The evolution of the scatter of the cosmic average color-magnitude relation: Demonstrating consistency with the ongoing formation of elliptical galaxies

0.7 MB·English

by  Christine Ruhland

ASTROPHYSICALJOURNALINPRESS: JANUARY27,2009
PreprinttypesetusingLATEXstyleemulateapjv.26/01/00
THEEVOLUTIONOFTHESCATTEROFTHECOSMICAVERAGECOLOR-MAGNITUDERELATION:
DEMONSTRATINGCONSISTENCYWITHTHEONGOINGFORMATIONOFELLIPTICALGALAXIES
CHRISTINERUHLAND1,ERICF.BELL1,BORISHÄUSSLER1,2,EDWARDN.TAYLOR3,MARCOBARDEN1,4,
DANIELH.MCINTOSH5,6
1Max-Planck-InstitutfürAstronomie,Königstuhl17,D-69117Heidelberg,Germany;[email protected]
2UniversityofNottingham,NottinghamNG72RDUnitedKingdom
3SterrewachtLeiden,LeidenUniversity,P.O.Box9513,NL-2300RALeiden
4InstitutfürAstro-undTeilchenphysik,UniversitätInnsbruck,Technikerstraße25/B,A-6020Innsbruck
5AstronomyDepartment,UniversityofMassachusetts,Amherst,MA01003USA
9 6DepartmentofPhysics,UniversityofMissouri-KansasCity,KansasCity,MO64110USA
0
ASTROPHYSICALJOURNALINPRESS: January27,2009
0
2 ABSTRACT

n We presentfirst measurementsof the evolution of the scatter of the cosmic averageearly-typegalaxy color–
a magnituderelation(CMR)fromz=1tothepresentday,findingthatitisconsistentwithmodelsinwhichgalaxies
J
are constantlybeingaddedto the red sequencethroughtruncationof star formationin blue cloudgalaxies. We

8 used a sample of over 700 red sequence, structurally-selected early-typegalaxies(defined to have Sérsic index
2
>2.5)withredshifts0<z<1takenfromtheExtendedChandraDeepFieldSouth(173galaxies)andtheSloan
DigitalSkySurvey(550galaxies),constructingrest-frameU- V colorsaccurateto<0.04mag. Wefindthatthe
]
O scatteroftheCMRofcosmicaverageearly-typegalaxiesis∼0.1maginrest-frameU- V colorat0.05<z<0.75,
andsomewhathigheratz=1. Wecomparedtheseobservationswithamodelinwhichnewredsequencegalaxies
C
are being constantlyaddedatthe rate requiredto match the observednumberdensityevolution, andfoundthat
.
h this model predicts the correct CMR scatter and its evolution. Furthermore, this model predicts approximately
p thecorrectnumberdensityof‘bluespheroids’—structurallyearly-typegalaxieswithbluecolors—albeitwith
- considerable model dependence. Thus, we conclude that both the evolution of the number density and colors
o
of the early-type galaxy population paint a consistent picture in which the early-type galaxy population grows
r
t significantlybetweenz=1andthepresentdaythroughthequenchingofstarformationinbluecloudgalaxies.
s
a Subjectheadings:galaxies:evolution—galaxies:general—galaxies:ellipticalandlenticular—galaxies:
[
stellarcontent—surveys

1
v 1. INTRODUCTION red sequence galaxy population (i.e., averaged over all envi-
0 ronments)buildsupinstellar massbyroughlyafactoroftwo
4 One of the best-knownand most powerfulscaling relations
overtheintervalz=1toz=0throughtheadditionofnewred
3 oftheearly-type(ellipticalandlenticular)galaxypopulationis
sequencegalaxies(Chenetal.2003;Belletal.2004b;Cimatti
4 the systematic reddeningof their colors with increasing lumi-
2006;Brownetal.2006a;Faberetal.2007;Scarlataetal.2007,
. nosity: thecolor–magnituderelation(CMR). Theslope of the
1 although some of the papers argue for a build-up in stellar
CMR is driven by a correlation between metallicity and mass
90 (Faber&Jackson1976;Kodama&Arimoto1997;Terlevichetal. mass only in galaxies with .1011M⊙). These ‘new’ red se-
quence galaxies are the result of truncation of star forma-
0 1999;Trageretal.2000;Gallazzietal.2006),whilethescatter
tion in some fraction of the blue cloud population (Belletal.
: isdeterminedbyscatterinbothageandmetallicity,whereitis
v 2007) through,e.g., galaxy-galaxymerging(Belletal. 2004b;
generallythoughtthatageisthedominantdriver(Boweretal.
i Faberetal. 2007; Hopkinsetal. 2007) or environmental pro-
X 1992;Trageretal.2000;Gallazzietal.2006,althoughTrageretal.
cesses such as strangulation or ram-pressure stripping (e.g.,
r 2000arguethatananticorrelationbetweenageandmetallicity
Kodama&Smail2001).
a keepsthescatteroftheearly-typegalaxyscalingrelationsrel-
Such a scenario makes strong predictions about what the
atively modest while allowing significant scatter in both age
scatteroftheCMRanditsevolutionshouldbeasafunctionof
and metallicity). The scatter in this correlation is relatively
redshift(vanDokkum&Franx2001); tofirstorderthe scatter
small(Baum1962;Visvanathan&Sandage1977;Boweretal.
isexpectedtobeconstantwithredshift.Theobjectofthispaper
1992; Terlevichetal. 2001; McIntoshetal. 2005b). Because
is to quantitativelytest this picture. We carefullymeasure the
thecolorofstellarpopulationsisstronglyaffectedbytheirages
CMRevolutionofgalaxiesselectedtohaveconcentratedlight
and metallicities (Worthey 1994), this correlation is a power-
profiles and red colors — taken as a proxy for the early-type
fulprobeofthe formationandevolutionofthe stellar popula-
galaxy population— from z=1 to the present day, and com-
tions in early-type galaxies. The small intrinsic scatter found
pare it to a toy modelof a growingred sequence. We use the
in some clusters (as little as σU- V = 0.04mag in Virgo and SDSSforthelow-redshiftCMRmeasurement,andasampleof
Coma;Boweretal.1992;Terlevichetal.2001;althoughother
galaxieswith spectroscopicredshiftsandaccurateHST colors
clusterscanhavescattersapproaching0.1mag;McIntoshetal.
fromtheextendedChandraDeepFieldSouth(CDFShereafter)
2005b) gaveconsiderablemomentumto the notionthatearly-
toprobetheCMRouttoz=1. Asitwasaprioriunclearhow
type galaxiesformedthe bulk of their stars at early times and
largetheCMRscattershouldhavebeen,weadoptedaconser-
thattheirstellarpopulationshaveagedessentiallypassivelyto
vativeapproachthatoptimizedrest-framecoloraccuracyatthe
thepresentday.
expense of sample size, choosing galaxies with spectroscopic
In the last few years, this position has been challenged by
redshifts and within relatively narrow redshift slices (to mini-
evidence from deep redshift surveys that the cosmic average
1
2 Ruhlandetal.
For this investigation, a sample of objects with reliable spec-
troscopicredshiftswascollectedfromavarietyofsources. In-
secureoruncertainspectroscopicredshiftswerecross-checked
withphotometricredshiftsfromtheCOMBO-173survey.The
spectroscopic selection criteria are described in the appendix
andresultinafinalsampleof3440galaxieswithspectroscopic
redshifts. We used3030galaxiesinwhatfollows;theremain-
ing 410 objects could not be used either because they lacked
datainoneormoreoftheHSTbands(211galaxies),orbecause
theobjecthadahalf-lightradiussmallerthan2pixels(204ob-
jects and5 objectssatisfied bothcriteria). Figure1 showsthe
redshiftdistributionofthe3030useableobjects.Wechoosethe
threebestpopulatedredshiftbinsofwidth∆z=0.1atz∼0.55,
0.7and1.0forouranalysis.Wemadethisselectionfortworea-
sons. Firstly,thebinshavetobequitenarrowtominimizethe
contributionofk-correction(thewavelengthrangeoverwhich
the interpolationmust be done)uncertaintiesto the final error
budget. Second,thebestpopulatedredshiftshadtobeusedin
ordertoobtainsufficientlypopulatedCMDsforderivingCMR
properties. InFigure1theseredshiftintervalsareindicatedby
theshadedareas.
Forfurtheranalysis,werejectedknownIRandX-raysources4.
FIG. 1.— The distribution of the spectroscopic redshift samples for the
intermediate-redshiftrange. Weusedgalaxieswithredshiftsaround0.55,0.7 IRsourceswereidentifiedbycomparisonwithMIPS24µmob-
and1.0asindicatedbytheshadedareas,inordertominimizethecontribution servationsoftheCDFSfromSpitzer(Papovichetal.2004).We
ofk-correctionuncertaintiestotheCMRscatter. use the 24µm band owing to its high sensitivity to obscured
starformationandAGNactivity. The80%completenesslimit
is 83µJy, corresponding to approximate obscured SFR limits
mize k-correction uncertainties) and with color HST imaging of(5, 10, 17)M yr- 1 atredshiftsof 0.55,0.7and1.0 respec-
(tominimizecolormeasurementerror). Thedataaredescribed ⊙
tively (Belletal. 2007) using a Kroupa (2001) IMF. We fur-
in§2. Wedescribethek-correctionsandtheiruncertaintiesfor
therexcludedgalaxiesdetectedindeepChandraimagingofthe
the intermediate redshift sample in §3. We present our mea-
CDFS.Thecoverageisnon-uniform,withanexposuretimeof
surements of the intercepts and scatter of the CMR for color
1Msinthecentralpointing,and250ksperpointingineachof4
and structurally selected samples as a function of redshift in
flankingfields. Thesedepthsaresufficienttodetectmoderate-
§ti4o.nImno§d5e,lswoefcinocmrepaasriengthceoombpsleerxvietdy,rfiensuallltys tcoomsteplalrairngpoitputolaa- luminosity AGNs (L0.5- 2keV = 1041- 1042 ergs s- 1) over the
wholeredshiftrangeofinterest(Lehmeretal.2005).
model for the growth of the red sequence through the trunca-
tion of star formation in blue cloud galaxies. We present our 2.1.1. ColorsandmagnitudesfromGEMSImages
conclusions in §6. The casual reader may wish to skip to §5
As the goal of this paper was to measure the scatter of the
directly. In what follows, we assume Ωm,0 =0.3, ΩΛ,0 =0.7, CMR as accurately as possible, we use high accuracy HST
andH =70kms- 1Mpc- 1andauniversally-applicableKroupa
0 colors for the construction of the CMR. For all objects with
(2001)stellarIMFforstellarpopulationmodeling.
spectroscopicredshiftsweusedGEMSpostagestampstomea-
sureaccuratemagnitudesintheF606WandF850LPpassbands.
2. DATA
We used the GALAPAGOS5 software package to cut postage
We use data from two differentsources, depending on red- stamps around the position of each object. Galaxy properties
shift. For galaxies with 0.5<z<1, we choose to determine were adopted from a single-component Sérsic model (Sérsic
accuratecolorsforgalaxieswithspectroscopicredshiftsinthe 1968) fit to the 2-D galaxy luminosity profile using the pack-
HST/GEMS survey of the CDFS. This is crucial for minimiz- age GALFIT (Pengetal. 2002). We estimate colors within
ingthecolormeasurementerror,placingthestrongestpossible the observed half-light radius (not the intrinsic half-light ra-
constraintsontheintrinsicscatteroftheCMR.Tocomplement dius r returned from fits to the light profile); such ob-
e,GALFIT
this dataset at low redshift, we use a sample drawn from the servedhalf-lightradiiaresubstantiallylargerthantheintrinsic
SDSSatz=0.05. half-light radii for compact galaxies. We determined the ob-
served half-lightradiusby performingaperture photometryin
2.1. Intermediateredshiftdata ellipses with the position angle and axis ratio given by GAL-
Fortheintermediateredshiftrange,uptoz=1,weusedata FIT, out to 10re,GALFIT on the F850LP-band image. The to-
takenintheExtendedChandraDeepFieldSouth(E-CDFS).A tal magnitude was defined as the aperture magnitude within
key ingredient is color HST imaging, taken from the GEMS1 10re,GALFIT. Theobservedhalf-lightradiuswasthendefinedto
and GOODS2 surveys. Thesedatawereusedtoestimateaccu- 3Classifying Objects by Medium-Band Observations in 17 Filters
rate galaxy colors within the half-light radius, and for selec- (Wolfetal.2003,2004)
tion bygalaxystructure. A secondkeyingredient,requiredto 4LeavinginIRandX-raysourcesgivessimilarresults;weconservatively
makeprecisek-corrections,isaccurateredshiftmeasurements. removesuchsourcesinordertominimizethecontributionofyoungstarsand
non-stellarlighttotheCMRscatter.
1GalaxyEvolutionfromMorphologyandSEDs(Rixetal.2004) 5GalaxyAnalysisoverLargeAreas:ParameterAssessmentbyGALFITting
2GreatObservatoriesOriginsDeepSurvey(Giavaliscoetal.2004) ObjectsfromSExtractor(M.Bardenetal.inpreparation)
EvolutionofEarly-typegalaxies 3
FIG. 2.—TheobservedF606W- F850LPcolorwithinthehalflightradius FIG. 3.—Anassessmentofthek-correctionuncertaintiesthroughcompar-
plottedasafunctionofredshift. Theredsequenceandbluecloudareclearly isonoftheobservedF775Wmagnitudeofthosesamplegalaxiesthatoverlap
visible. Thecutbetween thetwopopulations is schematically indicated by withtheGOODSfieldandtheF775WmagnitudepredictedusingInterRestus-
thedashedline(thiscutisonlyforillustrationpurposesandnotusedinwhat ingonlytheredshift,F606WandF850LPmagnitudesasinput.Inthisplotwe
followsforanyanalysis;theactualredshiftandmagnitude-dependentcutsare showthedifferencebetweenmeasuredandcalculatedmagnitudeinF775Was
giveninSec. 4.1).Thegrayshadedareasshowthethreeredshiftrangesused afunctionofredshift.ThediamondsymbolsindicateredobjectswithaSérsic
inthispaper. indexn>2.5.Theoutlieratz∼0.1isacompositemergingsystemwithboth
adust-reddenedandabluecomponent;suchacompositesystemistoocom-
plicatedtobedescribedbythesimpletemplatesusedhere. Thelongdashed
lineshowsthemeanofthesevaluesandtheshortdashedlinesshowtheRMS
bethesemi-majoraxisoftheellipsewithinwhichhalfoftheto- areaaroundthemeanvalue(bothvaluesarearound0.03). Therandomerror
tallightinF850LPwascontained. Inordertodetermineaccu- servesasanapproximationofthek-correctionuncertainty.
rateF606W- F850LPcolors,theF606W-imagewasconvolved
withadifferencePSF,determinedfromthePSFs(Jahnkeetal.
2004)inF606WandF850LP(thePSFcorrectionwasaccurate samemethodweusefortheintermediateredshiftdata;seeSec-
towithin1partinamillionintermsoftotalfluxonapixel-by- tion3).Rest-framemagnitudeswerecalculatedbyk-correcting
pixelbasis;seeHäußler2007section4.2.2fordetails),andthe Sérsic modelmagnitudes(Blantonetal. 2003) from the NYU
flux in F606W within the F850LP half-lightellipse was mea- VAGC;suchmagnitudesareclosertothetotalmagnitudesthan
sured. Figure 2 shows the distribution of the measuredcolors PetrosianorModelmagnitudes.Theformalrandomerrorinthe
against redshift. Uncertainties in the measured fluxes include finalU- V coloris<0.02magfromphotometricerror,withan
contributionsfromPoissonuncertainty,readnoise, anduncer- estimated calibrationerrorof <0.04mag(assuming0.01mag
tainty from inaccuraciesin the assumed sky level (this contri- calibration errors in g and r bands); random errors in MV are
butionisequaltothehalf-lightareainpixelstimestheskylevel ∼0.1mag,dominatedbysystematicerrorsinhowonedefines
uncertaintyincountsperpixel).Typicalvaluesforuncertainties skylevelsandtotalmagnitude.
inthedeterminedmagnitudesarearound0.007(slightlyhigher
3. K-CORRECTIONS
forhighredshiftsandlowerforsmallerredshifts).
Tocomparemeasurementsinaredshift-independentmanner,
2.2. Thelow-redshiftsamplefromtheSloanDigitalSky we k-correctthe observedframe measurementsinto restframe
Survey properties(throughoutthispaperweuseMV,rest and(U- V)rest
althoughourconclusionsdonotdependonthischoice). Todo
InordertoexplorethescatteroftheCMRatlowredshift,we
soweusetheIDLimplementedrestframeinterpolationcodeIn-
useasampleofgalaxiesdrawnfromtheSloanDigitalSkySur- terRestbyENT(http://www.strw.leidenuniv.nl/∼ent/InterRest;
vey (SDSS) Data Release 4 (Adelman-McCarthy 2006). We
this work is based on an earlier version of the code). To de-
choose a sample of galaxies from the publicly-available New
rive the redshift-dependent transformation between observed
York University Value-Added Galaxy Catalog (NYU VAGC;
and rest-frame colors (the algorithm is described in more de-
Blantonetal. 2005) in a very narrow redshift range 0.0495< tailin AppendixC of Rudnicketal. 2003), InterRestuses ob-
z<0.0505(2053galaxies). To maximize the accuracyof the served SEDs from a set of template galaxies: four empirical
colorinformation,weadoptcolorsderivedfrom‘Model’mag-
modelspectra from Colemanetal. (1980), and one additional
nitudes — such magnitudes use the best-fit de Vaucouleurs
starbursttemplatefromKinneyetal.(1996);thisisasubsetof
or exponential models in the r-band as a kernel for measur-
thedefaulttemplatesetwhichisusedtoavoiddegeneraciesin
ing fluxes in ugiz6. We k-correct the observed-frame ugriz
colorspace.
model colors to rest-frame U - V color using InterRest (the
These k-corrections were tested in two ways. Firstly, one
6Wealsousedaperturemagnitudeswithapertureradii5<r/arcsec<10, can use the k-correction routine to predict a F775W magni-
findingsimilarorlargerCMRscatter. tude for galaxies in GOODS (where one has F606W, F775W
4 Ruhlandetal.
andF850LP).WeshowsuchacomparisoninFig.3,whereone ourresultsremainunchangedifthesesystemsarenotexcluded
can see that the k-corrections give a scatter of ∼0.03 and an fromouranalysis). TheseobjectsareshownintheCMDswith
equal amount of mean color offset. Secondly, we can com- asterisks (X-ray) and diamonds(IR). The objects which qual-
pare the final rest-frame colors to the results of independent ified as red sequencegalaxiesafter these selection criteria are
k-correctioncodes. Comparisonto(loweraccuracy)COMBO- shown in black with error bars in the CMDs (number of RS
17 colors shows a scatter of 0.12 magnitudes and an offset galaxiesintheredshiftbins:563/38/102/31).
of 0.06mag, and comparison to a stellar population model-
derived k-correction by EFB and BH shows measurement-to- 4.2. FittingtheRedSequence
measurement scatter of less than 0.02 mag but overall rest-
ThegoalofthispaperistomeasuretheinterceptoftheCMR
frame color offsets of ∼0.1mag (this results primarily from
at a fiducial magnitude and its scatter, and to show the evo-
a difference between the 4000Å break structure of the stellar
lution of both the CMR intercept and scatter as a function of
population models and the observed ones used by InterRest).
redshift(see Figure 4). The interceptis the color value of the
We conclude that the k-corrections of the HST-derived colors
relationmeasuredataspecificmagnitude(eitherthesamemag-
areaccuratetoafewhundredthsofamagnitude(randomerror;
nitudevalueatallredshifts,orusingavariablemagnitudethat
thiscontributestothescatterontheCMR;Tayloretal.,2009,
attempts to account for the evolution of the population). The
submitted),withpossibleoverallsystematicsof.0.1mag(af- scatteriscalculatedusingtheIDLroutinerobust_sigma,which
fectingprimarilythezero-pointoftheCMR).Weassumethek-
givesanoutlier-resistantestimateofthedispersionofthecolor
correctionerrorstoscalewiththewavelengthrangeoverwhich
distribution using the median absolute deviation as an initial
theinterpolationisdone.
estimateandthenweightspointsusingTukey’sBiweightasan
robust estimator (this is the usual approach employed in this
4. RESULTS
field; e.g., Boweretal. 1992; McIntoshetal. 2005b). We fit
In this section we present our analysis of the red sequence a simple linear functionto the distributionof colorsand mag-
CMR scatter and its evolution. First, we explainthe selection nitudes of the non-star-formingearly-type galaxies under two
criteria appliedforred sequencegalaxies, then we discuss the assumptions:
actualmeasurementofthescatteroftheredsequenceatdiffer-
entredshifts0.05≤z≤1.05.Withourprecisemagnitudesand 1. Wefitthedatapointsineachredshiftbinseparately.
colors we have produced color-magnitude diagrams (CMDs)
2. Wechoosetoholdtheslopefixedatallredshifts≥0.5
forfourredshiftintervalsandplottheminFigure4.
tothevaluemeasuredatz=0.05fromtheSDSS.
4.1. SelectionofRedSequenceGalaxies The slope of the two methods are in some cases very differ-
ent, but as the SDSS sample has many more objects and a
Our selection criteria take care to choose only non-star-
larger dynamic range, this fit is much more reliable than the
forming,early-typegalaxiesrepresentingtheredsequenceand
fitsfortheotherbins. Furthersupportforthisassumedslopeis
torejectbluegalaxies,galaxieswithdiskstructure,andgalax-
ieswithongoingstarformationand/orAGNactivity. given by the best populated GEMS bin around z=0.7, which
shows nearly the same slope. We note that the determina-
First,weappliedacolorcuttoexcludegalaxieswithobvious
tionofthe interceptandscatter arenotsensitiveto ourchoice
signsofstarformationfromthesample. Forthiswemadeuse
of fitting method (Table 1)7. The histogram of color offsets
of the bimodality of the color distribution which is visible in
fromtheCMRwithredshift-independentslopeisshowninthe
theCMDsatallredshifts(Figure4). Thecolorcutwaschosen
inset panels of Fig. 4 for early-type galaxies (black) and for
tofallintothegapbetweenblueandredobjects(seealsohis-
all galaxies (gray). As the observed scatter contains contri-
tograms in Fig. 4). We used a tilted cut with the same slope
butionsfromintrinsicscatterandmeasurementuncertaintywe
for all samples. As the mean colorsof the populationsevolve
estimate the intrinsic color scatter by subtracting the random
with redshift we take this into account by allowing the cut to
color uncertainties in quadrature. The color uncertainties for
evolvecorrespondingly. Thecutappliedherecanbedescribed
as(U- V) >- 0.085·M - 0.65- 0.5·z.Smallchangesin thelow redshiftgalaxieswereestimated byscalingthe Model
rest V,rest u- r color uncertainties8 by d(U- V) /d(u- r), and adding
thepositionsofthecutsdonotinfluencethegeneralresults. In rest
in quadrature a small empirically-determined0.015 mag con-
thediagramsthecutismadevisiblebydifferentshadesofgray.
tribution accounting for real scatter in U- V at a given u- r:
The lightgraypointsare objectsbluerthen the colorcriterion
whereas the dark gray and black points indicate object on the δ(U- V)2 =(cid:2)δ(u- r)·d(U- V)/d(u- r)(cid:3)2+0.0152. If not fur-
redsideofthecut. therspecifiedwerefertotheintrinsicscatterhereafter.
A second selection criterion was applied to clean the sam- The colorintercepts(U- V) of the fitted CMR at a fixed
rest
ple of structurally late-type galaxies. For this the Sérsic in- M =- 22 are shown as a function of redshift in Figure 5.
V,rest
dexofthegalaxyis used(forthe GEMS galaxies, thisismea- The solid errorbarsdenote the formal error in the mean inter-
suredusingGALFIT,whilefortheSDSSgalaxiesweadoptthe cept, calculated using bootstrapping, although recall that the
Sérsic fits from Blantonetal. 2005). To be treated as part of actual,primarilysystematic,uncertaintyinthegalaxycolorsis
the red sequence a Sérsic index of n>2.5 is required. This
7FurthermoretheeffectofexcludingIRandX-raydetectionsfromthered
cut successfully weeds out edge-on spirals from the sample
sequenceisquitesmallanddoesnotaffectourresults. Theeffectontheinter-
(McIntoshetal.2005a). Theseobjectsareshownasdarkgray ceptsisaround1%. ThevaluesforintrinsicscatterwouldbeabitlargerifIR
points. RegardlessofcolorandSérsicindexwerejectgalaxies andX-raysourcesareincludedinthesample,changingforz=0.55from0.128
with X-ray or 24µm detections (for the CDFS data only; the to0.138,forz=0.7from0.126to0.133andforz=1.0from0.207to0.216.
SDSS sample we use lacks such information) as their colors 8RecallthatU- VisestimatedfromtheugrizModelcolorsusingInterRest.
Ourchoiceofscalingfromu- runcertaintyisreasonable: u,gandrarethe
maybe substantiallyaffectedbyUV-brightyoungstellar pop- maindeterminatsofU- V,wheregandrarerelativelywell-measuredandthe
ulationsand/oranaccretingsupermassiveblackhole(although ubanduncertaintyisfactorsofseverallarger.
EvolutionofEarly-typegalaxies 5
FIG. 4.—U- V restframecoloragainstMV forfourdifferentredshiftbins. Thelightgraypointsareobjectsbelowatiltedcut,dividingblueandredobjects.
Thiscuthasafixedslopeandaredshift-dependentintercept.DependingontheSérsicindextheredobjectsaredividedinadarkgray(n<2.5)andablacksample
(n>2.5;witherrorbarsforthethreeintermediateredshiftbins);then>2.5redgalaxiesareretainedinouranalysis. IndependentofcolorandSérsicindexIR
(diamonds)andX-ray(asterisks)detectionsarerejectedfromtheredsequencesample. Thedashedlinesarefitstotheredsequencesamplesforthethreeredshift
binswithz≥0.5. Inthez=0.05panelthefitisshownasasolidline(thepositionofthisfitisshownintheotherpanelsasthedottedline). Alinewiththesame
slopeisshiftedtothemeancolorvalueofthethreeotherpanels(solidline). Usingthese‘fits’wecalculatedinterceptsatMV =- 22. Thesmallhistogramsshow
thecolordistributionmeasuredasanoffsetfromtherelation. Thecompletedistributionisshowninlightgray,whereastheredsequence(theblackpointsinthe
CMDs)isshowninblack. Thedashedverticallineshowstheinterceptofthefit(dashedlineintheCMDs)atamagnitudevalueof- 22. Thesolidverticalline
showsthemeaninterceptswiththeCMRscatter(RMS)markedbythedottedverticallines.Thedash-dottedlinesshowtheCMRinterceptatz=0.05.Overplotted
isaGaussianwithmeanandσdefinedbythemeancolorandRMSoftheredsequencesample.
∼0.1mag.Thedotted‘errorbars’showourmeasurementofthe mentsfrom other studies (Blanton2006; Franzettietal. 2007;
CMRscatter,calculatedastheresistantdispersionofthecolor Cooletal.2006)areshowninthisplottogetherwithourdata.
offsets of the early-type galaxies from the CMR. The results In the case of Blanton (2006) and Cooletal. (2006), we have
are tabulated in Table 1. For comparison, intercept measure- k-corrected their values to rest-frame U - V color using the
6 Ruhlandetal.
TABLE1
Fit Fixedslope
measured intrinsic measured intrinsic
slope intercept scatter scatter slope intercept scatter scatter
z=0.05 - 0.087±0.006 1.457±0.005 0.124 0.117 - 0.087 1.457±0.005 0.124 0.117
z=0.55 - 0.015±0.028 1.206±0.021 0.126 0.124 1.248±0.022 0.130 0.129
z=0.70 - 0.066±0.014 1.178±0.010 0.127 0.127 1.184±0.011 0.126 0.126
z=1.00 0.010±0.047 1.097±0.041 0.210 0.206 1.103±0.036 0.212 0.208
Note.—Colorintercepts(atMV,rest=- 22)andscatterin(U- V)rest measuredwithtwodifferentmethods.‘Fixedslope’meansthattheslopeoftheCMRisfixed
tothez=0.05valueforallredshifts(solidlinesinFig.4),whileinthe‘Fit’columnstheredsequenceisfittedforeachbin(dashedlinesinFig.4).
thatsubtractioninquadratureoftheindividualgalaxymeasure-
menterrorsfromtheCMRscatteryieldsalmostunchangedre-
sults,evenforthelowredshiftSDSSsample(wherethescatter
coulddecrease to ∼0.09mag). This shows thatwe measured
a real scatter in the relation and not only a spread caused by
measurementuncertainties. Inparticular,oneshouldnotethat
fortheSDSS,spectralanalysisofthedriversoftheCMRscat-
terhavedemonstratedclearspectraldifferencesbetweenearly-
typegalaxiesofagivenmagnitudeattheredsideandblueside
of the CMR (Gallazzietal. 2006; Cooletal. 2006), demon-
stratingthatthebulkoftheCMRscatterisintrinsic.
5. INTERPRETATION
In the last sections, we described our measurements of the
CMRinterceptandscatterforcosmicaverageearly-typegalax-
ies at four redshifts between 1.0 and 0.05. We find a slowly-
evolving mean color, and an almost non-evolving scatter of
∼0.1mag in U-V rest-frame color. In this section, we build
some intuition about possible interpretation of this result us-
ing stellar population synthesis modeling. We show first the
evolutionofsinglebursts,orpopulationsofgalaxieswhosestar
FIG.5.—CMRinterceptsinU- Vasafunctionofredshift.Thesmallsolid formationistruncatedataparticulartime,in§5.1and5.2.Note
errorbarsdenotethestandarddeviationofallinterceptvaluescalculatedwith thatthepurposehereisnottotest‘monolithiccollapse’models
thebootstrapmethod. The‘errorbars’withdottedlinesindicatetheresistant (thosemodelsarealreadyruledoutbytheobservedbuildupof
dispersionofthecoloroffsetsfromthebest-fitCMR(i.e.,thescatterofthe
thered sequencepopulation),ratheritis toestablish the basic
CMR).Theothersymbolsshowmeasurements oftheCMRintercepts from
otherpapers,asexplainedinthelegend.ThemeasurementsfromBlantonand modelingredients.In§5.3and5.4weaskandanswerasimple
CoolweretransformedintoU- Vrest usingkcorrect. Theerrorbarsreflectthe question(similarinspirittovanDokkum&Franx2001):ifthe
uncertaintiesintroducedbythistreatment.
redsequenceformsthroughongoingandcontinioustruncation
of star formation in previously star-forming systems, can one
simultaneouslyreproducethe build-upof red sequence galax-
kcorrect software package, written by M. Blanton. We made
iesandthescatteroftheCMR?
surethatthereisnosignificantdifference(.0.03mag)between
therest-framecolorsderivedwithkcorrectandInterRest.
5.1. Theevolutionofsinglebursts
We find that the intercept of the color-magnitude relation
evolves by ∼0.3 mag in U- V color between z=1 and z= To get our bearings, we focus first on the evolution of the
0.05,inroughagreementwithpreviousstudies(e.g.Belletal. CMR intercept using single bursts of star formation. In what
2004a;Franzettietal.2007;Blanton2006;Tayloretal.2008), follows, we use the stellar populationmodel PÉGASE 10 (Ver-
although recall that systematic errors in the intercepts of the sion 2.0, see Fioc&Rocca-Volmerange1997, forthe descrip-
CMR are significant, ∼ 0.1 mag in U - V rest-frame color. tionofanearlierversionofthemodel)topredicttheevolution
Moreimportantly,we finda scatter ofσU- V ∼0.1mag(Table ofgalaxycolorsandabsolutemagnitudesasafunctionofred-
1) at all z<0.75; the scatter at z=1 appearsto be somewhat shift.
larger(beingconsistentwith Tayloretal.2008). Thesevalues The resultsare showninFigure6 forthreedifferentforma-
aresomewhatlargerthanthescattermeasuredforlocalgalaxy tion redshifts and for various metallicities. One can see that
clusters(0.04<σU- V <0.1,wherethescatterappearstovary the evolutionof the interceptof the CMR followsroughlythe
fromcluster to cluster; e.g. McIntoshetal. 2005b)9. We note trendsexpectedforthepassivereddeningandfadingofancient
stellar populations. In the contextof single bursts, the rate of
9Thepossible trend towards abluer CMRintercept atverylarge cluster- changeoftheCMRinterceptwithredshiftisrelatedprimarily
centricradii,arguablyanenvironmentaleffect,wouldalsoincreasethescatter
ofthecosmicaverageCMRrelativetotheclusterCMR(e.g.,Terlevichetal. 10Projetd’EtudedesGAlaxiesparSynthèseEvolutive
2001;Pimbbletetal.2002).
EvolutionofEarly-typegalaxies 7
FIG.6.—Theevolutioninrest-framecolorofsingle-burststellarpopulationsformedatthreedifferentredshifts,andwithdifferentmetallicities(whereZ=0.02is
solarmetallicity). Theasterisksdenotethemeasuredinterceptsfromourpaper;thegrayasterisksarethesameasinFig.5,whereastheblackasterisksshowcolor
interceptsmeasuredataredshift-dependentabsolutemagnitude(tocompensateforfadingofstellarpopulationsasthegalaxypopulationages;onecanthinkofthis
asmeasuringtheinterceptatapproximatelyconstantstellarmass).Theothergraysymbolsshowdatafromotherpapers,measuredinasimilarfashiontoourgray
datapoints(seethelegendsofFig.5or7).
to formation history, whereas the overallinterceptis sensitive
primarilytometallicity,withsomesensitivitytoage.
Tocompensateforthepassivefadingoftheearly-typepop-
ulation, we also measure the CMR intercept at a redshift-
dependentabsolutemagnitude(blackasterisksinFigure6).We
choose to adopta modelwith metallicityZ =0.008and a for-
mationredshiftof2toestimatetheevolutionoftheluminosity
ofanearly-typegalaxyasafunctionofredshift11,andusethis
tocalculatetheabsolutemagnitudevaluesatwhichwemeasure
the interceptof the CMR (these absolute magnitudesare - 22,
- 21.5,- 21.3,and- 20.8atz=1.0,0.75,0.55and0.05respec-
tively). Onecanthinkoftheseinterceptsasbeingmeasuredat
a given, redshift-independent,stellar mass. Because these in-
terceptsreflecttheevolutionatagivenstellarmass,wechoose
tofocusonthesevaluesinwhatfollows,asamoreintuitivere-
flectionofthelikelyevolutionofthecolorofagivengalaxy(or
amass/metallicitybinintheevolvinggalaxypopulation).
5.2. Theevolutionofgalaxieswithtruncatedstarformation
Motivated by the observational evidence for truncation of
star formationin blue sequencegalaxies, leadingto the ongo-
ingbuild-upoftheredsequencegalaxiesatredshiftsz<1(e.g. FIG. 7.—Theredshiftevolutionofrest-framecolorfordifferenttruncation
Belletal.2004b;Borchetal.2006;Belletal.2007),westudy times.Foralllines,starformationstartsatz=2andthedifferentlinesdenote
theevolutionofthecolorsofgalaxieswhosestarformationhas avarietyofdifferenttruncationredshifts(fromlefttoright:0.2to1.2insteps
of0.2).Thetinyblackdotsonthelinesindicatethepointontheevolutionary
been truncatedat a variety of redshifts z.1. The purpose of
trackagalaxyhasreached0.5,1and2Gyr,respectively,afterthetruncation
this section is to get a feeling for the ingredients used for the ofstarformation(aslabeledonthesecondlinefromtheright). Thesymbols
modelingofthe CMR evolutiondescribedin the nextsection. arethesameasinFigures5and6.
Figure7showstherest-framecolorevolutionofa stellarpop-
ulation which formsstars at a constantrate fromz =2 to the
f
truncation redshift z . We plot the evolution of seven dif- in steps of 0.2. A general feature of such truncation models
trunc
ferent truncation histories which all have a constant metallic- is a period of relatively rapid evolution onto the red sequence
ity of Z =0.02. The rightmost track has a truncation redshift (timescales.1Gyr,ascanbeseeninFig.7andBlanton2006;
very close to the formation redshift of the model, namely at Schweizer&Seitzer1992),andthenrelativelyslowsubsequent
z=1.95. The other lines show the evolution of galaxies with fadingandreddeningofthepopulation.
smallertruncationredshifts(fromlefttoright)from0.2to1.2
5.3. ExpectationsfortheScatterMeasurement
11Thechoicebetweentheformationredshiftsintherangeshownintheplot
doesnothaveagreatinfluenceontheresults;tochoosezf =3insteadwould WiththeseSFmodelingingredientsinplace,wearenowina
leadtoinaslightlysmallerevolutioninmagnitudes,buttheresultingdifference positiontoaskwhattheevolutionoftheinterceptandscatterof
ininterceptsissmallerthan0.02forallredshifts. Adifferentchoiceinmetal-
theCMRcantellusabouttheevolutionoftheearly-typegalaxy
licityhasalsoonlyverysmalleffects. TochooseZ=0.02(solarmetallicity)
population. Obviously,wewillbeunabletoaddressthisissue
wouldchangetheresultsevenlessthanthechangeofformationredshift.
8 Ruhlandetal.
FIG.8.—Theintegratednumberoftruncated(pre-redsequence)galaxiesas FIG. 10.—Colorsofindividualgalaxiescalculatedinthesamewayasfor
afunctionofcosmicage(tgal,trunc=13.5Gyristhepresentday). Assuming Figure9butassumingascatterinmetallicity. Thelinesshowthemeanvalue
thataftertruncationofstarformationgalaxiesfadeontotheredsequencein1 incolorandthescatterofthecolordistribution. Recallthatwehaveuseda
Gyr,onereproduces(byconstruction)theobservedevolutioninstellarmass redshift-dependent luminositycutasdescribedinSection5.1tomeasurethe
densityontheredsequence(insetpanel). intercepts.
completely, as we have seen that many factors influence the isusedtoestimatethetruncationratebyshiftingthetimeaxis
colorsandmagnitudesofgalaxies:whenstarformationstarted, by- 1Gyr-approximatelythetimetakentoreddenenoughto
metallicity,when(if!) starformationends,andwhetherornot satisfyourredsequencecut(followingBlanton2006;seealso
thereisanyresidualstarformation. Fig. 7). In this way, we have a truncation rate history that is
Instead,welimitourselvestoonewell-definedquestion.Re- consistentwithBorchetal.(2006)andcanbeusedtoestimate
cent observations have measured a significant increase in the the evolution of the CMR scatter. To describe the truncation
total stellar mass in the red sequence galaxy population since rateforepochsnotcoveredbyBorchetal.(2006),wechooseto
z = 1 (Chenetal. 2003; Belletal. 2004b; Bundyetal. 2005; modelthetruncationrateasaconstantlyincreasingfunctionof
Brownetal.2006b;Borchetal.2006;Faberetal.2007). This timefromz ∼5.5untilz =0.9.Theinfluenceofthischoice
f trunc
evolution manifests itself primarily in terms of an increasing ontheresultsisnegligible. Theresultingnumberoftruncated
space density of red sequence galaxies at . L∗ (Borchetal. (pre-redsequence)galaxies–theintegralofthetruncationrate
2006;Faberetal.2007),andismostnaturallyinterpretedasbe- –asafunctionofcosmicepochisalsogiveninFig.8.
ingfedbythetruncationorquenchingofstarformationinmas- The next step is to build a more realistic truncation model
sive blue galaxies (Belletal. 2004b, 2007; Faberetal. 2007). (c.f. Fig. 7): insteadofchoosingoneparticulartruncationtime
Insuchascenario,oneexpectsasignificantscatterintheCMR, asin§5.2,weinsteaddrawtruncationtimesfromthetruncation
because of the constantflow of recently star-forminggalaxies time distribution in Fig. 8. We choose 12 ‘observation’ red-
onto the red sequence. Here, we will predict the CMR scat- shiftsbetweenz=0andz=1.1;ateachwedraw1000galaxies
terimpliedbyaconstantlygrowingredsequence,andcompare fromthistruncation13historyshowninFig.8resultinginsam-
this predicted scatter with the observations. Such an exercise plesofgalaxieswithdifferenttruncationredshifts,butthesame
wascarriedoutbyvanDokkum&Franx(2001)forearly-type formationredshiftz =3forallgalaxies14.Duetothisvariety
start
galaxiesinclusters;here,weextendtheirworktoacosmicav- oftruncationredshiftsthegalaxiesinthesamplesexperienced
erageenvironment. periodsofpassiveevolutionofdifferentlength.Thisthengives
Our first ingredient is a toy model for the build up in the a distribution of galaxy colors at each redshift of interest; for
number of red sequence galaxies as a function of time. We displaypurposesinFigs.9and10wehaveaddedasmallran-
assumei)thatthegrowthinthetotalmassontheredsequence dom offset in redshift. We assume no ongoing low-level star
is driven entirely by adding blue galaxies that have had their formationinredsequencegalaxies;whilepotentiallyunrealis-
SF recentlytruncated,andii)redsequencegalaxiesare added tic,itallowsustoestimatetheexpectedscatterfromtruncation
at all stellar masses equally12. We describe the evolution of
13Theresultsofthispaperdonotchangesignificantlyifaburstofstarforma-
the number of red sequence galaxies with a simple linear fit
tionoccursbeforetruncation,asmightbeexpectedinagas-richgalaxymerger.
(in redshift) as shown in the small panel of Fig. 8, compared
14Notethatthischoiceofzstart differsfromzf insection5.1. Incontrastto
with the measurements of the integrated stellar mass density thisformerzf,whichwasusedtosimulatethepassiveevolutionafteraninitial
ofBorchetal.(2006). Wethendeterminethederivativeofthis starburst,zstartindicatesthestartingpointofalongerperiodofstarformation.
relationtogetthechangeinstellarmassdensitywithtime.This
12In fact the CMR scatter and mass build-up are both measured at ∼
1011M⊙,reducingtheimportanceofthisassumption.
EvolutionofEarly-typegalaxies 9
FIG.9.—ColorsofindividualgalaxiescalculatedusingthetruncationhistoryshowninFig.8usingonefixedmetallicityforeachplot.Thecolorsweremeasured
forcertainredshiftvaluesandareshownherespreadoutinredshifttoillustratethedensityincolorspace.Themetallicitiesarefromlefttoright0.008,0.02(solar)
and0.05.Thereisabimodalityatsomeredshifts,asaresultofkinksintheevolutionarytracksatsomevaluesofage/metallicity.
TABLE2
Fit Fixedslope Simulation
measured intrinsic measured intrinsic
scatter scatter scatter scatter
z=0.05 0.124 0.117 0.124 0.117 0.115
z=0.55 0.126 0.124 0.130 0.129 0.126
z=0.70 0.127 0.127 0.126 0.126 0.132
z=1.00 0.210 0.206 0.212 0.208 0.167
Note. —Forbettercomparisonthemeasurementvaluesforthemeasuredandintrinsicredsequencescatterarepresentedheretogetherwiththevaluesforthe
simulatedscatter.
Inordertoseparatebetweentheeffectsofageandmetallicity
scatterontheCMRscatter,wefirstconsidertheeffectsoffor-
mationhistoryaloneinFig.9. Onecanseeaconsiderablecolor
scatterfromtheongoingaccretionofrecently-truncatedgalax-
ies,alongwithsomelow-levelbimodalitiescausedbykinksin
the time evolution of colors for some metallicities (see, e.g.,
Fig. 6). For solar metallicity Z =0.02 the color evolution is
smooth, giving no ’pile-ups’in colorspace. The stronginflu-
enceofmetallicityonthecoloroftheredsequencecanalsobe
seeninthisplot.
In Fig. 10, we show our expectation for the evolution of
the CMR intercept and scatter as a function of redshift. We
havedrawngalaxiesfromalog-normaldistributioninmetallic-
itywithmean[Fe/H]=- 0.12andscatter0.1dexwhichisheld
constant over redshift (Fig. 11)16. This distribution was cho-
sen to approximately match the observed CMR intercept and
scatter, but it is interesting to note that this value of metallic-
ity scatter is consistent with the estimated intrinsic scatter in
metallicityofpresent-dayearly-typegalaxiesof∼0.1dexfrom
withthisapproach.Suchanargumenthasmerit,butwouldneglect(aswealso
have)theinfluenceofanyage/metallicityanti-correlationontheCMRscatter
FIG.11.—MetallicitydistributionforthemodeledgalaxysampleinFigure (asobservedbye.g.Trageretal.2000)
10.Themeanvaluehlog10Z/Z⊙iis- 0.12andstandarddeviationis0.1.Solar 16Our assumption of a redshift-independent scatter is clearly an over-
metallicityistakentobe0.02. simplification;yet,inthecontextofourmodelinwhicheachgalaxyhasitsown
singlemetallicityitisadefensibleone. Inreality,themetallicitymayevolve
ifthereisanylowlevelresidualstarformationinearly-typegalaxies(indeed,
alone15. ifthere is anage-metallicity relation in thestars in anindividual galaxy, its
light-weighted agecanevolveasthegalaxyagesevenintheabsenceofstar
15OnecouldarguewewillestimatelowerlimitstothescatteroftheCMR formation).
10 Ruhlandetal.
Gallazzietal. (2006). We show the mean and scatter (calcu- theimplicationsofthegrowthoftheredsequencethroughthe
lated with the same estimation algorithm as the scatter in the truncation of star formation in blue galaxies. Here we have
observed relations) of the distribution as solid lines. The re- shownthatsuchamodelreproducessimultaneouslytheevolu-
sulting distribution agrees well with the scatter measurements tionoftheinterceptandscatterofthecolor-magnituderelation
at the redshifts 0.05, 0.55 and 0.7. At z=1.0, the measured since z=1 and the blue spheroid fraction at intermediate red-
scatterexceedsthemodelprediction(allowingformorescatter shift. Suchananalysislendsconsiderableweighttothenotion
in star formationhistories). Theresultsarepresentedin Table that the early-type galaxy population has grown considerably
2. between redshift one and the present day through the trunca-
Itisinterestingtocompareourresultswithasimilaranalysis tionofstarformationinbluegalaxies(throughmergersorsome
ofearly-typegalaxiesinclusterscarriedoutbyvanDokkum&Franxotherphysicalprocess).
(2001). Theyuse asimilar modelofaconstantly-growingred
sequencetopredictboththemass-to-lightratioandcolorevolu- 6. DISCUSSIONANDCONCLUSIONS
tion(andscatter)oftheearly-typegalaxypopulation,findinga The evolution of the scatter of the red sequence is an im-
relativelyslowcolorevolutionandarelativelyconstantscatter. portantsourceofinformationabouttheevolutionaryhistoryof
Our results are in qualitative accord with their results for the the red sequence/early-type galaxy population. In this paper,
cluster early-type galaxy population, but are representative of weconstructedhigh-accuracycolor–magnituderelationsatfour
thecosmic-averagedearly-typegalaxypopulationandarecon- differentredshiftrangesusingaccuratecolorandspectroscopic
strained to reproduce the observed build-up of the early-type redshiftinformation. We useda sampleofover3000galaxies
galaxypopulation. in the CDFS, in conjunction with a local reference sample of
galaxiesfromtheSDSS,tounderstandtheredshiftevolutionof
5.4. BlueSpheroids CMR scatter. We used images from the GEMS survey taken
Sofar,wehavemadenoparticularassumptiononthemech- with the ACS onboard HST to provide both high-resolution
anism by which galaxies quench their star formation and join morphologies(to classify galaxies as early-type) and to mea-
theredsequence.Inthissection,weexplorearathermorespe- sureaccuratecolorswithinthehalf-lightradius.Inordertocal-
cificscenario:galaxiesstructurallytransformintoanearly-type culateaccuratek-correctionstorest-framepassbands,weused
galaxy (e.g., through galaxy merging) before reddening on to spectroscopicredshiftscompiledfromavarietyofsources. At
the red sequence. Such a scenario predicts that there should allredshifts,weapplyastructureandcolorcuttoisolateearly-
be a non-negligiblepopulationof blue spheroids– i.e., galax- type red-sequence galaxies; at intermediate redshift we were
iesthatarestructurallyearly-typebuthavebluecolors. Inthis able also to excise star-forming galaxies and AGN from the
context,wepresentarangeofpredictionsfortheirabundance, sampleusingX-rayand24µminformation.
requiring that blue spheroids i) have colors at least 0.25 mag Theresultingscatterofthecolormagnituderelationis∼0.1
bluer inU- V than the locus of red sequence galaxies at that mag in U - V color at z = 0.05, 0.55 and 0.7, and some-
redshift,andii)areatleastagiventimet fromthetrun- what higher at z = 1.0. This scatter is comparable to those
recognize
cation (or spheroid creation) event. This latter criterion is in-
troduced to allow for a delay t between the event that
recognize
truncatedstarformation(e.g. agalaxymerger)andthegalaxy
becomingrecognizablyearlytype;inwhatfollowsweexplore
the range0≤t ≤0.4 Gyr, motivatedby simulationsof
recognize
galaxymergers.Theratioofbluespheroidstothetotalnumber
ofspheroidalgalaxies(redandbluespheroids)N /(N +N )
BS RS BS
ismeasuredasafunctionofredshiftandisshowninFig. 12for
3differentvaluesoft .
recognize
TherearetwokeypointstotakeawayfromFig.12. First,the
predicted blue spheroid fraction depends sensitively on one’s
choice of t (and therefore, also, details of the star for-
recognize
mation history and dust content of the galaxy)17. Second,
despite this uncertainty, the range in model prediction is in
reasonable agreement with observed blue spheroid fractions
(e.g. N /(N +N )∼0.06atz∼0.6fromHäußler200718).
BS RS BS
ThefractionobservedbyBamfordetal.(2008)fortherelevant
mass range is slightly higher than in our models, but as they
usedadifferentmethodthesevaluesmightnotbedirectlycom-
parable. Recallthatthistoymodelwasconstructedtoexplore
17In fact, for long trecognize, the blue spheroid fraction decreases towards
higherredshiftbecausetrecognizebecomescomparabletothetimetakentotran-
sitionbetweenthebluecloudandredsequence.
18Herewearecomparingwiththebluespheroidfractionofrelativelymas- FIG. 12.—The predicted ratio ofblue spheroids to the total number of
sivespheroidalgalaxies,whichhaveamassrangeconsistentwithourredse- spheroids as a function of redshift for ourtoy model for the growth ofthe
quencegalaxies(seeHäußler2007,Fig.4.13).AsHäußler2007(seeparagraph redsequence. Thethreecurvesshowtheeffectofthreedifferentchoicesfor
4.5.1)foundmanyoftheworksquotingahigherbluespheroidfractionarein- trecognize,thetimetakenforagalaxytobecomerecognizablyearlytypeafter
cludinglow-mass/low-densityobjectsthatcanneverturnintoapresent-day theeventthattruncatesstarformation.DespitethedependenceofNBS/(NRS+
bulge-dominatedredsequencegalaxy(e.g.,Abrahametal.1999;Schadeetal. NBS)ontrecognize,itisremarkablethatthepredictedbluespheroidfractionis
1999;Imetal.2002). intherangeoftheobservations(e.g.Häußleretal.2007).