions Galaxies such as Sculptor were probably not the dominantcontributors to the halo
stars that span the full range of metallicities displayedby the Galactic field halo population
We revisit the halo comparison with the presentMDF for Sculptor Figure 9 shows the metal-poortail ([FeH] lt minus2) of the MRS synthesis-based Sculp-tor MDF presented here the CaT-based SculptorMDF (Helmi et al 2006) and the MW halo MDF(Schoerck et al 2008) As observed in the compar-isons to other dSphs presented by Schoerck et al thehalo seems to have a steeper metal-poor tail than theCaT-based Sculptor MDF despite the evidence thatCaT-based metallicities overpredict [FeH] at [FeH] minus22 (eg Koch et al 2008 Norris et al 2008) Thesynthesis-based MDF does not rely on empirical calibra-tions and the technique has been shown to work at leastdown to [FeH] = minus3 (Kirby et al 2008b)
This MDF shows that the halo has a much steepermetal-poor tail than Sculptor This result is consistentwith a merging scenario wherein several dwarf galax-ies significantly larger than Sculptor contributed mostof the stars to the halo field (eg Robertson et al 2005Font et al 2006) In these models the more luminousgalaxies have higher mean metallicities Galaxies witha Sculptor-like stellar mass are minority contributors tothe halo field star population Less luminous galaxiesare even more metal-poor (Kirby et al 2008b) There-fore Sculptor conforms to the luminosity-metallicity re-lation for dSphs and the difference between SculptorrsquosMDF and the MW halo MDF does not pose a problemfor hierarchical assembly
52 Alpha Element Abundances
The discrepancy between halo and dSph abundancesextends beyond the MDF In the first HRS study
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Fig 10mdash Multi-element abundances in Sculptor (black) Thepoint sizes reflect the quadrature sum of the errors on [FeH] and[XFe] where larger points have smaller errors The bottom panelshows the average of the four elements shown in the other panelsFor comparison the red error bars show the means and standarddeviations from the seven GCs of KGS08 Because the Sculptorand GC abundances were measured in the same way the compar-ison demonstrates that [XFe] declines with increasing [FeH] inSculptor but not the GCs
of stars in a dSph Shetrone Bolte amp Stetson (1998)found that the [CaFe] ratio of metal-poor stars inDraco appeared solar in contrast to the enhancedhalo field stars Shetrone Cote amp Sargent (2001) andShetrone et al (2003) confirmed the same result in Sex-tans Ursa Minor Sculptor Fornax Carina and Leo Iand they included other α elements in addition to Ca
Here we present the largest sample of [αFe] measure-ments in any dSph Figure 10 shows [MgFe] [CaFe]and [TiFe] versus [FeH] for Sculptor The figure alsoshows the mean and standard deviations of all of the in-dividual stellar abundance measurements for each of theseven GCs in the sample of KGS08 All of the modifi-cations to the KGS08 technique described in Secs 3 and4 apply to the GC measurements in Fig 10 Althoughour discussion in the appendix demonstrates that our
minus05
00
05
10
[Mg
Fe]
model Lanfranchi amp Matteucci (2009)HRS Geisler et al (2005)HRS Shetrone et al (2003)MRS trendMRS
Fig 11mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The points with error barsshow published high-resolution data (Shetrone et al 2003 blueand Geisler et al 2005 green) The green line is the inversevariance-weighted average of at least 20 stars within a window of∆[FeH] = 025 The red line shows the chemical evolution modelof Lanfranchi amp Matteucci (2004 updated 2009) The onset ofType Ia SNe causes the decline in [XFe] with [FeH] Mg declinessteadily because it is produced exclusively in Type II SNe but SiCa and Ti are produced in both Type Ia and II SNe
measurements are accurate on an absolute scale by com-paring to several different HRS studies in Sculptor it isalso instructive to compare abundances measured withthe same technique in two types of stellar systems Allfour element ratios slope downward with [FeH] in Sculp-tor but remain flat in the GCs Additionally the largerspread of [MgFe] than other element ratios in the GCs isnot due to larger measurement uncertainties but to theknown intrinsic spread of Mg abundance in some GCs(see the review by Gratton et al 2004) [SiFe] [CaFe]and [TiFe] are more slightly sloped than [MgFe] inSculptor because both Type Ia and Type II SNe pro-duce Si Ca and Ti but Type II SNe are almost solelyresponsible for producing Mg (Woosley amp Weaver 1995)Finally to maximize the SNR of the element ratio mea-surements we average the four ratios together into onenumber called [αFe] The [αFe] ratio is flat across theGCs but it decreases with increasing [FeH] in Sculptor
Quantitative models of chemical evolution in dwarf
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 13
minus05
00
05
10
[Mg
Fe]
Sculptor (MRS) Milky Way thin diskMilky Way thick diskMilky Way haloVenn et al (2004)
Fig 12mdash As in Fig 10 the black points show medium-resolutionmulti-element abundances in Sculptor The colored points showdifferent components of the Milky Way (Venn et al 2004) the thindisk (red) the thick disk (green) and the field halo (cyan) Thedashed lines are moving averages of the MW data in 075 dex binsof [FeH] In Sculptor [αFe] falls at lower [FeH] than in the haloindicating that the halo field stars were less polluted by Type IaSNe and therefore formed more rapidly than Sculptor stars
galaxies are consistent with these trends At a certaintime corresponding to a certain [FeH] in the evolutionof the dSph Type Ia begin to pollute the interstellarmedium with gas at subsolar [αFe] More metal-richstars that form from this gas will have lower [αFe]than the more metal-poor stars Lanfranchi amp Matteucci(2004) have developed a sophisticated model that in-cludes SN feedback and winds They predicted theabundance distributions of six dSphs including Sculp-tor Figure 11 shows our measurements with their pre-dictions (updated with new SN yields G Lanfranchi2009 private communication) As predicted the rangeof [MgFe] is larger than the range of [CaFe] or [SiFe]because Mg is produced exclusively in Type II SNewhereas Si and Ca are produced in both Type Ia andII SNe (Woosley amp Weaver 1995) We do not observestrong evidence for a predicted sharp steepening in slopeof both elements at [FeH] sim minus18 but observationalerrors and intrinsic scatter may obscure this ldquokneerdquoAlso the observed [FeH] at which [MgFe] begins todrop is higher than the model predicts indicating a
less intense wind than used in the model Note thatthe element ratios [XFe] become negative (subsolar)at high enough [FeH] as predicted by the modelsLanfranchi amp Matteucci (2004) do not predict [TiFe]because it behaves more like an Fe-peak element thanan α element
In addition to trends of [αFe] with [FeH]Marcolini et al (2006 2008) predicted the distributionfunctions of [FeH] and [αFe] of a Draco-like dSph Therange of [FeH] they predicted is nearly identical to therange we observe in Sculptor and the shapes of bothdistributions are similar The outcome of the models de-pends on the mass of the dSph Sculptor is ten timesmore luminous than Draco (Mateo 1998) and thereforemay have a larger total mass [However Strigari et al(2008) find that all dSphs have the same dynamical masswithin 300 pc of their centers It is unclear whether thetotal masses of the original unstripped dark matter ha-los are the same] In principle these chemical evolutionmodels could be used to measure the time elapsed sincedifferent epochs of star formation and their durationsWe defer such an analysis until the advent of a modelbased on a Sculptor-like luminosity or mass
In Fig 12 we compare individual stellar abundancesin Sculptor to MW halo and disk field stars (compilationby Venn et al 2004) As has been seen in many pre-vious studies of individual stellar abundances in dSphs[αFe] falls at a significantly lower [FeH] in Sculptorthan in the MW halo The drop is particularly appar-ent in [MgFe] which is the element ratio most sensitiveto the ratio of the contributions of Type II to Type IaSNe The other element ratios also drop sooner in Sculp-tor than in the halo but appear lower than in the haloat all metallicities Along with the MDF comparison inSec 513 this result is consistent with the suggestion byRobertson et al (2005) that galaxies significantly moremassive than Sculptor built the inner MW halo Theirgreater masses allowed them to retain more gas and expe-rience more vigorous star formation By the time Type IaSNe diluted [αFe] in the massive halo progenitors themetallicity of the star-forming gas was already as highas [FeH] = minus05 In Sculptor the interstellar [FeH]reached only minus15 before the onset of Type Ia SNe pol-lution
53 Radial Abundance Distributions
Because dSphs interact with the MW they can losegas through tidal or ram pressure stripping (Lin amp Faber1983) The gas preferentially leaves from the dSphrsquos out-skirts where the gravitational potential is shallow Ifthe dSph experiences subsequent star formation it mustoccur in the inner regions where gas remains Sculp-torrsquos MDF suggests a history of extended star formationSculptor might then be expected to exhibit a radial abun-dance gradient in the sense that the inner parts of thedSph are more metal-rich than the outer parts
The detection of a radial metallicity gradient inSculptor has been elusive In a photometric studyHurley-Keller (2000) found no evidence for an age ormetallicity gradient Based on HRS observations offive stars (the same sample as Shetrone et al 2003)Tolstoy et al (2003) found no correlation between [FeH]and spatial position Finally in a sample of 308 starswith CaT-based metallicities T04 detected a significant
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
14 Kirby et al
minus30
minus25
minus20
minus15
minus10
minus05
[Fe
H]
0 2 4 6 8 10elliptical radius (arcmin)
minus06minus04
minus02
minus00
02
04
0608
[αF
e]
Fig 13mdash Spatial abundance distributions in Sculptor Pointsizes are larger for stars with smaller measurement uncertaintiesThe red points reflect the mean values in 1 arcmin bins along withthe errors on the means The red lines are the least-squares linearfits We detect a gradient of minus0030 plusmn 0003 dex per arcmin in[FeH] and +0013 plusmn 0003 dex per arcmin in [αFe]
segregation in Sculptor a centrally concentrated rela-tively metal-rich component and an extended relativelymetal-poor component Westfall et al (2006) arrived atthe same conclusion and Walker et al (2009) confirmedthe existence of a [FeH] gradient in a sample of 1365Sculptor members
In order to detect a gradient those studies targetedSculptor stars at distances of more than 20 arcmin Themaximum elliptical radius of this study is 11 arcminTherefore this study is not ideally designed to detectradial gradients Figure 13 shows the radial distributionof [FeH] and [αFe] in Sculptor The x-axis is the lengthof the semi-major axis of an ellipse defined by Sculptorrsquosposition angle and ellipticity (Mateo 1998) Althoughthis study is limited in the spatial extent of targets we dodetect a gradient of minus0030plusmn0003 dex per arcmin Thisestimate is very close to the gradient observed by T04Walker et al (2009) measure a shallower gradient butthey present their results against circular radius insteadof elliptical radius
Marcolini et al (2008) predict radial gradients in both[FeH] and [αFe] in dSphs In particular they expectshallower [FeH] gradients for longer durations of starformation The gradient we observe is stronger than anyof their models They also expect very few stars withlow [αFe] at large radius Given that [αFe] decreaseswith [FeH] and [FeH] decreases with distance it seemsreasonable to expect that [αFe] increases with radius Infact we detect an [αFe] gradient of +0013plusmn 0003 dexper arcmin
6 CONCLUSIONS
Sculptor is one of the best-studied dwarf spheroidalsatellites of the Milky Way In the past ten years at leastfive spectroscopic campaigns at both low and high res-olution have targeted this galaxy More than any otherdSph Sculptor has aided in the understanding of thechemical evolution of dSphs and the construction of theMilky Way stellar halo
We have sought to increase the sample of multi-elementabundances in Sculptor through MRS The advantagesover HRS include higher throughput per resolution ele-ment the ability to target fainter stars and multiplex-ing The large sample sizes will enable detailed compar-isons to chemical evolution models of [αFe] and [FeH]in dSphs The disadvantages include larger uncertain-ties particularly for elements with few absorption linesin the red and the inability to measure many elementsaccessible to HRS MRS is not likely to soon provide in-sight into the evolution of neutron-capture elements indSphs
In order to make the most accurate measurements pos-sible we have made a number of improvements to thetechnique of Kirby Guhathakurta amp Sneden (2008a)We have consulted independent HRS of the same starsto confirm the accuracy of our measurements of [FeH][MgFe] [CaFe] and [TiFe] In the case of [FeH]and the average [αFe] our MRS measurements are onlyslightly more uncertain than HRS measurements
Some of the products of this study include
1 An unbiased metallicity distribution forSculptor Because the synthesis-based abun-dances do not rely on any empirical calibrationtheir applicability is unrestricted with regard to[FeH] range The MDF is asymmetric with a longmetal-poor tail as predicted by chemical evolutionmodels of dSphs Furthermore fits to simple chem-ical evolution models shows that Sculptorrsquos MDFis consistent with a model that requires no pre-enrichment
2 The largest sample of [αFe] and [FeH]measurements in any single dSph 388 starsWe have confirmed the trend for [αFe] to decreasewith [FeH] as shown by Geisler et al (2007) withjust nine stars from the studies of Shetrone et al(2003) and Geisler et al (2005) Chemical evolu-tion models may be constructed from these mea-surements to quantify the star formation history ofSculptor
3 The detection of radial [FeH] and [αFe]gradients Our sample probes a smaller rangethan previous studies nonetheless we find aminus0030 plusmn 0003 dex per arcmin gradient in [FeH]and a +0013 plusmn 0003 dex per arcmin gradient in[αFe]
4 The discovery of a Sculptor member starwith [FeH]= minus380plusmn 028 This discovery sug-gests that since-disrupted galaxies similar to Sculp-tor may have played a role in the formation of theMilky Way metal-poor halo High-resolution spec-troscopy of individual stars will confirm or refutethis indication
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 15
minus2 minus1 0 1 2x = ([FeH]i minus [FeH]j) (δ[FeH]i
2 + δ[FeH]j 2)12
0
5
10
15
N(lt
x)
Fig 14mdash Cumulative distribution of differences between the re-peat measurements of [FeH] for 17 stars divided by the estimatederror of the difference The curve is the integral of a unit GaussianThe curve matches the distribution well indicating that the errorsare estimated properly
minus1 0 1y = ([αFe]i minus [αFe]j) (δ[αFe]i
2 + δ[αFe]j2)12
0
5
10
15
N(lt
y)
Fig 15mdash Same as Fig 14 for [αFe] which is the average of[MgFe] [SiFe] [CaFe] and [TiFe]
Much more can be done with this technique inother galaxies The stellar population of a dSphdepends heavily on its stellar mass For instanceLanfranchi amp Matteucci (2004) and Robertson et al(2005) predict that more massive satellites have an [αFe]ldquokneerdquo at higher [FeH] In the next papers in this serieswe intend to explore the multi-element abundance distri-butions of other dSphs and compare them to each otherWe will observe how the shapes of the MDFs and the[αFe]ndash[FeH] diagrams change with dSph luminosity orstellar mass These observations should aid our under-standing of star formation chemical evolution and theconstruction of the Galaxy
We thank Kyle Westfall for providing the photometriccatalog Gustavo Lanfranchi and Francesca Matteucci forproviding their chemical evolution model David Lai forthoughtful conversations and the anonymous referee forhelpful comments that improved this manuscript Thegeneration of synthetic spectra made use of the Yale HighPerformance Computing cluster Bulldog ENK is grate-ful for the support of a UC Santa Cruz Chancellorrsquos Dis-sertation Year Fellowship PG acknowledges NSF grantAST-0307966 AST-0607852 and AST-0507483 CS ac-knowledges NSF grant AST-0607708
Facility KeckII (DEIMOS)
APPENDIX
ACCURACY OF THE ABUNDANCE MEASUREMENTS
In order to quantify the accuracy of the MRS measurements we examine the spectra of stars observed more thanonce and stars with previous HRS measurements
Duplicate Observations
The repeat observations of 17 stars provide insight on the effect of random error on the measurements of [FeH]and [αFe] Figures 14 and 15 summarize the comparisons of measurements of different spectra of the same starsThey show the cumulative distribution of the absolute difference between the measured [FeH] and [αFe] for eachpair of spectra divided by the expected error of the difference (see Sec 49) The solid curve is the integral of a unitGaussian which represents the expected cumulative distribution if the estimated errors accurately represent the truemeasurement errors In calculating the expected error of the difference we apply the systematic error to only one ofthe two stars Even though the same technique is used to measure abundances in both stars some systematic error isappropriate because the wavelength range within a pair of spectra differs by 300ndash400 A The different Fe lines in theseranges span a different range of excitation potentials and the Levenberg-Marquardt algorithm converges on differentsolutions
Comparison to High-Resolution Measurements
The most reliable test of the MRS atmospheric parameter and abundance estimates is to compare with completelyindependent observations and analyses of the same stars Table 6 lists the previous HRS measurements of nineSculptor members (Shetrone et al 2003 Geisler et al 2005) as well as the DEIMOS measurements of the same starsUnfortunately these two HRS studies share no stars in common and therefore cannot be compared with each other
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
16 Kirby et al
TABLE 6Abundances of Stars with Previous High-Resolution Spectroscopy
star Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Of Teff log g and ξ any spectroscopic abundance measurement is most sensitive to Teff In general underestimatingTeff leads to an underestimate of [FeH] Shetrone et al (2003 hereafter S03) determine Teff spectroscopically byminimizing the slope of the derived abundance for each line versus excitation potential Geisler et al (2005 hereafterG05) determine Teff photometrically with empirical color-temperature relations Figure 16 shows Teff from thosestudies and this one for each of the nine stars in common The MRS temperatures do not follow the temperatures ofeither HRS study better than the other
Both S03 and G05 measure log g spectroscopically from demanding ionization equilibrium [FeH] measured fromFe I lines must match that measured from Fe II lines However our red spectra have very few measurable Fe II linesAlternatively log g may be determined from a starrsquos absolute magnitude and Teff via the Stefan-Boltzmann law Eventhough gravity depends on the inverse square of Teff and the inverse square root of luminosity luminosity imposesa stronger constraint on log g because of its larger range on the RGB than Teff Even accounting for the error inthe distance modulus to Sculptor the typical error on photometric log g is sim 01 dex Therefore we determine log gfrom photometry alone Figure 17 shows the comparison between log g used by S03 and G05 and this study Theagreement is not particularly good with discrepancies up to 06 dex However the photometric values of log g aremore accurate than can be determined from the medium-resolution red spectra which show very few lines of ionizedspecies Furthermore as discussed below errors in log g influence the abundance measurements much less than errorsin Teff
Both S03 and G05 measure microturbulent velocity (ξ) by forcing all Fe lines to give the same abundance regardlessof their reduced width We have fixed ξ to log g with an empirical relation (Eq 2) Figure 18 compares the HRSmicroturbulent velocities (ξ) to our adopted values The largest discrepancy is 03 km sminus1
Figure 19 shows the comparison between HRS and MRS [FeH] measurements for the same stars The agreement isvery good (σ = 014 dex) Just two stars out of nine do not fall within 1σ of the one-to-one line
The MRS [FeH] for star 770 is larger than the HRS [FeH] The MRS Teff is also significantly larger than theHRS Teff for this star Similarly the MRS Teff for star H461 is lower than the HRS Teff forcing the MRS [FeH]lower than the HRS [FeH] In fact even the smaller deviations from the [FeH] one-to-one line can be attributed todeviations from the Teff one-to-one line No such correlation can be attributed to deviations in log g or ξ The closecorrespondence between Figs 16 and 19 demonstrates that Teff is the dominant atmospheric parameter in determiningmetallicity
B08b published a catalog of VLTFLAMES [FeH] measurements based on both the EW of the infrared Ca II triplet(CaT) and HRS (Hill et al in preparation) The two resolution modes of FLAMES (R sim 6500 and R sim 20000)allowed them to complete both MRS and HRS analyses with the same instrument Their high-resolution spectroscopicsample and ours overlap by 47 stars which are shown in Fig 20 The agreement (σ = 014 dex) is as good as theprevious comparison to HRS studies
The B08b HRS measurements rely on atmospheric parameters determined from both five-band photometry andspectroscopy We also measure Teff spectrophotometrically Our methods may be similar although we do not useinfrared photometry There appears to be a small systematic trend such that our MRS measurements are lower thanthe B08b HRS measurements of [FeH] at both low and high [FeH] The average discrepancy at the extrema of theresiduals is 02 dex We withhold a detailed investigation of these residuals until publication of the details of the HRS
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 17
3800
4000
4200
4400
4600
4800T
effM
RS
(K)
1446
195 H
482 H45
9
H47
9
982
H40
0
H46
1
770
Shetrone et al (2003)Geisler et al (2005)
3800 4000 4200 4400 4600 4800TeffHRS (K)
minus200
minus100
0
100
200
Tef
fMR
S minus
Tef
fHR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 16mdash Comparison between effective temperature (Teff ) usedin previous HRS abundance analyses and photometric Teff used forthis workrsquos MRS abundance analysis Symbol shape indicates thereference for the HRS abundances Star names from Tab 1 areprinted to the upper left of each point
00
05
10
15
(log
g)M
RS
(cm
sminus2 )
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
00 05 10 15(log g)HRS (cm sminus2)
minus06
minus04
minus02
00
02
04
06
(log
g)M
RS
minus (lo
g g)
HR
S
1446
195
H48
2
H45
9
H47
9982
H40
0
H46
1
770
Fig 17mdash Same as Fig 16 except for surface gravity (log g) Theerror bars represent photometric error and they are given by replac-ing Teff with log g in Eq 6
studyB08b share seven stars in common with S03 and G05 To emphasize the accuracy of our MRS analysis we note that
the scatter of the differences between the two sets of HRS studies (σ = 016 dex) is in fact larger than the scatter inthe comparison between the MRS [FeH] and the same seven stars of S03 and G05 (σ = 014 dex) This small sampledoes not indicate that the MRS measurements are more accurate than any HRS measurements but it does suggestthat the accuracy is competitive
Figure 21 shows the comparison between the MRS and HRS (S03 and G05) values of [MgFe] [SiFe] [CaFe] and[TiFe] In addition Fig 22 shows unweighted averages of those four element ratios where available The agreementis good in all cases Furthermore the error bars seem to be reasonable estimates of the actual random and systematicerror
The agreement between HRS and MRS [αFe] is very good (σ = 013 dex) Even though Fe lines outnumber αelements lines the ratio [αFe] can be measured about as accurately as [FeH] because α and Fe respond similarly toerrors in atmospheric parameters whereas Teff and [FeH] exhibit strong covariance
In addition to [FeH] B08b have published HRS measurements of [CaFe] Figure 23 shows the comparison betweenthe stars we share in common (σ = 020 dex) The larger vertical scatter than horizontal scatter demonstrates that anMRS analysis is noisier than an HRS analysis when the number of measurable lines is small Regardless the degree ofcorrelation is high with a linear Pearson correlation coefficient of 053 indicating that the medium-resolution spectrahave significant power to constrain [CaFe]
REFERENCES
Anders E amp Grevesse N 1989 Geochim Cosmochim Acta 53197
Battaglia G Helmi A Tolstoy E Irwin M Hill V ampJablonka P 2008a ApJ 681 L13
Battaglia G Irwin M Tolstoy E Hill V Helmi A LetarteB amp Jablonka P 2008b MNRAS 383 183 (B08b)
Battaglia G et al 2006 AampA 459 423
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
18 Kirby et al
16
18
20
22
24ξ M
RS
(km
sminus1 )
1446
195
H48
2
H45
9
H47
9
982
H40
0H
461 77
0
16 18 20 22 24ξHRS (km sminus1)
minus03
minus02
minus01
00
01
02
03
ξ MR
S (k
m sminus
1 ) minus
ξ HR
S (k
m sminus
1 )
1446
195
H48
2
H45
9 H47
9
982
H40
0H
461
770
Fig 18mdash Same as Fig 16 except for microturbulent velocity (ξ)The error bars are found by propagating the error on log g throughEq 2
minus25
minus20
minus15
minus10
minus05
[Fe
H] M
RS
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus25 minus20 minus15 minus10 minus05[FeH]HRS
minus02
minus01
00
01
02
[Fe
H] M
RS
minus [F
eH
] HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 19mdash Comparison between [FeH] derived from previous HRSabundance analyses and [FeH] derived from this workrsquos MRS abun-dance analysis Symbols are the same as in Fig 16
Castelli F 2005 Memorie della Societa Astronomica ItalianaSupplement 8 34
Castelli F Gratton R G amp Kurucz R L 1997 AampA 318 841Castelli F amp Kurucz R L 2004 ArXiv Astrophysics e-prints
arXivastro-ph0405087Cohen J G amp Huang W 2009 ApJ 701 1053Demarque P Woo J-H Kim Y-C amp Yi S K 2004 ApJS
155 667Faber S M et al 2003 Proc SPIE 4841 1657Font A S Johnston K V Bullock J S amp Robertson B E
2006 ApJ 638 585Frebel A Collet R Eriksson K Christlieb N amp Aoki W
2008 ApJ 684 588Frebel A F et al 2009 ApJ submitted arXiv09022395Fuhr J R amp Wiese W L 2006 Journal of Physical and
Chemical Reference Data 35 1669Fulbright J P 2000 AJ 120 1841Geisler D Smith V V Wallerstein G Gonzalez G amp
Charbonnel C 2005 AJ 129 1428 (G05)Geisler D Wallerstein G Smith V V amp Casetti-Dinescu
D I 2007 PASP 119 939Girardi L Bertelli G Bressan A Chiosi C Groenewegen
M A T Marigo P Salasnich B amp Weiss A 2002 AampA391 195
Gratton R Sneden C amp Carretta E 2004 ARAampA 42 385Grevesse N amp Sauval A J 1998 Space Science Reviews 85
161Guhathakurta P et al 2006 AJ 131 2497Helmi A et al 2006 ApJ 651 L121 (H06)Holtzman J A Afonso C amp Dolphin A 2006 ApJS 166 534Hurley-Keller D A 2000 PhD Thesis University of Michigan
Johnson J A 2002 ApJS 139 219Kirby E N 2009 PhD Thesis University of California Santa
CruzKirby E N Guhathakurta P amp Sneden C 2008a ApJ 682
1217 (KGS08)Kirby E N Simon J D Geha M Guhathakurta P amp
Frebel A 2008b ApJ 685 L43Koch A Grebel E K Gilmore G F Wyse R F G Kleyna
J T Harbeck D R Wilkinson M I amp Wyn Evans N2008 AJ 135 1580
Kurucz R 1993 ATLAS9 Stellar Atmosphere Programs and 2kms grid Kurucz CD-ROM No 13 Cambridge MassSmithsonian Astrophysical Observatory 1993 13
Lai D K Johnson J A Bolte M amp Lucatello S 2007 ApJ667 1185
Lanfranchi G A amp Matteucci F 2004 MNRAS 351 1338Lin D N C amp Faber S M 1983 ApJ 266 L21Lynden-Bell D 1975 Vistas in Astronomy 19 299Majewski S R Ostheimer J C Kunkel W E amp Patterson
R J 2000 AJ 120 2550Marcolini A DrsquoErcole A Battaglia G amp Gibson B K 2008
MNRAS 386 2173Marcolini A DrsquoErcole A Brighenti F amp Recchi S 2006
MNRAS 371 643Markwardt C B 2009 in ASP Conf Ser arXiv09022850
Astronomical Data Analysis Software and Systems XVIII edD Bohlender P Dowler amp D Durand (San Francisco CAASP)
Mateo M L 1998 ARAampA 36 435
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 19
minus25
minus20
minus15
minus10
[Fe
H] M
RS
minus25 minus20 minus15 minus10[FeH]HRS (Battaglia et al 2008b)
minus04
minus02
00
02
04
[Fe
H] M
RS
minus [F
eH
] HR
S
Fig 20mdash Comparison between the HRS spectral synthesis measurements of [FeH] of Battaglia et al (2008b) and the synthesis-basedmedium resolution measurements of [FeH] (this work) for the stars observed in both studies
Norris J E Gilmore G Wyse R F G Wilkinson M IBelokurov V Evans N W amp Zucker D B 2008 ApJ 689L113
Pagel B E J 1997 Nucleosynthesis and Chemical Evolution ofGalaxies (Cambridge UP)
Pietrzynski G et al 2008 AJ 135 1993Prantzos N 2003 AampA 404 211Prantzos N 2008 AampA 489 525Queloz D Dubath P amp Pasquini L 1995 AampA 300 31Ramırez I amp Melendez J 2005 ApJ 626 465Robertson B Bullock J S Font A S Johnston K V amp
Hernquist L 2005 ApJ 632 872Salvadori S amp Ferrara A 2009 MNRAS 395 L6Schlegel D J Finkbeiner D P amp Davis M 1998 ApJ 500
525Schmidt M 1963 ApJ 137 758Schoerck T et al 2008 AampA submitted arXiv08091172Searle L amp Zinn R 1978 ApJ 225 357Shetrone M D Bolte M amp Stetson P B 1998 AJ 115 1888Shetrone M D Cote P amp Sargent W L W 2001 ApJ 548
592Shetrone M D Siegel M H Cook D O amp Bosler T 2009
AJ 137 62Shetrone M D Venn K A Tolstoy E Primas F Hill V amp
Kaufer A 2003 AJ 125 684 (S03)Simon J D amp Geha M 2007 ApJ 670 313Sneden C A 1973 PhD Thesis University of Texas at Austin
Sneden C Kraft R P Prosser C F amp Langer G E 1992AJ 104 2121
Strigari L E Bullock J S Kaplinghat M Simon J D GehaM Willman B amp Walker M G 2008 Nature 454 1096
Thevenin F amp Idiart T P 1999 ApJ 521 753Tolstoy E et al 2003 AJ 125 707Tolstoy E et al 2004 ApJ 617 L119 (T04)van den Bergh S 1962 AJ 67 486VandenBerg D A Bergbusch P A amp Dowler P D 2006
ApJS 162 375Venn K A amp Hill V M 2005 From Lithium to Uranium
Elemental Tracers of Early Cosmic Evolution 228 513Venn K A amp Hill V M 2008 The Messenger 134 23Venn K A Irwin M Shetrone M D Tout C A Hill V amp
Tolstoy E 2004 AJ 128 1177Walker M G Mateo M amp Olszewski E W 2009 AJ 137
3100Walker M G Mateo M Olszewski E W Gnedin O Y
Wang X Sen B amp Woodroofe M 2007 ApJ 667 L53Westfall K B Majewski S R Ostheimer J C Frinchaboy
P M Kunkel W E Patterson R J amp Link R 2006 AJ131 375
White S D M amp Rees M J 1978 MNRAS 183 341Woosley S E amp Weaver T A 1995 ApJS 101 181
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
20 Kirby et al
minus04
minus02
00
02
04
06
08[M
gF
e]M
RS
1446
195
H48
2
H47
9
770
(a)
minus04 minus02 00 02 04 06 08[MgFe]HRS
minus03
minus02
minus01
00
01
02
03
[Mg
Fe]
MR
S minus
[Mg
Fe]
HR
S
1446
195
H48
2
H47
9
770
minus04
minus02
00
02
04
06
08
[SiF
e]M
RS
1446
195
H48
2
H47
9
H46
1
770
(b)
minus04 minus02 00 02 04 06 08[SiFe]HRS
minus02
minus01
00
01
02
[SiF
e]M
RS
minus [S
iFe]
HR
S
1446
195
H48
2
H47
9
H46
1
770
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
(c)
minus04 minus02 00 02 04 06 08[CaFe]HRS
minus02
minus01
00
01
02
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H46
177
0
minus04
minus02
00
02
04
06
08
[TiF
e]M
RS
1446
195
H48
2
H45
9H
479
982
H40
0
H46
1
770
(d)
minus04 minus02 00 02 04 06 08[TiFe]HRS
minus02
00
02
[TiF
e]M
RS
minus [T
iFe]
HR
S
1446
195
H48
2 H45
9H
479
982
H40
0 H46
1
770
Fig 21mdash Same as Fig 19 except for [MgFe] (upper left) [SiFe] (upper right) [CaFe] (lower left) and [TiFe] (lower right) Onlythose measurements with estimated errors less than 045 dex are shown
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
Abundances in the Sculptor dSph 21
minus04
minus02
00
02
04
06[α
Fe]
MR
S
1446
195
H48
2
H45
9H47
9
982
H40
0
H46
1
770
minus04 minus02 00 02 04 06[αFe]HRS
minus02
minus01
00
01
02
[αF
e]M
RS
minus [α
Fe]
HR
S
1446
195
H48
2
H45
9
H47
9
982
H40
0
H46
1
770
Fig 22mdash Same as Fig 19 except for an average of the α elements
minus04
minus02
00
02
04
06
08
[Ca
Fe]
MR
S
minus04 minus02 00 02 04 06 08[CaFe]HRS (Battaglia et al 2008b)
minus06
minus04
minus02
00
02
04
06
[Ca
Fe]
MR
S minus
[Ca
Fe]
HR
S
Fig 23mdash Comparison between the HRS measurements of [CaFe]of Battaglia et al (2008b) and the synthesis-based medium resolu-tion measurements of [CaFe] (this work) for the stars observed inboth studies
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
22
Kirb
yet
al
TABLE 6Multi-Element Abundances in Sculptor
RA Dec M T2 Teff log g ξ [FeH] [MgFe] [SiFe] [CaFe] [TiFe](K) (cm sminus2) (km sminus1) (dex) (dex) (dex) (dex) (dex)
Note mdash Table 6 is published in its entirety in the electronic edition of the Astrophysical Journal A portion is shown here for guidance regarding form and content
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