FERMILAB-PUB-18-443-PPD

DES-2017-0291Draft version November 8, 2018Preprint typeset using LATEX style emulateapj v. 12/16/11

FIRST COSMOLOGY RESULTS USING TYPE IA SUPERNOVAE FROM THE DARK ENERGY SURVEY:EFFECTS OF CHROMATIC CORRECTIONS TO SUPERNOVA PHOTOMETRY ON MEASUREMENTS OF

COSMOLOGICAL PARAMETERS

J. Lasker1,2, R. Kessler1,2, D. Scolnic2, D. Brout3, C. B. D’Andrea3, T. M. Davis4, S. R. Hinton4, A. G. Kim5,C. Lidman6, E. Macaulay7, A. Möller8,6, M. Sako3, M. Smith9, M. Sullivan9, J. Asorey10, B. A. Bassett11,12,

D. L. Burke13,14, J. Calcino4, D. Carollo15, M. Childress9, J. Frieman16,2, J. K. Hoormann4, E. Kasai17,12,T. S. Li16,2, M. March3, E. Morganson18, E. S. Rykoff13,14, E. Swann7, B. E. Tucker8,6, W. Wester16,

T. M. C. Abbott19, S. Allam16, J. Annis16, S. Avila7, K. Bechtol20, E. Bertin21,22, D. Brooks23,A. Carnero Rosell24,25, M. Carrasco Kind26,18, J. Carretero27, F. J. Castander28,29, L. N. da Costa25,30,

C. Davis13, J. De Vicente24, H. T. Diehl16, P. Doel23, A. Drlica-Wagner16,2, B. Flaugher16, J. Garćıa-Bellido31,E. Gaztanaga28,29, D. Gruen13,14, R. A. Gruendl26,18, J. Gschwend25,30, G. Gutierrez16, D. L. Hollowood32,

K. Honscheid33,34, D. J. James35, S. Kent16,2, E. Krause36, R. Kron16,2, K. Kuehn37, N. Kuropatkin16, M. Lima38,25,M. A. G. Maia25,30, J. L. Marshall39, P. Martini33,40, F. Menanteau26,18, C. J. Miller41,42, R. Miquel43,27,

A. A. Plazas44, E. Sanchez24, V. Scarpine16, I. Sevilla-Noarbe24, R. C. Smith19, M. Soares-Santos45,F. Sobreira46,25, E. Suchyta47, M. E. C. Swanson18, G. Tarle42, D. L. Tucker16, A. R. Walker19

(DES Collaboration)1 Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637, USA

2 Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA3 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA

4 School of Mathematics and Physics, University of Queensland, Brisbane, QLD 4072, Australia5 Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA

6 The Research School of Astronomy and Astrophysics, Australian National University, ACT 2601, Australia7 Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK

8 ARC Centre of Excellence for All-sky Astrophysics (CAASTRO)9 School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK

10 Korea Astronomy and Space Science Institute, Yuseong-gu, Daejeon, 305-348, Korea11 African Institute for Mathematical Sciences, 6 Melrose Road, Muizenberg, 7945, South Africa

12 South African Astronomical Observatory, P.O.Box 9, Observatory 7935, South Africa13 Kavli Institute for Particle Astrophysics & Cosmology, P. O. Box 2450, Stanford University, Stanford, CA 94305, USA

14 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA15 INAF, Astrophysical Observatory of Turin, I-10025 Pino Torinese, Italy

16 Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, IL 60510, USA17 Department of Physics, University of Namibia, 340 Mandume Ndemufayo Avenue, Pionierspark, Windhoek, Namibia

18 National Center for Supercomputing Applications, 1205 West Clark St., Urbana, IL 61801, USA19 Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, Casilla 603, La Serena, Chile

20 LSST, 933 North Cherry Avenue, Tucson, AZ 85721, USA21 CNRS, UMR 7095, Institut d’Astrophysique de Paris, F-75014, Paris, France

22 Sorbonne Universités, UPMC Univ Paris 06, UMR 7095, Institut d’Astrophysique de Paris, F-75014, Paris, France23 Department of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT, UK

24 Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain25 Laboratório Interinstitucional de e-Astronomia - LIneA, Rua Gal. José Cristino 77, Rio de Janeiro, RJ - 20921-400, Brazil

26 Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, IL 61801, USA27 Institut de F́ısica d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra

(Barcelona) Spain28 Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain

29 Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain30 Observatório Nacional, Rua Gal. José Cristino 77, Rio de Janeiro, RJ - 20921-400, Brazil

31 Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain32 Santa Cruz Institute for Particle Physics, Santa Cruz, CA 95064, USA

33 Center for Cosmology and Astro-Particle Physics, The Ohio State University, Columbus, OH 43210, USA34 Department of Physics, The Ohio State University, Columbus, OH 43210, USA

35 Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA36 Department of Astronomy/Steward Observatory, 933 North Cherry Avenue, Tucson, AZ 85721-0065, USA

37 Australian Astronomical Optics, Macquarie University, North Ryde, NSW 2113, Australia38 Departamento de F́ısica Matemática, Instituto de F́ısica, Universidade de São Paulo, CP 66318, São Paulo, SP, 05314-970, Brazil

39 George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, and Department of Physics andAstronomy, Texas A&M University, College Station, TX 77843, USA

40 Department of Astronomy, The Ohio State University, Columbus, OH 43210, USA41 Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA

42 Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA43 Institució Catalana de Recerca i Estudis Avançats, E-08010 Barcelona, Spain

44 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109, USA45 Brandeis University, Physics Department, 415 South Street, Waltham MA 02453

46 Instituto de F́ısica Gleb Wataghin, Universidade Estadual de Campinas, 13083-859, Campinas, SP, Brazil47 Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831

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Draft version November 8, 2018

ABSTRACT

Calibration uncertainties have been the leading systematic uncertainty in recent analyses usingtype Ia Supernovae (SNe Ia) to measure cosmological parameters. To improve the calibration, wepresent the application of Spectral Energy Distribution (SED)-dependent “chromatic corrections” tothe supernova light-curve photometry from the Dark Energy Survey (DES). These corrections dependon the combined atmospheric and instrumental transmission function for each exposure, and theyaffect photometry at the 0.01 mag (1%) level, comparable to systematic uncertainties in calibrationand photometry. Fitting our combined DES and low-z SN Ia sample with Baryon Acoustic Oscillation(BAO) and Cosmic Microwave Background (CMB) priors for the cosmological parameters Ωm (thefraction of the critical density of the universe comprised of matter) and w (the dark energy equationof state parameter), we compare those parameters before and after applying the corrections. We findthe change in w and Ωm due to not including chromatic corrections are −0.002 and 0.000, respectively,for the DES-SN3YR sample with BAO and CMB priors, consistent with a larger DES-SN3YR-likesimulation, which has a w-change of 0.0005 with an uncertainty of 0.008 and an Ωm change of 0.000with an uncertainty of 0.002 . However, when considering samples on individual CCDs we find largeredshift-dependent biases (∼ 0.02 in distance modulus) for supernova distances.Subject headings: cosmology:dark energy – cosmology:observations –supernovae:general – techniques:

photometric

1. INTRODUCTION

Supernova cosmologists uses type Ia Supernovae(SNe Ia) as standardizable candles to measure distancesover a wide range of redshifts, which, when combinedwith a measurement of the redshift, are used to trace theexpansion history of the Universe. The SN Ia distancesand redshifts are fit to a model that is typically param-eterized in terms of the fraction of the universe’s energythat is in matter (ΩM) versus that which is in dark en-ergy (ΩΛ), as well as the equation of state parameter ofdark energy, w.

The recovery of cosmological parameters from SNe issensitive to calibration in two ways. First, cosmologi-cal constraints depend on comparing the relative bright-nesses of SNe at different redshifts. As the rest frame SNspectrum is redshifted, we observe it in different band-passes which must be calibrated relative to each other.Second, we observe SNe at different positions on thesky, different locations on our focal plane, and in dif-ferent weather conditions. Non-uniformity of these ob-servations can introduce potential cosmological biases.Together, these calibration uncertainties make up thelargest source of systematic uncertainty on cosmologicalparameters derived from SN Ia distances.

The impact of the systematic uncertainty from calibra-tion is well illustrated in the recent analysis of the Pan-theon sample (Scolnic et al. 2017), which is the largestcombined sample of spectroscopically confirmed SNe Iaanalyzed to date. For the dark energy equation of stateparameter w, the Pantheon analysis’ calibration uncer-tainty of 2-6 mmag, depending on sample, contributesσw = 0.02, half of their total uncertainty on w.

The samples included in this analysis are from the Pan-STARRS 1 (PS1, Rest et al. 2014) Medium Deep Survey,the Sloan Digital Sky Survey II (SDSS-II, Sako et al.2014), the Supernova Legacy Survey (SNLS, Conley et al.2011), HST (Riess et al. 2004, 2007; Rodney et al. 2014),the Center for Astrophysics low redshift surveys (CFA3and CFA4, Hicken et al. 2009 and Hicken et al. 2012),the Carnegie Supernova Project (CSP, Stritzinger et al.2011), and the HST Cluster Supernova Survey (Suzuki

et al. 2012).It’s critical to note that while the calibration uncer-

tainties from these samples are a factor of 50 below thedistance uncertainties, the binned distance uncertaintiesthat constrain cosmology are reduced as (

√NSN), unlike

the calibration error.It is important to reduce calibration uncertainties in

order to utilize the improved statistical power in mea-suring cosmological parameters from surveys with largersamples. The Dark Energy Survey Supernova Program(DES-SN, Kessler et al. 2015) is measuring multi-bandlight curves of a photometric sample of thousands ofSNe Ia, as well as a spectroscopically classified sampleof several hundred SNe Ia. Furthermore, the Large Syn-optic Survey Telescope (LSST, Ivezić and the LSST Sci-ence Collaboration 2013), which is expected to begin sur-vey operations in 2022, will discover 104 SNe Ia withhigh-quality light curves in its deep-drilling fields, as wellas over a million SNe Ia with sparser light curves in thewide-fast-deep survey.

Calibration of astronomical images is fundamentallythe transformation of a number of ADU (Analog/DigitalUnits) from a source in a CCD image to a top-of-the-atmosphere brightness. This process has undergonemany different iterations throughout the last 20 years ofwide area astrophysical sky surveys. We briefly summa-rize these below.

The Sloan Digital Sky Survey (SDSS,York et al. 2000)made many innovations for the calibration procedures ofwide-area sky surveys. They developed the ugriz filtersystem (Fukugita et al. 1996) that has been used withminor variations by many other surveys, including DES(Flaugher et al. 2015), PS1 (Tonry et al. 2012) and SNLS(Regnault et al. 2009). The Ubercal method (Padmanab-han et al. 2008) accounted for the flat field variation andamplifier gain variation while absorbing the atmosphericeffects into a linear (in magnitude) airmass correction.This method made use of repeated observations of starsduring the survey to achieve 1% relative calibration (con-sistency in the natural magnitude system) across the sur-vey footprint. Since Vega was too bright to be observedby SDSS, they tied their absolute photometry to the AB

3

system (Oke and Gunn 1983), a hypothetical flat refer-ence spectrum which has a constant value of 3631 Jy (1Jy = 10−26 Wm2Hz ) as would be measured at the top of theatmosphere. The AB system provides a more practicalpath to apply the absolute calibration through observa-tions of fainter flux standards like BD+17-4708, whichcan be observed by large survey instruments without sat-urating the CCDs.

PS1 improved on the Ubercal method that SDSS usedfor its relative calibration by adopting a different sur-vey strategy (Magnier et al. 2013). This included largerareas of overlap between exposures and spacing repeatobservations of a field both on 15 minute timescaleswithin a night and at 6 month separations. These over-laps enabled PS1 to obtain high-quality calibration onnights with poor conditions as explained in Schlafly et al.(2012). PS1 used their improved photometry and over-laps of their fields with those of SDSS to recalibrate SDSSto PS1-levels of precision using a method called Hyper-calibration (Finkbeiner et al. 2016).

To further improve the absolute calibration, PS1 mea-sured the full transmission function including instrument(telescope + CCD) and atmosphere. They measured theinstrumental transmission using in-dome monochroma-tor scans of the telescope and CCDs without filters, andthey also utilized the vendor scans of the filter through-put (Tonry et al. 2012). For the atmospheric compo-nent, they included MODerate resolution atmosphericTRANsmission (MODTRAN, Berk et al. 1987) modelsin their method to allow for specific contributions fromaerosols, water vapor, and ozone to the linear airmass ex-tinction. PS1 used repeated observations of many HSTCalSpec (Bohlin et al. 2014) standard stars inside of thefootprint to tie its photometry to the AB system (Scolnicet al. 2015). Hereafter “transmission” refers to the fullinstrumental + atmospheric transmission function unlessotherwise specified.

For the Dark Energy Survey (The Dark Energy SurveyCollaboration 2005) at the Cerro Tololo InteramericanObservatory (CTIO), a new calibration method has beendeveloped based on a forward modeling approach. Thismethod is called the Forward Global Calibration Method(FGCM, Burke et al. 2018, B18 hereafter). While SDSSand PS1 account for the effect of the atmosphere aver-aged over each night, FGCM models the full DES trans-mission function for each CCD and each exposure, thusaccounting for dependence of the transmission functionon focal plane position as well as its time variation.FGCM uses approximately bimonthly measurements ofthe system throughput in each passband for each CCD(DECals, Marshall et al. 2013). More information aboutthe variation in the instrumental transmission functionacross the focal plane is obtained from star flats as de-scribed in Drlica-Wagner et al. 2018. To monitor atmo-spheric changes, FGCM uses data from a GPS receiver atCTIO (Blake and Shaw 2011; Flaugher et al. 2015). Thedata is analyzed by SuomiNet1, which provides measure-ments of atmospheric precipitable water vapor (PWV)in 30 minute time windows. It uses this information inconjunction with data from bright stars in normal DESobservations. FGCM achieves relative calibration at the

1 http://www.suominet.ucar.edu

∼ 4.5 mmag level. This is based on a comparison ofthe DES catalogs to those of Gaia DR2 averaged oversmall patches of sky and is likely an upper bound for theuncertainty.

FGCM determines its absolute calibration by compar-ing observed magnitudes of the CalSpec standard C26202with the “synthetic” magnitudes obtained by multiply-ing the CalSpec spectrum with each filter’s model FGCMtransmission function. C26202 is located within one ofthe DES-SN deep fields that has been observed over 100times during the survey and it is faint enough to not sat-urate in most of the exposures. The flux scaling for eachexposure, usually expressed as the logarithmic zeropoint,is obtained by integrating the product of the exposure’stransmission function with a reference spectrum. Despiteusing C26202 to determine the absolute calibration, DESuses the flat AB spectrum as its reference.

This zeropoint is precisely correct only if the sourceSED is the reference spectrum or if it is observed underthe exact conditions that define the reference transmis-sion functions. The reference transmission functions arechosen during the FGCM fitting process to represent theaverage DES transmission function in each band. Forother sources and other observing conditions, the opti-mal calibration requires additional corrections that de-pend on the SED of the source being observed. We callthese “chromatic corrections.”

There are two observational effects that contribute tothe need for chromatic corrections. First, the atmo-spheric transmission as a function of wavelength variesbetween observations. Those variations are illustratedin the uppermost panel of Fig. 3 from Li et al. (2016)(hereafter, L16). This figure shows the ratio between thetransmission functions at PWV = 3 mm and PWV = 10mm. This plot shows a maximum of 50% fractional vari-ation in the transmission function in z-band due to thePWV variation. Second, the Dark Energy Camera (DE-Cam Flaugher et al. 2015) filter transmission functionvaries across the focal plane as shown in Fig. 6 of L16.This figure shows a shift of the edge of the i-band trans-mission function of up to 6 nm as a function of distancefrom the center of the focal plane.

Color differences between astrophysical point sourcesand the reference standard affect the size of these chro-matic corrections. This is particularly important for su-pernovae, as supernova SEDs are much redder than thereference standard, are very diverse, have strong broadfeatures, vary with time, and vary significantly in colordue to the wide range of redshifts observed as well red-dening due to dust in the SN host galaxy. The variationof SN Ia spectra with redshift is shown here in Fig. 1.The objective of this paper is to demonstrate the appli-cation of the chromatic corrections to DES-SN data andcharacterize the effects of the corrections in single-epochphotometry, light curves, and cosmology.

The outline of the paper is as follows. The formalismof chromatic corrections is described in §2.1. We describethe dataset to which these SED-based corrections are ap-plied in §2.2. We show the method with which the SN Ialight curves are fit, including the application of the chro-matic corrections, in §2.3. In §3, we show our resultsincluding: demonstrating the effect of the corrections onthe single-epoch photometry (§3.1); the effect on the nui-sance parameters α and β as well as a cross-check of those

4

parameters with those of Pantheon in §3.2; the effect onthe supernova light curves and cosmology (§3.3); and theeffect of the corrections on SN Ia simulated on individualCCDs (§3.4). Finally we examine several cross checks onour analysis in §3.5.

0.0

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Fig. 1.— SN Ia SEDs at peak brightness for (a) low, (b) interme-diate, and (c) high redshift model spectra from SALT2 Guy et al.2007, and (d) the AB spectrum, which is proportional to 1/λ2.Overplotted on all spectra are the DES griz standard bandpasses.

2. METHODS + DATA SAMPLE

2.1. Application of Chromatic Corrections

Here we describe the exact form of the chromatic cor-rections and the manner in which they are applied to thesupernova photometry.

The typical definition of the magnitude, mb, in a band,b, of a source with flux (photon counts normalized bytelescope aperture and exposure time), Fb, in an imagewith zeropoint, ZPb, is

mb = −2.5 log10(Fb) + ZPb. (1)

In the AB system, this definition can be further ex-

panded such that:

mb = −2.5 log10∫ ∞

0

Fν,src(λ)φb,tot(λ)λ−1dλ

+2.5 log10

∫ ∞0

Fν,ref(λ)φb,tot(λ)λ−1dλ,

(2)

where Fν,src(λ) is the SED (in units ofW

m2Hz ) of the sourceobject being observed, and Fν,ref(λ) is the SED of the ref-erence object for the photometric system. For DES, weuse the AB spectrum (Fig. 1d). φb,tot(λ) is the dimen-sionless total transmission function.

This definition of the magnitude forms the basis forthe chromatic corrections in L16:

δmb =mstd −mobs =

−2.5 log10

∫∞0Fν,src(λ)φ

atmobs (λ)φ

instb,obs(λ)λ

−1dλ∫∞0Fν,src(λ)φatmref (λ)φ

instb,ref(λ)λ

−1dλ(3)

+2.5 log10

∫∞0Fν,ref(λ)φ

atmobs (λ)φ

instb,obs(λ)λ

−1dλ∫∞0Fν,ref(λ)φatmref (λ)φ

instb,ref(λ)λ

−1dλ.

In Eq. 3, mstd is the ”standard” magnitude of the ob-ject being observe transformed as though it was observedunder the reference conditions, mobs is the magnitudethat was observed under the actual conditions, Fν,src andFν,ref are the same as in Eq. 2, φ

atmobs (λ) and φ

instb,obs(λ)

are the atmospheric and instrumental2 components ofφb,tot(λ) at the location of the source on the focal planefrom Eq. 2 such that φatmobs (λ)φ

instb,obs(λ) = φb,tot(λ) , and

φatmref (λ) and φinstb,ref(λ) are the reference atmospheric and

DECam transmission functions within a given band, b,respectively. The reference transmission functions arechosen during the FGCM process to represent the mostprobable conditions over the course of the survey (seeFig. 4 in B18).

Due to this choice of reference transmission, the aver-age chromatic correction for a single object over an infi-nite number of observations should trend to zero. How-ever, SNe Ia are time varying and the shape of the lightcurve is important for standardization. Therefore, trendsin atmospheric parameters that depend on time (e.g sea-sonal variations, El Niño, and degradation of the primarymirror) could produce effects that will not average tozero. The light curve sampling requirements result innon-uniform sampling of events over the course of thesurvey and therefore seasonal variations in atmosphericproperties could potentially result in chromatic correc-tions whose effect on SN Ia distance does not average tozero.

The correction in Eq. 3 is defined so that it is equal tozero for observations of the reference source with the ref-erence transmission function. The atmospheric transmis-sion functions are informed by our PWV measurementsand the DECam transmission functions are measured bythe DECal scans with additional input on the focal planevariation from star flats. The correction is added to thezeropoint based on the SED of the source.

2 telescope, instrument, filter, and CCD

5

These chromatic corrections are an improvement overthe previous linear atmospheric correction3 in two ma-jor ways. First, they account for variation in the at-mospheric conditions over the course of each night ofobserving whereas the linear correction coefficients werefit nightly. Second, the chromatic corrections incorpo-rate SED information allowing for the correction of non-blackbody spectra and objects whose spectra have strongfeatures

Using a small data sample, L16 shows that the effectof these chromatic corrections on SNe Ia can be as largeas 10 mmag (1%) in z-band and several mmag in r and ibands for high redshifts and large atmospheric water va-por. This study illustrates that for SEDs that differ sig-nificantly from the reference, the chromatic correctionscan be comparable or larger than to the non-uniformityof the calibration (≈ 4.5 mmag).

The middle row of panels in Fig. 7 from L16 showsthat the variation in the corrections described in Eq. 3matches the observed variation in stellar magnitude vs.stellar color to mmag precision. The typical color rangeobserved in SNe Ia is 0.5 < g−i < 3.5, which includes theentire range of that figure. This test demonstrates thatchromatic corrections improve the calibration for sourceswhose SED differs from the reference SED.

2.2. Data Sample

The Dark Energy Survey includes a 5000 deg2 (“wide”)survey (DES 2018) and a 27 deg2, time domain, super-nova survey (Bernstein et al. 2012; Kessler et al. 2015),which are run concurrently between August and Febru-ary beginning in 2013 and ending in 2018. The wide sur-vey alone will continue operations into 2019. The widesurvey is conducted in 5 bands (grizY ) of which the 4bluest bands (griz) are used in the supernova survey.Survey observations are conducted on the Victor Blanco4m telescope using the Dark Energy Camera (DECam)at the CTIO in Chile.

The supernova fields are observed when the predictedpoint spread function (PSF) is above 1.1′′ or when a fieldhits a “deadman” trigger meaning that it has not beenobserved for 7 days. The atmospheric conditions of thesupernova survey are illustrated in Fig. 2, whose threepanels shows the distribution of PWV, atmospheric op-tical depth due to aerosols (τ), and PSF respectively.While PWV and τ are comparable to the median DESwide area conditions, the median PSF is about a tenthof an arcsecond above the median PSF of the wide areasurvey.

Atmospheric parameters PWV and τ were computedby B18 for exposures satisfying quality requirements forthe wide-area, and thus 10% of supernova survey obser-vations do not have the atmospheric parts of the correc-tion. However, all exposures are corrected for instrumen-tal transmission variation. Atmospheric information forall exposures will be included in a future paper that willcover the calibration of the full five seasons of DES.

The DES SNe are discovered in the “real-time” differ-ence imaging pipeline (DIFFIMG, Kessler et al. 2015),where deep coadded template images are subtracted fromeach supernova survey image. In this paper we use 214spectroscopically confirmed SNe Ia discovered from the

3 http://classic.sdss.org/dr7/algorithms/jeg photometric eq dr1.html

first three years of DES-SN. The spectroscopic selectionof the sample is described in D’Andrea et al (2018, inprep.). The 2% calibration uncertainty for DIFFIMGphotometry is sufficient for SN discovery and monitoring,but is not sufficient for the cosmology analysis. There-fore, DES has developed a version of “scene modeling”photometry (SMP, Brout et al. 2018), originally devel-oped by SDSS (Holtzman et al. 2008) and later used bySNLS (Astier et al. 2013), for use in the offline analysiswith the goal of achieving sub-percent precision. In thisanalysis we are using the SMP photometry.

To improve the cosmological parameter determination,the spectrscopically confirmed subset of the DES-SNsample is combined with 126 low redshift (low-z) super-novae from surveys including CFA3, CFA4, and CSP.This sample is taken from the Pantheon analysis (Scolnicet al. 2017) with additional cuts described in DES Col-laboration 2018. We do not apply chromatic correctionsto the low-z sample because we do not have the infor-mation necessary to make these corrections. Instead, weuse the original survey calibration. The combination ofthe DES-SN sample and the low-z sample is referred toas “DES-SN3YR.”

In order to study the effect of chromatic correctionswith large statistics in all areas of parameter space(e.g. SN parameters like redshift, color, and stretch aswell as observing conditions like τ and PWV), we uti-lize a DES-SN3YR-like sample produced by the simula-tion code in the SuperNova ANAlysis (SNANA4, Kessleret al. 2009, Kessler et al. 2018) software package. We usethis simulation to generate a large number of SEDs, ap-proximately 120x the size of the DES-SN3YR sample, forwhich we can assess the impact of chromatic corrections.

These simulated supernovae are generated using thecolor and stretch distributions of Scolnic and Kessler(2016), the volumetric rate from Perrett et al. (2012),the spectroscopic selection function from D’Andrea et al.in Prep., host galaxy library from Gupta et al. (2016),and the intrinsic scatter model from Guy et al. (2010);Kessler et al. (2013). This simulation uses randomly cho-sen sky coordinates over the supernova fields, selects arandom CCD from the focal plane, and uses DES obser-vation dates. The date and focal plane location are usedto determine chromatic corrections (Eq. 3) in the samemanner as for the data.

Fig. 3 shows the redshift and maximum signal to noiseratio (SNR) distributions for the DES-SN sample. Thesimulations agree well with the data for the DES-SN sam-ple. A similar plot for the low-z sample is shown in Fig. 7.of (Kessler et al. 2018)

2.3. Light-Curve and Cosmology fitting

The SNANA software package provides light-curve fit-ting code using the Spectral Adaptive Lightcurve Tem-plate 2 (SALT2) model first developed by Guy et al.(2007). We use the most recently trained SALT2 modelthat was developed for the Joint Light-curve Analysis(JLA, Betoule et al. 2014). However, to see the effect ofthe chromatic corrections on z-band in the lowest red-shift DES supernovae, we use the Near Infrared (NIR)extension of this model from Hounsell et al. (2017). Thelight-curve fitting code determines the stretch (x1), color

4 snana.uchicago.edu for manual and other information

http://classic.sdss.org/dr7/algorithms/jeg_photometric_eq_dr1.html

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Fig. 2.— The distribution of atmospheric precipitable water vapor (PWV), optical depth due to aerosols (τ), and PSF FWHM for DESobservations of the supernova fields during the first three seasons. The black solid and red dashed lines represent the median conditionsover the first three seasons of the survey for DES and DES-SN respectively, and the green dotted and dashed line represents the referenceatmosphere (there is no standard PSF size). All four bands (griz) are included.

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Fig. 3.— The distribution of redshift (left) and maximum signal to noise (right) for SNe Ia in the DES-SN data sample (black circleswith error bars) and simulation (light blue bars).

7

(c), amplitude (x0), and time of peak brightness (t0) foreach supernova light-curve, both for the DES-SN3YRdata sample and the simulated sample described in §2.2.Distance moduli are calculated by the Tripp estimator(Tripp 1998):

µ = M0 +mB + αx1 − βc, (4)where mB = −2.5 log10(x0), α is the stretch-magnitudestandardization parameter, and β is the color-magnitudestandardization parameter.

In the first step of the analysis, the light curves are fitwithout chromatic corrections to determine the SED ateach epoch using the SALT2 spectral model. Next, thelight curves are fit with corrections (Eq. 3) applied.

After light curve fitting, the standardization parame-ters α and β and a Hubble diagram which is correctedfor biases due to selection effects and light curve fittingare determined simultaneously from a global fit to theset of DES-SN3YR light curve parameters (c, x1, mB).This global fit is performed with the BEAMS with BiasCorrection (BBC, Kessler and Scolnic 2017) formalismwith 20 logarithmically spaced redshift bins from 0.01 to0.85.

The binned distances and uncertainties are passed towFit, a fast χ2 minimization program using MINUIT(James and Roos 1975), which outputs marginalized cos-mology parameters w and Ωm based on a wCDM model,a flat universe with varying dark energy equation of stateparameter, w, and cold dark matter. These parametersare obtained with priors from BAO (Eisenstein et al.2005) and CMB (Komatsu et al. 2009). The cosmo-logical parameters are blinded so that we only examinedifferences due to the chromatic corrections. These sim-plifications are used because they are significantly fasterand sufficiently accurate for differential studies. How-ever, we do not use these simplifications in the nomi-nal DES-SN3YR cosmology analysis (DES Collaboration2018).

For each SN, we calculate the change in the BBC dis-tance modulus µ and the three parameters x1, c, andmB due to the chromatic corrections. The light-curve fitparameters x1 and c are multiplied by the nuisance pa-rameters α and β to give them the same units (mag) as µand mB . α and β are fit separately with BBC before andafter corrections are applied; however, they do not sig-nificantly change due to the corrections. Therefore, weadopt a single value for alpha and beta when calculatingthe differences. These differences are defined below:

∆µ = µnoCorr − µcorr (5)

∆αx1 = αx1,noCorr − αx1,corr (6)

∆βc = βcnoCorr − βccorr (7)

∆mB = mB,noCorr −mB,corr. (8)We characterize the ∆ parameter dependence on red-

shift using a linear fit (∆ vs. redshift) to the unbinnedSN sample in order to obtain a simple one parameterquantification of the effect of the corrections. These val-ues and their slopes can be seen in Figs. 6, 7, 8, and 12.

Since the fitting uncertainty on the slopes of the bestfit lines does not account for correlations (e.g. betweenx1,noCorr and x1,corr), the uncertainty is determined em-pirically. We generate 50 data-sized simulations of theDES-SN3YR sample. Then, after running those samplesthrough the same analysis as the data, we collect the fit-ted values of the ∆ parameter slopes vs. redshift and ∆cosmological parameters. We use the standard deviationof the slopes and cosmological parameters among the 50simulations to estimate the uncertainty. We believe thisis valid since the distribution of these 50 slopes is con-sistent with a normal distribution. We also use thoseuncertainty estimates for the larger simulated sample.However, for that larger sample we scale down the un-certainty by the square root of the ratio of the size ofthe larger sample to the size of the DES-SN3YR sample.Applying corrections based on these linear relationshipsis not a substitute for applying the full integrated cor-rection to each supernova epoch. However, calculatingthe slopes is useful to check whether the simulated SNechange similarly to the data events as well as to checkwhether the redshift trend (or lack thereof) in parameterchanges indicates that there should or should not be acosmological parameter bias.

We define changes in the wFit output cosmological pa-rameters w and Ωm:

∆w = wnoCorr − wcorr (9)

∆Ωm = Ωm,noCorr − Ωm,corr. (10)

Following the method for determining the uncertaintieson the slopes above, the uncertainties on ∆w and ∆Ωmare the standard deviation in these quantities from 50DES-SN3YR sized simulations. These uncertainties arealso scaled by the square root of the sample size.

3. RESULTS

We begin this section with the impact of the correc-tions on the single-epoch photometry and show the de-pendence on SN color, redshift, and atmospheric PWV.Next we show a comparison of the SALT2 nuisance pa-rameters α and β between this analysis and the Pan-theon analysis, as well as the change in those parametersdue to the chromatic corrections. Finally, we present thechanges in light-curve fit parameters, distance moduli,and cosmological parameters due to these corrections.

3.1. Impact on single-epoch photometry

We apply the corrections described in §2.1 to the DES-SN3YR sample and examine the effects on single-epochphotometry. Since the z band includes water absorptionlines, we present those results here. The g, r, and i bandsshow a median chromatic correction consistent with zeroat all values of redshift, PWV, and observed r − i (forg and r band) or i− z (for i band) color. The standarddeviation of all chromatic corrections in g, r, and i bandsrespectively are 11.1, 3.3, and 4.4 mmag.

The upper left panel of Figure 4 shows the average (z-band) chromatic correction as a function of PWV andi − z color when applied to the DES-SN3YR sample.PWV and i−z are divided into 10 evenly spaced bins overthe range of observed parameter space. Those panels are

8

further subdivided into panels based on the SN redshift.These plots include all SN epochs regardless of phaserelative to peak brightness in the model B band.

There is a trend of about 1 mmag per mm of PWVat low redshifts and that trend reverses to −1 mmag permm of PWV at highest redshifts. To see the δmz effectwith higher statistics, the upper right panel of Figure 4shows a prediction using a simulation of 120 DES-SN3YRsamples. This simulation confirms the trend observedin the data. There is no statistically significant trendwith light-curve fit color in data or simulation. Thedata sample appears to have very low scatter in somePWV/color+redshift bins because it only has one or twoevents that fall in that bin. The simulated scatter ismore representative of the true scatter in the chromaticcorrections.

In order to further illustrate the effect of the chromaticcorrections due to atmospheric and CCD variations, inFig. 5 we present the distribution of corrections for twoselected SN SEDs integrated for each atmospheric trans-mission function observed during DES. These SN SEDsare from Figs. 1 b and 1 c, with redshifts 0.36 and 0.85,respectively. We present two panels for each of the twosample SEDs: the first set of panels takes its instrumen-tal transmission function from 6 interior CCDs and theother takes its instrumental transmission function fromthe 6 outer CCDs. The median of the chromatic correc-tion distribution is significantly different when consider-ing the inner CCDs vs. the outer CCDs and the shapeof the distribution is much wider for the lower redshiftSN than the higher redshift SN.

The width of the low-redshift chromatic correction dis-tribution is driven primarily by PWV variations between0.5 and 15 mm. Within the z-band wavelength range, theAB spectrum is nearly flat, while the SN spectra are sig-nificantly more tilted, and thus PWV variations, whichaffect the region near λ ∼ 9500Å, have a larger effecton the AB spectrum. The distribution for high redshift(lower panels) is much narrower due to the fortuitousbump in the exact location of the PWV feature. Wehave checked that without this bump, the width of thechromatic correction distribution is much larger and alsoreproduces the secondary peak that we observe in thelow redshift distribution.

3.2. Result for BBC fitted SALT2 nuisance parameters

Table 1 shows the nuisance parameters α and β fromthe BBC fits of the DES-SN3YR sample, as well as thosefrom the Pantheon Sample. We compare these parame-ters to check our fitting method without unblinding thecosmological parameter fit. α and β are statisticallyconsistent between DES-SN3YR and Pantheon, and thechromatic corrections result in negligible shifts (< 1%).The table also includes the intrinsic scatter of supernovabrightness (σint) which is calculated as the amount ofadditional error that needs to be added during the fitto get the reduced χ2 to be equal to one. This value isalso comparable to the scatter in Pantheon (Scolnic et al.2017).

3.3. Effect of chromatic corrections on light-curve fitparameters distances, and cosmology

Here we propagate both the DES-SN3YR and simu-lated samples through the analysis and show the effects

TABLE 1BBC nuisance parameters for DES-SN3YR and Pantheon

samples.

Dataset α β σintDES Uncorrected 0.144± 0.008 3.12 ± 0.104 0.097DES Correcteda 0.145± 0.008 3.11 ± 0.10 0.097

Pantheon 0.156 ± 0.006 3.02 ± 0.06 0.09

aChromatic corrections described in §2.1.

of the chromatic corrections as a function of redshift onthe fit parameters.

Figure 6 shows the redshift dependence of the effectof the chromatic corrections on the measured distancemodulus (∆µ), as well as on the light-curve fit param-eters (∆x1, ∆c, and ∆mB) for the data. The slopes ofthe shift vs. redshift given on the top of each panel showthat each slope is consistent with zero.

Figure 7 shows the same quantities as in Fig. 6, but forthe simulated DES-SN3YR sample, which has slope un-certainties that are almost an order of magnitude smallerthan those of the data. For the simulated SNe, ∆mBshows a nonzero slope with 3-σ significance (0.6 ± 0.2mmag). This effect does not propagate to any signif-icant redshift trend in distance modulus vs. redshift.The remaining light-curve fit parameters have slopes vs.redshift that are consistent with zero at a 1-σ level. Allof the slopes for the simulated sample parameters areconsistent with the slopes of the data sample parametersas shown in the top two rows of each panel of Fig. 8.While the mean of the chromatic corrections is small,the scatters in these plots exhibit the range of the chro-matic corrections on the individually measured distancemoduli and fitted light-curve parameters.

To examine the relative effects of the atmospheric andinstrumental corrections, we made the corrections for thesimulated sample using the standard atmosphere, zero-ing out the atmospheric correction, and then we madea second set of corrections that are the differences be-tween the full (atmospheric + instrumental) correctionsand the instrumental only corrections. The effect of thesecorrections on distance modulus are shown in Fig. 9 andFig. 10 below.

These figures (Fig. 9 and 10) show that the trend indistance correction vs. redshift is mostly due to the at-mospheric effects, but the oscillatory features are mostlydue to the instrumental effects. We have examined thetrend of ∆µ vs. redshift for individual CCDs, and wefind that the oscillations are present in each CCD andare not an artifact of stacking all of the CCDs.

For the data, the shifts in the cosmological parametersΩm and w due to the chromatic corrections (∆Ωm and∆w as in Equations 9 and 10) are ∆w = −0.002 and∆Ωm = 0.000. These changes are consistent with oursimulated results where the mean change in w over our 50simulated DES-SN3YR-sized simulations is 0.007 with anstandard error in the mean of 0.008. Similarly, the meanΩm change is 0.001 with a standard error in the mean of0.001. The simulation results are consistent with zero asexpected. They are also consistent with the data basedon our limited sample size. The results are visualized inthe top two rows of each panel of Fig. 11.

9

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Fig. 4.— For DES z band, δmz dependence on PWV (top) and i− z color (bottom). Each set of 4 panels shows a different redshift rangefor data (left) and simulations (right). The white solid lines connect the median chromatic correction in each PWV/color bin, the reddashed line is zero, and the colored band represents the standard deviations within each bin.

For an SN Ia-only analysis, we find ∆Ωm and ∆w are0.005 and -0.0294. However, since the shift occurs alongthe direction of the SN Ia-only contour degeneracy, theeffect on the combined SN Ia, CMB, and BAO results arenegligible for the DES data set. Furthermore the shiftis still negligible in an SN Ia-only analysis relative to theparameter uncertainties, 0.07 and 0.35 respectively forΩm and w.

3.4. Results on individual CCDs

There is no significant trend in ∆µ vs redshift as shownin Figs. 6 and 7. However, this is not the case for individ-

ual CCDs in the simulated sample. The data sample istoo small to get meaningful results for individual CCDs,so we use a simulated sample. Fig. 12 shows ∆µ vs red-shift for 4 different CCDs at different distances from thecenter of the focal plane. CCD 35 is near the center,CCD 52 is halfway between the center and the edge, andCCDs 1 and 62 are at the far edge of the focal plane onopposite sides. These 4 CCDs were chosen to sample theradial transmission function variation as shown in L16.These simulations show that some CCDs have a strongtrend in ∆µ vs. redshift.

The results of fitting these redshift trends for the data,

10

10 0 10 20mz (mmag)

0250500750

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Inner CCDsOuter CCDs

10 0 10 20mz (mmag)

0

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2000

3000

4000

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6000SN @ z = 0.849

Inner CCDsOuter CCDs

Fig. 5.— For DES z band, δmz distribution for the SN spectrum in Fig. 1 b (left) and Fig. 1 c (right). Each set of panels shows a differentset of CCDs (inner CCDs as black dots and outer CCDs as blue bands).

simulation, and subsets of the simulation for each of thechosen CCDs are summarized in the bottom four rows ofeach panel of Fig. 8. The scatter among the individualCCD samples is large and in many cases the CCDs areboth inconsistent with each other and with zero. Theindividual corrections show a strong oscillatory behaviorwith redshift that comes from features of the SED movinginto and out of the bandpasses with redshift.

3.5. Cross Checks

Since our redshift cutoff of 0.85 is a function of the DESspectroscopic selection function (D’Andrea et al 2018 inprep.) and is not related to the chromatic correctionsor the supernovae themselves, we have also tested theeffect of changing this cutoff to lower redshift. There isno significant change in ∆w and ∆Ωm with decreasingredshift cutoff.

To obtain the spectra used in the chromatic correc-tions, we use the spectral templates from the SALT2model. This SED model is constructed from spline basisfunctions and thus may alter some of the SN spectral fea-tures. To check if our chromatic corrections are sensitiveto the SALT2 SED representation, we have performeda cross-check based on the spectral time series createdby Hsiao et al. (2007). Mosher et al. (2014) constructeda model from the Hsiao spectral time series using theSALT2 stretch and color law relations while preservingthe spectral features. Using this model results in correc-tions consistent with those based on the SALT2 modelspectra: the ∆µ (Eq.5) agree to within 0.25 mmag for−0.3 < c < +0.3.

4. CONCLUSION

In this paper, we presented the first application of thechromatic corrections described in B18 to type Ia su-pernova cosmology. We applied the corrections to theDES-SN3YR supernova sample as defined in the DES

Collaboration 2018 analysis. The effect of the chromaticcorrections on distance modulus is not significant in ei-ther data or simulation. The 1σ limit on the mediansize of the chromatic correction on the single epoch pho-tometry is a less than 2 mmag change in correction overthe redshift range from z = 0 to z = 1. This limit isvalid for the DES-SN3YR sample and is not necessar-ily valid for other samples, although this has not beentested. The application of chromatic corrections, whilenecessary to achieve the precision photometry in B18,results in a change in w of −0.002± 0.008 and a changein Ωm of 0.000 ± 0.002, for the combined SN Ia, BAO,and CMB analysis, which is not statistically significant.Examining the effect of the corrections on single CCDsboth in ∆µ trends vs. redshift and cosmological param-eters shows that this effect would become significant ona targeted survey where the observations are placed ona single CCD or subset of CCDs. This is assuming thatsuch a survey would use the FGCM calibration of DESand would not recalibrate itself to a reference spectrumbased only on the CCDs it used.

James Lasker is grateful for support from the ARCS(Acheivement Rewards for College Scholars) foundationand its donors. James Lasker, Rick Kessler, Dan Scol-nic, and Josh Frieman are grateful for the support of theUniversity of Chicago Research Computing Center forassistance with the calculations carried out in this workand to the Kavli Institute for Cosmological Physics.

Dan Scolnic is supported by NASA through HubbleFellowship grant HST-HF2-51383.001 awarded by theSpace Telescope Science Institute, which is operated bythe Association of Universities for Research in Astron-omy, Inc., for NASA, under contract NAS 5-26555.

Funding for the DES Projects has been provided bythe U.S. Department of Energy, the U.S. National Sci-

11

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d mB/dz = (0.1 ± 1.3) mmag

Fig. 6.— The redshift dependence of ∆µ, ∆αx1, ∆βc, and ∆mB (Eqs. 5, 6, 7, and 8 respectively) for the DES-SN3YR SN Ia sample.Each dot is an individual SN from the DES-SN3YR sample. The black line connects the median ∆ for the SNe in each redshift bin, itserror bars represent the standard deviation of the chromatic correction in each bin, the red solid line is zero, and the green dotted line isthe best fit line whose slope and uncertainty are given above each panel.

ence Foundation, the Ministry of Science and Educationof Spain, the Science and Technology Facilities Coun-cil of the United Kingdom, the Higher Education Fund-ing Council for England, the National Center for Super-computing Applications at the University of Illinois atUrbana-Champaign, the Kavli Institute of CosmologicalPhysics at the University of Chicago, the Center for Cos-mology and Astro-Particle Physics at the Ohio State Uni-versity, the Mitchell Institute for Fundamental Physicsand Astronomy at Texas A&M University, Financiadorade Estudos e Projetos, Fundação Carlos Chagas Filho

de Amparo à Pesquisa do Estado do Rio de Janeiro,Conselho Nacional de Desenvolvimento Cient́ıfico e Tec-nológico and the Ministério da Ciência, Tecnologia e In-ovação, the Deutsche Forschungsgemeinschaft and theCollaborating Institutions in the Dark Energy Survey.

The Collaborating Institutions are Argonne NationalLaboratory, the University of California at Santa Cruz,the University of Cambridge, Centro de InvestigacionesEnergéticas, Medioambientales y Tecnológicas-Madrid,the University of Chicago, University College London,the DES-Brazil Consortium, the University of Edin-

12

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)

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d( x1)/dz = (-0.7 ± 0.7) mmag

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)

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d mB/dz = (0.8 ± 0.2) mmag

Fig. 7.— Same as Fig. 6, but for the simulated DES-SN3YR-like sample.

burgh, the Eidgenössische Technische Hochschule (ETH)Zürich, Fermi National Accelerator Laboratory, the Uni-versity of Illinois at Urbana-Champaign, the Institut deCiències de l’Espai (IEEC/CSIC), the Institut de F́ısicad’Altes Energies, Lawrence Berkeley National Labora-tory, the Ludwig-Maximilians Universität München andthe associated Excellence Cluster Universe, the Univer-sity of Michigan, the National Optical Astronomy Ob-servatory, the University of Nottingham, The Ohio StateUniversity, the University of Pennsylvania, the Univer-sity of Portsmouth, SLAC National Accelerator Labora-tory, Stanford University, the University of Sussex, TexasA&M University, and the OzDES Membership Consor-

tium.Based in part on observations at Cerro Tololo Inter-

American Observatory, National Optical Astronomy Ob-servatory, which is operated by the Association of Uni-versities for Research in Astronomy (AURA) under a co-operative agreement with the National Science Founda-tion.

The DES data management system is supported bythe National Science Foundation under Grant Num-bers AST-1138766 and AST-1536171. The DES partic-ipants from Spanish institutions are partially supportedby MINECO under grants AYA2015-71825, ESP2015-66861, FPA2015-68048, SEV-2016-0588, SEV-2016-0597,

13

30 20 10 0 10 20ddz

CCD1

CCD35

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30 20 10 0 10 20d x1dz

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Fig. 8.— The slope of the ∆µ, ∆αx1 (upper right), ∆βc (lower left), and ∆mB (lower right) (Equations 5, 6, 7, and 8) vs. redshift forthe data sample, simulated sample, and subsets of the simulated sample for 4 individual CCDs.and MDM-2015-0509, some of which include ERDFfunds from the European Union. IFAE is partiallyfunded by the CERCA program of the Generalitat deCatalunya. Research leading to these results has re-ceived funding from the European Research Councilunder the European Union’s Seventh Framework Pro-gram (FP7/2007-2013) including ERC grant agreements240672, 291329, and 306478. We acknowledge supportfrom the Australian Research Council Centre of Ex-cellence for All-sky Astrophysics (CAASTRO), throughproject number CE110001020, and the Brazilian Insti-

tuto Nacional de Ciência e Tecnologia (INCT) e-Universe(CNPq grant 465376/2014-2).

This manuscript has been authored by Fermi ResearchAlliance, LLC under Contract No. DE-AC02-07CH11359with the U.S. Department of Energy, Office of Science,Office of High Energy Physics. The United States Gov-ernment retains and the publisher, by accepting the arti-cle for publication, acknowledges that the United StatesGovernment retains a non-exclusive, paid-up, irrevoca-ble, world-wide license to publish or reproduce the pub-lished form of this manuscript, or allow others to do so,for United States Government purposes.

REFERENCES

D. M. Scolnic, D. O. Jones, and A. Rest, ArXiv e-prints (2017),arXiv:1710.00845.

A. Rest, D. Scolnic, R. J. Foley, et al., ApJ 795, 44 (2014),arXiv:1310.3828.

http://arxiv.org/abs/1710.00845http://dx.doi.org/10.1088/0004-637X/795/1/44http://arxiv.org/abs/1310.3828

14

0.0 0.2 0.4 0.6 0.8redshift

20

10

0

10

20 (m

mag

)d /dz = (4.3 ± 7.9) mmag

Fig. 9.— Same as Fig. 7 upper left panel, but for atmospheric corrections only, and only for the four chosen CCDs (1,35,52,62).

0.0 0.2 0.4 0.6 0.8redshift

20

10

0

10

20

(mm

ag)

d /dz = (-0.1 ± 7.9) mmag

Fig. 10.— Same as Fig. 9, but for instrumental corrections only.

15

0.0050 0.0025 0.0000 0.0025 0.0050 0.0075 0.0100 0.0125m

data

sim

CCD 35

CCD 52

CCD 62

CCD 1

0.0050 0.0025 0.0000 0.0025 0.0050 0.0075 0.0100 0.0125w

data

sim

CCD 35

CCD 520.051CCD 62

CCD 1

Fig. 11.— ∆Ωm and ∆w (Equations 9 and 10) for the labeled samples. ∆w for CCD62 is out of view so its value is printed next to anarrow.

16

0.0 0.2 0.4 0.6 0.8redshift

20

10

0

10

20

(mm

ag)

DES Simulation: CCD 35

d /dz = (16.9 ± 8.5) mmag

0.0 0.2 0.4 0.6 0.8redshift

20

10

0

10

20

(mm

ag)

DES Simulation: CCD 52

d /dz = (-4.6 ± 5.5) mmag

0.0 0.2 0.4 0.6 0.8redshift

20

10

0

10

20

(mm

ag)

DES Simulation: CCD 62

d /dz = (6.8 ± 6.4) mmag

0.0 0.2 0.4 0.6 0.8redshift

20

10

0

10

20

(mm

ag)

DES Simulation: CCD 1

d /dz = (-3.7 ± 9.0) mmag

Fig. 12.— For simulated DES-like supernova, ∆µ (Equation 5) vs. redshift for the labeled CCDs.

M. Sako, B. Bassett, A. C. Becker, et al., ArXiv e-prints (2014),arXiv:1401.3317 [astro-ph.CO].

A. Conley, J. Guy, M. Sullivan, et al., ApJS 192, 1 (2011),arXiv:1104.1443 [astro-ph.CO].

A. G. Riess, L.-G. Strolger, J. Tonry, et al., ApJ 607, 665 (2004),astro-ph/0402512.

A. G. Riess, L.-G. Strolger, S. Casertano, et al., ApJ 659, 98(2007), astro-ph/0611572.

S. A. Rodney, A. G. Riess, L.-G. Strolger, et al., AJ 148, 13(2014), arXiv:1401.7978.

M. Hicken, P. Challis, S. Jha, et al., ApJ 700, 331 (2009),arXiv:0901.4787 [astro-ph.CO].

M. Hicken, P. Challis, R. P. Kirshner, et al., ApJS 200, 12(2012), arXiv:1205.4493.

M. D. Stritzinger, M. M. Phillips, L. N. Boldt, et al., AJ 142, 156(2011), arXiv:1108.3108.

N. Suzuki, D. Rubin, C. Lidman, et al., ApJ 746, 85 (2012),arXiv:1105.3470 [astro-ph.CO].

R. Kessler, J. Marriner, M. Childress, et al., AJ 150, 172 (2015),arXiv:1507.05137 [astro-ph.IM].

Ž.. Ivezić and the LSST Science Collaboration, “Lsst sciencerequirements document,” (2013).

D. G. York, J. Adelman, J. E. Anderson, Jr., et al., AJ 120, 1579(2000), astro-ph/0006396.

M. Fukugita, T. Ichikawa, J. E. Gunn, et al., AJ 111, 1748(1996).

B. Flaugher, H. T. Diehl, K. Honscheid, et al., AJ 150, 150(2015), arXiv:1504.02900 [astro-ph.IM].

J. L. Tonry, C. W. Stubbs, K. R. Lykke, et al., ApJ 750, 99(2012), arXiv:1203.0297 [astro-ph.IM].

N. Regnault, A. Conley, J. Guy, et al., A&A 506, 999 (2009),arXiv:0908.3808 [astro-ph.IM].

http://arxiv.org/abs/1401.3317http://dx.doi.org/10.1088/0067-0049/192/1/1http://arxiv.org/abs/1104.1443http://dx.doi.org/10.1086/383612http://arxiv.org/abs/astro-ph/0402512http://dx.doi.org/10.1086/510378http://dx.doi.org/10.1086/510378http://arxiv.org/abs/astro-ph/0611572http://dx.doi.org/10.1088/0004-6256/148/1/13http://dx.doi.org/10.1088/0004-6256/148/1/13http://arxiv.org/abs/1401.7978http://dx.doi.org/10.1088/0004-637X/700/1/331http://arxiv.org/abs/0901.4787http://dx.doi.org/10.1088/0067-0049/200/2/12http://dx.doi.org/10.1088/0067-0049/200/2/12http://arxiv.org/abs/1205.4493http://dx.doi.org/10.1088/0004-6256/142/5/156http://dx.doi.org/10.1088/0004-6256/142/5/156http://arxiv.org/abs/1108.3108http://dx.doi.org/10.1088/0004-637X/746/1/85http://arxiv.org/abs/1105.3470http://dx.doi.org/ 10.1088/0004-6256/150/6/172http://arxiv.org/abs/1507.05137http://ls.st/LPM-17http://ls.st/LPM-17http://dx.doi.org/10.1086/301513http://dx.doi.org/10.1086/301513http://arxiv.org/abs/astro-ph/0006396http://dx.doi.org/10.1086/117915http://dx.doi.org/10.1086/117915http://dx.doi.org/ 10.1088/0004-6256/150/5/150http://dx.doi.org/ 10.1088/0004-6256/150/5/150http://arxiv.org/abs/1504.02900http://dx.doi.org/10.1088/0004-637X/750/2/99http://dx.doi.org/10.1088/0004-637X/750/2/99http://arxiv.org/abs/1203.0297http://dx.doi.org/10.1051/0004-6361/200912446http://arxiv.org/abs/0908.3808

17

N. Padmanabhan, D. J. Schlegel, D. P. Finkbeiner, et al., ApJ674, 1217-1233 (2008), astro-ph/0703454.

J. B. Oke and J. E. Gunn, ApJ 266, 713 (1983).E. A. Magnier, E. Schlafly, D. Finkbeiner, et al., ApJS 205, 20

(2013), arXiv:1303.3634 [astro-ph.IM].E. F. Schlafly, D. P. Finkbeiner, M. Jurić, et al., ApJ 756, 158

(2012), arXiv:1201.2208 [astro-ph.IM].D. P. Finkbeiner, E. F. Schlafly, D. J. Schlegel, et al., ApJ 822,

66 (2016), arXiv:1512.01214 [astro-ph.IM].A. Berk, L. S. Bernstein, and D. C. Robertson, Space Science

Instrumentation, Tech. Rep. (1987).R. C. Bohlin, K. D. Gordon, and P.-E. Tremblay, PASP 126, 711

(2014), arXiv:1406.1707 [astro-ph.IM].D. Scolnic, S. Casertano, A. Riess, et al., ApJ 815, 117 (2015),

arXiv:1508.05361 [astro-ph.IM].The Dark Energy Survey Collaboration, ArXiv Astrophysics

e-prints (2005), astro-ph/0510346.D. L. Burke, E. S. Rykoff, S. Allam, et al., AJ 155, 41 (2018),

arXiv:1706.01542 [astro-ph.IM].J. L. Marshall, J.-P. Rheault, D. L. DePoy, et al., ArXiv e-prints

(2013), arXiv:1302.5720 [astro-ph.IM].A. Drlica-Wagner, I. Sevilla-Noarbe, E. S. Rykoff, et al., ApJS

235, 33 (2018), arXiv:1708.01531.C. H. Blake and M. M. Shaw, PASP 123, 1302 (2011),

arXiv:1109.6703 [astro-ph.IM].T. S. Li, D. L. DePoy, J. L. Marshall, et al., AJ 151, 157 (2016),

arXiv:1601.00117 [astro-ph.IM].J. Guy, P. Astier, S. Baumont, et al., A&A 466, 11 (2007),

astro-ph/0701828.Dark energy survey operations: years 4 and 5 , Vol. 10704 (2018).J. P. Bernstein, R. Kessler, S. Kuhlmann, et al., ApJ 753, 152

(2012), arXiv:1111.1969.D. Brout, M. Sako, D. Scolnic, et al., (2018), arXiv:1811.02378

[astro-ph].

J. A. Holtzman, J. Marriner, R. Kessler, et al., AJ 136, 2306(2008), arXiv:0908.4277.

P. Astier, P. El Hage, J. Guy, et al., A&A 557, A55 (2013),arXiv:1306.5153 [astro-ph.IM].

DES Collaboration, ArXiv e-prints (2018), arXiv:1811.02374.R. Kessler, J. P. Bernstein, and D. Cinabro, PASP 121, 1028

(2009), arXiv:0908.4280.R. Kessler, J. Asorey, D. Brout, et al., (2018), arXiv:1811.02379

[astro-ph].D. Scolnic and R. Kessler, ApJ 822, L35 (2016),

arXiv:1603.01559.K. Perrett, M. Sullivan, A. Conley, et al., AJ 144, 59 (2012),

arXiv:1206.0665.C. D’Andrea, M. Smith, M. Sullivan, et al., in Prep.R. R. Gupta, S. Kuhlmann, E. Kovacs, et al., AJ 152, 154

(2016), arXiv:1604.06138.J. Guy, M. Sullivan, A. Conley, et al., A&A 523, A7 (2010),

arXiv:1010.4743.R. Kessler, J. Guy, J. Marriner, et al., ApJ 764, 48 (2013),

arXiv:1209.2482.M. Betoule, R. Kessler, J. Guy, et al., A&A 568, A22 (2014),

arXiv:1401.4064.R. Hounsell, D. Scolnic, R. J. Foley, et al., ArXiv e-prints (2017),

arXiv:1702.01747 [astro-ph.IM].R. Tripp, A&A 331, 815 (1998).R. Kessler and D. Scolnic, ApJ 836, 56 (2017), arXiv:1610.04677.F. James and M. Roos, Computer Physics Communications 10,

343 (1975).D. J. Eisenstein, I. Zehavi, D. W. Hogg, et al., ApJ 633, 560

(2005), astro-ph/0501171.E. Komatsu, J. Dunkley, M. R. Nolta, et al., ApJS 180, 330

(2009), arXiv:0803.0547.E. Y. Hsiao, A. Conley, D. A. Howell, et al., ApJ 663, 1187

(2007), astro-ph/0703529.J. Mosher, J. Guy, R. Kessler, et al., ApJ 793, 16 (2014),

arXiv:1401.4065

http://dx.doi.org/10.1086/524677http://dx.doi.org/10.1086/524677http://arxiv.org/abs/astro-ph/0703454http://dx.doi.org/10.1086/160817http://dx.doi.org/ 10.1088/0067-0049/205/2/20http://dx.doi.org/ 10.1088/0067-0049/205/2/20http://arxiv.org/abs/1303.3634http://dx.doi.org/ 10.1088/0004-637X/756/2/158http://dx.doi.org/ 10.1088/0004-637X/756/2/158http://arxiv.org/abs/1201.2208http://dx.doi.org/10.3847/0004-637X/822/2/66http://dx.doi.org/10.3847/0004-637X/822/2/66http://arxiv.org/abs/1512.01214http://dx.doi.org/10.1086/677655http://dx.doi.org/10.1086/677655http://arxiv.org/abs/1406.1707http://dx.doi.org/10.1088/0004-637X/815/2/117http://arxiv.org/abs/1508.05361http://arxiv.org/abs/astro-ph/0510346http://dx.doi.org/10.3847/1538-3881/aa9f22http://arxiv.org/abs/1706.01542http://arxiv.org/abs/1302.5720http://dx.doi.org/10.3847/1538-4365/aab4f5http://dx.doi.org/10.3847/1538-4365/aab4f5http://arxiv.org/abs/1708.01531http://dx.doi.org/10.1086/662980http://arxiv.org/abs/1109.6703http://dx.doi.org/10.3847/0004-6256/151/6/157http://arxiv.org/abs/1601.00117http://dx.doi.org/10.1051/0004-6361:20066930http://arxiv.org/abs/astro-ph/0701828http://dx.doi.org/10.1117/12.2312113http://dx.doi.org/ 10.1088/0004-637X/753/2/152http://dx.doi.org/ 10.1088/0004-637X/753/2/152http://arxiv.org/abs/1111.1969http://arxiv.org/abs/1811.02378http://arxiv.org/abs/1811.02378http://dx.doi.org/ 10.1088/0004-6256/136/6/2306http://dx.doi.org/ 10.1088/0004-6256/136/6/2306http://arxiv.org/abs/0908.4277http://dx.doi.org/10.1051/0004-6361/201321668http://arxiv.org/abs/1306.5153http://arxiv.org/abs/1811.02374http://dx.doi.org/10.1086/605984http://dx.doi.org/10.1086/605984http://arxiv.org/abs/0908.4280http://arxiv.org/abs/1811.02379http://arxiv.org/abs/1811.02379http://dx.doi.org/10.3847/2041-8205/822/2/L35http://arxiv.org/abs/1603.01559http://dx.doi.org/10.1088/0004-6256/144/2/59http://arxiv.org/abs/1206.0665http://dx.doi.org/ 10.3847/0004-6256/152/6/154http://dx.doi.org/ 10.3847/0004-6256/152/6/154http://arxiv.org/abs/1604.06138http://dx.doi.org/10.1051/0004-6361/201014468http://arxiv.org/abs/1010.4743http://dx.doi.org/10.1088/0004-637X/764/1/48http://arxiv.org/abs/1209.2482http://dx.doi.org/10.1051/0004-6361/201423413http://arxiv.org/abs/1401.4064http://arxiv.org/abs/1702.01747http://dx.doi.org/10.3847/1538-4357/836/1/56http://arxiv.org/abs/1610.04677http://dx.doi.org/10.1016/0010-4655(75)90039-9http://dx.doi.org/10.1016/0010-4655(75)90039-9http://dx.doi.org/10.1086/466512http://dx.doi.org/10.1086/466512http://arxiv.org/abs/astro-ph/0501171http://dx.doi.org/10.1088/0067-0049/180/2/330http://dx.doi.org/10.1088/0067-0049/180/2/330http://arxiv.org/abs/0803.0547http://dx.doi.org/10.1086/518232http://dx.doi.org/10.1086/518232http://arxiv.org/abs/astro-ph/0703529http://dx.doi.org/10.1088/0004-637X/793/1/16http://arxiv.org/abs/1401.4065

ABSTRACT1 introduction2 Methods + Data Sample2.1 Application of Chromatic Corrections2.2 Data Sample2.3 Light-Curve and Cosmology fitting

3 RESULTS3.1 Impact on single-epoch photometry3.2 Result for BBC fitted SALT2 nuisance parameters3.3 Effect of chromatic corrections on light-curve fit parameters distances, and cosmology3.4 Results on individual CCDs3.5 Cross Checks

4 CONCLUSION