University of Groningen

Understanding disk galaxies with the Tully-Fisher relationPonomareva, Anastasia

IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.

Document VersionPublisher's PDF, also known as Version of record

Publication date:2017

Link to publication in University of Groningen/UMCG research database

Citation for published version (APA):Ponomareva, A. (2017). Understanding disk galaxies with the Tully-Fisher relation. RijksuniversiteitGroningen.

CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).

Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.

Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.

Download date: 08-01-2021

Chapter 3The Multi–WavelengthTully–Fisher relation withspatially resolved Hikinematics

— Anastasia Ponomareva, Marc Verheijen, Reynier Peletier,Albert Bosma —

92 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Abstract

In this chapter we investigate the statistical properties of the Tully-Fisher relation for a sample of 32 galaxies with measured distances fromthe Cepheid period–luminosity relation and/or TRGB stars. We takeadvantage of panchromatic photometry in 12 bands (from FUV to 4.5 µm)and of detailed Hi kinematics. We use these data together with threekinematic measures (W i, Vmax and Vflat) extracted from the global Hiprofiles or rotation curves, so as to construct 36 correlations allowing us toselect the one with the least scatter. We introduce a tightness parameterσ⊥ of the TFr, in order to get a slope–independent measure of the goodnessof fit. We find that the tightest correlation occurs when we select the 3.6µm photometric band together with the Vflat parameter extracted from theHi rotation curve. The residuals do not show any correlation with globalgalaxy properties.

3.1. Introduction 93

3.1 Introduction

The Tully-Fisher relation (TFr) is a power–law correlation between theluminosity and the rotation velocity of late-type galaxies (Tully & Fisher1977). It was empirically established as a powerful tool to measure distancesto galaxies independently from their redshift. Knowing only a galaxy’srotational velocity from the width of its neutral hydrogen (Hi) line profile,one can recover the distance modulus to this galaxy by inferring the totalintrinsic luminosity from a calibrator sample. Thus, to obtain accuratedistances, a number of studies of the statistical properties of the TFr weredone in the past, aiming to reduce as much as possible the observed scatterin the relation, e.g. the Cosmic Flows program (Courtois et al. 2011;Courtois & Tully 2012; Tully & Courtois 2012).

Understanding the origin of the TFr is one of the main challenges fortheories of galaxy formation and evolution. From a theoretical point ofview, a perfect correlation between the intrinsic luminosity and rotationalvelocity of a galaxy is currently explained as a relation between the hostingdark matter halo and its baryonic content, assuming a direct link betweenluminosity and baryonic mass. The detailed statistical properties of theTFr provide important constraints to semi-analytical models and numericalsimulations (Navarro & Steinmetz 2000; Vogelsberger et al. 2014; Schayeet al. 2015; Maccio et al. 2016). It is thus an important test for the theory ofgalaxy formation and evolution to reproduce the slope, scatter and the zeropoint of the TFr in different photometric bands simultaneously. The TFrcan also constrain theories about the distribution of mass within galaxies,e.g. it was shown by Courteau et al. (2003) that barred and unbarredgalaxies follow the same TFr, even though barred galaxies could be lessdark matter dominated within their optical radius (Weiner et al. 2001).

Over the past decades, the scatter in the observed TFr was decreasedsignificantly by more accurate photometric measures. As first suggested byAaronson et al. (1979), the TFr can be tightened by moving from opticalto NIR bands, where the old stars peak in luminosity and provide a goodproxy for the stellar mass of the galaxies (Peletier & Willner 1991). Theadvent of infra-red arrays shifted photometry to the JHK bands and thento space-based infrared photometry, e.g. with the Spitzer Space Telescope(Werner et al. 2004). However, despite the obvious advantages of deepnear-infrared luminosities, it is still not clear at which NIR wavelengthsthe smallest scatter in the TFr can be achieved. For example, Bernstein

94 Chapter 3. The Multi–Wavelength Tully–Fisher relation

et al. (1994), using 23 spirals in the Coma cluster found that the H-bandTFr does not have less scatter than the I-band relation. Sorce et al. (2013)claim that the 3.6 µm TFr has even larger scatter than the I-band TFr(Tully & Courtois 2012, hereafter TC12). Consequently, accurate infraredphotometry led to the point where the measurement errors on the totalluminosity no longer explain the observed scatter.

Yet, sofar, very little attention has been given to improve the mea-surements of the rotation velocity which is, as mentioned before, thoughtto be strongly related dynamically to the dark matter halo. Notably, thewidth and shape of the global Hi profile are determined by the detaileddistribution of the Hi gas in the disk, the shape of a galaxy’s rotation curve,and the presence of non-circular motions and/or a warp. It is impossible totake into account all these important aspects while inferring the rotationalvelocity of a galaxy from the integrated global Hi profile. This notion hasmotivated observational studies which took advantage of optical rotationcurves, using Hα long slit spectroscopy (Rubin et al. 1980, 1985; Pizagnoet al. 2007). However, the rotational velocity at the optical radius doesnot probe the dark matter halo potential properly, since the data do notextend far enough in radius. Of course, for an axisymmetric galaxy witha monotonically rising rotation curve that reaches a constant flat part inthe non-warped outer gas disk, the rotational velocity is reasonably well-defined and can be estimated from the corrected width of the global Hiprofile. Unfortunately, galaxies often are not that well–behaved and thecolumn–density distribution and kinematic structure of their gas disks maysignificantly affect the shape and width of the global Hi profiles, introducingerrors on the derived rotational velocity that can not be corrected for.

Detailed studies of galactic rotation curves using 21-cm synthesisimaging (Bosma 1981; van Albada et al. 1985; Begeman 1989; Broeils& van Woerden 1994; Verheijen 2001; Swaters et al. 2002; Noordermeer2006; de Blok et al. 2014), show that the shape of the rotation curvestrongly depends on the morphology and surface brightness of the galaxy,introducing deviations from the classical flat rotation curve. For instance,it is well known that dwarf and low surface brightness galaxies have slowlyrising rotation curves. In this case the observed maximal rotational velocity(Vmax) will underestimate the velocity of the halo, simply because therotation curve is not reaching the flat part (Vflat). The other extremecase are massive early–type spirals, which usually show a fast rise of therotation curve until the maximum velocity (Vmax) is reached, usually within

3.2. The Sample 95

the optical disk, beyond which the rotation curve significantly declines,reaching the flat part with much lower velocity (Bosma 1981; Casertano& van Gorkom 1991; Verheijen 2001; Noordermeer 2006). In this case,the velocity of the halo, if taken to be Vmax, will be overestimated for themost massive galaxies, which can cause a curvature in the TFr (Neill et al.2014). It was shown by Verheijen (2001) with a study of spiral galaxies inthe Ursa Major cluster, that the statistical properties of the TFr depend onthe shape of the rotation curves, and that the observed scatter is reducedsignificantly when extended Hi rotation curves are available to substitutethe corrected width of the global Hi profile with Vflat from the rotationcurve as a kinematic measure.

It is very important to realise that the literature contains manyobservational results on the TFr which are often inconsistent with eachother. This is largely due to different corrections applied to the observables,e.g. for extinction or inclination, due to different photometric systems, dueto different observing techniques or due to different samples. This makesit very complicated to compare the various studies in a simple manner.In this chapter we establish TFrs based on a homogeneous analysis of dataobtained in 12 photometric bands from UV to IR, while taking advantage ofspatially resolved Hi kinematics as reported in Chapter 2 (Ponomareva et al.2016). We study the statistical properties of the TFr to investigate the linkbetween the host DM halo and various stellar populations of galaxies, whichpeak in different bands. Such a homogeneous study allows us to obtain abetter understanding of the physical phenomenon of the TFr especially asa tool to study the internal structure of galaxies.

3.2 The Sample

In our study we are interested in the slope and intrinsic tightness of the TFr.We are not aiming to maximise the number of galaxies in the sample, butrather to increase the quality of the kinematic measures for a representativesample of galaxies with independent distance measurements. Thus,we analysed aperture synthesis imaging Hi data to derive high–qualityrotation curves (Ponomareva et al. 2016). The independent distances toour galaxies were measured from the Cepheid period–luminosity relation(Freedman et al. 2001) or/and from the tip of the red giant branch(Rizzi et al. 2007) and are provided by The Extragalactic DistanceDatabase (EDD). Independently measured distances reduce the error on

96 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0 50 100 150 200 250 300 350

Radius (arcsec)

15

20

25

30

µ(mag/arcsec2

)4.5 µm3.6 µmKsHJzirguNUVFUV

Figure 3.1 – Surface brightness profiles of NGC3351 for 12 photometric bands. Theregion within which the exponential disk fit was done is indicated with arrows. Blacklines show the exponential disk fit to the profile. Profiles are terminated at their Rlim(see Section 3.3.2).

the absolute magnitude of a galaxy and therefore reduce the impact ofdistance uncertainties on the observed scatter of the TFr. For example,in our case, distance uncertainties contribute only σdist = 0.07 mag to thetotal observed scatter of the TFr, which is much lower in comparison withσdist = 0.41 mag if the Hubble distances are adopted. We adopt a sampleof 32 large, relatively nearby galaxies from the zero point (ZP) calibratorsample described in TC12. Their selection criteria for galaxies includedin the sample completely satisfy our requirements: 1) morphological typesSab and later (Figure 2.1), 2) inclinations no less than 45◦, 3) Hi profileswith adequate S/N, 4) global Hi profiles without evidence of distortionor blending. Their selection criteria give us confidence that the adoptedgalaxies are kinematically well-behaved with regularly rotating, extendedHi disks. In Ponomareva et al. (2016) it was found that this confidence waslargely justified. Global parameters of the sample galaxies are summarisedin Table 2.1.

3.3. Photometric data 97

3.3 Photometric data

To study the wavelength dependence of the statistical properties of the TFrrequires not only a representative sample, but a systematic, homogeneousapproach in deriving the main photometric properties of galaxies. We use12 bands per galaxy (FUV, NUV, u, g, r, i, z, J, H, Ks, 3.6, 4.5 µm) for 21galaxies, and 7 bands for the remaining 11 galaxies in our sample due to theabsence of SDSS imaging data. This broad wavelength coverage allows usto measure the relative luminosity of old and young stars within a galaxy.

The FUV and NUV images were collected from the various GalaxyEvolution Explorer (GALEX, Martin et al. (2005)) space telescope dataarchives. UV light comes from regions where hot and young stars resideand therefore it is often used as a tracer of star formation within galaxies,although it can be severely affected by dust extinction. Since young starshave a very low contribution to the total mass of a galaxy, a very largescatter in the UV–based TFrs might be expected. Nevertheless, we considerthese bands in our study.

To obtain optical photometry, we use the SDSS Data Release 9 (DR9,Ahn et al. (2012)), but note that SDSS photometry is only available for21 galaxies in our sample. Therefore we consider TFrs in the SDSS bandsfor a smaller number of galaxies. However, we point out that the SDSS–subsample still spans a wide luminosity range.

We collected a wide range of NIR images: J , H, Ks bands from theTwo-Micron All Sky Survey (2MASS, Skrutskie et al. (2006)) and 3.6 µmand 4.5 µm from the Spitzer Survey for Stellar Structure in Galaxies (S4G,Sheth et al. (2010)). All data were gathered from the IRSA archive. Itis evident in Figure 3.1 that S4G data are significantly deeper than the2MASS data. As was already mentioned in the introduction, NIR bands arewidely used to study the statistical properties of the TFr because they areconsidered to be the best tracers of old stellar populations which dominatethe baryonic mass of spiral galaxies. However, the contribution by othercomponents such as NIR emission from PAH (Shapiro et al. 2010), warmdust or AGB stars can be significant and varies across the NIR bands,especially at the longer wavelengths. For instance, Querejeta et al. (2015)showed that around 10–30 % of the total light in the 3.6 µm band can beassociated with dust emission (see Section 6.3 for further discussion).

98 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0.8 1.0 1.2 1.4 1.6 1.8

u – g

0.1

0.2

0.3

0.4

0.5

r–

i

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

g – r

−0.2

−0.1

0.0

0.1

0.2

0.3

0.4

0.5

i–z

0.0 0.1 0.2 0.3 0.4 0.5 0.6

K – [3.6]

−0.10

−0.05

0.00

0.05

0.10

[3.6

]–[4

.5]

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

g – r

2.0

2.5

3.0

i–[3

.6]

2 3 4 5 6 7 8 9

NUV – [3.6]

0.0

0.2

0.4

0.6

0.8

1.0

FU

V–

NU

V

0.0 0.1 0.2 0.3 0.4 0.5

H – K

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

J–

K

2.2hTOT

Figure 3.2 – Colour-Colour diagrams, based on our photometry. Grey symbols indicatecolours for the apparent magnitudes within 2.2h and black symbols for total magnitudes.Dashed lines delineate the empirical relations constructed for a large number of galaxies.SDSS colours from Hansson et al. (2012), 2MASS from Jarrett et al. (2000), GALEXfrom Bouquin et al. (2015) and Spitzer from Querejeta et al. (2015).

3.3. Photometric data 99

3.3.1 Photometric analysis

Since galaxies do not have well–defined edges it is impossible to accuratelymeasure their total light. Thus, the integrated flux is usually measuredwithin a chosen isophote or aperture. However it is possible to estimatethe total magnitude of a galaxy by adding the missing light. This missinglight is usually calculated under the assumption of a purely exponentialdisk as the extrapolation of the surface brightness profile (SBP) beyond achosen aperture radius to infinity, and depends only on the number of diskscale lengths within the aperture radius (Giovanelli et al. 1994; Tully et al.1996).

All photometrically calibrated images of our sample galaxies wereanalysed homogeneously. First, masks were designed for each galaxyin every band to remove foreground and background objects. Then, asingle master mask was constructed for each galaxy by combining themasks from all bands. This master mask was applied to all bands ofa galaxy and allowed to censor images for background and foregroundobjects independently of the band they contaminate. We summarisedinformation from two dimensional images into 1D radial surface brightnessprofiles (SBPs) by calculating the azimuthally averaged pixel values withinellipses with fixed position and inclination angles, adopted from the tilted–ring fitting to the Hi velocity fields (Ponomareva et al. 2016). Differencesbetween kinematic and optical values for position and inclination anglesare shown in Figure 5 of Ponomareva et al. (2016). This procedure wasrepeated for all bands and all galaxies in the sample.

Figure 3.1 shows an example of the resulting profiles from our analysisfor NGC 3351. With grey lines the exponential disk fitting is shown inevery band. From Figure 3.1 it is clear that the radial extent of the profilesmay vary from band to band. It mostly depends on the quality and depthof the data.

3.3.2 From aperture to total magnitudes

The aperture magnitudes (map) were calculated by integrating the surfacebrightness profile in each band within a fixed radius (Rlim). Rlim was chosenafter a visual inspection of every profile, as the largest radius at which thesurface brightness (µlim) is still reliable. Given the varying quality of thedata, Rlim may differ for various bands. In Figure 3.1 the SBPs are shownwithin their Rlim. The azimuthally averaged pixel values over a fixed radial

100 Chapter 3. The Multi–Wavelength Tully–Fisher relation

range of the outer flat part of the profiles, well beyond Rlim, were adoptedas the “sky” background value and subtracted. The standard deviationfrom the mean sky value over this radial range (σsky) resulted in errors onthe surface brightness as σ(µ) = 2.5× (σsky/Ln10× cnts).

While the extrapolation to total magnitudes for HSB galaxies is smalland insignificant, for LSB objects it can play a crucial role in recoveringthe total light. The quality of the data also plays an important role.For instance, for the shallow surveys an extrapolation to obtain the totalmagnitudes is always necessary. Thus, linear fits were made to the outerpart of each SBP (except for the 2MASS data, see below), which is notaffected by the contribution from the bulge light and characterizes theexponential drop of surface brightness of a galaxy due to the pure diskcomponent. The radial range within which the fit was made was identifiedthrough visual inspection and is shown in Figure 3.1 with vertical arrows.This procedure is in essence the “mark the disk” procedure describedby de Jong (1996). We assume that beyond Rlim the SBP continues todrop exponentially without any truncations and/or breaks. Under thisassumption Tully et al. (1996) showed that the extended magnitude doesnot depend on the scale length of the disk or on the ellipticity of the galaxy,but only on the number ∆n of disk scale lengths within Rlim. Hence it canbe calculated as :

∆mext = 2.5 log[1− (1 + ∆n)e−∆n], (3.1)

with

∆n = (µlim − µ0)/1.086. (3.2)

Then, the total magnitudes follow from mtot = map + ∆mext.As was mentioned above, the quality of the data has a significant impact

on how deep one can recover the surface brightness profile of a galaxy.Unfortunately, 2MASS survey images are too shallow and the SBPs donot extend enough to apply the method of recovering the total light asdescribed above. Therefore, we measured magnitudes in the J,H,K bandswithin 2.2 disk scale lengths (h) and calculated colours J − [3.6], H − [3.6]and K−[3.6] within this radius. We fixed the colours and calculated 2MASS

total magnitudes as MJHKtot = M

[3.6]tot + (JHK2.2h − [3.6]2.2h).

Various studies have shown that surface brightness profiles of spiralgalaxies might have truncations and breaks (Martın-Navarro et al. 2012;

3.4. Hi data 101

Munoz-Mateos et al. 2016; Kim et al. 2014). Munoz-Mateos et al. (2016)described three morphological types of surface brightness profiles: singleexponential (Type I), down–bending (Type II) and up–bending (TypeIII). While most of the galaxies from our sample have single exponentialprofiles, six galaxies (NGC 3319, NGC 3351, NGC 4244, NGC 4639, NGC4725 and NGC 5584) appear to have Type II surface brightness profilesaccording to classification by Munoz-Mateos et al. (2016). These profilesare characterised by a break beyond which the profile becomes steeper.However in most cases (including ours) the break lies in the outer parts ofthe disk and is mostly characterised by the presence of a bar in a galaxy.Since we performed an exponential disk fit to extrapolate to the totalmagnitude in the outer parts of the profile, our measurement is not affectedby the break. Therefore, the extrapolated magnitude for these galaxies isnot overestimated. However, to asses the quality of our total magnitudemeasurements, we compare colours based on total magnitudes with thecolours based on magnitudes, measured within 2.2 scale lengths (2.2h) thatare not affected by uncertainties in the extrapolation. The scale length isusually defined as the radius at which the brightness of a galaxy at theparticular wavelength has decreased by a factor of e from the centre. Inour study we measure the 1 scale length as Rlim/∆n, and using the value of2.2h as measured from the 3.6 µm surface brightness profiles for all bands,even though the scale length changes with the band.

Colour-colour diagrams based on magnitudes within 2.2h as well as totalmagnitudes are shown in Figure 3.2. Both types of colours show similartrends in the diagrams. This leads us to conclude that the galaxies from oursample do not have a significantly different colour gradient beyond 2.2h,with the exception of the UV colours for which the colours based on the totalmagnitudes are systematically bluer, indicating longer scale lengths for theFUV and NUV profiles. The range in our colours is in good agreementwith various observational studies (Jarrett et al. 2000; Hansson et al. 2012;Querejeta et al. 2015; Bouquin et al. 2015).

3.4 Hi data

We are interested in studying the statistical properties of the TFr at variouswavelengths based on rotational velocities derived from global Hi profilesand high–quality rotation curves. The ideal data for this work are Hi radio

102 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Sab Sbc Scd Sdm Im

Hubble-type

0

2

4

6

8

10

Nu

mb

er

Figure 3.3 – Rotation curves morphology distribution within the sample. The lighthatched region shows galaxies with declining rotation curves. The dark shaded areacorresponds to galaxies with rising rotation curves.

synthesis–imaging data which provide the global Hi profiles, as well as thespatially resolved rotation curves.

We collected the Hi radio synthesis–imaging data for 29 galaxies fromthe literature. Most of these galaxies were observed previously as partof larger Hi surveys (THINGS, WHISP, HALOGAS, etc). We observedthe remaining three galaxies with the Giant Radio Metrewave Telescope(GMRT) in March 2014. All data cubes were analysed homogeneously andthe following data products were delivered for all galaxies in our sample:global Hi profiles, integrated Hi column–density maps, Hi surface–densityprofiles and high–quality rotation curves derived from highly–resolved, two–dimensional velocity fields.

These data products, along with a detailed description of the observa-tions, data reduction and analyses, are presented in Chapter 2 (Ponomarevaet al. 2016). Here, we summarize the relevant kinematic information,obtained from the Hi data.

3.4.1 Rotational velocities

There are several ways to measure the rotational velocities of spiral galaxiesusing Hi data. First, from the width of the Hi 21cm line profile, where thecorrected width of the profile relates to the rotational velocity as W i =2Vrot. Second, from the resolved Hi velocity fields. While the former ismuch faster to obtain observationally and can therefore be used for a largenumber of galaxies, the latter allows to derive the spatially resolved rotationcurve of a galaxy.

3.4. Hi data 103

0 20 40 60 80 100

Radius (kpc)

0

50

100

150

200

250

300

350

Vrot

(km

s−1)

Figure 3.4 – Compilation of rotation curves of our sample galaxies plotted on the samelinear scale. Blue curves belong to galaxies with Rrc (Vmax < Vflat) and red curves aredeclining rotation curves (Vmax > Vflat).

104 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Amongst others, Verheijen (2001) showed that rotation curves of spiralgalaxies have different shapes, which mostly depend on the morphologicaltype and luminosity of a galaxy. The advantage of our sample is that itcovers all types of rotation curves: rising (Rrc) for dwarf galaxies (Vmax <Vflat), classical flat (Frc) for the intermediate types (Vmax = Vflat), anddeclining (Drc) for the early–type spirals (Vmax > Vflat). The “family”of rotation curves of our sample is shown in Figure 3.4. Moreover, Figure3.3 demonstrates that declining rotation curves tend to belong mainly tomassive early type spirals, while rising rotation curves are common for latetype galaxies (Casertano & van Gorkom 1991; Verheijen 2001; Noordermeeret al. 2007; Oh et al. 2008; Swaters et al. 2009; de Blok et al. 2014).

To quantitatively describe the shape of a rotation curve, we measure theslope of the outer part of a rotation curve between the radius at 2.2 diskscale lengths, measured from the 3.6.µm SBP, and the outermost point:

S2.2h,lmp =Log(V2.2h/Vlmp)

Log(R2.2h/Rlmp)(3.3)

where V2.2h and Vlmp are the rotational velocities at the radius equal to 2.2h(R2.2h) and at the radius of the last measured point Rlmp. Thus, a slopeequal to zero belongs to a flat rotation curve, a positive slope to a risingrotation curve and a negative slope to a declining rotation curve. Figure 3.5demonstrates S2.2h,lmp as a function of global galactic properties. There areprominent correlations with Hubble type (as was suggested earlier) and withthe absolute magnitude. In grey we show a compilation of various samplesfrom previous studies (Casertano & van Gorkom 1991; Verheijen & Sancisi2001; Spekkens & Giovanelli 2006; Noordermeer et al. 2007; Swaters et al.2009), to point out that our sample is not in any way peculiar and followsthe same trends found in previous studies.

The shape of the global Hi profile can indicate the shape of the rotationcurve in two cases. First, a boxy or Gaussian shape profile is an indicationfor a rising rotation curve for which the velocity of the dark matter halois underestimated from the profile width. Figure 2.6 demonstrates thedifference in the velocity obtained using W50 (corrected for inclination),compared to Vmax (upper panel) and Vflat (bottom panel) from the rotationcurves. It is clear that the main outliers are the galaxies with either risingor declining rotation curve. Thus, the rotational velocity measured fromW50 will be underestimated in comparison with Vmax, and overestimatedin comparison with Vflat. Therefore, one should take into account that the

3.4. Hi data 105

Sab Sbc Scd Sdm Im

Hubble type

−0.4

−0.2

0.0

0.2

0.4

0.6

log

Slop

e

−26−24−22−20−18−16−14

M

−0.4

−0.2

0.0

0.2

0.4

0.6

log

Slop

e

MR-2.95M[3.6]

0 2 4 6 8 10 12

scale length (kpc)

−0.4

−0.2

0.0

0.2

0.4

0.6

14 16 18 20 22 24

µ0(mag/arcsec−2)

−0.4

−0.2

0.0

0.2

0.4

0.6µ0(R)-3.16µ0[3.6]

Figure 3.5 – Slopes of outer rotation curves and their correlation with galaxy parameters.Our sample is shown with black dots. Absolute magnitude and disk central surfacebrightness are measured in the 3.6 µm band. A compilation of various observationalsamples (Casertano & van Gorkom 1991; Verheijen & Sancisi 2001; Spekkens & Giovanelli2006; Noordermeer et al. 2007; Swaters et al. 2009) is shown with grey symbols. Forthe reference samples, the absolute magnitude and disk central surface brightness aremeasured in theR band and then matched to our sample using the colour term (R−[3.6] =2.95 and µ0(R) − µ0[3.6] = 3.16).

106 Chapter 3. The Multi–Wavelength Tully–Fisher relation

rotational velocity derived from the width of the global profile may differfrom the velocity measured from the spatially resolved rotation curve.

3.5 Corrections to observables

3.5.1 Photometry

As a photometric measure for the TFr we use the corrected absolute totalmagnitudes M b,i

T (λ) :

M b,iT (λ) = mT (λ)−Abλ −Aiλ −DM, (3.4)

where mT (λ) is the apparent total magnitude, Abλ is the Galactic extinctioncorrection, Aiλ is the internal extinction correction and DM is the distancemodulus, based on the distance given in Table 2.1. Further details aredescribed in the subsections below.

Galactic extinction correction

The Galactic extinction correction depends only on the galactic coordinatesof the object and on the bandpass in which the galaxy is observed. Thusthe extinction at a given wavelength λ is usually described as

Abλ = R(λ)× E(B − V ), (3.5)

where R(λ) is the extinction at wavelength λ relative to E(B -V). Thevalues of E(B -V) were obtained using the “Galactic dust reddening andextinction” tool provided by the NASA/IPAC infrared science archive. Thisservice provides 100µm cirrus maps with new estimates for the galacticdust extinction from Schlafly & Finkbeiner (2011). The R(λ) extinctioncoefficients for multiple passbands were calibrated using the Fitzpatrickextinction law with extinction coefficient R(V ) = 3.1 and reddening E(B−V ) = 0.4 for a 7,000 K source spectrum (Fitzpatrick 1999).

Internal extinction correction

The correction for internal extinction in spiral galaxies is somewhatuncertain because it depends on various galactic parameters. Giovanelliet al. (1995) showed that the internal obscuration of a galaxy stronglydepends on its total luminosity. Furthermore, its inclination plays a

3.5. Corrections to observables 107

significant role as a galaxy seen more inclined will be much more obscured.The internal extinction correction can be expressed as:

Aiλ = γλ log(a/b), (3.6)

where γλ is an extinction amplitude parameter (Tully et al. 1998) and a/b isthe projected ellipticity of a galaxy. Note that this prescription correspondsto no internal extinction for face–on galaxies.

Tully et al. (1998) calibrated the γλ parameter as a function of the widthW i

50 of the Hi 21–cm line profile, corrected for inclination. Thus, from Tullyet al. (1998) and Sorce et al. (2012) we adopt the calibrated values of γλ asa function of W i

50 for some of the passbands of our interest:

γr = 1.15 + 1.88(logW i50 − 2.5). (3.7)

γi = 0.92 + 1.63(logW i50 − 2.5). (3.8)

γKs = 0.22 + 0.40(logW i50 − 2.5), (3.9)

γ[3.6] = 0.10 + 0.19(logW i50 − 2.5). (3.10)

Note, that γλ can be zero, but cannot be negative. For instance, Sorceet al. (2012) assume γ[3.6] = 0 in case of W i

50 < 94 kms−1. For the J and Hbands we adopt γJ = 0.3 + γKs and γH = 0.1 + γKs respectively (Masterset al. 2003). For the g -band we use an average internal extinction ofspiral galaxies from face-on to edge-on of Aig = 0.6 mag, assuming internalextinction in the z -band of Aiz = 0.3 mag (Masters et al. 2010). We donot apply an extinction correction to the UV bands (FUV to u) due to thelarge uncertainties and high extinction in these bands.

3.5.2 Hi kinematics

In this section we summarize the main corrections that were applied to thekinematic measures.

The global Hi linewidths were corrected for:

108 Chapter 3. The Multi–Wavelength Tully–Fisher relation

1. Instrumental broadening, which depends on the instrumental velocityresolution and on the steepness of the wings of the velocity profile,following Verheijen & Sancisi (2001).

2. Turbulent motions, which depend on the level at which the width ofthe profile was measured 20% or 50% of the peak flux (Verheijen& Sancisi 2001). Figure 2.6 demonstrates the difference betweencorrected (right panels) and non-corrected (left panels) widths of theintegrated Hi profile and the velocity derived from the rotation curve.

3. Inclination, the linewidths were corrected for inclination accordingto the formula W i

50,20 = W50,20/sin(ikin), where ikin is a kinematicinclination angle, in order to represent the rotational velocity asW i

50,20 = 2Vrot (see Section 4.1).

Prior to the rotation curve derivation, Gaussian velocity fields werecensored for skewed velocity profiles (high h3) measured from the Gauss–Hermit polynomial velocity fields. A skewness of the velocity profilesmight be present mostly due to beam–smearing and non–circular motions.Thus, censoring for the high h3 allowed us to derive high–quality rotationcurves, representing the actual rotational velocity of a galaxy, not affectedby the effects mentioned above. The details can be found in Chapter 2(Ponomareva et al. 2016).

3.6 The Tully-Fisher relations

In this section we present the statistical properties of the multi-wavelengthTFrs using the different kinematic measures W50, Vmax and Vflat. First, wediscuss the fitting method. Second, we discuss the slope and vertical scatter(σ) of the TFrs. Then, we introduce the slope independent tightness (σ⊥)of the TFrs. We conclude with the search for a 2nd parameter that maycorrelate with the residuals.

3.6.1 Fitting method

The study of the statistical properties of the TFr requires establishing theslope and zero point of the relation. However, there is no general agreementwhich fitting method is best suited. For example, it was shown that theslope of the TFr is affected by a Malmquist bias (TC12) which can be

3.6. The Tully-Fisher relations 109

resolved by applying an inverse least squares regression (Willick 1994).Moreover, it is important to note that the vertical scatter of the TFr, whichis crucial for the distance measure, is highly dependent on the slope. Thus,an intrinsically tight TFr may introduce a larger vertical scatter due to asteeper slope (Verheijen 2001). As we are interested in the tightness ofthe TFr, while the Malmquist bias is minimal for our sample, we apply anorthogonal regression where the best-fit model minimises the orthogonaldistances from the points to the line. We apply the fitting method withbivariate correlated errors and intrinsic scatter (BCES, Akritas & Bershady(1996)) using the python implementation developed by Nemmen et al.(2012). The main advantages of this method are that it takes errors in bothdirections into account, it permits the measurement errors of both variablesto be dependent (for example uncertainties due to the inclination) and itassigns less weight to outliers and data points with large errors.

In order to accurately calculate the (intrinsic) scatter and tightnessof the relations, the following measurement uncertainties were taken intoaccount:

1. the errors in total magnitudes M bT , i(λ) due to the sky background,

distance uncertainties and the uncertainty in the photometric zero–point.

2. the errors on the rotational velocity measures Vmax, Vflat and W50,see Table 2.5.

3. the error on the kinematic inclination which affects both the internalextinction correction and the kinematic measure, introducing covari-ance in the errors.

3.6.2 Slope, scatter and tightness

We measure the slope, scatter and tightness of the TFrs in 12 differentbands with different kinematic measures, using the weighted orthogonalregression fit and taking correlated errors in both directions into account.It is important to point out that the comparisons are made for the sampleswith different numbers of galaxies: 32 for the UV and IR bands and 21 forthe SDSS bands (see Section 3). However, we present the comparisons forthe SDSS subsample of 21 galaxies for all bands in Appendix A.

It has been suggested for some time that the slope of the TFr steepensfrom blue to red wavelengths (Aaronson et al. 1979; Tully et al. 1982;

110 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Fuv Nuv u g r i z J H K 3.6 4.5

Band

−10

−9

−8

−7

−6

−5

Slop

e(M

λ)

N=32N=21 (SDSS)

W50

Vmax

Vflat

Figure 3.6 – Slope of the TFr as a function of wavelength, calculated using differentrotation measures. With black points indicated slopes measured for the TFr based onW50, with green based on Vmax and with red based on Vflat. Independently of band, theTfr based on Vflat demonstrates the steepest slope.

Fuv Nuv u g r i z J H K 3.6 4.5

Band0.0

0.2

0.4

0.6

0.8

1.0

σ(m

ag)

W50

Vmax

Vflat

Figure 3.7 – Vertical scatter of the TFr as a function of wavelength, calculated usingdifferent rotation measures. With black points indicating the scatter measured for theTFr based on W50, with green based on Vmax and with red based on Vflat.

3.6. The Tully-Fisher relations 111

Table 3.1 – The results of the orthogonal fits of the TFrs.

Band Slope (Mag) Slope (dex)

W50 Vmax Vflat W50 Vmax VflatFUV -7.12±0.86 -7.04±0.98 -7.87±1.27 2.36±0.38 2.32±0.37 2.59±0.47NUV -6.45±0.76 -6.36±0.86 -6.91±0.94 1.93±0.40 1.91±0.40 2.06±0.41u -6.06±0.64 -6.30±0.60 -6.95±0.67 1.69±0.44 1.75±0.46 1.91±0.52g -6.11±0.33 -6.43±0.57 -7.12±0.6 1.9 ±0.33 1.97±0.4 2.17±0.44r -6.76±0.25 -7.09±0.51 -7.87±0.56 2.26±0.23 2.36±0.3 2.61±0.33i -7.02±0.32 -7.29±0.49 -8.14±0.57 2.12±0.38 2.19±0.44 2.42±0.49z -7.89±0.40 -8.17±0.52 -9.12±0.61 2.82±0.16 2.91±0.22 3.25±0.24J -8.73±0.52 -8.55±0.39 -9.22±0.4 3.23±0.26 3.16±0.20 3.41±0.19H -8.99±0.52 -8.83±0.42 -9.47±0.38 3.43±0.24 3.36±0.18 3.61±0.15Ks -9.26±0.50 -9.08±0.41 -9.77±0.41 3.51±0.23 3.44±0.18 3.81±0.193.6 µm -9.05±0.45 -8.86±0.37 -9.52±0.32 3.52±0.19 3.44±0.15 3.7 ±0.114.5µm -9.04±0.46 -8.81±0.38 -9.51±0.33 3.52±0.19 3.45±0.16 3.7 ±0.12

Band Zero Point (Mag) Zero point (log(L(L�)))

W50 Vmax Vflat W50 Vmax VflatFUV 0.18±2.17 -0.09±2.44 1.77±3.12 7.53±0.95 7.66±0.93 7.05±1.16NUV -1.78±1.92 -2.07±2.15 -0.88±2.32 6.36±1.03 6.47±1 6.11±1.04u -2.45±1.62 -1.91±1.53 -0.41±1.71 4.71±1.13 4.59±1.2 4.21±1.32g -4.27±0.83 -3.55±1.42 -1.94±1.51 4.96±0.86 4.79±1.03 4.33±1.13r -3.24±0.63 -2.49±1.28 -0.67±1.39 4.28±0.59 4.07±0.78 3.49±0.84i -2.94±0.81 -2.32±1.25 -0.35±1.44 4.74±0.99 4.58±1.12 4.04±1.25z -0.87±1.01 -0.24±1.31 1.97±1.52 3.07±0.41 2.85±0.56 2.08±0.62J 0.1 ±1.28 -0.44±0.99 1 ±0.99 1.92±0.67 2.13±0.52 1.59±0.49H 0.08±1.29 -0.42±1.06 0.92±0.94 1.70±0.61 1.90±0.45 1.38±0.37Ks 0.52±1.24 0.00±1.04 1.44±0.038 1.58±0.6 1.78±0.46 1.22±0.443.6 µm 2.4±1.1 1.40±1.41 3.61±1.73 1.67±0.49 1.88±0.37 1.33±0.294.5 µm 2.92±1.13 2.36±0.97 3.73±0.83 1.66±0.50 1.88±0.39 1.33±0.31

Notes. Upper panel. Column (1): photometrical band; Column (2)-Column(4): slopes ofthe TFrs based on W50, Vmax and Vflat, measured in magnitudes; Column (5)-Column(7):slope of the TFrs based on W50, Vmax and Vflat, measured in dex. Lower panel. Column(1): photometrical band; Column (2)-Column(4): zero points of the TFrs based on W50,Vmax and Vflat, measured in magnitudes; Column (5)-Column(7): zero points of the TFrsbased on W50, Vmax and Vflat, measured in dex.

112 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Table 3.2 – Vertical scatter of the TFrs in different photometrical bands measured inmagnitudes and in dex

Band σ (Mag) σ (dex)

W50 Vmax Vflat W50 Vmax VflatFUV 0.87±0.14 0.89±0.15 0.97±0.17 0.30±0.09 0.31±0.09 0.33±0.1NUV 0.74±0.13 0.76±0.14 0.77±0.15 0.25±0.09 0.26±0.09 0.26±0.09u 0.44±0.15 0.47±0.14 0.44±0.15 0.19±0.11 0.19±0.12 0.19±0.12g 0.27±0.11 0.34±0.14 0.32±0.14 0.14±0.1 0.15±0.11 0.15±0.11r 0.22±0.09 0.31±0.13 0.29±0.13 0.12±0.08 0.14±0.1 0.13±0.1i 0.25±0.1 0.3 ±0.12 0.31±0.13 0.11±0.06 0.12±0.08 0.12±0.08z 0.29±0.11 0.32±0.13 0.33±0.14 0.12±0.07 0.13±0.08 0.13±0.09J 0.39±0.11 0.4 ±0.09 0.39±0.09 0.15±0.08 0.16±0.07 0.15±0.06H 0.41±0.11 0.44±0.1 0.38±0.09 0.16±0.07 0.17±0.06 0.15±0.06K 0.41±0.1 0.44±0.1 0.40±0.09 0.16±0.07 0.17±0.06 0.16±0.063.6 0.39±0.1 0.41±0.09 0.33±0.08 0.15±0.06 0.16±0.05 0.13±0.054.5 0.40±0.1 0.42±0.09 0.34±0.08 0.16±0.06 0.16±0.05 0.13±0.05

Notes. Column (1): photometrical band; Column (2)-Column(4): scatters of theTFrs based on W50, Vmax and Vflat, measured in magnitudes; Column (5)-Column(7):tightnesses of the TFrs based on W50, Vmax and Vflat, measured in dex.

Table 3.3 – Tightness of the TFrs in different photometrical bands measured in dex

Band σ⊥ (dex)

W50 Vmax VflatFUV 0.12±0.045 0.124±0.022 0.122±0.022NUV 0.12±0.048 0.123±0.024 0.117±0.024u 0.099±0.062 0.099±0.031 0.091±0.031g 0.068±0.044 0.071±0.022 0.066±0.022r 0.05±0.03 0.055±0.015 0.05±0.015i 0.042±0.018 0.044±0.009 0.041±0.009z 0.043±0.02 0.045±0.01 0.042±0.01J 0.047±0.016 0.049±0.013 0.045±0.013H 0.047±0.015 0.050±0.012 0.042±0.012K 0.046±0.022 0.049±0.011 0.042±0.0113.6 0.043±0.019 0.046±0.01 0.036±0.014.5 0.044±0.02 0.047±0.01 0.036±0.01

Notes. Column (1): photometrical band; Column (2)-Column(4): tightness of the TFrsbased on W50, Vmax and Vflat, measured in dex;

3.6. The Tully-Fisher relations 113

Fuv Nuv u g r i z J H K 3.6 4.5

Band0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14�?

(dex

)W50

Vmax

Vflat

Fuv Nuv u g r i z J H K 3.6 4.5

Band0.030

0.035

0.040

0.045

0.050

0.055

�?

(dex

)

Fuv Nuv u g r i z J H K 3.6 4.5

Band0.030

0.035

0.040

0.045

0.050

0.055

�?

(dex

)

Figure 3.8 – Orthogonal tightness of the TFr as a function of wavelength, calculatedusing different rotation measures. With black points indicated scatter measured for theTFr based on W50, with green on Vmax and with red on Vflat. Independently in eachband the relation is “tighter”, when it is based on the Vflat as a rotation measure

Verheijen 2001). We confirm this result by our study, which covers a muchbroader wavelength range. The variation of the slope with passband ispresented in Figure 3.6. Our result suggests a “flattening” of the slope as afunction of wavelength in the mid–infrared bands. Moreover, the TFr basedon Vflat is always showing the steepest slope in every passband (Figure 3.6).The steepest slope is found in the K -band and is consistent with −10.

The vertical scatter (σ) in every passband was measured using each ofthe three velocity measures W50, Vmax and Vflat. The total observed scatterwas calculated according to the following equation:

σ =

√χ2

N − 1, (3.11)

where χ2 is∑(M b,i

T − (a · log(Vcirc) + b))2,

here Vcirc stands for one of the three velocity measures W50, 2Vmax or 2Vflat,a and b are the fitted slope and zero point of the relation respectively, and

114 Chapter 3. The Multi–Wavelength Tully–Fisher relation

N − 1 is the number of degrees of freedom. Errors on the scatter wereestimated following a full error propagation calculation. The vertical scatterin magnitudes, which is relevant for distance measurements, is shown inFigure 3.7 as a function of wavelength. It is clear from Figure 3.7 thatthe vertical scatter is reasonably “flat” in the mid–IR bands, suggestingthat there might be no difference which mid–IR band to use as a distanceindicator. Therefore the preference should be given to the one whichsuffers least from dust extinction and non–stellar contamination. However,one can argue that the r–band TFr based on W50 should be used as adistance estimation tool, since it demonstrates the smallest vertical scatter.Interestingly, Verheijen (2001) had found a very similar result. Yet, it isimportant to keep in mind that the vertical scatter is a slope–dependentmeasure, while an intrinsically tight TFr will demonstrate a large verticalscatter if the slope of the relation is steep. Moreover, it is remarkablethat for the UV and optical bands (FUV to z) the vertical scatter maybe smaller when the relation is based on W50, with the smallest σ = 0.23mag in the r band. However, for red bands (J to 4.5µm) the smallestvertical scatter σ = 0.33 mag is found in the 3.6 µm band TFr based on2Vflat. This is due to the fact that when the relation is based on 2Vflat,the slope steepens more significantly for the UV and optical bands than forthe infrared.

The tightness (σ⊥) of the TFr is the perpendicular scatter betweenthe data points and the linear model, which provides information onhow “tight” the data are spread around the regression line. It is slopeindependent and has been recently used for testing galaxy formationand evolution models (Papastergis et al. 2016). Therefore, the tightnessprovides important information on the intrinsic properties of the TFr. Wecalculate tightness using the following formula:

σ⊥ =

√ ∑d2i

N − 2, (3.12)

where N − 2 is the amount of degrees of freedom and di is a perpendiculardistance of each point to a model line:

di =

√(xi + ayi − ab

a2 + 1− xi

)2

+

(a · xi + ayi − ab

a2 + 1+ b− yi

)2

,

3.6. The Tully-Fisher relations 115

1.8 2.0 2.2 2.4 2.6 2.8 3.0Log(W50)

−22

−20

−18

−16

−14

M[3

.6]

slope= -9.05σ = 0.39σ⊥ = 0.044

1.8 2.0 2.2 2.4 2.6 2.8 3.0Log(2Vmax)

−22

−20

−18

−16

−14

M[3

.6]

slope= -8.87σ = 0.41σ⊥ = 0.047

1.8 2.0 2.2 2.4 2.6 2.8 3.0

Log(2Vflat)

−22

−20

−18

−16

−14

M[3

.6]

slope= -9.52σ = 0.34σ⊥ = 0.036

Figure 3.9 – The 3.6µm TFrs based on the different kinematic measure W50 –left, Vmax– middle,Vflat – right. With green symbols indicated three galaxies with rising rotationcurves (Vmax < Vflat). These galaxies were not included in the fit model.

here xi and yi are the coordinates of each measured point, in our caselog(Lλ/L�) and log(Vcirc) respectively, a and b are the slope and the zeropoint of a model line. Errors on the tightness were estimated following afull error propagation calculation. The tightness of the TFr as a function ofwavelength is shown in Figure 3.8. It also “flattens” in the mid–IR bandswith the tightest correlation at 3.6 µm equal to σ⊥ = 0.036 dex. Moreover,independently of the photometric band, the TFrs tend to be tighter whenbased on 2Vflat (Figure 3.8).

3.6.3 A closer look at the 3.6µm Tully–Fisher relation

Figure 3.9 shows the TFr in the 3.6 µm band based on W50, Vmax and Vflat.

According to our fit, the MT,b,i[3.6] –Vflat correlation can be described as :

MT,b,i[3.6] = (−9.52± 0.32) ∗ log(2Vflat) + 3.3± 0.8 (3.13)

and LT,b,i[3.6] (L�)–Vflat as

log(LT,b,i[3.6] ) = (3.7± 0.11) ∗ log(2Vflat) + 1.3± 0.3, (3.14)

based on M�(3.6µm) = 3.24 mag (Oh et al. 2008). Here MT,b,i[3.6] is the

total magnitude, corrected for Galactic and internal extinction, and LT,b,i[3.6]is luminosity, presented in solar luminosities, Vflat is the rotational velocityof the flat part of the rotation curve in km/s.

Eqn. 3.13 describes the tightest of the TFrs, with an observed tightnessequal to σ⊥,obs = 0.036± 0.010 dex. Without considering the observational

116 Chapter 3. The Multi–Wavelength Tully–Fisher relation

−10 −5 0 5 10

d⊥/ε⊥

0

1

2

3

4

5

6

7

8

9

Nu

mb

er

zero σ⊥,intdata

Figure 3.10 – Histogram of the perpendicular distances from the data points to theline (d⊥,i) in the LT,b,i[3.6] (L�)–Vflat relation, normalised by the perpendicular errors ε⊥,i.The standard normal distribution, which would be expected for a zero intrinsic tightnessis shown with a black line. The data best–fit is shown with the dashed line with thestandard deviation of 1.9.

errors, σ⊥,obs presents an upper limit on the intrinsic tightness of theTFr[3.6],Vflat : σ⊥,int < σ⊥,obs = 0.036 dex. This is 0.02 dex smaller thanthe observed tightness of the Baryonic TFr for gas–rich galaxies, found byPapastergis et al. (2016), using W50 as a rotational velocity measure.

Further, we can estimate the intrinsic tightness of the TFr[3.6],Vflat bycomparing the perpendicular distance from each data point to the modelline d⊥,i with the measurement error ε⊥,i, where ε⊥,i is based on the ob-servational errors on the luminosity (εL[3.6],i

) and on the rotational velocity(εVflat,i) of each data point, projected onto the direction perpendicular tothe model line:

ε2i = (εlog(L[3.6]),i ·1

1 + a2)2 + (εlog(2Vflat),i ·

a

1 + a2)2, (3.15)

where a is the slope of the line and the uncertainty due to the distancemeasurement is included in the error on the total luminosity. For moredetails on the derivation of Eqn. 15 see Papastergis et al. (2016). If theobserved tightness of the relation would be only due to the measurement

3.6. The Tully-Fisher relations 117

errors, the histogram of d⊥,i/ε⊥,i would then follow a standard normaldistribution. Yet, it is clear from Figure 3.10 that the spread of d⊥,i/ε⊥,iis larger than expected from a standard normal distribution which hasa standart deviation of 1, with the measured standard deviation of 1.9.Therefore, a small but non–zero intrinsic perpendicular scatter (σ⊥) ispresent in the TFr[3.6],Vflat . To obtain the best estimate for the intrinsictightness, we present it as follows :

σ⊥,int =√σ2⊥,obs − σ2

⊥,err, (3.16)

where σ⊥,err = 0.025 dex is the perpendicular scatter due to themeasurement errors only.

Thus, we obtain an estimate for the intrinsic perpendicular scatterσ⊥,int ∼ 0.026 dex. It is important to keep in mind that this result dependson how accurately the observational errors can be determined. Therefore,any underestimate of the observational errors will lead to a decrease of theintrinsic tightness and vice versa.

As was already mentioned before, previous studies (Meidt et al. 2012;Querejeta et al. 2015) concluded that Spitzer 3.6 µm luminosities representnot only the old stellar population. Up to 30% of the 3.6 µm light mightbe coming from warm dust which is heated by young stars and re–emittedat longer wavelengths. Moreover, AGB stars appear to peak at 3.6 µm aswell. To test the effect of contamination by dust and/or AGB stars on thetightness of the TFr, we constructed a subsample of 18 galaxies from oursample. These galaxies were studied as part of the S4G Pipeline analysis byQuerejeta et al. (2015). In this study the 3.6 µm images were decomposedinto stellar and non-stellar contributions using an Independent ComponentAnalysis described in Meidt et al. (2012). We compared the statisticalproperties of the TFrs in the observed 3.6 µm band and in the 3.6 µm bandcorrected for non–stellar contamination, as demonstrated in Figure 3.11.The results of the comparison can be found in Table 3.4. It is clear thatthe scatter and tightness of the TFr at 3.6 µm can be slightly reduced if thenon–stellar contamination is taken into account, especially when the TFris based on Vflat as a rotational velocity measure. However, the differencein the scatter (∆σ = 0.03 mag) and tightness (∆σ⊥ = 0.004 dex) is toosmall (∼ 10%) to draw definite conclusions. Hence, a more detailed studyof this subject should be done with a larger sample of galaxies for which adecomposition into stellar and non–stellar emission has been performed.

118 Chapter 3. The Multi–Wavelength Tully–Fisher relation

2.0 2.5 3.0

Log(2Vflat)

−22

−20

−18

−16

M[3.6

](m

ag)

not correctedcorrected

2.0 2.5 3.0

Log(2Vflat)

−0.5

−0.4

−0.3

−0.2

−0.1

0.0

∆M

[3.6

](m

ag)

correction

Figure 3.11 – Left panel: The MT,b,i[3.6] –Vflat relation is shown with blue points. The

relation using total magnitudes corrected for non–stellar contamination is shown withred points. Right panel: The correction for non–stellar contamination as a function ofrotational velocity 2Vflat.

Table 3.4 – Slope scatter and tightness of the TFrs, constructed for 19 galaxies in theobserved 3.6µm band and in the 3.6µm band, corrected for the non–stellar contamination

N=19 Observed CorrectedW50 Vmax Vflat W50 Vmax Vflat

slope (mag) -8.52 -8.56 -9.20 -8.77 -8.77 -9.47σ (mag) 0.40 0.45 0.32 0.38 0.41 0.29σ⊥ (dex) 0.043 0.046 0.036 0.043 0.046 0.031

Notes. Slope, scatter and tightness of the TFrs, constructed for 19 galaxies inthe observed 3.6 µm band and in the 3.6 µm band, corrected for the non–stellarcontamination. Column(1): name of the parameter; Column (2-4): slope, scatter andtightness of the TFrs in the observed 3.6 µm band (based on different velocity measures);Column (5-7):slope ,scatter and tightness of the TFrs in the 3.6 µm band, corrected fornon–stellar emission (based on different velocity measures);

3.6. The Tully-Fisher relations 119

3.6.4 Need for a 2nd parameter?

For several decades it was suggested that the scatter in the TFr can bereduced by adding a second parameter (Rubin et al. 1985; Tully & Pierce2000). This parameter is usually derived from the correlations of theresiduals of the TFr with global galactic properties. It has been shownthat the residuals of the TFr based on W50 correlate well with the colouror morphological type of galaxies (Aaronson & Mould 1983; Rubin et al.1985; Russell 2004). The correlations are usually found in the blue bandswhich tend to have much larger scatter, and found to be completely absentin the red bands where the scatter is already very small (Tully & Pierce2000; Verheijen 2001). However, Sorce et al. (2012) found a colour termpresent in the residuals of the 3.6 µm TFr, which allowed them to reducethe observed scatter by 0.05 mag.

We examine the residuals ∆Mλ of the TFrs in each band based onVflat and investigate possible correlations with global galactic propertiessuch as SFR, central surface brightness, and the outer slope of the rotationcurve. First, we consider in detail two extremes ∆MNUV and ∆M[3.6]

based on Vflat. From Figure 3.12 it is clear that while NUV residuals havestrong hints for correlations with all galactic parameters, these strong hintsdisappear for the 3.6 µm residuals. It is not surprising, that some of thecorrelations show opposite trends, for instance with the star formation rate.Here ∆MNUV show a hint for a correlation with the star formation rate,while at 3.6 µm there is a small hint but for an anti–correlation, as NUVband traces young regions of the star formation in galaxies, whicle 3.6 µmband traces the old stellar population, which is not associated with the starformation.

To quantitatively describe the strengths of the correlations between TFrresiduals and global galactic properties, we calculate Pearson’s coefficientsr, a measure of the linear correlation between two variables. We considerthe correlation to have place when the Pearson’s coefficient is reachingthe value of 0.6 and higher or -0.6 and lower for anti–correlation. Figure3.13 shows the Pearson’s coefficients r as a function of wavelength for thecorrelations between ∆Mλ and various galactic properties such as i− [3.6]colour, the outer slope of the rotation curve (see Section 5.2), centralsurface brightness at 3.6 µm, star formation rate and morphological type.It is clear from Figure 3.13 that the Pearson’s coefficients do not suggestany strong correlations between residuals of the TFrs and various galactic

120 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Sab Sbc Scd Sdm Im

Hubble type

−2

−1

0

1

2

∆M

[3.6

]

Sab Sbc Scd Sdm Im

Hubble type

−2

−1

0

1

2

∆M

NUV

2.0 2.2 2.4 2.6 2.8 3.0

i - [3.6]

−2

−1

0

1

2∆

M[3.6

]

2.0 2.2 2.4 2.6 2.8 3.0

i - [3.6]

−2

−1

0

1

2

∆M

NUV

−0.4 −0.2 0.0 0.2 0.4 0.6

log Slope

−2

−1

0

1

2

∆M

[3.6

]

−0.4 −0.2 0.0 0.2 0.4 0.6

log Slope

−2

−1

0

1

2

∆M

NUV

13 14 15 16 17 18 19 20 21 22

µ[3.6]0

−2

−1

0

1

2

∆M

[3.6

]

13 14 15 16 17 18 19 20 21 22

µ[3.6]0

−2

−1

0

1

2

∆M

NUV

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0

log SFR

−2

−1

0

1

2

∆M

[3.6

]

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0

log SFR

−2

−1

0

1

2

∆M

NUV

Figure 3.12 – Residuals of the TFrs in the NUV and 3.6 µm bands as a function ofglobal galactic properties.

3.7. Discussion and Conclusions 121

Fuv Nuv u g r i z J H K 3.6 4.5

Band−1.0

−0.5

0.0

0.5

1.0

r

i-[3.6]Slrcµ0

SFRT-type

Figure 3.13 – Pearson’s correlation coefficients between MT (λ)– log(2Vflat) and globalgalactic properties ([i-3.6 µm] colour, outer slope of the rotation curve, central surfacebrightness, star formation rate and morphological type) as a function of wavelength.[i-3.6 µm]

properties in any band, except for the FUV where a prominent correlationwith the colour term is found. This result is in agreement with previousstudies for blue bands. However, there is no evidence for a significantcorrelation between ∆M[3.6] and the i − [3.6] colour (r = −0.29), despitethe previous suggestions by Sorce et al. (2012). Nonetheless, the strengthfor the correlation between ∆M[3.6] and the i−[3.6] colour was not presentedin Sorce et al. (2012) study, therefore we can not perform a quantitativecomparison. In conclusion, we do not find any second parameter, whichwould help to reduce the scatter in the near–infrared TFr.

3.7 Discussion and Conclusions

In this chapter, we present an empirical study of the multi–wavelengthTully–Fisher relation, taking advantage of spatially resolved Hi kinematics.This study aims to investigate the statistical properties of the TFrs in 12photometric bands, using three rotational velocity measures: W50 from theglobal Hi profile, and Vmax and Vflat from high–quality, spatially–resolvedHi rotation curves. The galaxies in our sample were selected to haveindependently measured Cepheid or/and TRGB distances. This allowed

122 Chapter 3. The Multi–Wavelength Tully–Fisher relation

us to calibrate the TFr with minor distance uncertainties (σdist = 0.07mag, instead of σdist = 0.41 mag when using Hubble flow distances).

First, we present a slope–independent perpendicular scatter (σ⊥) ofthe TFr, which describes how tight the data points are spread aroundthe model line. We study the tightness as a function of wavelength forTFrs based on different rotational velocity measures (Section 6.2). We findthat the tightness σ⊥ of the TFr improves significantly from the blue tothe infrared bands, but it “flattens” for the near–infrared bands, with thelargest σ⊥ = 0.043 dex in the H–band and the smallest σ⊥ = 0.036 dexin the 3.6 µm band, using Vflat as a rotational velocity measure. We findthat the later is not consistent with a zero intrinsic perpendicular scatterindicating that the measured σ⊥,obs can not be completely explained by themeasurement errors (see Section 6.3). Nevertheless, the TFr based on the3.6 µm luminosities and Vflat provides the tightest constraint on theories ofgalaxy formation and evolution. Indeed, such a tight correlation betweenthe 3.6 µm luminosity of a galaxy with the velocity of the outer most pointof the rotation curve suggests an extremely tight correlation between themass of the dark matter halo and its baryonic content. Certainly, 3.6 µmlight has been considered as the best tracer of the total stellar mass ofgalaxies which dominates the baryonic mass. However, many observationalstudies have shown, that not only old stars, but also hot dust and AGBstars might contribute to this light by 30% in some cases. We have shownthat the observed tightness and scatter of the TFr can be somewhat reducedif the 3.6 µm light is corrected for non–stellar contamination (see Section6.3). However, more studies should be done to further investigate thiseffect, using a larger sample of galaxies for which the decomposition of thelight into old stars and contamination can be performed.

An obvious next step in studying the tightness of the TFr is to measurethe slope, scatter and tightness of the baryonic TFr (BTFr) and comparethis with measurements derived for the 3.6 µm band. However, thisapproach introduces more uncertainties related to estimating the stellarmass. For instance, Papastergis et al. (2016) found a larger perpendicularscatter of the BTFr, even though they considered a sample of heavilygas–dominated galaxies for which uncertainties in stellar mass are lesssignificant. However, that study was done using only W50 as a rotationalvelocity measure. Therefore, the next chapter discusses the statisticalproperties of the BTFr with resolved Hi kinematics.

3.7. Discussion and Conclusions 123

Next, we study the slope of the TFr as a function of wavelength, usingW50, Vmax and Vflat (see Section 6.2). We confirm the results of previousstudies (Aaronson et al. 1979; Tully et al. 1982; Verheijen 2001), that theslope of the TFr steepens toward longer wavelengths. Furthermore, webroadened the study over a wider wavelength range. The steepening ofthe slope results from the fact that redder galaxies are much brighter thanbluer galaxies at longer wavelengths. Moreover, galaxies that are bright inthe infrared tend to rotate more rapidly. Therefore, at longer wavelengthsthe high–mass end of the TFr will rise faster than the low–mass end. Inaddition, we find that the TFr based on Vflat as a rotational velocitymeasure has the steepest slope in every photometric band. Massive galaxiestend to have declining rotation curves with Vmax > Vflat (see Section4.1, Figure 2.6). Hence, if Vflat is used as a rotation velocity measure,bright galaxies have lower velocities than when measured with W50 and/orVmax. This difference, therefore, reduces the velocity range over which thegalaxies are distributed. Thus, this effect steepens the slope of the TFras well. Similar results were found by Verheijen (2001) and Noordermeeret al. (2007). Moreover, the use of Vflat “straightens” the TFr and removesa possible curvature in the TFr at the high–mass end (Neill et al. 2014;Noordermeer & Verheijen 2007).

Subsequently, we discussed the vertical scatter (σ) of the TFr as afunction of wavelength, using three rotational velocity measures (see Section6.2). It is well known, that the vertical scatter of the TFr is stronglydependent on the slope. Thus, even an intrinsically tight correlationcan be found to have a large vertical scatter if the slope is steep. Thevertical scatter of the TFr is mostly discussed in the context of determiningdistances to galaxies. We find the smallest vertical scatter in the r–band,using W50 as a rotational velocity measure, confirming the result found byVerheijen (2001). Moreover, we find that the vertical scatter in the 3.6 µmband (σ = 0.39mag) to be lower than previously reported by Sorce et al.(2012) for the 3.6 µm band (σ = 0.44mag) and by Neill et al. (2014) forthe 3.4 µm band(σ = 0.54 mag). These comparisons are done using W50 asa rotational velocity measure. Besides, we find σ to be smaller when usingW50 as a velocity measure for the FUV and optical bands (FUV − z). Forthe infrared bands (J to 4.5µm), σ is smaller when the TFr is based onVflat. This result suggests that σ in the infrared bands is less sensitive tothe slope steepening with Vflat.

124 Chapter 3. The Multi–Wavelength Tully–Fisher relation

We searched for a second parameter that can possibly help to reduce thevertical scatter of the TFr. We considered the residuals of the TFrs (∆Mλ–Vflat ) in every band (see Section 6.4) and find no significant correlationsbetween the residuals of the TFrs and main galactic properties (SFR, centralsurface brightness, outer slope of the rotation curve, morphological type andi− [3.6] colour ) (see Figure 3.13). Even though the UV bands show hintsfor correlations between the residuals and some of the global properties suchas SFR (see Figure 3.12), no correlations are found in the red bands. Thissuggests that these correlations are triggered by different stellar populationsin early–type and late–type galaxies of the same UV luminosity and notby the difference in Vflat governed by the dark matter halo. Lastly, it isimportant to mention that we do not find any correlation between the TFrresiduals ∆M[3.6]–W50 and the colour term i − [3.6] (Pearson’s coefficientr = 0.1), contrary to the result reported previously by Sorce et al. (2012).

As was shown by Sorce & Guo (2016), the size of the sample may havea significant impact on the scatter of the TFr. Therefore, it is necessary topoint out that the limited size of our sample might cause the uncertaintiesin the slope, scatter and zero point of the TFrs. However, it is veryexpensive to establish a large sample of spiral galaxies which have bothindependently measured distances and resolved Hi kinematics. Nonetheless,this challenge will be possible to address with the Hi imaging surveys thatare planned for new observational facilities, such as Apertif (Verheijen et al.2008), MeerKAT (de Blok et al. 2009) and ASKAP (Johnston et al. 2007),providing resolved Hi kinematics for many thousands of galaxies.

Acknowledgements

I thank Pauline Barmby for sharing Spitzer images of M31. I am alsograteful to Emmanouil Papastergis for fruitful discussions and usefulcomments.

Appendix 3.A The Tully-Fisher relations for the SDSSsubsample

In this Appendix we present the results for the smaller SDSS sample. Inthis subsample we consider only 21 galaxies which have photometry fromall 12 bands. This allows us to compare the slope, scatter and tightness of

3.A. The Tully-Fisher relations for the SDSS subsample 125

Fuv Nuv u g r i z J H K 3.6 4.5

Band

−11

−10

−9

−8

−7

−6

−5

Slop

e(m

ag)

Fuv Nuv u g r i z J H K 3.6 4.5

Band0.0

0.2

0.4

0.6

0.8

1.0

σ(m

ag)

Fuv Nuv u g r i z J H K 3.6 4.5

Band)0.00

0.02

0.04

0.06

0.08

0.10

0.12

σ⊥

(dex

)

Figure A.1 – Slope, scatter and tightness of the TFr of the SDSS subsample as a functionof wavelength, calculated using different rotation measures. With black points indicatedvalues measured for the TFr based on W50, with green based on Vmax and with red basedon Vflat.

126 Chapter 3. The Multi–Wavelength Tully–Fisher relation

the TFrs at various wavelengths for the same number of galaxies. We recallthat the lack of SDSS data for our full sample resulted in this smaller SDSSsubsample. Figure A.1 demonstrates the slope, scatter and tightness of theTFrs for this subsample. Even though the number of galaxies is smaller,there is no significant difference in trends compared to results based on thefull sample. Table A.1 summarises the measurements for the reduced TFrsample.

3.A. The Tully-Fisher relations for the SDSS subsample 127Table

A.1

–T

he

slop

e,sc

att

eran

tightn

ess

for

the

SD

SS

sam

ple

Band

Slo

pe

(Mag)

W50

Vmax

Vflat

FU

V-7

.65±

1.1

1-8

.73±

1.2

0-9

.89±

1.9

4N

UV

-6.4

4±

1.0

2-7

.39±

1.2

0-7

.82±

1.1

2u

-6.1

9±

0.6

5-6

.45±

0.6

1-7

.09±

0.6

9g

-6.1

9±

0.3

3-6

.54±

0.5

9-7

.21±

0.6

3r

-6.7

4±

0.2

6-7

.11±

0.5

4-7

.83±

0.5

8i

-7.1

9±

0.2

9-7

.52±

0.4

9-8

.32±

0.5

6z

-7.8

5±

0.4

2-8

.18±

0.5

5-9

.06±

0.6

3J

-8.1

4±

0.4

5-8

.51±

0.5

9-9

.44±

0.7

2H

-8.4

4±

0.5

3-8

.85±

0.6

5-9

.80±

0.7

7K

-8.6

1±

0.5

4-9

.01±

0.6

6-1

0.0±

0.8

13.6

-8.3

2±

0.4

8-8

.67±

0.5

7-9

.62±

0.5

24.5

-8.3

1±

0.5

1-8

.67±

0.5

9-9

.61±

0.7

2

Band

Sca

tter

(Mag)

Tig

htn

essσ⊥

(dex

)W

50

Vmax

Vflat

W50

Vmax

Vflat

FU

V0.9

6±

0.3

81.1

3±

0.4

01.1

7±

0.3

40.1

32±

0.0

91

0.1

35±

0.0

45

0.1

25±

0.0

45

NU

V0.7

8±

0.4

70.9

4±

0.4

80.8

6±

0.4

00.1

38±

0.0

97

0.1

41±

0.0

49

0.1

29±

0.0

49

u0.4

3±

0.3

00.4

5±

0.2

90.4

3±

0.3

10.0

94±

0.1

24

0.0

93±

0.0

62

0.0

85±

0.0

61

g0.2

7±

0.2

20.3

4±

0.2

80.3

2±

0.2

90.0

69±

0.0

89

0.0

72±

0.0

45

0.0

67±

0.0

47

r0.2

3±

0.1

90.3

2±

0.2

70.3

0±

0.2

70.0

52±

0.0

60

0.0

58±

0.0

30

0.0

53±

0.0

33

i0.2

5±

0.2

00.3

1±

0.2

50.3

0±

0.2

70.0

42±

0.0

36

0.0

46±

0.0

18

0.0

42±

0.0

20

z0.3

0±

0.2

30.3

3±

0.2

70.3

3±

0.2

90.0

45±

0.0

41

0.0

46±

0.0

21

0.0

43±

0.0

20

J0.3

3±

0.3

20.3

8±

0.2

90.3

9±

0.2

90.0

47±

0.0

43

0.0

50±

0.0

37

0.0

47±

0.0

40

H0.3

6±

0.3

20.4

2±

0.3

00.4

2±

0.2

90.0

44±

0.0

40

0.0

49±

0.0

35

0.0

44±

0.0

37

K0.3

6±

0.3

10.4

2±

0.3

00.4

2±

0.2

90.0

42±

0.0

54

0.0

47±

0.0

32

0.0

43±

0.0

34

3.6

0.3

3±

0.3

00.3

7±

0.2

80.3

7±

0.2

70.0

41±

0.0

49

0.0

43±

0.0

30

0.0

40±

0.0

30

4.5

0.3

4±

0.3

00.3

8±

0.2

90.3

9±

0.2

70.0

42±

0.0

50

0.0

45±

0.0

30

0.0

41±

0.0

30

Note

s.C

olu

mn

(1):

band;

Colu

mn

(2)-

Colu

mn

(4):

slop

esof

the

TF

rsbase

donW

50,Vmax

andVflat,

mea

sure

din

magnit

udes

;C

olu

mn

(5)-

Colu

mn(7

):sc

att

erof

the

TF

rsbase

donW

50,Vmax

andVflat,

mea

sure

din

magnit

udes

;C

olu

mn

(8)-

Colu

mn

(10):

tightn

ess

of

the

TF

rsbase

donW

50,Vmax

andVflat,

mea

sure

din

dex

;

128 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Appendix 3.B The Tully-Fisher relations using 2.2hmagnitudes

In this Appendix we briefly present the results of the TFrs, basedon magnitudes measured within 2.2 disk scale lengths. Figure B.1demonstrates the slope, scatter and tightness of these TFrs. It is clearfrom the figures, that even though the trends remain the same, the errorson the scatter and tightness significantly increase. Moreover, usage ofmagnitudes measured within 2.2 disk scale lengths did not decrease thescatter or improve the tightness of the TFrs in comparison with totalmagnitudes. Table B.1 summarises the measurements for the TFrs, basedon 2.2h magnitudes.

3.B. The Tully-Fisher relations using 2.2h magnitudes 129

Fuv Nuv u g r i z J H K 3.6 4.5

Band

−11

−10

−9

−8

−7

−6

−5

Slop

e(m

ag)

Fuv Nuv u g r i z J H K 3.6 4.5

Band0.0

0.2

0.4

0.6

0.8

1.0

σ(m

ag)

Fuv Nuv u g r i z J H K 3.6 4.5

Band)0.00

0.02

0.04

0.06

0.08

0.10

0.12

σ⊥

(dex

)

Figure B.1 – Slope, scatter and tightness of the TFr based on magnitudes measuredat 2.2h, as a function of wavelength, calculated using different rotation measures. Withblack points indicated values measured for the TFr based on W50, with green based onVmax and with red based on Vflat.

130 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Table

B.1

–T

he

slop

e,sc

att

eran

tightn

ess

for

the

SD

SS

sam

ple

Band

Slo

pe

(Mag)

W50

Vmax

Vflat

FU

V-7

.63±

1.7

3-7

.33±

1.7

4-8

.39±

2.2

0N

UV

-6.9

5±

1.0

4-6

.69±

1.1

0-7

.46±

1.3

8u

-7.8

2±

1.3

8-7

.95±

1.1

1-8

.76±

1.2

7g

-7.1

7±

0.5

5-7

.38±

0.4

7-8

.21±

0.5

4r

-7.7

6±

0.4

6-8

.01±

0.4

2-8

.92±

0.5

1i

-8.1

5±

0.5

4-8

.38±

0.4

7-9

.36±

0.5

9z

-8.5

8±

0.6

9-8

.81±

0.6

0-9

.85±

0.7

4J

-8.9

3±

0.5

1-9

.12±

0.5

7-9

.97±

0.6

7H

-8.9

9±

0.5

6-9

.22±

0.6

7-9

.99±

0.6

1K

-9.3

8±

0.5

4-9

.61±

0.6

3-1

0.4

6±

0.6

83.6

-9.5

6±

0.4

6-9

.37±

0.4

2-1

0.0

8±

0.4

04.5

-9.6

5±

0.5

3-9

.44±

0.4

3-1

0.1

6±

0.4

1

Band

Sca

tter

(Mag)

Tig

htn

essσ⊥

(dex

)W

50

Vmax

Vflat

W50

Vmax

Vflat

FU

V1.1

3±

0.4

01.1

0±

0.4

01.2

1±

0.4

40.1

43±

0.1

22

0.1

44±

0.0

61

0.1

40±

0.0

61

NU

V0.9

0±

0.3

10.8

7±

0.3

20.9

3±

0.3

50.1

25±

0.0

79

0.1

25±

0.0

39

0.1

21±

0.0

39

u0.6

9±

0.4

30.6

5±

0.3

90.6

2±

0.4

10.0

87±

0.1

38

0.0

82±

0.0

69

0.0

71±

0.0

69

g0.3

2±

0.2

70.3

2±

0.2

50.3

1±

0.2

70.0

44±

0.0

55

0.0

43±

0.0

27

0.0

38±

0.0

27

r0.2

8±

0.2

50.2

9±

0.2

40.2

8±

0.2

60.0

46±

0.0

46

0.0

46±

0.0

23

0.0

42±

0.0

23

i0.3

1±

0.2

70.3

0±

0.2

50.3

0±

0.2

80.0

48±

0.0

55

0.0

46±

0.0

27

0.0

39±

0.0

27

z0.3

7±

0.3

10.3

4±

0.2

80.3

6±

0.3

20.0

45±

0.0

86

0.0

43±

0.0

43

0.0

42±

0.0

43

J0.3

8±

0.2

20.4

3±

0.2

30.4

3±

0.2

50.0

48±

0.0

42

0.0

47±

0.0

21

0.0

44±

0.0

21

H0.3

9±

0.2

30.4

6±

0.2

60.4

1±

0.2

40.0

46±

0.0

71

0.0

51±

0.0

35

0.0

44±

0.0

35

K0.4

1±

0.2

20.4

7±

0.2

50.4

5±

0.2

50.0

44±

0.0

45

0.0

49±

0.0

23

0.0

43±

0.0

23

3.6

0.4

2±

0.2

00.4

4±

0.1

90.3

8±

0.1

90.0

43±

0.0

38

0.0

46±

0.0

19

0.0

37±

0.0

19

4.5

0.4

5±

0.2

10.4

6±

0.2

00.4

0±

0.1

90.0

47±

0.0

44

0.0

48±

0.0

22

0.0

40±

0.0

22

Note

s.C

olu

mn

(1):

band;

Colu

mn

(2)-

Colu

mn

(4):

slop

esof

the

TF

rsbase

donW

50,Vmax

andVflat,

mea

sure

din

magnit

udes

;C

olu

mn

(5)-

Colu

mn(7

):sc

att

erof

the

TF

rsbase

donW

50,Vmax

andVflat,

mea

sure

din

magnit

udes

;C

olu

mn

(8)-

Colu

mn

(10):

tightn

ess

of

the

TF

rsbase

donW

50,Vmax

andVflat,

mea

sure

din

dex

;

3.C. Data tables and plots 131

Appendix 3.C Data tables and plots

In this Appendix we present tables with our photometric measurementsfor each galaxy in every band together with the surface brightnessprofiles. Table C.0 compiles information on the photometric measurements: Column(1): NGC number. Column(2): photometric band. Column(3-5): magnitude at 2.2h, total magnitude and extrapolation total magnitudebeyond Rlim. Column(6): central surface brightness of the disk, correctedfor inclination. Column(7): Log scale length in arcsec. Figures C1-C32present the surface brightness profiles for each galaxy in every band. Theexponential disk fits are shown with black lines.

132 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Table C.0 – Photometric measurements of the sample.

name band m2.2h mtot mext µ0 ∆n Log(h)mag mag mag/ arsec

arcsec2

NGC55 FUV 11.643±0.001 11.387±0.045 -0.002 22.42 8.45 2.24NUV 11.303±0.001 11.047±0.045 -0.002 22.08 8.45 2.24J 6.82 ±0.03 6.4 ±0.11 – — — —H 6.267±0.075 5.847±0.13 – — — —K 6.023±0.064 5.603±0.121 – — — —3.6 5.903±0.031 5.483±0.074 -0.162 18.53 3.47 2.454.5 5.844±0.19 5.466±0.527 -0.134 18.38 3.69 2.43

NGC 224 u 6.451±0.049 6.139±0.323 -0.023 19.865 5.786 2.516g 4.026±0.019 3.798±0.111 -0.023 17.421 5.770 2.517r 2.877±0.002 2.699±0.033 -0.001 13.858 9.300 2.310i 2.278±0.012 2.094±0.079 -0.016 15.443 6.175 2.4883.6 0.182±0.270 −0.451±0.076 -0.776 14.770 1.645 2.8634.5 0.268±0.401 −0.419±0.107 -0.831 14.915 1.569 2.883

NGC247 FUV 11.735±0.001 10.670±0.045 -0.004 21.332 7.702 2.113NUV 11.334±0.002 10.339±0.136 -0.005 20.967 7.633 2.11J 8.108±0.026 7.474±0.01 – — — —H 7.412±0.092 6.778±0.18 – — — —K 7.373±0.062 6.739±0.13 – — — —3.6 6.921±0.017 6.287±0.080 -0.086 17.725 4.236 2.2184.5 6.961±0.025 6.291±0.101 -0.105 17.868 3.989 2.244

NGC 253 FUV 12.557±0.001 10.487±0.040 -0.050 24.465 4.870 2.426NUV 11.710±0.001 9.876±0.061 -0.045 23.362 4.994 2.41J 5.507±0.001 4.935±0.002 – – – –H 4.701±0.001 4.129±0.003 – – – –K 4.353±0.002 3.781±0.001 – – – –3.6 3.913±0.001 3.341±0.028 -0.006 13.553 7.315 2.0904.5 3.915±0.003 3.336±0.132 -0.005 13.369 7.454 2.081

NGC 300 FUV 10.622±0.001 9.634±0.037 -0.002 20.390 8.759 2.057NUV 10.353±0.001 9.415±0.095 -0.002 20.282 8.825 2.05J 7.168±0.017 6.527±0.111 – – – –H 6.566±0.021 5.925±0.11 – – – –K 6.435±0.044 5.794±0.093 – – – –3.6 6.271±0.003 5.630±0.028 -0.030 17.422 5.454 2.1084.5 6.244±0.060 5.637±0.842 -0.014 16.725 6.337 2.043

NGC 925 FUV 12.913±0.002 11.923±0.075 -0.002 19.905 8.485 1.673NUV 12.592±0.005 11.640±0.219 -0.002 19.555 8.495 1.67J 9.097±0.041 8.399±0.18 – – – –H 8.448±0.052 7.75 ±0.176 – – – –K 8.269±0.048 7.571±0.13 – – – –3.6 8.046±0.003 7.348±0.062 -0.015 17.152 6.303 1.8024.5 8.069±0.007 7.344±0.255 -0.005 16.676 7.490 1.727

Notes.

3.C. Data tables and plots 133

NGC 1365 FUV 12.688±0.001 12.038±0.109 -0.002 21.118 8.852 1.734NUV 12.200±0.002 11.668±0.653 -0.000 17.858 12.688 1.57J 7.666±0.061 7.416±0.346 – – – –H 7.170±0.929 6.92 ±0.345 – – – –K 6.728±0.204 6.478±0.424 – – – –3.6 6.547±0.040 6.297±0.209 -0.075 17.829 4.393 1.8344.5 6.511±0.041 6.290±0.234 -0.068 17.850 4.503 1.823

NGC 2366 FUV 12.829±0.002 12.548±0.013 -0.038 22.596 5.206 1.885NUV 12.687±0.006 12.387±0.029 -0.052 22.729 4.816 1.91J 10.224±0.399 10.76 ±0.333 – – – –H 9.562±0.367 10.165±0.953 – – – –K 9.402±0.245 10.03 ±0.588 – – – –3.6 10.111±0.028 9.513±0.065 -0.178 20.429 3.359 2.0174.5 10.333±0.052 9.509±0.088 -0.412 21.170 2.366 2.170

NGC 2403 FUV 10.447±0.003 9.866±0.016 -0.063 21.960 4.593 2.183NUV 10.209±0.007 9.676±0.050 -0.056 21.652 4.735 2.16u 10.537±0.030 10.059±0.154 -0.070 21.374 4.477 2.127g 9.068±0.046 8.612±0.272 -0.060 20.353 4.647 2.110r 8.614±0.029 8.205±0.177 -0.054 19.855 4.784 2.098i 8.349±0.027 7.960±0.169 -0.051 19.584 4.836 2.093z 8.234±0.051 7.864±0.360 -0.045 19.434 5.004 2.078J 7.139±0.059 6.784±0.186 – – – –H 6.499±0.060 6.144±0.177 – – – –K 6.320±0.063 5.965±0.122 – – – –3.6 5.891±0.005 5.536±0.044 -0.038 17.452 5.179 2.0984.5 5.857±0.006 5.487±0.053 -0.051 17.496 4.842 2.127

NGC 2541 FUV 14.669±0.001 12.686±0.004 -0.174 22.729 3.392 1.770NUV 14.343±0.001 12.502±0.007 -0.148 22.429 3.579 1.74u 15.927±0.020 14.407±0.143 -0.155 22.890 3.525 1.75g 13.296±0.006 11.968±0.057 -0.113 21.786 3.901 1.709r 12.561±0.009 11.350±0.089 -0.099 21.069 4.066 1.691i 12.312±0.015 11.243±0.300 -0.048 20.694 4.929 1.608z 12.402±0.022 11.325±0.331 -0.064 20.830 4.585 1.639J 11.299±0.042 10.41 ±0.654 – – – –H 10.677±0.102 9.788±0.653 – – – –K 10.427±0.055 9.538±0.552 – – – –3.6 9.995±0.033 9.106±0.490 -0.013 16.445 6.445 1.3944.5 9.964±0.027 9.080±0.538 -0.006 15.721 7.354 1.337

NGC 2841 FUV 13.612±0.001 12.580±0.013 -0.333 25.197 2.617 2.138NUV 12.991±0.001 12.201±0.015 -0.183 24.172 3.326 2.03u 12.453±0.022 11.784±0.258 -0.063 21.683 4.595 1.939g 10.125±0.028 9.625±0.797 -0.019 19.691 6.013 1.822r 9.267±0.025 8.801±0.792 -0.018 18.901 6.090 1.817i 8.892±0.009 8.431±0.296 -0.017 18.539 6.150 1.813z 8.585±0.019 8.148±0.586 -0.017 18.244 6.106 1.816J 7.380±0.004 6.971±0.081 – – – –H 6.666±0.008 6.257±0.081 – – – –K 6.428±0.005 6.019±0.077 – – – –3.6 6.101±0.001 5.692±0.029 -0.021 15.466 5.860 1.7764.5 6.159±0.004 5.677±0.038 -0.049 15.864 4.902 1.853

134 Chapter 3. The Multi–Wavelength Tully–Fisher relation

NGC 2976 FUV 13.115±0.001 12.612±0.022 -0.178 23.733 3.360 1.812NUV 12.734±0.001 12.417±0.046 -0.024 22.171 5.709 1.58u 12.728±0.005 12.213±0.134 -0.053 21.858 4.796 1.717g 11.049±0.004 10.478±0.099 -0.040 20.305 5.124 1.688r 10.471±0.005 9.877±0.113 -0.036 19.582 5.241 1.678i 10.130±0.006 9.526±0.172 -0.027 19.038 5.586 1.650z 9.957±0.008 9.393±0.257 -0.019 18.684 5.974 1.621J 8.789±0.006 8.303±0.09 – – – –H 8.165±0.013 7.679±0.09 – – – –K 7.931±0.012 7.445±0.085 – – – –3.6 7.521±0.002 7.035±0.018 -0.066 16.163 4.552 1.5824.5 7.453±0.010 6.989±0.106 -0.046 15.802 4.976 1.543

NGC 3031 FUV 12.339±0.001 10.376±0.068 -0.119 25.936 3.845 2.494NUV 11.619±0.001 10.013±0.116 -0.116 25.812 3.871 2.49u 10.574±0.038 9.666±0.148 -0.142 21.531 3.635 2.342g 7.807±0.027 7.262±0.198 -0.055 19.553 4.767 2.224r 7.027±0.020 6.563±0.194 -0.035 18.610 5.296 2.179i 6.434±0.010 6.006±0.099 -0.031 17.938 5.416 2.169z 6.507±0.045 5.679±0.168 -0.323 19.830 2.653 2.479J 5.080±0.008 4.686±0.073 – – – –H 4.401±0.008 4.007±0.073 – – – –K 4.137±0.008 3.743±0.068 – – – –3.6 3.766±0.002 3.372±0.026 -0.036 15.527 5.252 2.1244.5 3.827±0.004 3.423±0.039 -0.039 15.626 5.173 2.131

NGC 3109 FUV 11.711±0.002 11.115±0.220 -0.009 22.124 6.923 2.136NUV 11.408±0.010 10.825±2.391 -0.003 21.661 8.057 2.07J 9.310±0.112 8.645±0.319 – – – –H 8.972±0.155 8.307±0.36 – – – –K 8.697±0.170 8.032±0.498 – – – –3.6 8.370±0.006 7.705±0.030 -0.067 18.333 4.523 2.0434.5 8.271±0.013 7.673±0.029 -0.105 17.764 3.990 2.097

NGC 3198 FUV 13.775±0.000 12.266±0.034 -0.012 22.483 6.505 1.885NUV 13.306±0.001 11.969±0.257 -0.004 21.757 7.835 1.80u 13.763±0.010 12.849±0.166 -0.039 21.436 5.171 1.763g 11.592±0.009 10.799±0.147 -0.039 20.335 5.165 1.764r 10.986±0.008 10.311±0.188 -0.026 19.675 5.627 1.726i 10.642±0.008 10.026±0.251 -0.019 19.354 6.011 1.698z 10.430±0.010 9.835±0.247 -0.023 19.170 5.802 1.713J 9.209±0.015 8.696±0.289 – – – –H 8.479±0.037 7.966±0.267 – – – –K 8.301±0.041 7.788±0.208 – – – –3.6 7.979±0.011 7.466±0.174 -0.027 16.409 5.601 1.6494.5 7.956±0.078 7.412±0.942 -0.037 16.535 5.216 1.680

IC 2574 FUV 12.391±0.006 11.603±0.056 -0.105 24.132 3.987 2.098NUV 12.200±0.006 11.517±0.063 -0.077 23.771 4.353 2.06J 0.000±0.000 9.263±0.101 – – – –H 0.000±0.000 9.063±1.154 – – – –K 0.000±0.000 8.863±0.12 – – – –3.6 8.655±0.105 8.113±0.232 -0.214 20.272 3.143 2.1554.5 8.603±0.145 8.112±0.381 -0.164 20.190 3.460 2.114

3.C. Data tables and plots 135

NGC 3319 FUV 13.912±0.002 12.706±0.009 -0.120 22.836 3.836 1.717NUV 13.575±0.003 12.431±0.010 -0.131 22.579 3.729 1.72u 14.49 ±0.042 13.447±0.143 -0.150 22.671 3.563 1.749g 12.443±0.041 11.520±0.160 -0.142 21.829 3.633 1.740r 12.028±0.058 11.194±0.246 -0.124 21.419 3.796 1.721i 11.770±0.069 10.965±0.304 -0.125 21.226 3.783 1.723z 11.715±0.069 11.059±0.533 -0.059 20.955 4.667 1.631J 10.581±0.040 9.921±0.124 – – – –H 9.766±0.064 9.106±0.319 – – – –K 9.705±0.095 9.045±0.233 – – – –3.6 9.548±0.049 8.888±0.148 -0.091 18.169 4.163 1.6504.5 9.546±0.107 8.877±0.337 -0.069 17.874 4.494 1.616

NGC 3351 FUV 13.458±0.003 12.718±0.086 -0.010 22.403 6.696 1.651NUV 12.663±0.003 12.101±0.158 -0.006 21.570 7.370 1.60u 12.646±0.019 12.081±0.157 -0.054 21.898 4.771 1.719g 10.621±0.025 10.105±0.246 -0.041 20.385 5.111 1.689r 9.883±0.025 9.395±0.260 -0.038 19.695 5.184 1.683i 9.505±0.023 9.043±0.242 -0.037 19.334 5.237 1.678z 9.246±0.022 8.805±0.267 -0.031 19.097 5.417 1.664J 7.899±0.011 7.482±0.09 – – – –H 7.194±0.026 6.777±0.114 – – – –K 6.948±0.021 6.531±0.985 – – – –3.6 6.726±0.004 6.309±0.051 -0.030 16.552 5.470 1.6594.5 6.743±0.011 6.301±0.094 -0.045 16.664 5.002 1.698

NGC 3370 FUV 14.861±0.014 13.745±0.369 -0.028 21.771 5.558 1.334NUV 14.306±0.023 13.269±0.290 -0.057 21.539 4.725 1.40u 14.36 ±0.018 13.624±0.054 -0.184 21.019 3.320 1.323g 12.758±0.006 12.130±0.017 -0.161 20.197 3.480 1.303r 12.282±0.007 11.751±0.022 -0.133 19.707 3.711 1.275i 12.027±0.010 11.526±0.034 -0.129 19.491 3.743 1.271z 11.809±0.017 11.392±0.064 -0.098 19.191 4.073 1.235J 10.571±0.013 10.24 ±0.086 – – – –H 9.909±0.015 9.58 ±0.093 – – – –K 9.669±0.023 9.34 ±0.259 – – – –3.6 9.218±0.005 8.889±0.034 -0.050 16.487 4.880 1.1924.5 9.173±0.012 8.870±0.095 -0.036 16.290 5.260 1.159

NGC 3621 FUV 13.067±0.001 11.936±0.007 -0.080 22.110 4.318 1.841NUV 12.350±0.002 11.343±0.018 -0.065 21.382 4.562 1.81J 7.995±0.006 7.528±0.374 – – – –H 7.331±0.009 6.864±0.09 – – – –K 7.091±0.011 6.624±0.093 – – – –3.6 6.708±0.003 6.241±0.048 -0.026 15.803 5.649 1.6954.5 6.668±0.006 6.200±0.240 -0.008 15.404 6.951 1.605

136 Chapter 3. The Multi–Wavelength Tully–Fisher relation

NGC 3627 FUV 12.428±0.000 11.747±0.001 -0.378 25.412 2.469 2.250NUV 11.690±0.004 11.393±0.069 -0.070 23.753 4.471 1.99u 11.595±0.016 11.166±0.185 -0.041 21.531 5.095 1.861g 10.049±0.009 9.597±0.216 -0.021 20.167 5.896 1.797r 9.322±0.008 8.874±0.170 -0.023 19.506 5.754 1.808i 8.901±0.007 8.446±0.235 -0.013 18.835 6.448 1.758z 8.736±0.007 8.174±0.053 -0.082 19.321 4.293 1.935J 7.053±0.007 6.743±0.205 – – – –H 6.385±0.017 6.075±0.086 – – – –K 6.100±0.012 5.79 ±0.082 – – – –3.6 5.813±0.001 5.503±0.021 -0.026 15.989 5.630 1.7934.5 5.787±0.004 5.469±0.057 -0.030 16.020 5.456 1.807

NGC 4244 FUV 12.732±0.059 12.193±0.742 -0.007 20.702 7.214 2.255NUV 12.109±0.051 11.601±0.711 -0.005 19.911 7.491 2.23u 12.57 ±0.030 11.976±0.139 -0.122 22.322 3.817 2.497g 10.910±0.021 10.352±0.090 -0.119 21.187 3.841 2.494r 10.397±0.020 9.876±0.100 -0.100 20.655 4.050 2.471i 10.072±0.021 9.574±0.108 -0.091 20.309 4.158 2.460z 10.147±0.034 9.606±0.149 -0.106 20.502 3.983 2.478J 9.016±0.045 8.488±0.106 – – – –H 8.413±0.059 7.885±0.374 – – – –K 8.199±0.071 7.671±0.084 – – – –3.6 7.708±0.035 7.180±0.234 -0.051 17.618 4.843 2.4284.5 7.717±0.054 7.196±0.305 -0.057 17.624 4.723 2.439

NGC 4258 FUV 11.617±0.013 11.172±0.238 -0.000 18.148 10.787 1.870NUV 11.112±0.014 10.716±0.273 -0.000 17.810 10.762 1.87u 10.69 ±0.023 10.332±0.121 -0.022 20.497 5.811 2.110g 8.945±0.017 8.652±0.143 -0.013 19.285 6.417 2.067r 8.273±0.021 8.016±0.202 -0.009 18.476 6.824 2.041i 7.902±0.021 7.627±0.165 -0.024 19.000 5.723 2.117z 7.654±0.021 7.338±0.107 -0.056 19.270 4.744 2.198J 6.445±0.022 6.16 ±0.155 – – – –H 5.769±0.041 5.484±0.205 – – – –K 5.537±0.048 5.252±0.077 – – – –3.6 5.251±0.017 4.966±0.110 -0.063 17.596 4.595 2.2274.5 5.259±0.012 5.023±0.095 -0.037 17.289 5.215 2.172

NGC 4414 FUV 12.540±0.001 11.638±0.189 -0.017 22.181 6.124 1.666NUV 13.678±0.001 12.794±0.328 -0.011 23.084 6.656 1.63u 13.462±0.000 12.588±0.000 -0.156 22.907 3.523 1.754g 11.270±0.000 10.567±0.000 -0.078 21.230 4.340 1.663r 10.554±0.000 9.918±0.000 -0.077 20.666 4.355 1.662i 10.153±0.000 9.525±0.000 -0.092 20.427 4.151 1.682z 9.864±0.000 9.344±0.000 -0.051 19.932 4.851 1.615J 8.327±0.003 7.965±0.128 – – – –H 7.598±0.004 7.236±0.097 – – – –K 7.293±0.004 6.931±0.318 – – – –3.6 7.062±0.003 6.700±0.029 -0.030 14.906 5.469 1.3414.5 7.028±0.003 6.671±0.034 -0.028 14.810 5.560 1.334

3.C. Data tables and plots 137

NGC 4535 FUV 13.202±0.004 12.151±0.067 -0.022 21.709 5.846 1.680NUV 12.713±0.004 11.809±0.088 -0.013 21.122 6.425 1.63u 13.153±0.124 12.358±0.932 -0.018 21.235 6.047 1.616g 11.098±0.048 10.352±0.587 -0.035 20.203 5.285 1.674r 10.463±0.024 9.765±0.259 -0.042 19.717 5.085 1.691i 10.093±0.039 9.433±0.442 -0.039 19.379 5.173 1.684z 9.921±0.063 9.387±8.386 -0.002 18.159 8.677 1.459J 8.608±0.021 8.034±0.147 – – – –H 7.887±0.047 7.313±0.154 – – – –K 7.671±0.029 7.097±0.165 – – – –3.6 7.418±0.004 6.844±0.050 -0.028 16.556 5.553 1.6534.5 7.397±0.005 6.826±0.065 -0.027 16.520 5.587 1.650

NGC 4536 FUV 14.142±0.003 12.866±0.050 -0.037 22.073 5.221 1.729NUV 13.659±0.006 12.510±0.259 -0.014 21.489 6.338 1.64u 13.984±0.022 13.065±0.387 -0.049 21.924 4.897 1.708g 11.762±0.025 10.951±0.340 -0.054 20.631 4.787 1.717r 11.049±0.024 10.359±0.353 -0.045 19.995 4.994 1.699i 10.493±0.027 9.897±0.680 -0.024 19.343 5.747 1.638z 10.541±0.050 9.783±0.296 -0.122 19.915 3.815 1.816J 9.072±0.014 8.698±0.098 – – – –H 8.362±0.017 7.988±0.128 – – – –K 8.029±0.028 7.655±0.095 – – – –3.6 7.575±0.003 7.201±0.047 -0.018 16.098 6.070 1.6144.5 7.506±0.005 7.149±0.081 -0.015 15.955 6.261 1.601

NGC 4605 FUV 12.712±0.001 12.263±0.070 -0.080 24.153 4.310 1.812NUV 12.258±0.000 11.809±0.053 -0.033 22.780 5.373 1.71u 12.622±0.015 12.142±0.794 -0.001 19.836 9.711 1.347g 11.115±0.018 10.568±6.236 -0.002 18.812 8.695 1.395r 10.665±0.018 10.105±0.122 -0.003 18.375 7.976 1.432i 10.407±0.021 9.832±2.715 -0.004 18.180 7.652 1.450z 10.239±0.017 9.702±0.726 -0.004 18.302 7.647 1.450J 9.121±0.005 8.67 ±0.521 – – – –H 8.434±0.011 7.983±0.131 – – – –K 8.230±0.014 7.779±0.088 – – – –3.6 7.828±0.010 7.377±0.060 -0.055 15.647 4.763 1.4984.5 7.773±0.009 7.339±0.058 -0.048 15.541 4.908 1.485

NGC 4639 FUV 14.724±0.001 13.702±0.010 -0.138 22.683 3.665 1.435NUV 14.283±0.001 13.433±0.018 -0.073 21.958 4.429 1.35u 14.354±0.033 13.814±0.750 -0.019 20.765 5.999 1.028g 12.432±0.055 11.877±0.366 -0.101 20.289 4.039 1.199r 11.746±0.133 11.291±0.765 -0.074 19.177 4.401 1.162i 11.389±0.243 11.014±1.705 -0.029 17.919 5.520 1.064z 11.212±0.686 10.928±0.911 -0.065 18.647 4.557 1.147J 9.902±0.010 9.55 ±0.16 – – – –H 9.200±0.047 8.848±0.146 – – – –K 9.008±0.025 8.656±0.119 – – – –3.6 8.759±0.007 8.407±0.057 -0.044 16.216 5.017 1.2024.5 8.781±0.006 8.429±0.058 -0.042 16.216 5.078 1.197

138 Chapter 3. The Multi–Wavelength Tully–Fisher relation

NGC 4725 FUV 13.871±0.006 12.257±0.186 -0.125 24.554 3.779 1.966NUV 13.354±0.004 11.913±0.100 -0.131 23.944 3.727 1.97u 12.979±0.007 12.059±0.077 -0.105 22.522 3.987 1.943g 10.460±0.007 9.719±0.069 -0.083 20.964 4.269 1.913r 9.532±0.004 8.878±0.044 -0.070 20.034 4.471 1.893i 9.224±0.006 8.620±0.071 -0.060 19.696 4.649 1.876z 9.167±0.017 8.382±0.091 -0.152 19.919 3.547 1.994J 7.589±0.008 7.119±0.099 – – – –H 6.816±0.012 6.346±0.097 – – – –K 6.630±0.009 6.16 ±0.117 – – – –3.6 6.502±0.007 6.032±0.034 -0.072 16.164 4.441 1.7504.5 6.557±0.010 6.091±0.054 -0.065 16.126 4.563 1.738

NGC 5584 FUV 14.219±0.002 13.491±0.051 -0.009 20.600 6.878 1.241NUV 13.844±0.008 13.149±0.205 -0.008 20.296 6.987 1.23u 14.485±0.054 13.868±0.475 -0.000 20.140 10.647 1.051g 12.767±0.006 12.035±0.047 -0.056 20.552 4.742 1.403r 12.315±0.009 11.596±0.059 -0.065 20.265 4.557 1.420i 12.066±0.015 11.345±0.089 -0.081 20.168 4.303 1.445z 11.925±0.071 11.260±0.517 -0.061 19.974 4.645 1.412J 10.592±0.017 9.961±0.36 – – – –H 9.800±0.023 9.169±0.521 – – – –K 9.709±0.028 9.078±0.124 – – – –3.6 9.616±0.017 8.985±0.466 -0.017 17.459 6.112 1.3894.5 9.571±0.034 8.939±0.922 -0.017 17.373 6.146 1.387

NGC 7331 FUV 14.020±0.008 12.662±0.013 -0.745 24.902 1.689 2.170NUV 13.176±0.009 12.313±0.018 -0.407 23.928 2.381 2.02u 11.979±0.019 11.513±0.096 -0.069 21.648 4.497 1.824g 9.883±0.009 9.509±0.051 -0.068 20.235 4.516 1.822r 9.021±0.008 8.683±0.044 -0.071 19.575 4.462 1.827i 8.556±0.005 8.261±0.029 -0.058 19.095 4.701 1.804z 8.210±0.039 7.811±0.133 -0.135 19.213 3.690 1.910J 7.173±0.015 6.932±1.154 – – – –H 6.377±0.049 6.136±0.16 – – – –K 6.094±0.034 5.853±0.107 – – – –3.6 5.754±0.008 5.513±0.056 -0.058 16.630 4.704 1.8044.5 5.743±0.011 5.490±0.067 -0.063 16.698 4.597 1.814

NGC 7793 FUV 11.579±0.001 10.556±0.003 -0.111 21.549 3.930 1.882NUV 11.269±0.001 10.329±0.004 -0.087 21.189 4.212 1.85J 8.179±0.011 7.485±0.131 – – – –H 7.611±0.017 6.917±0.099 – – – –K 7.432±0.026 6.738±0.09 – – – –3.6 7.164±0.003 6.470±0.028 -0.033 16.379 5.373 1.7464.5 7.137±0.005 6.459±0.054 -0.023 16.124 5.791 1.714

Notes. Column(1): NGC number. Column(2): photometric band. Column(3-5):magnitude at 2.2h, total magnitude and extrapolation total magnitude beyond Rlim.Column(6): central surface brightness of the disk, corrected for inclination. Column(7):Log scale length in arcsec.

3.C. Data tables and plots 139

0 200 400 600 800 1000 1200 1400 1600

Radius (arcsec)

16

18

20

22

24

26

28

30

32

µ(mag/arcsec2

)

NGC 554.5 µm3.6 µmKsHJNUVFUV

Figure C.1

0 500 1000 1500 2000 2500

Radius (arcsec)

10

15

20

25

µ(mag

.arcsec2

)

NGC 2244.5 µm3.6 µmirgu

Figure C.2

140 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0 200 400 600 800 1000

Radius (arcsec)

15

20

25

30

µ(mag

.arcsec2

)NGC 247

4.5 µm3.6 µmKsHJNUVFUV

Figure C.3

0 200 400 600 800 1000 1200 1400

Radius (arcsec)

10

15

20

25

30

35

µ(mag

.arcsec2

)

NGC 2534.5 µm3.6 µmKsHJNUVFUV

Figure C.4

3.C. Data tables and plots 141

0 200 400 600 800 1000

Radius (arcsec)

15

20

25

30

35

µ(mag

.arcsec2

)

NGC 3004.5 µm3.6 µmKsHJNUVFUV

Figure C.5

0 50 100 150 200 250 300 350 400 450

Radius (arcsec)

16

18

20

22

24

26

28

30

µ(mag

.arcsec2

)

NGC 9254.5 µm3.6 µmKsHJNUVFUV

Figure C.6

142 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0 100 200 300 400 500

Radius (arcsec)

15

20

25

30

µ(mag

.arcsec2

)

NGC 13654.5 µm3.6 µmKsHJNUVFUV

Figure C.7

0 100 200 300 400 500

Radius (arcsec)

18

20

22

24

26

28

30

µ(mag

.arcsec2

)

NGC 23664.5 µm3.6 µmKsHJNUVFUV

Figure C.8

3.C. Data tables and plots 143

0 200 400 600 800 1000

Radius (arcsec)

15

20

25

30

35

µ(mag

.arcsec2

)

NGC 24034.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.9

0 50 100 150 200

Radius (arcsec)

18

20

22

24

26

28

µ(mag

.arcsec2

)

NGC 25414.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.10

144 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0 100 200 300 400 500 600

Radius (arcsec)

10

15

20

25

30

35

µ(mag

.arcsec2

)NGC 2841

4.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.11

0 50 100 150 200 250 300 350 400

Radius (arcsec)

16

18

20

22

24

26

28

30

32

µ(mag

.arcsec2

)

NGC 29764.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.12

3.C. Data tables and plots 145

0 200 400 600 800 1000 1200

Radius (arcsec)

10

15

20

25

30

µ(mag

.arcsec2

)

NGC 30314.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.13

0 200 400 600 800 1000

Radius (arcsec)

18

20

22

24

26

28

30

32

µ(mag

.arcsec2

)

NGC 31094.5 µm3.6 µmKsHJNUVFUV

Figure C.14

146 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0 100 200 300 400 500

Radius (arcsec)

15

20

25

30

µ(mag

.arcsec2

)NGC 3198

4.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.15

0 100 200 300 400 500 600

Radius (arcsec)

18

20

22

24

26

28

30

32

µ(mag

.arcsec2

)

IC 25744.5 µm3.6 µmKsHJNUVFUV

Figure C.16

3.C. Data tables and plots 147

0 50 100 150 200 250

Radius (arcsec)

16

18

20

22

24

26

28

30

µ(mag

.arcsec2

)

NGC 33194.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.17

0 50 100 150 200 250 300 350

Radius (arcsec)

15

20

25

30

µ(mag

.arcsec2

)

NGC 33514.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.18

148 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0 20 40 60 80 100 120 140

Radius (arcsec)

14

16

18

20

22

24

26

28

30

µ(mag

.arcsec2

)NGC 3370

4.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.19

0 50 100 150 200 250 300 350

Radius (arcsec)

12

14

16

18

20

22

24

26

28

30

µ(mag

.arcsec2

)

NGC 36214.5 µm3.6 µmKsHJNUVFUV

Figure C.20

3.C. Data tables and plots 149

0 50 100 150 200 250 300 350 400 450

Radius (arcsec)

10

15

20

25

30

µ(mag

.arcsec2

)

NGC 36274.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.21

0 200 400 600 800 1000 1200

Radius (arcsec)

16

18

20

22

24

26

28

30

32

µ(mag

.arcsec2

)

NGC 42444.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.22

150 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0 100 200 300 400 500 600 700 800 900

Radius (arcsec)

10

15

20

25

30

µ(mag

.arcsec2

)NGC 4258

4.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.23

0 50 100 150 200 250 300 350

Radius (arcsec)

10

15

20

25

30

µ(mag

.arcsec2

)

NGC 44144.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.24

3.C. Data tables and plots 151

0 50 100 150 200 250 300

Radius (arcsec)

15

20

25

30

µ(mag

.arcsec2

)

NGC 45354.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.25

0 50 100 150 200 250 300

Radius (arcsec)

10

15

20

25

30

µ(mag

.arcsec2

)

NGC 45364.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.26

152 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0 50 100 150 200 250 300

Radius (arcsec)

16

18

20

22

24

26

28

30

32

µ(mag

.arcsec2

)NGC 4605

4.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.27

0 20 40 60 80 100

Radius (arcsec)

10

15

20

25

30

µ(mag

.arcsec2

)

NGC 46394.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.28

3.C. Data tables and plots 153

0 50 100 150 200 250 300 350 400

Radius (arcsec)

10

15

20

25

30

µ(mag

.arcsec2

)

NGC 47254.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.29

0 20 40 60 80 100 120

Radius (arcsec)

16

18

20

22

24

26

28

30

32

µ(mag

.arcsec2

)

NGC 55844.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.30

154 Chapter 3. The Multi–Wavelength Tully–Fisher relation

0 50 100 150 200 250 300

Radius (arcsec)

10

15

20

25

30

µ(mag

.arcsec2

)NGC 7331

4.5 µm3.6 µmKsHJzirguNUVFUV

Figure C.31

0 50 100 150 200 250 300 350 400 450

Radius (arcsec)

15

20

25

30

µ(mag

.arcsec2

)

NGC 77934.5 µm3.6 µmKsHJNUVFUV

Figure C.32

References 155

References

Aaronson, M., Huchra, J., & Mould, J. 1979, ApJ, 229, 1Aaronson, M. & Mould, J. 1983, ApJ, 265, 1Ahn, C. P., Alexandroff, R., Allende Prieto, C., et al. 2012, ApJS, 203, 21Akritas, M. G. & Bershady, M. A. 1996, ApJ, 470, 706Begeman, K. G. 1989, A&A, 223, 47Bernstein, G. M., Guhathakurta, P., Raychaudhury, S., et al. 1994, AJ,

107, 1962Bosma, A. 1981, AJ, 86, 1791Bouquin, A. Y. K., Gil de Paz, A., Boissier, S., et al. 2015, ApJL, 800, L19Broeils, A. H. & van Woerden, H. 1994, A&AS, 107Casertano, S. & van Gorkom, J. H. 1991, AJ, 101, 1231Courteau, S., Andersen, D. R., Bershady, M. A., MacArthur, L. A., & Rix,

H.-W. 2003, ApJ, 594, 208Courtois, H. M. & Tully, R. B. 2012, ApJ, 749, 174Courtois, H. M., Tully, R. B., & Heraudeau, P. 2011, MNRAS, 415, 1935de Blok, E., Booth, R., & Frank, B. 2009, in Panoramic Radio Astronomy:

Wide-field 1-2 GHz Research on Galaxy Evolution, 7de Blok, W. J. G., Jozsa, G. I. G., Patterson, M., et al. 2014, A&A, 566,

A80de Jong, R. S. 1996, A&AS, 118, 557Fitzpatrick, E. L. 1999, PASP, 111, 63Freedman, W. L., Madore, B. F., Gibson, B. K., et al. 2001, ApJ, 553, 47Giovanelli, R., Haynes, M. P., Salzer, J. J., et al. 1994, AJ, 107, 2036Giovanelli, R., Haynes, M. P., Salzer, J. J., et al. 1995, AJ, 110, 1059Hansson, K. S. A., Lisker, T., & Grebel, E. K. 2012, MNRAS, 427, 2376Jarrett, T. H., Chester, T., Cutri, R., et al. 2000, AJ, 119, 2498Johnston, S., Bailes, M., Bartel, N., et al. 2007, PASA, 24, 174Kim, T., Gadotti, D. A., Sheth, K., et al. 2014, ApJ, 782, 64Maccio, A. V., Udrescu, S. M., Dutton, A. A., et al. 2016, MNRAS, 463,

L69Martin, D. C., Fanson, J., Schiminovich, D., et al. 2005, ApJL, 619, L1Martın-Navarro, I., Bakos, J., Trujillo, I., et al. 2012, MNRAS, 427, 1102Masters, K. L., Giovanelli, R., & Haynes, M. P. 2003, AJ, 126, 158Masters, K. L., Nichol, R., Bamford, S., et al. 2010, MNRAS, 404, 792Meidt, S. E., Schinnerer, E., Knapen, J. H., et al. 2012, ApJ, 744, 17Munoz-Mateos, J. C., Sheth, K., Gil de Paz, A., et al. 2016, ApJ, 818, 101

156 Chapter 3. The Multi–Wavelength Tully–Fisher relation

Navarro, J. F. & Steinmetz, M. 2000, ApJ, 538, 477Neill, J. D., Seibert, M., Tully, R. B., et al. 2014, ApJ, 792, 129Nemmen, R. S., Georganopoulos, M., Guiriec, S., et al. 2012, Science, 338,

1445Noordermeer, E. 2006, PhD thesis, Groningen: RijksuniversiteitNoordermeer, E., van der Hulst, J. M., Sancisi, R., Swaters, R. S., & van

Albada, T. S. 2007, MNRAS, 376, 1513Noordermeer, E. & Verheijen, M. A. W. 2007, MNRAS, 381, 1463Oh, S.-H., de Blok, W. J. G., Walter, F., Brinks, E., & Kennicutt, Jr.,

R. C. 2008, AJ, 136, 2761Papastergis, E., Adams, E. A. K., & van der Hulst, J. M. 2016, A&A, 593,

A39Peletier, R. F. & Willner, S. P. 1991, ApJ, 382, 382Pizagno, J., Prada, F., Weinberg, D. H., et al. 2007, AJ, 134, 945Ponomareva, A. A., Verheijen, M. A. W., & Bosma, A. 2016, MNRASQuerejeta, M., Meidt, S. E., Schinnerer, E., et al. 2015, ApJS, 219, 5Rizzi, L., Tully, R. B., Makarov, D., et al. 2007, ApJ, 661, 815Rubin, V. C., Burstein, D., Ford, Jr., W. K., & Thonnard, N. 1985, ApJ,

289, 81Rubin, V. C., Burstein, D., & Thonnard, N. 1980, ApJL, 242, L149Russell, D. G. 2004, ApJ, 607, 241Schaye, J., Crain, R. A., Bower, R. G., et al. 2015, MNRAS, 446, 521Schlafly, E. F. & Finkbeiner, D. P. 2011, ApJ, 737, 103Shapiro, K. L., Falcon-Barroso, J., van de Ven, G., et al. 2010, MNRAS,

402, 2140Sheth, K., Regan, M., Hinz, J. L., et al. 2010, PASP, 122, 1397Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163Sorce, J. G., Courtois, H. M., & Tully, R. B. 2012, AJ, 144, 133Sorce, J. G., Courtois, H. M., Tully, R. B., et al. 2013, ApJ, 765, 94Sorce, J. G. & Guo, Q. 2016, MNRAS, 458, 2667Spekkens, K. & Giovanelli, R. 2006, AJ, 132, 1426Swaters, R. A., Sancisi, R., van Albada, T. S., & van der Hulst, J. M. 2009,

A&A, 493, 871Swaters, R. A., van Albada, T. S., van der Hulst, J. M., & Sancisi, R. 2002,

A&A, 390, 829Tully, R. B. & Courtois, H. M. 2012, ApJ, 749, 78Tully, R. B. & Fisher, J. R. 1977, A&A, 54, 661Tully, R. B., Mould, J. R., & Aaronson, M. 1982, ApJ, 257, 527

References 157

Tully, R. B. & Pierce, M. J. 2000, ApJ, 533, 744Tully, R. B., Pierce, M. J., Huang, J.-S., et al. 1998, AJ, 115, 2264Tully, R. B., Verheijen, M. A. W., Pierce, M. J., Huang, J.-S., & Wainscoat,

R. J. 1996, AJ, 112, 2471van Albada, T. S., Bahcall, J. N., Begeman, K., & Sancisi, R. 1985, ApJ,

295, 305Verheijen, M. A. W. 2001, ApJ, 563, 694Verheijen, M. A. W., Oosterloo, T. A., van Cappellen, W. A., et al.

2008, in American Institute of Physics Conference Series, Vol. 1035,The Evolution of Galaxies Through the Neutral Hydrogen Window, ed.R. Minchin & E. Momjian, 265–271

Verheijen, M. A. W. & Sancisi, R. 2001, A&A, 370, 765Vogelsberger, M., Genel, S., Springel, V., et al. 2014, MNRAS, 444, 1518Weiner, B. J., Sellwood, J. A., & Williams, T. B. 2001, ApJ, 546, 931Werner, M. W., Roellig, T. L., Low, F. J., et al. 2004, ApJS, 154, 1Willick, J. A. 1994, ApJS, 92, 1