Submittedto ApJ Letters PreprinttypesetusingLATEXstyleemulateapjv.5/2/11 REVEALING VELOCITY DISPERSION AS THE BEST INDICATOR OF A GALAXY’S COLOR, COMPARED TO STELLAR MASS, SURFACE MASS DENSITY OR MORPHOLOGY David. A. Wake1, Pieter G. van Dokkum1 Marijn Franx2, Submitted to ApJ Letters ABSTRACT UsingdataofnearbygalaxiesfromtheSloanDigitalSkySurveyweinvestigatewhetherstellarmass 2 (M ), central velocity dispersion (σ), surface mass density (Σ), or the Sersic n parameter is best 1 star correlatedwith a galaxy’srest-frame color. Specifically, we determine how the mean color of galaxies 0 2 varieswithoneparameterwhenanotherisfixed. WhenMstar isfixedweseethatstrongtrendsremain with all other parameters, whereas residual trends are weaker when Σ, n, or σ are fixed. Overall σ n is the best indicator of a galaxy’s typical color, showing the largest residual color dependence when a any of the other three parameters are fixed, and M is the poorest. Other studies have indicated J star that both the halo and black hole properties are better correlated with σ than with Mstar, Σ or n. 4 Therefore,ourresultsareconsistentwithapicturewhereagalaxy’sstarformationhistoryandpresent 2 star formation rate are determined to some significantdegree by the currentproperties and assembly history of its dark matter halo and/or the feedback from its central super massive black hole. ] O Subject headings: galaxies: fundamental parameters — galaxies: formation — galaxies: kinematics and dynamics — galaxies: statistics C . h p 1. INTRODUCTION Bell 2008; Wuyts et al. 2011; van Dokkum et al. 2011; - It is well established that the stellar populations Bell et al. 2011). o Although it seems clear that the correlation between of galaxies in the nearby Universe correlate with r color and mass is weaker than the correlations between t their luminosities and masses, such that the stars in s color and Σ, σ, or n, it is not clear which of these pa- more massive galaxies are on average older and more a rameters is the best predictor of a galaxy’s color. This [ metal-rich(e.g., Bower et al. 1992; Blanton et al. 2003a; Kauffmann et al. 2003). The old ages of the most lu- is important to establish as it provides information on 1 minous galaxies are somewhat puzzling, as it implies the physical processes that govern galaxy evolution. As v thattheremustbesomemechanismresponsibleforshut- an example, if n best correlates with color (as suggested 8 byBell et al.2011)itmayimplythatthemergerhistory tingofftheirstarformation(e.g.,Kauffmann & Haehnelt 9 determinesthestarformationhistory,whereasifσ isthe 2000; Croton et al. 2006; Naab et al. 2007; Kereˇs et al. 9 key parameter it would suggest that the star formation 2005). Another puzzle is that the correlation between 4 history is influenced (or even determined) by the dark star formation history and mass is complex: low mass . matter halo or the central supermassive black hole. 1 galaxiesaretypicallyyoungerandhighmassgalaxiesare 0 typicallyolder,withabimodaltransitionregionat∼3× InthisLetterweinvestigatewhichofthefourparame- 2 1010M⊙ (Kauffmann et al. 2003). This bimodality and ters Mstar, Σ, σ, or n is most closely correlated with the 1 the associated transition mass scale have been the sub- star formation history, as parameterized by the color. : jectofintensedebateinthepastyears(e.g.,Bundy et al. We determine this by fixing each parameter in turn and v measuringtowhatextentthecolordependsontheother i 2006; Peng et al. 2010; Brammer et al. 2011). X An intriguing possibility is that luminosity and mass three parameters. The homogeneous, large datasets re- quired for this study are now available from the 7th r arenotthe“right”parameterstointerpretgalaxyevolu- a tion, and that there exist other parameters that show datareleaseoftheSloanDigitalSkySurvey(SDSSDR7; Abazajian et al. 2009). more straightforward correlations with stellar popula- tion parameters. As demonstrated by Kauffmann et al. 2. DATA (2003,2006),thestarformationhistoriesofgalaxiesshow Thegalaxydatausedinthisanalysisaregatheredfrom less scatter when the structure of galaxies is taken into the seventh data release of the SDSS (Abazajian et al. account. Inparticular,the agesandstarformationrates 2009). We begin with the Large Scale Structure sam- of galaxies are better correlated with their surface den- ples of the DR7 NYU Value Added Galaxy catalogue sities Σ (which is proportional to M∗/re2 with re the (VAGC Blanton et al. 2005). The sample we use has size of the galaxy) than with mass alone. Franx et al. an r band magnitude range of 14.5 < r < 17.6. In (2008)findthatthestrongcorrelationbetweencolorand addition the NYU VAGC gives k-corrected (to z=0.1) M∗/re2 (and M∗/re) persists all the way to z ∼ 2. Sim- absolutemagnitudes(Blanton et al.2003a),velocitydis- ilar trends have been found for velocity dispersion and persion measurements from the Princeton Spectroscopic for the Sersic (1968) index n (e.g., Blanton et al. 2003a; pipeline, andcircularizedsersicfits for eachgalaxyallof 1DepartmentofAstronomy,YaleUniversity,NewHaven,CT which we make use of in this analysis. For estimates of the stellar mass we make use of the 06520 2SterrewachtLeiden,LeidenUniversity,NL-2300RALeiden, MPA/JHUDR7valueaddedcatalogwhichprovidesstel- TheNetherlands. larmassestimates basedonstellarpopulationfits to the 2 Wake et al. tion of each parameter. We have applied to this figure (and all subsequent figures) a V/Vmax weight for each galaxy to correct for the varying stellar mass complete- ness limit with redshift. We plot the color distributions as a function of log(M ), log(Σ), log(σ2) and log(n2). star We have chosen these units as they are all approxi- mately linearly proportional to one an other. This is illustrated in Figure 2 were we show the relationships between these four parameters. The contours show the full distributions and the points show the mean of y in bins of x (black) and y in bins of x (red). Whilst we may expect Σ and σ2 to be approximately linearly pro- portionalto M andeachother,we findthat n2 shows star the same trends overa broadrangein those parameters. Therefore we can meaningfully compare the predictive power of n2 to that of the other three parameters. Figure 1 shows that there is a clear color dependence on each parameter but with significant scatter. It also illustrates,ashasbeenpreviouslyfound(e.g.,Kauffmann et al. 2003),that M is a relatively poor discriminator star of a galaxy’s color, particularly around the “transition mass” of ∼ 3×1010M⊙. It is important to note that distributions become noisy at both low M and low star σ. The number of galaxies becomes increasing small at low masses, due to the apparent magnitude limit of the SDSS, which also strongly affects the sample at low σ duetothe tightcorrelationbetweenthe twoparameters. Figure 1. Theu−rcolordistributionasafunctionofMstar, σ measurements also become more uncertain below 65 σ2, Σ and n2, for SDSSDR7 galaxies with 0.04<z<0.113. km/s due to the resolution of the SDSS spectra. For Theu−r color is positively correlated with all four parame- these reasons we limit the remainder of the analysis to tneerasr.MThstearc∼or3re×lat1i0o1n0wMit⊙h.MTshtaerdhoatsteladrglienescsasthtoerw,pthareticcuutlsarwlye gaWlaxeieaslswoirtehmMovsetared>ge10o1n0Mdis⊙kagnadlaxσie>sf6r5omkmo/usr.sample apply in Mstar and σ to defineourprimary sample. to minimize the influence of dust on our measurements SDSS photometry (Kauffmann et al. 2003; Salim et al. (e.g.,Patel et al.2011),althoughweexpectthedustcon- 2007). The overlap between the MPA/JHU and NYU tribution to be low in the local universe. We make a cut VAGs is close to but to quite 100% and so we remove using the Galaxy Zoo P parameter limiting it to be edge the regions where they do not match from the analysis. < 0.3. We note that this cut changes our results very Wealsoremoveanyregionofthesurveythathasaspec- little and has no effect on any of our conclusions. troscopic completeness less than 70%. This leaves an areaof7640deg2 anda totalsampleof521,313galaxies. 4. WHICHPARAMETERCORRELATESBESTWITH COLOR? The SDSS velocity dispersions are measured within the 3” diameter SDSS fiber. We correct to a com- In order to determine which parameter shows the mon aperture of one eighth of an effective radius (r ), strongest correlation with color we determine whether e the central velocity dispersion, using the relation σ0 = thereremainsanycolordependenceonMstar,Σ,σ,andn σ (8r /r )0.066 where r = 1.”5 (Cappellari et al. wheneachofthese parametersareheld fixed. We divide ap ap e ap 2006). re istakenfromthebestfittingcircularizedSersic ourparentsample(0.02<z < 0.11,Mstar >1010M⊙, σ profile fit. > 65km/s, Pedge < 0.3)into a seriesofsamples selected Throughout we use u−r color from the K-corrected tohavenarrowrangesineachparameter. Weselectbins NYU VAGC absolute magnitudes. As already stated of 0.05 in log(Mstar) and log(Σ), 0.025 in log(σ) and 0.2 these are corrected to z = 0.1; although they are not in n. We then calculate the mean u−r color of galaxies quite u−r at rest we will refer to them as u−r col- in each of these narrow binned samples as of function of ors. We also make use of the morphological classifica- theotherthreeparameters,wherethemeaniscalculated tions from Galaxy Zoo (Lintott et al. 2011) which pro- in bins of 300 galaxies. videsmultiplevisualclassificationsforeachgalaxyinthe SDSSspectroscopicsample. Theparameterweuseisthe 4.1. Residual Correlations probability that a galaxy is an edge on disk (Pedge) (see We show the resulting relationships between mean Lintott et al. 2011, for details). colorandM ,Σ,nandσ inFigures3and4. Eachrow star showsapairofparameterswiththebinningandabscissa 3. DEPENDENCEOFCOLORONMstar,σ,Σ,ANDN parameter switched. That is, in each row the left panel We wish to understand how the typical color of a shows the effect of varying parameter 1 at fixed param- galaxy depends on its stellar mass, central velocity dis- eter 2, and the right panel shows the effect of varying persion, surface mass density, and Sersic profile. We be- parameter 2 at fixed parameter 1. The left and right gininFigure1 wereweshowthe u−r colordistribution panel therefore essentially show the same information, for all SDSS galaxies with 0.02 < z < 0.11 as a func- but highly the trends in a complimentary way. If the 3 Figure 2. TherelationshipsbetweenMstar,Σ,σ2andn2forallSDSSDR7galaxieswith0.02<z <0.11. GalaxiesareV/Vmax weighted to correct for the redshift dependent stellar mass completeness limit. The black points show the mean of y in bins of x containing 500 galaxies, where as the red points show the mean of x in bins of y. We can see that over a significant range of each parameter they are all approximately linearly proportional to oneanother. trends of all of the binned samples lie on top of each ThebottompanelsofFigure3concernΣandn. Atlow other in any of the plots it would mean that the color n there is a very strong relationship between color and wouldbe independent ofthe parameterusedforthe bin- ΣwithhigherΣgalaxiesbeingredder. Whilstthistrend ning. Similarly,iftheabscissaparameterisunimportant remains for all n the slope of this correlation reduces as each of the individual binned trends will be flat. n increases. There is a similar dependence of color on n Turning to the first pair of parameters at the top of at fixed Σ, although the relation becomes very weak at Figure 3, Σ and M , we can see something close to the highest Σ. star this extreme situation. When M is held fixed (left In Figure 4 we show how the color depends on σ at star panel) there remains a clear trend with Σ, such that fixed M , Σ, and n on the left and how color depends star higher Σ galaxies are redder. The trend is particularly on M , Σ, and n at fixed σ on the right. It is striking star strong at low M and gradually decreases at the high- howtightallofthe trends areinthe left panels andhow star est masses, resulting in some spread but a generally low separated they are in the right panels. This indicates dispersion between the M bins. The same trend is that the mean galaxy color is more strongly dependent star visible when Σ is held fixed; there is only a very weak on σ than M , Σ or n. This is particularly true at star dependenceofmeanu−r coloronM withmoremas- σ(>200km/s)whereallthetrendsliealmostcompletely star sive galaxies being redder. The individual Σ bins are on top of each other on the left and are very close to well separated, showing the strong color dependence on flat on the right. At lower σ interesting trends emerge; Σ, and are generally parallel. It appears that Σ is a perhaps surprisingly the mean color becomes bluer as better indicator of a galaxy’s color than its stellar mass M increases,withthistrendincreasingasσdecreases. star is. This probably reflects an increasing disk component in We next consider M and n, shown in the middle moremassive galaxiesatfixed σ. At low σ (<175km/s) star panelofFigure3. Forlown(<2.5)thereisastrongde- a trend emerges with Σ such that galaxies with higher pendence of the color on n at fixed M , but for higher Σatfixedσ havereddercolors,withthetrendbecoming star nthetrendswithM areallthesamewithnondepen- more significant as σ decreases. There is also a trend star dence. Atallnthereisatrendformoremassivegalaxies with n when n < 2.5 such that galaxies with higher n to be redder on average, although this is very weak for are redder. There is no color dependence on n at fixed galaxies with log(M ) < 11. Again M appears a σ for higher n galaxies. Whilst some trends with M , star star star poorerindicatorofagalaxiescolorthann,althoughthis Σ and n emerge in some regions of the parameter space is less true at high n or high M . thereisalwaysastrongdependenceofthemeancoloron star 4 Wake et al. Figure 3. The relationship between mean u−r color and mass surface density at fixed stellar mass (top left), stellar mass at fixed mass surface density (top right), stellar mass at fixed sersic n (middle left), sersic n at fixed stellar mass (middle right), mass surface density at fixed sersic n (bottom left) and sersic n at fixed mass surface density (bottom right). 5 Figure 4. The relationship between mean u−r color and velocity dispersion at fixed stellar mass (top left), stellar mass at fixed velocity dispersion (top right), velocity dispersion at fixed mass surface density (middle left) and mass surface density at fixedvelocity dispersion (middle right),velocity dispersion at fixedsersic n (bottom left) and sersic at fixedvelocity dispersion (bottom right). 6 Wake et al. σ over the full range of the other parameters. Bell et al. 2011), call into question whether “mass quenching” (e.g., Peng et al. 2010) and other mass- 4.2. Quantifying the Residual Correlations driven effects are actually manifestations of underlying We show in Figure 5 an attempt to both simplify and trends with velocity dispersion. The velocity dispersion quantify the trends that are displayed in Figures 3 and may in turn reflect a yet more fundamental parameter. 4. In narrow bins of one parameter we calculate the dif- It is known to correlate well with central black hole ference in the mean u−r color of the galaxies lying in mass (e.g., Ferrarese & Merritt 2000; Gebhardt et al. the lowest and highest 10 percentiles of the other three 2000) and also with the properties of dark matter halos parameters. Since the size of the range of the second (Wake et al. 2012). Taken together, all these results parameter may vary with the first and between the dif- suggest a simple scenario where the mass of the dark ferent parameters we calculate this color difference per matter halodetermines both the centralblack hole mass unit log(M ), log(Σ), log(σ2) and log(n2). For exam- and the star formation history of galaxies. star ple the blue points in the top left panel of 5 show the This study can be extended and improved in many difference between the mean u−r color of galaxies with ways. The dispersions are currently corrected to a com- the 10% highest Σ and 10% lowest Σ per unit log(Σ) in monaperturewithreasonableassumptions,butitwould narrow bins of σ. This is essentially the vertical scatter beveryusefultomeasureradialtrendsindispersionina in the center left panel ofFigure 4 or the gradientof the systematicway. Thisisparticularlyrelevantforlowmass individual trends in the center right panel. galaxies and star forming galaxies, as they have signif- The color gradients shown in Figure 5 reinforce the icant disks which presumably dominate at large radii. conclusions we have already drawn. When σ is fixed Blue disks may well be the cause of the peculiar fact (top left panel) the magnitude of the color gradient is that, at low σ, more massive galaxies are bluer at fixed always less than 0.5, showing that there is only a weak dispersion(seeFig.4). Modelingofthe effectsofvarious dependenceofcoloronM ,Σornatconstantσ. This physicalprocesses (such as merging)on the velocity dis- star is particularly true at high σ (> 200 km/s) where the persion may help us understand why velocity dispersion gradient is essentially zero for both Σ and n. When the is so well correlated with many aspects of galaxies. One other three parameters are held fixed the color gradient possibilityisthatσ maywellbeindicatingboththehalo with σ is always the largest and is greater than 0.5 re- mass(orotherhaloproperties),inasimilarormorepre- gardless of the values of the other parameters. Clearly cise manner than Mstar (Wake et al. 2012), and at the there is a significantly larger dependence of the color of same time be an indicator of the relative bulge to disk galaxies on σ than on Mstar, Σ or n. components. So at fixed Mstar a higher σ galaxy has a Figure 5 again confirms the negative color gradients larger bulge to disk ratio and so is redder, whereas at with M at low σ (red points in top left panel), such fixedn a higherσ galaxytypically occupiesa more mas- star thatmoremassivegalaxiesarebluerwhenσ isfixed. We sive dark matter halo and so is also redder. σ is then also see negative color gradients with n for the highest the best of the four parameters at encapsulating both Σ galaxies. Otherwise it is always the case that galaxies colordependences (halo massandbulge to diskratio)as with higher Mstar or n are redder, and always the case illustrated by the tightness of the σ - Mstar and σ - n that galaxies with higher σ or Σ are redder when the relations shown in Figure 2. other parameters are fixed. Finally, it would be very interesting to do similar sys- tematicstudiesatearliercosmicepochs,extendingthose 5. DISCUSSION pioneered by Franx et al. (2008) and Bezanson et al. The central result of this paper is that the colors of (2011), which will give further insight into the physical galaxiesdepend more stronglyonσ than onM , Σ, or parameters which drive galaxy formation and evolution. star n. We have demonstrated this by examining, for eachof these parameters, how strong residual correlations with REFERENCES theotherthreeparametersarewhentheparameterunder consideration is held fixed. 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