Morphological Evolution and the Ages of Early-Type Galaxies in Clusters

13 Pages·0.25 MB·English

by  Pieter G. van Dokkum

ACCEPTEDFORPUBLICATIONINTHEASTROPHYSICALJOURNAL
PreprinttypesetusingLATEXstyleemulateapj
MORPHOLOGICALEVOLUTIONANDTHEAGESOFEARLY-TYPEGALAXIESINCLUSTERS
PIETERG.VANDOKKUM1
CaliforniaInstituteofTechnology,MS105-24,Pasadena,CA91125
AND
MARIJNFRANX
LeidenObservatory,P.O.Box9513,NL-2300RA,Leiden,TheNetherlands
AcceptedforpublicationinTheAstrophysicalJournal
1 ABSTRACT
0 Morphologicalandspectroscopicstudiesofhighredshiftclustersindicatethatasignificantfractionofpresent-
0 dayearly-typegalaxieswastransformedfromstarforminggalaxiesatz<1.Ontheotherhand,theslowluminos-
2
ityevolutionofearly-typegalaxiesandthelowscatterintheircolor-magnituderelationindicateahighformation

n redshift of their stars. In this paper we construct models which reconcile these apparently contradictory lines
a of evidence, and we quantify the effects of morphologicalevolution on the observedphotometric propertiesof
J
early-typegalaxiesindistantclusters. We showthatin thecase ofstrongmorphologicalevolutiontheapparent

6 luminosityandcolorevolutionofearly-typegalaxiesaresimilartothatofasingleagestellarpopulationformed
2 atz=∞,irrespectiveofthetruestarformationhistoryofthegalaxies. Furthermore,thescatterinage,andhence

the scatter in color and luminosity, is approximately constant with redshift. These results are consequencesof
1
the“progenitorbias”: theprogenitorsoftheyoungestlowredshiftearly-typegalaxiesdropoutofthesampleat
v
highredshift. Weconstructmodelswhichreproducetheobservedevolutionofthenumberfractionofearly-type
8
galaxies in rich clusters and their color and luminosity evolution simultaneously. Our modelling indicates that
6
4 ∼50% ofearly-typegalaxieswere transformedfromothergalaxytypesat z<1, andtheir progenitorgalaxies
1 mayhavehadroughlyconstantstarformationratespriortomorphologicaltransformation. Theeffectofthepro-
0 genitorbias on the evolutionof the meanM⁄L ratio andcolor can be estimated. Theprogenitorbias is a linear
1 functionofthescatterinthecolor-magnituderelationproducedbyagevariations,andismaximaliftheobserved
0 scatterisentirelyduetoagedifferences. AftercorrectingtheobservedevolutionofthemeanM⁄L ratioforthe
B
h/ maximum progenitor bias we find that the mean luminosity weighted formation redshift of stars in early-type
p galaxieshz∗i=3.0+- 00..95forΩm=0.3andΩΛ=0,andhz∗i=2.0-+00..23forΩm=0.3andΩΛ=0.7.Ouranalysisplaces
- thestarformationepochofearly-typegalaxieslaterthanpreviousstudieswhichignoredtheeffectsofprogenitor
o
bias. The resultsare consistentwith the idea that(some) Ly-breakgalaxiesare star formingbuildingblocksof
r
t massiveearly-typegalaxiesinclusters.
s
a
keywordsgalaxies:evolution,galaxies:ellipticalandlenticular,cD,galaxies:structureof,galaxies:clusters
:
v
Xi 1. INTRODUCTION IMF.FurthermorethelowscatterincolorsandM⁄Lratiosim-
pliesthatthescatterin agesatanyredshiftisverysmall(e.g.,
r Early-type galaxies (elliptical and S0 galaxies) constitute
a Ellisetal.1997,Stanfordetal.1998).
∼80%ofthegalaxypopulationinthecentralregionsofnearby
Ontheotherhand,evidenceisaccumulatingthatmanyearly-
richclusters(Dressler1980),andstudiesofnearbyanddistant
type galaxies in clusters were relatively recently transformed
clustershaveprovidedstrongconstraintsontheirevolutionand
fromstarforminggalaxies. Dressleretal.(1997)reportahigh
formation.
fraction of spiral galaxies in clusters at 0.3<z<0.5. These
Theclusterobservationshavebeenusedtoconstrainthestel-
galaxies are nearly absent in nearby rich clusters (Dressler
laragesofearly-typegalaxies.Ononehand,thereisverygood
1980),andhencemusthavetransformedintoearly-typegalax-
evidence that early-type galaxies form a very homogeneous,
ies between z= 0.5 and z= 0. Other studies (e.g., Couch et
slowlyevolvingpopulation: thescatterintheircolorsissmall,
al. 1998, van Dokkumet al. 2000)have confirmedthis trend,
bothatlowredshift(e.g.,Bower,Lucey,&Ellis1992),andat
and extended it to z= 0.8. Dressler et al. (1997) found that
high redshift(Ellis et al. 1997; Stanford, Eisenhardt, & Dick-
the increased fraction of spiral galaxies at high redshift was
inson 1998), the scatter in their mass-to-lightratios is equally
accompaniedby a low fraction of S0 galaxies, and concluded
small(e.g.,Luceyetal.1991,Pahre,Djorgovski,&deCarvalho
that the z≈0.4 spiral galaxies transformed into S0 galaxies.
1998, Kelson et al. 2000), and the evolution of their mass-to-
Otherstudieshavefoundevidenceformergingandinteractions
light ratiosis slow (vanDokkum& Franx 1996, Kelson et al.
inhighredshiftclusters(Lavery&Henry1988;Lavery,Pierce,
1997,Benderetal.1998,vanDokkumetal.1998a). Thesere-
&McClure1992;Dressleretal.1994;Couchetal.1998;van
sults indicatea veryhighredshiftof formationforthe starsin
Dokkum et al. 1999). These transformations may provide a
early-typegalaxies. Asanexample,vanDokkumetal(1998a)
way to form young elliptical galaxies in the clusters at late
foundfromtheevolutionoftheFundamentalPlanerelationto
times. Themorphologicalevidenceforrecentandrapidevolu-
z=0.83thatthestarsinmassiveearly-typegalaxiesmusthave
formedatz>2.8forΩm=0.3,ΩΛ=0,andaSalpeter(1955) tionintheclustergalaxypopulationissupportedbyphotomet-
1HubbleFellow
1
2 Early-TypeGalaxiesinClusters
ric and spectroscopic studies, which have found a significant galaxy can be described by three parameters: the time when
increase of the numberfractions of star formingand post star star formation starts, the time when star formation stops, and
burstgalaxiesfromz=0toz=1(e.g.,Butcher&Oemler1978, the variationof star formationbetweenthe startand end. The
1984, Dressler & Gunn 1983, Couch & Sharples 1987, Post- star formationis allowedto increaseor decreasewith time. It
man,Lubin,&Oke1998,Poggiantietal.1999,vanDokkumet isassumedthatthegalaxyisclassifiedasanearly-typegalaxy
al 2000). Hencethe evidenceappearssecure thatmanyearly- sometimeafterthecessationofstarformation.Weassumethat
type galaxies in clusters were transformed from star forming the galaxiesdo notstop their star formationat the same time,
galaxiesatfairlyrecenttimes. butratherhaveadistributionofcessationtimes.
The purpose of this paper is to produce models which can This descriptionis fairly genericfor manydetailedtheories
bringtheseapparentlydifferentlinesofevidenceregardingthe of galaxy formation. We do not define the processes driving
ages into agreement. Specifically, we analyse the effects of themorphologicaltransformationandthecessationofstarfor-
latemorphologicaltransformationsasfoundbyDressleretal., mation. Various processes have been invoked, including gas
and others, on the observedevolution of colors and luminosi- strippingof spiralgalaxies(e.g., Gunn& Gott1972, Tytler &
tieswithredshift. Weshowthattheeffectof“progenitorbias” Vidal 1978, Abadi, Moore, & Bower 1999, Kodama & Smail
(Franx&vanDokkum1996;vanDokkumetal.2000)canbe 2000),tidalinteractions(e.g., Fried 1988, Mooreet al. 1996),
very significant: if early-typegalaxieswere transformedfrom andmergers(e.g.,Laveryetal.1992,vanDokkumetal.1999).
other galaxy types at late times, the youngest progenitors of Itdoesnotmatterinouranalysiswhatprocesscausesthecessa-
present-dayearly-typegalaxiesdropoutofthesampleofearly- tionofstarformation,andweallowforburstsofstarformation
type galaxies at high redshift. Hence the samples of galaxies toaccompanythisevent.
at low and high redshift are not the same, and in particular, Thetransitionphasebetweenstarforminggalaxyandearly-
the high redshift samples might be biased towards the oldest type galaxy is assumed to last for a significant time. Imme-
progenitorsofpresent-dayearly-typegalaxies. Thepurposeof diatelyafter the cessationof star formationgalaxiesare likely
this paper is to quantify the effects of progenitor bias, and to to show tidalfeatures(in case of an interactionor merger),or
estimate the corrections which are required for models which weakspiralarms.Themorphologiesof“E+A”orpoststarburst
ignoremorphologicalevolution.Tothatend,weconstructrela- galaxiesseemtobeconsistentwiththisscenario. Theygener-
tivelysimplemodelsforthehistoryofstarformationandmor- ally areclassified as early-typespiralsortidally distortedsys-
phological type of cluster early-type galaxies. We show that tems(Poggiantietal.1999;Fabricantetal.2000;vanDokkum
the observed slow luminosity evolution and low scatter in the etal.2000).Itisnotwellknownhowlongittakesbeforethese
color-magnituderelationand theFundamentalPlaneare natu- structuresfadeordisperse;weassumethatearly-typegalaxies
ralconsequencesofrecentandongoingassemblyofearly-type arefirstclassifiedassuch∼1.5Gyrafterstarformationintheir
galaxies. We correcttheobservedevolutionfortheprogenitor progenitorsceased.
bias,andderivethecorrectedmeanageofthestarsinearly-type InthecurrentSectionwedonotspecifywhetherthemodels
galaxies. applytoellipticalgalaxies,S0galaxies,orboth. Observation-
Our models are extensions of the earlier work by van ally,theearly-typegalaxyfractionismorerobustthantherel-
Dokkumetal(1998b),Boweretal.(1998),andShioya&Bekki ativenumbersofellipticalgalaxiesandS0galaxies(e.g.,Fab-
(1998). These authorsconsideredcomplexstar formationhis- ricant,Franx,&vanDokkum2000,vanDokkumetal.2000).
tories of cluster galaxies, but did notinvestigatethe effectsof If differenthistories apply to the two classes of galaxies, two
morphological transformations on the observed properties of separatemodelswillbeneededforeachsub-class. Weexplore
early-typegalaxiesathighredshift. Theprogenitorbiasisim- suchmodelsinSection5.
plicitlyincludedintheverydetailedsemi-analyticalmodelsby, The generic effects of late morphologicaltransitions are il-
forexample,Kauffman&Charlot(1998)andBaugh,Cole, & lustrated in Fig. 1. In panel (a), the evolution of the mass-to-
Frenk (1996). In these complex models it is difficult to iso- light ratio is shown for a population of galaxies with a small
late and quantify specific effects, such as the progenitor bias. rangeinage,withoutanylatemorphologicaltransitions.Ascan
The main contributionof our work is that we use simple ana- be seen, galaxies with young stellar populations evolve more
lytic modelswith only three free parameters, which allows us rapidly than galaxies with old stellar populations, and hence
to provide explicit estimates for the effects of morphological thespreadinM⁄Lratiosincreaseswithredshift(panelb). The
evolutionontheobservedcolorsandluminositiesofearly-type mean evolution is faster than that of a single age population
galaxies. formedatz=∞, whichis indicatedby the dashedline in (b).
Thistype of modellinghas beenused extensivelyto constrain
theagesofearly-typegalaxiesinclusters: iftherearenomor-
2. MODELING phologicaltransitions,theevolutionofthemeancolororlumi-
We construct simple models for the evolution of early-type nosity constrainsthe meanage of early-typegalaxies, and the
galaxies, which parameterizeboth their star formationhistory scatterconstrainsthespreadinages(e.g.,Bower,Lucey,&El-
and morphological evolution. Our models allow the full his- lis1992,Ellisetal.1997,vanDokkumetal.1998(a,b),Bower
tory to be quantifiedby three parameters. They are not based etal.1998,Stanfordetal.1998,Ferreras&Silk2000).
onafullphysicaldescriptionoftheformationandevolutionof In panel (c), a model is shown in which galaxies are trans-
galaxiesasderivedby,e.g., Kauffmann,White, & Guiderdoni formedintoearly-typegalaxiesataconstantrate. Thebroken
(1993)andBaughetal.(1996). linesindicategalaxiesbeforetheyarerecognizedasearly-type
galaxies. It can easily be seen that the sample of early-type
galaxies at high redshift is a small subsample of all galaxies
2.1. BasicDescription
which are classified as early-type galaxies at z=0. The two
Weassumethatearly-typegalaxieshavesimilarhistoriesof samples are therefore not directly comparable, and erroneous
starformationandmorphology. Thehistoryofeachindividual
vanDokkum&Franx 3
Fig. 1.—Illustrationoftheevolutionofearly-typegalaxiesintraditionalmodels(a,b)andinmodelswithmorphologicalevolution(c,d). Lines
in(a)and(c)showtheevolutionofindividualgalaxies, witharangeofages. Thedashedsectionsofthecurvesin(c)indicatethatthegalaxies
arenot yet recognized asearly-typegalaxies. Panels(b)and (d)show theevolutionof themeanM⁄Lratiointhesetwomodels. Thescatteris
indicatedbythewidthofthehatchedregions. Thedashedlineshowstheevolutionofasingleagestellarpopulationformedatz=∞. Inmodels
withmorphologicalevolutionthemeanM⁄Lratioevolvesslowlyandthescatterisroughlyconstant,becausemoreandmoreyounggalaxiesdrop
outofthesampleathighredshift.
results are derived if morphological evolution is ignored. As galaxy:
a result, the evolutionin the meanM⁄L ratio of the early-type t
galaxiesisveryslow(paneld).TheslopeoftheM⁄L–zrelation P(tstop)∝exp(cid:18)- τ (cid:19). (1)
stop
iscomparabletotheslopeforasinglestellarpopulationwhich
Weshowlaterthatthisexpressioncanprovideasatisfactoryfit
formedatz=∞(indicatedbythedashedline),eventhoughthe
tothedata.Ifτ ≪t ,witht thepresentageoftheUniverse,
meanformationredshiftofthestarsinallearly-typegalaxiesat stop 0 0
star formation in the progenitors terminated at very high red-
z=0islowathz∗i≈2. Evenmoreremarkableisthefactthat
thescatterinM⁄Lratiosisvirtuallyconstant. Theseeffectsare shift. Attheotherextreme,τstop=∞correspondstoaconstant
transformationrate.Foreachindividualgalaxy,themorpholog-
causedbythefactthattheyoungestgalaxiescontinuouslydrop
ical transformation to early-type galaxy occurs at t +0.1t ,
outofthesamplegoingtohigherredshifts. Inthesubsections stop 0
i.e.,∼1.5Gyraftertruncationofstarformation.
below we specify a broader range of models, and explore the
consequences. The parameter f∗ characterizesthe variationof the star for-
mationrate. Thestarformationhistoryofthegalaxiescanin-
cludebursts,andincreasingordecreasingcontinuousformation
2.2. ModelParametersandMethodology
ratesasafunctionoftime. Afterstarformationceases,thelu-
Thefullmodelsarequantifiedbythreeparameters:t ,the minosity and color evolution of such a complex population is
start
timewhenstarformationstarts,τ ,thetimescalewhichchar- wellapproximatedbyasingleagepopulationofstarswiththe
stop
acterizes the distribution of times when star formation stops, same luminosity weighted mean age (e.g., van Dokkum et al.
and f∗,whichdescribesthestarformationratebetweenthestart 1998b).
andendofstarformation. Thelasttwoparametersaredefined Hence for each galaxywe approximatethe evolutionof the
inthefollowingway. complexpopulationby thatofa singleage populationformed
The parameter τstop determines the probability distribution att=t∗,with
of tstop, the time when star formation stops for an individual t∗= f∗tstop+(1- f∗)tstart. (2)
4 Early-TypeGalaxiesinClusters
For f∗≈1,thestellarpopulationisdominatedbyaburstatthe metallicity. In this paper we will limit the discussion to rest
endofthestarformationhistory,andfor f∗≈0thepopulation frame B band luminosities, and rest frameU- B colors. Our
isdominatedbyaburstatthestartofthestarformationhistory. resultscaneasilybeexpressedinother(restframe)bands.The
Ifthestarformationrateisapproximatelyconstantfromt=t Worthey(1994)modelsgiveκ =0.91andκ =1.07forsolar
start B U
tot=tstop,then f∗≈0.5. metallicityandaSalpeter(1955)IMF.Thecolorevolutioncan
We tested the accuracy of our approach by calculating the beapproximatedby
luminosity and color evolution of galaxies with complex star
formationhistories(e.g.,anexponentiallydecliningstarforma- LB ∝(t- t∗)κU- κB. (4)
tion rate followed by a star burst), and comparing the results L
U
topredictionsfromsingleburstmodelswiththesamevaluesof
f∗.Aftertransformationtoearly-typegalaxy(i.e.,>1.5Gyraf- Expressed in magnitudes, color and luminosity evolution are
terstarformationhasceased)ourapproximationofluminosity relatedthrough
andcolorevolutionisaccuratetoafewpercent.Threepossible
starformationhistoriesofearly-typegalaxiesareshowninFig. ∆(U- B) = (κU- κB)κ-B1∆B (5)
2. The model with f∗ =0.7 has a star burst at the end of its ≈ 0.18∆B (6)
starformationhistory,andmaybeappropriateforspiralgalax-
ies falling into clusters, or mergers. Although these histories inthesemodels. Theevolutionofthemeancolorandscatterin
are quite complex, >1.5Gyr after star formation has ceased thecolorwillthereforebesimilartothescaledevolutionofthe
∼
theirevolutionissimilartothatofsingleagestellarpopulations meanM⁄Lratioanditsscatter.
formedatt∗= f∗tstop+(1- f∗)tstart. In the following, we use Monte-Carlosimulationsto calcu-
late model predictions for given values of τstop, f∗, and tstart.
This approach has the advantage that the mean and scatter in
colorsandluminositiesatagiventimecanbecomputedusing
the same methodsas for the observations. In the simulations,
all galaxies start out as star forming objects at t =t . Each
start
galaxyisassignedavaluefort ,thetimewhenstarformation
stop
ceases.Thedistributionoft isgivenbyEq.1,withboundary
stop
condition0<t <0.9t , witht the presentage of the Uni-
stop 0 0
verse. At each timestept, objects which satisfy the condition
t +0.1t <t are selected as early-type galaxies. Using Eq.
stop 0
3 and 4 these galaxies are assigned a luminosity and a color.
The central value and the spread of the color and luminosity
distribution at time t are calculated with the biweight statistic
(Beers, Flynn,&Gebhardt1990). Thisstatistic wasalsoused
byStanfordetal.(1998)andvanDokkumetal.(1998b,2000)
tocalculatethescatterinthehighredshiftcolor-magnitudere-
lation. We note that the evolution of the mean M⁄L ratio and
colorsofearly-typegalaxiescanalsobeevaluatedanalytically.
InAppendixAwegiveapproximateexpressionswhichcanbe
usedformostapplications.
2.3. ExamplesofModelswithProgenitorBias
WecalculatethepredictedevolutionoftheM⁄Lratioandits
scatter for several models. To demonstrate the effects of pro-
genitorbiasweconsidertwoclassesofmodels,onewithmild
Fig. 2.—Illustrationofourparameterization. Galaxiesstartforming morphologicalevolution(τ =0.2t )andonewithstrongmor-
starsatt ,andstarformationterminatesatt .Galaxiesdonotstop stop 0
start stop phologicalevolution(τ =0.5t ). Figure3showstheresults.
their star formation at the same time, but have a distribution of ces- stop 0
sationtimes,parameterizedbythetransformationtimescaleτ . The In models with τstop =0.2t0 morphologicalevolution is not
stop
starformationhistorybetweent andt canbequitecomplex,and veryimportantto z=1, and ≈80% of present-dayearly-type
start stop
mayincludestarbursts.Itisparameterizedbytheparameter f∗,which galaxieswerealreadyinplaceatthatredshift. Inmodelswith
describeswhetherstarformationismoreweightedtowardststartortstop. τstop=0.5t0,ontheotherhand,only≈50%ofearly-typegalax-
ies were in place at z=1. In all panels of Fig. 3 brokenlines
show the class of models with mild morphologicalevolution,
Ourparameterizationallowsstraightforwardcomputationof andsolidlinesshowmodelswithstrongmorphologicalevolu-
luminositiesandcolorsofgalaxies,becausetheluminosityevo- tion.
lutionofasingleagestellarpopulationcanbeapproximatedby
apowerlaw(e.g.,Tinsley1980,Worthey1994). Therefore,to
goodapproximation, 2.3.1. EffectofVaryingtheStarFormationHistory
1 Panels (a), (b), and (c) show the effectof changingthe star
L∝ . (3) formationhistory,whilekeepingthetimeofonsetofstarforma-
(t- t∗)κ
tionfixedatt =0. Theresultsfortheevolutionofthemean
start
The coefficient κ depends on the passband, the IMF, and the M⁄Lratioareshowninpanel(a). Quiteremarkably,nearlyall
vanDokkum&Franx 5
Fig. 3.—PredictedevolutionofthemeanM⁄Lratioanditsscatterinvariousmodelswithprogenitorbias. Inallpanels,solidlinesshowmodels
withstrongmorphologicalevolutiontoz=1(τ =0.5t )andbrokenlinesshowmodelswithmildmorphologicalevolution(τ =0.2t ). Panels
stop 0 stop 0
(a,b,c)demonstratetheeffectofvaryingthestarformationhistory,parameterizedby f∗.TheevolutionofthemeanM⁄Lratio(panela)isremarkably
similarinallmodels,whereasthescatter(panelb)andtheprogenitorbias(panelc)areverysensitivetothestarformationhistory. Panels(d,e,f)
showtheeffectofvaryingthetimeofonsetofstarformation,t . Varyingt hasalargeeffectontheevolutionofthemeanM⁄Lratio,aswell
start start
asonthescatterandtheprogenitorbias. Themodelsindicatethattheobservedtransformationrateandtheobservedscattersufficetopredictthe
progenitorbias.
modelpredictionslieveryclosetothelineforoldpopulations eragescatterislarge,becauseitisastrongfunctionofthestar
whichformedatthestartoftheUniverse(z =∞). Wefind formationhistoryofgalaxies. Aswewillseelater,thisimplies
form
littledependenceonthetranformationtimescaleτstoporon f∗, thatobservationsofthescatterputimportantconstraintsonthe
whichcharacterizesthestarformationhistory.Thisresultillus- models. For galaxies with later star formation, f∗ increases,
trates the dramatic effects of the progenitorbias, as the mean andthescatterincreasesalmostlinearlywith f∗. Forthelimit-
stellarageofthegalaxiesatz=0canbeaslowashalftheage ing case of a constanttransformationrate (τ =∞), we find
stop
oftheUniverse(for f∗=1),andyettheapparentevolutionfol- thatthescatteriswellapproximatedbyσ(lnM⁄LB)∼0.3f∗(see
lowstherelationforveryoldpopulationsformedatinfinitered- Appendix).Thescatterisnotstronglydependentonredshiftbe-
shift.Thereasonforthisbehaviouristhattheformationmodels causeofthescale-freenatureofthemodels. Insuchscale-free
arealmostscalefree. Inmodelswithaconstanttransformation models, the relative agedifferencesbetweenearly-typegalax-
rate, at any time the youngest half of the galaxies have been ies at any epoch is fairly constant. The scatter is proportional
addedtothesampleinthelasthalfoftheageoftheUniverseat totheagedifferencesbetweengalaxiesrelativetothemeanage
thattime. Asaresult,themeanstellarageofthegalaxiesisan (e.g.,vanDokkumetal.1998b). Asgalaxiesarecontinuously
almostconstantfractionoftheageoftheUniverse,independent addedtothesample,therangeinagesincreasesatthesamerate
of the star formation histories of individual galaxies, and the asthemeanage;hencethespreadinagesrelativetothemean
meanmass-to-lightratiosandcolorswillevolveasif thestars age remains constant. In the Appendix this effect is demon-
formedatveryhighredshift. IntheAppendixwedemonstrate strated analytically. Only in models with mild morphological
this effect analytically. The absolute colors and mass-to-light evolutionto z=1 (indicatedby the brokenlines in Fig. 3) we
ratios at z=0 will be differentfor these models, butthese are findanincreaseofthescatterwithredshift.Inthesemodelsthe
notoriouslydifficultto interpretuniquely(e.g.,Worthey1994, scatterisverylowatz=0,andatz>0.5reachesvaluessimilar
Faberetal.1999). tothoseinmodelswithstrongmorphologicalevolution.
Fortunately,thescatterinM⁄Lratiosandcolorsismuchmore Theprogenitorbiasofthemodelsisshowninpanel(c). We
sensitivetothetransformationtimescaleandstarformationhis- definetheprogenitorbiasatgivenredshiftasthedifferencebe-
tories. We show the scatter in M⁄L ratios in panel (b). For a tweentheM⁄Lratioofearly-typegalaxiesandtheM⁄Lratioof
givenmorphologicaltransformationratethevariationintheav- all progenitorsof present-day early-type galaxies. This is the
6 Early-TypeGalaxiesinClusters
“error”intheobservedM⁄Lratiothatiscausedbythelatead- evolutiondependingonclustertype. InthisSectionwedonot
ditionofearly-typegalaxiestothesample.Asthefigureshows, distinguishelliptical galaxiesand S0 galaxieswithin the class
thebiasincreaseswithincreasingtranformationtimescaleτ , ofearly-typegalaxies. In Sect. 5 we exploremodelsinwhich
stop
andincreasing f∗. Bothparametersalsocausethescattertoin- bothclassesaremodeledseparately.
crease. For models with strong morphological evolution the Theevolutionoftheearly-typegalaxyfractionispossiblyin-
progenitorbiascanbeapproximatedby fluencedbytheinclusionoflowmassgalaxiesundergoingstar
bursts. Sincethesamplesaremagnitudeselected,thepresence
bias(lnM⁄LB)≈1.3×scatter(lnM⁄LB)×z (7) ofsuchgalaxiesathighredshiftwoulddecreasethefractionof
early-typegalaxies,andwouldbeunrelatedtotheevolutionof
Thisapproximationisaccurateto∼<10%forτstop>0.5t0.This massive galaxies. For the cluster MS1054- 03 at z=0.83 we
resultsuggeststhattheprogenitorbiascanbeestimatedonthe havealargedatasetofconfirmedmemberswithaccuratecol-
basisoftheobservedtransformationrate,andtheobservedscat- ors(vanDokkumetal.2000),andwetestedtheimportanceof
ter. The star formation history is the individual galaxies, as thiseffectbydeterminingtheearly-typegalaxyfractionamong
parametrizedby f∗,isnotneededtoestimatetheeffect.Thisis redgalaxiesalone. Ifwelimittheanalysistoredgalaxieswith
averyusefulresult,asitisdifficulttoconstrainthevalueof f∗ (U- B) > 0.3 the early-type fraction changes from 45% to
z
directlyfromtheobservedcolorsandluminosities. 52%. This result indicates that the brightening of low mass
galaxieshasaminoreffectonthefractionofearly-typegalax-
ies. Othereffectsmayhavetheoppositeeffect.Asanexample,
2.3.2. EffectofVaryingtheTimeofOnsetofStarFormation
biases introduced by the selection of the clusters themselves
Panels(d), (e), and(f)showtheeffectofchangingthetime probablycause ustounderestimatethe evolutionofthe early-
ofonsetofstarformationt ,whilekeepingthestarformation typegalaxyfraction(see,e.g.,Kauffmann1995).
start
history constant at f∗ =0.5 (i.e., approximately constant star The evolution of the rest frame M⁄LB ratio with redshift is
formationfromt tot ). TheevolutionofthemeanM⁄Lra- showninFig.4(b)andistakenfromvanDokkumetal.(1998a).
start stop
tioforthevariousmodelsisshowninpanel(f). Theevolution Data are from Jørgensen et al. (1996), van Dokkum & Franx
isverysensitivetothetimeofonsetofstarformation: thereis (1996), Kelson et al. (1997), and van Dokkum et al. (1998a).
analmostlinearrelationbetweenthetimewhenstarformation The M⁄L ratio evolution is derived from the evolution of the
commencesandtherateofM⁄Levolution. Thereasonforthis zeropointoftheFundamentalPlanerelation(seevanDokkum
behaviour is that the mean age of the stellar population in all &Franx1996). Theevolutioniswelldetermined,becausethe
galaxies is lower for higher values of t . As will be shown FundamentalPlanehasverysmallscatter.
start
inSect.3theobservedevolutionofthemeanM⁄Lratioplaces Thescatterinln(M⁄L )isshowninFig.4(c).Thedatapoint
B
strongconstraintsonthetimewhenstarformationcommenced atz≈0 isfromJørgensenetal. (1996). Data pointsathigher
inearly-typegalaxies. redshiftare from Kelson et al. (2000)(z=0.33), Kelson et al.
The scatter and the progenitorbias are shown in panels (e) (1997) (z=0.58), and van Dokkum et al. (1998a) (z=0.83).
and (f). They both depend on the value of t , such that the The highest redshift points have considerable uncertainty, be-
start
scatterishigherandtheprogenitorbiasstrongerforlateronset causetheyarederivedfromsmallsamples.
ofstarformation. Asaresultofthisdualdependencetherela- The scatter in the U- B color-magnitude relation is taken
tion betweentheprogenitorbiasandthe observedscatter (Eq. from van Dokkumet al. (2000)and shown in Fig. 4(d). Data
7)isnotverysensitivetothevalueoft ,onceagainindicat- arefromStanfordetal.(1998),Bower,Lucey,&Ellis(1992),
start
ing that the observed rate of morphologicalevolution and the Ellisetal.(1997),vanDokkumetal.(1998b),andvanDokkum
observedscattersufficetoestimatetheprogenitorbias. etal.(2000).Theobservationswerebroughttoacommon(rest
frame) band by using σ(U- B)=1.4σ(B- V) and σ(U- B)=
0.6σ(U- V),asderivedfromtheWorthey(1994)models. The
3. APPLICATIONTOOBSERVATIONS scatter is roughly constant with redshift, at σ(U- B) ≈ 0.03
ThemodelsdescribedinthepreviousSectioncanbeapplied magnitudes.
to observationsof early-typegalaxiesin clustersat 0<z<1.
Parameters to fit are the evolution of (i) the early-type galaxy 3.2. ConstraintsonModelParameters
fraction,(ii)themeanM⁄L ratio,asdeterminedfromtheFun-
B 3.2.1. TransformationTimeScale
damental Plane, (iii) the scatter in M⁄L , and (iv) the scatter
B
in the color-magnituderelation. Free parametersare the mor- Theobservedevolutionoftheearly-typegalaxyfractiondi-
phologicaltransformationrate(parameterizedbyτstop),andthe rectly constrains the transformation time scale τstop. This is
starformationhistoriesofgalaxiespriortothetransformations demonstratedinFig.3(a),whichshowstheredshiftdependence
(parameterizedby f∗ andtstart). of the transformed galaxy fraction for different values of the
transformationtimescale.
Wevariedthetransformationtimescalebetweenτ =0and
3.1. Data stop
τ =∞. Ifτ =0allmorphologicaltransformationsoccurat
stop stop
Theevolutionoftheearly-typegalaxyfractioninclustersis veryhighredshiftandifτ =∞thetransformationrateiscon-
stop
showninFig.4(a)(takenfromvanDokkumetal.2000). Data stant. Theobservedevolutionoftheearly-typegalaxyfraction,
points are from Dressler (1980), Andreon, Davoust, & Heim shown in Fig. 4(a), gives a best fitting value of τ ≈0.5t .
stop 0
(1997), Dressler et al. (1997), Lubin et al. (1998), Fabricant Values between 0.3t and 1.7t are consistent with the data at
0 0
et al. (2000), and van Dokkum et al. (2000). The early-type the90%confidencelevel.
fraction decreases by a factor ∼2 from z =0 to z= 1. The The clusters in Fig. 4(a) form a very heterogeneous sam-
scatteraroundthedownwardtrendissignificant,anditwillbe ple, and a potential worry is that the evolution is severely af-
interestinginthefuturetoexploresystematicdifferencesinthe fected by selection biases. As a test of the robustness of the
vanDokkum&Franx 7
Fig. 4.—Comparisonofobservationstomodelpredictions. Shownaretheevolutionoftheearly-typegalaxyfraction(a),theevolutionofthe
meanM⁄L ratio(b),thescatterinln(M⁄L ),asderivedfromthescatterintheFundamentalPlaneofearly-typegalaxies(c),andthescatterinthe
B B
U- Bcolor-magnituderelation(d). Sourcesofthedataaredescribed inthetext. Thesolidlinesshow thebestfittingmodel, withτ =0.5t ,
stop 0
f∗=0.5(i.e.,aconstantstarformationrate),andtstart=0. Thismodelprovidesanexcellentfittothedata. Thebrokenlinesshowamodelwith
f∗=0.25(i.e.,adecliningstarformationrate).ThismodelallowsforadditionalscatterintheFPandtheCMrelationasaresultof,e.g.,metallicity
variationsormergers. Theprogenitorbiasisshowninpanel(e). Itisastrongfunctionof f∗,andhencethescatter. Theobservedscatterprovides
anupperlimittothebiasof≈0.2inln(M⁄L )atz=1.
B
transformation rate we fitted all clusters with high X-ray lu- As was demonstrated in Sect. 2 the star formation history
minosities separately. Solid symbols in Fig. 4(a) are clusters betweent andt isconstrainedbytheobservedscatterin
start stop
withL >1044.5h- 2ergss- 1(seevanDokkumetal.2000).This M⁄L ratio andcolor. Thisstrongdependenceof thescatter on
X 50
samplegivesaverysimilarbestfitvalueofτ ≈0.45t . We thestarformationhistorywasdiscussedearlierbyvanDokkum
stop 0
note,however,thatthemorphologicaltransformationrateisone etal.(1998b)andBoweretal.(1998)inthecontextof“tradi-
ofthemainuncertaintiesinourstudy.Wewillreturntothisis- tional”modelswhichdonotincludemorphologicalevolution.
sueinSect.5. Ifallscatterinthecolor-magnituderelationandtheFundamen-
tal Plane is producedby age variations, the best fitting model
3.2.2. StarFormationHistories has f∗ = 0.52 (i.e., an approximately constant star formation
rate), with values to f∗ =0.62 consistent with the data at the
Wenextexploremodelswiththebestfittransformationtime 90%confidencelevel. ThelinesinFig.4(c)and(d)showthe
τstop=0.5t0,andwevarythetimeofonsetofstarformationtstart modelwith f∗ =0.5. Forvaluesof f∗ lowerthan0.5the scat-
andtheparameterdescribingthestarformationhistory f∗. terisunderpredicted,andadditionalscatterdueto,e.g.,merg-
AsdemonstratedinthepreviousSection,therateofevolution ing, metallicity variations, ordustis allowed. As an example,
ofthemeanM⁄Lratiohasanapproximatelylineardependence the brokenlines show a modelwith τ =0.5t , t =0, and
stop 0 start
onthevalueoftstart.Theobservedevolution,showninFig.4(b), f∗=0.25.Thepreferredvaluesof f∗≤0.5correspondtograd-
is very slow. The dashed line indicates a simple single burst ualstarformationhistoriessimilartothosedepictedintheup-
model with zform =∞. This model provides a good fit to the pertwopanelsofFig.2.
data, as was previouslyshown by vanDokkumetal. (1998a).
We find a best fitting value of t =0.03t . Values between
start 0 3.3. TheProgenitorBias
t =0andt =0.2t areconsistentwiththedataatthe90%
start start 0
confidence level. The implication is that star formation com- Ourbestfittingmodelhasτstop=0.5t0,t0=0,and f∗ ≤0.5.
menced at high redshift (z>2.5) in early-type galaxies. The The progenitor bias, expressed as the difference between the
lineinFig.4(b)showsthebestfittingmodelwitht =0. observed M⁄L ratio of early-type galaxies and the M⁄L ratio
start
8 Early-TypeGalaxiesinClusters
of all progenitors of early-type galaxies in nearby clusters, is for Ωm = 0.3 and ΩΛ = 0, or ∆lnhM⁄LBi =(- 1.1±0.1)z for
showninFig.4(e). Theprogenitorbiasismaximalif f∗=0.5, Ωm=0.3andΩΛ=0.7. Theevolutionafterapplyingthemax-
in which case the scatter in the CM relation and the FP is en- imumcorrectionforprogenitorbiasis∆lnhM⁄L i≈- 1.1z,or
B
tirely produced by age variations. In this extreme model the ∆lnhM⁄L i≈ - 1.3z for positive cosmological constant. We
B
progenitorbiasisapproximately0.2×zinlnM⁄L ,or0.04×z concludethattheprogenitorbiashasasmall(<20%),butnon-
B ∼
inU- Bcolor. negligible effect on the observed evolution of the mean M⁄L
Westressthatthesevaluesareupperlimits,becausethescat- ratiofromz=0to z=1. Thecorrectionsareupperlimits, be-
ter can be caused by other effects than age. As shown in the causeitisassumedthatthescatterinluminositiesandcolorsis
previous Section, the progenitor bias scales linearly with the entirelyduetoagevariationsamongthegalaxies.
scatterintroducedbyagevariations. Forexample,if f∗ =0.25 The observedevolutionof the mean color and M⁄L ratio of
the scatter due to ageis onlyhalfthe observedscatter. In this early-typegalaxiesindicatesa veryhigh redshiftof formation
casetheprogenitorbiasisonly0.1×zinlnM⁄L (indicatedby fortheirstars(e.g.,vanDokkum&Franx1996,Schade,Barri-
B
thebrokenlineinFig.4e). entos,& Lopez-Cruz1997,Stanfordetal. 1998,vanDokkum
Itisinterestingtocomparetheseresultstothesimplescaling et al. 1998a, Kodamaet al. 1998). Because the true evolution
with the observed scatter that was derived in Sect. 2.3.1. Us- ofearly-typegalaxiesis underestimatedas a resultofthe pro-
ing the observed scatter of ≈0.15 in lnM⁄L Eq. 2.3.1 gives genitorbias,theagesoftheirstarsareoverestimated.
B
a progenitor bias of ∼0.2z, identical to the value we derived We constrain the formation epoch of the stars in early-type
from the full fitting of the models to the observations. This galaxies from the corrected evolution of the mean M⁄L ratio.
remarkableagreementdemonstratesquantitativelythattheob- First we assume that the scatter in the color-magnitude rela-
served transformation rate and the observed scatter suffice to tionandtheFundamentalPlaneisentirelycausedbyagevari-
predicttheprogenitorbias. Inparticular,knowledgeofthede- ations. Using ∆lnhL i=1.1z in Eq. 3 we find that the mean
B
tailedstarformationhistoriesofthegalaxies(tstartand f∗inour luminosity weighted formation time of the stars in early-type
models)isnotrequired. galaxiesht∗i=0.16t0, orhz∗i=3.0-+00..59 whenexpressedinred-
shift. ForΩm =0.3andΩΛ=0.7∆lnhLBi=1.3z,andwefind
3.4. DependenceonCosmology hz∗i=2.0-+00..23. Asacheckonourprocedure,wealsocomputed
themeanformationepochdirectlyfromtheMonte-Carlosim-
WeusedΩm=0.3andΩΛ=0tocalculatethemodelpredic- ulation which gave the best fit to the observations. The age
tionsandthedatapointsshownin Fig.4. Themodelsdepend derivedfromthesimulationisidenticaltotheagederivedfrom
onthecosmologicalmodelbecauseoftheconversionfromtime thecorrectedevolutionoftheM⁄Lratio.
toredshift. TheobservedevolutionofthemeanM⁄Lratioalso Ifthescatterinthecolor-magnituderelationandtheFunda-
dependson the cosmology, because effective radii of galaxies mentalPlaneisnotentirelycausedbyagevariations,themean
are measuredinarcseconds. Asdemonstratedin Benderetal. age of the stars is higher. Both the mean age and the scatter
(1998)andvanDokkumetal.(1998a)thedependenciescanbe haveanapproximatelylineardependenceon f∗(Eq.2andA9).
quitestrong,andtheobservedevolutionoflnM⁄LBprovidesan Therefore, for a given morphological transformation rate the
upper limit on Ωm (assuming the slope of the IMF is not sig- mean age of the stars is to good approximationa linear func-
nificantlysteeperthantheSalpeter(1955)value).Notethatthe tionofthescatter atz=0. Fromthe Monte-Carlosimulations
modelsanddatashowninFig.4arenotdependentontheHub- withτ =0.5t wefind
stop 0
bleconstant,becausetheluminosityevolutionofstellarpopu-
lationscanbeapproximatedbyapowerlawandalldatapoints ht∗i⁄t0 ∼ 2×σlnM⁄L(B) (8)
arerelativetonearbyclusters. ∼ 10×σU- B (9)
OurresultsareverysimilarforaUniversewithacosmolog-
icalconstant(Ωm=0.3andΩΛ=0.7). Thepredictedevolution tfioornΩsmto=th0e.3scaantdterΩiΛs=ne0g.l7ig.ibIlfeththeeccoonrtrreibcutitoionnfoorfpargoegevnaritioa-r
of the early-typegalaxy fraction remains virtually unaffected,
and the best fitting value for the transformationtime scale re- biasisnegligibleaswell, andwefindhz∗i≈6.5forΩm =0.3
mainsτ ≈0.5t . TheobservedevolutionofthemeanM⁄L andΩΛ=0,andhz∗i≈2.6forΩm=0.3andΩΛ=0.7(cf.van
stop 0 B Dokkumetal.1998a). Unfortunatelyitisobservationallydif-
ratioismorerapidinthiscosmology,andisnolongerwellfitted
ficulttodisentanglethecontributionsofageandmetallicityto
bymodelswithextremelyhighformationredshiftofthestellar
theobservedscatter(e.g.,Trageretal.2000).
population (see also van Dokkum et al. 1998a). Models with
t =0 predicttoo slow evolution, and good fits are obtained
start
fort =0.15t . Becausethestellar populationsofearly-type 5. SEPARATINGELLIPTICALANDS0GALAXIES
start 0
galaxiesare youngerfortstart >0 the predictedscatter in M⁄L InthepreviousSectionswehavetreatedearly-typegalaxies
ratiosandcolorsishigherforagivenvalueof f∗. Asaresult, asoneclass. However,Dressleretal.(1997)separatedtheevo-
theobservedscatterisbestfittedfor f∗≈0.4inthiscosmology, lutionofellipticalandS0 galaxies,andfoundthatthe ratioof
as comparedto f∗ ≈0.5 for a Universe withoutcosmological thefractionsofS0andellipticalgalaxiesevolvesrapidlyfrom
constant. z=0toz≈0.55.
Figure 5 shows the evolutionof the numberfractionsof S0
galaxiesandellipticalgalaxiesseparately,fortheDressleretal.
4. CORRECTINGFORPROGENITORBIAS
(1997)clusters(solidsymbols). Thedottedlinesarelinearfits
TheevolutionoftheM⁄Lratiocanbecorrectedforprogen- tothedata.Ascanbeseen,theS0fractionincreasesbyafactor
itor bias. Our best fitting model indicates that the observed of ∼ 5 towards lower redshift, whereas the elliptical fraction
evolution of the M⁄L ratio underestimates the true evolution dropsby∼30%fromredshiftz=0.55toz=0. Dressleretal.
by ≈ 0.2×z in ∆lnhM⁄L i, and ≈ 0.04×z in ∆hU - Bi. (1997) interpret the rapid evolution of the S0 fraction as evi-
B
van Dokkum et al. (1998b)found ∆lnhM⁄L i=(- 0.9±0.1)z dencefortransformationofspiralgalaxiestoS0galaxiessince
B
vanDokkum&Franx 9
z=0.55.AspointedoutbyFabricantetal.(2000)thedecrease tremelyhighredshiftinthismodel,whereastheS0galaxiesare
in the elliptical galaxy fraction over time requires substantial continuouslytransformedfromstarforminggalaxies.
accretionontoclusterssincez=0.55. Thisresultisinconflictwithstudiesofluminousearly-type
We model this evolution in the following way: we assume cluster galaxies at low and intermediate redshift, which indi-
thatthefractionofellipticalsisconstantwithtime,andthatS0 cate very little differencein luminosityweightedage between
galaxiesareformedfromthespiralgalaxiesthatarepresentin luminousellipticalandS0galaxiesinthecoresofrichclusters
theclustersatz=0.55. We ignorethefactthatinfallingspiral (e.g., Jørgensen, Franx, & Kjærgaard 1996, Ellis et al. 1997,
galaxies are also transformed into S0 galaxies. The evolution van Dokkum et al. 1998a, Jones, Smail, & Couch 2000, Kel-
oftheS0galaxiesisapproximatedreasonablywellbyamodel sonetal. 2000). OtherstudieshavereportedS0 galaxieswith
with a constant transformation rate (Fig. 5). The overpredic- younger stellar populations, but these tend to have low lumi-
tionof thefractionofS0 galaxiesathighredshiftimpliesthat nosities (e.g., Caldwell et al. 1993, van Dokkumet al. 1998b,
weunderestimatethedifferencesbetweentheellipticalandS0 Kuntschner&Davies1998).
galaxies.
Fig.6.—PredictedevolutionofthemeanM⁄L ratioforamodelwith
B
different evolutionary histories for elliptical galaxies and S0 galax-
ies. Itisassumedthatallellipticalgalaxiesformedatextremelyhigh
redshift,whereasS0galaxiesarecontinuouslytransformedfromstar
forminggalaxies. Thismodelpredictsadifferenceof∆ln(M⁄L )≈
B
0.24betweenluminous ellipticalgalaxiesandS0galaxiesat allred-
shifts.
Thereareseveralwaysinwhichthisconflictcanbesolved.
First, we canadaptthe starformationhistories. Themodelas-
sumes that star formation in elliptical and S0 galaxies com-
mencedatz=∞,andthattheirstarformationratewasapprox-
imatelyconstantfromt tot . Ifstarformationinelliptical
start stop
galaxies commenced at a later time the systematic difference
betweenellipticalandS0galaxiesisreduced.Ift =0.2t for
start 0
Fig. 5.—Evolutionofthenumberfractionofellipticalgalaxiesand elliptical galaxies (i.e., star formation commenced at z≈2.5)
S0 galaxies separately, from Dressler et al. (1997) (solid symbols). thesystematicdifferenceinM⁄LratiobetweenellipticalandS0
TheS0fractiondecreaseswithredshift,whereastheellipticalfraction galaxiesatz=0 is verysmall. However,it increasesto ≈0.3
increases. Thedottedlinesarelinearfitstothedata. Thesolidlines
inln(M⁄L )atz=0.8. Thiscorrespondstoasystematicdiffer-
showtheevolutioninourhybridmodel. B
enceinU- Bcolorof0.06,whichisinconsistentwiththelow
scatterintheCMrelationofearlytypegalaxiesatz=0.83(van
In our first models, we assume that the star formation rate
for the spiral galaxies is constant in time (f∗ =0.5), and that Dokkumetal.2000).
Analternativeexplanationforthesmallobserveddifference
starformationstartsatt =0forallgalaxies. Figure6shows
theevolutionofthemeasntarMt ⁄Lratiointhismodel,forelliptical betweenluminousellipticalandS0galaxiesisthatmostoftheir
starswereformedatveryhighredshift.Inourmodels,thiscor-
galaxies(dottedline), S0 galaxies(dashedline), andelliptical
and S0 galaxiescombined(solid line). Themodelreproduces respondstolowvaluesof f∗,theparameterdescribingthestar
the observedevolutionofthe M⁄L ratioofthe combinedsam- formationhistory.ThesystematicdifferenceinM⁄Lratioscales
ple of elliptical galaxies and S0 galaxies. However, elliptical linearlywith f∗, andforvaluesof f∗ ∼<0.2thesystematicage
galaxies in this model have systematically higher M⁄L ratios difference between elliptical and S0 galaxies is ∼< 5% at all
redshifts.Thisexplanationcanbetestedwiththehelpofdirect
and redder colors than S0 galaxies at all redshifts. The dif-
ference is ≈0.24 in lnM⁄L , or ≈0.05 in U- B color. This measurementsofthestarformationratesofthespiralgalaxies
B inintermediateredshiftclusters.
differencecorrespondstoadifferenceof≈20%inluminosity
Athirdpossibilityisthattheeffectsofmetallicitycancelthe
weightedage(e.g.,Wortheyetal.1994). Thislargedifference
effectsofage(e.g.,Worthey,Trager,&Faber1996,Shioya&
arises because all elliptical galaxies formed their stars at ex-
10 Early-TypeGalaxiesinClusters
Bekki1998,Trageretal.2000). Thespiralgalaxieswouldbe z<1, starformationcommencedatearlytimes(z>2.5),and
enriched in metals compared to the elliptical galaxies of the starformationwasapproximatelyconstantpriortotransforma-
same luminosity, and hence their colors would be redder, and tion. Suchgradualstar formationhistoriesareconsistentwith
theirM⁄Lratioshigherthanthatofellipticalgalaxieswith the thelownumbersofstarburstgalaxiesseeninintermediatered-
sameage. Thissolutionrequiresexactfinetuningbetweenage shift clusters (e.g., Abraham et al. 1996, Balogh et al. 1998,
andmetallicitytokeepthescattersmall. Itcanbetestedbydi- Ellingsonetal.2000),althoughsomestarburstscouldbecon-
rect observations of absorption line strengths of elliptical and cealedbydust(Poggiantietal.1999).
S0 galaxies in nearby and distant clusters. The first studies The observed color and luminosity evolution of early-type
do notappeartoindicate significantdifferencesbetweenmas- galaxiescanbecorrectedfortheeffectsofprogenitorbias. We
siveellipticalandS0galaxies(e.g.,Kuntschner&Davies1998, haveshownthatforagivenmorphologicaltransformationrate
Jonesetal.2000,Kelsonetal.2001). the progenitor bias is proportional to the scatter in M⁄L ratio
Finally,theseparationofellipticalsandS0’sisverydifficult, or color. The correction is maximal if the scatter in the CM
and itis notclear whethera clear distinctioncan be madebe- relationandtheFPatz=0isentirelyduetoagevariationsbe-
tween elliptical galaxies and S0 galaxieswith L∗ luminosities tween galaxies. This maximumcorrection to the evolution of
(e.g.,Jørgensen&Franx1994,Rix&White1990). Thelatter restframe∆lnhM⁄L iisapproximately- 0.2×z,andthecor-
B
studydemonstratedthatmanyellipticalgalaxiescontainsignif- rectiontotheevolutionofrestframe∆hU- Biisapproximately
icant disks, and would be classified as S0 galaxieswhen seen - 0.04×z. Thesecorrectionscaneasilybecomputedforother
edge-on. JorgensenandFranxarguedthatthe Coma elliptical restframebandsusingstellarpopulationsynthesismodels. As
and S0 galaxies can be approximatedwell by a population of anexample,theWorthey(1994)andBruzual&Charlot(2000)
galaxies which has a homogeneousdistribution in the ratio of modelsgive∆(U- V)≈1.7∆(U- B)forsolarmetallicityand
bulge light to total light. In this case, no clearcut distinction Salpeter(1955)IMF. Therefore,the correctionto ∆hU- Vi is
wouldexistbetweenS0galaxiesandellipticalgalaxies,andthe ∼- 0.07×z. The correctionsare upper limits, because varia-
evolutionary histories would not be so different between the tionsindustcontentandmetallicityprobablycontributetothe
galaxies. This might also explain the fact that the classifica- scatter. Ontheotherhand,aspointedoutby,e.g.,Trageretal.
tionsbetweendifferentauthorsagreewellwhenthetotalfrac- (2000) variations in metallicity and age may conspire to pro-
tion of elliptical and S0 galaxies is considered, but not when ducealowscatter. Ifthisisconfirmedthecorrectionsmaybe
the classes are separated (e.g., Andreon1998, Fabricantet al. largerthanthevaluesgivenhere.
2000).Quantitativeclassificationswouldbeabletoresolvethis Becausethemeanluminosityandcolorevolutionareunder-
issue, especially if detailed attentionis givento the classifica- estimated,themeanageofthestarsinearly-typegalaxiesthatis
tionuncertaintiesduetoprojectioneffects. derivedfrom them is overestimatedin traditionalmodels. We
find that the mean luminosity weighted formation redshift of
6. SUMMARYANDCONCLUSIONS aenardlyΩ-tΛyp=e0g,aolarxhize∗sic=an2.b0e-+00a..23sfloowrΩamsh=z∗0i.3=a3n.0d+-Ω00..95Λf=or0Ω.7m,i=f0th.3e
Inthispaperwehavequantifiedtheeffectsofmorphological scatterintheCMrelationandtheFPisentirelycausedbyage
evolution on the observed properties of early-type galaxies in variations. This result is important, because previous studies
clusters at 0<z<1. A manifestation of morphologicalevo- whichignoredtheeffectsofprogenitorbiasfoundmuchearlier
lutionisthe“progenitorbias”: athighredshift,theprogenitors formation epochs of the stars in early-type galaxies (e.g., El-
oftheyoungestpresent-dayearly-typegalaxiesdropoutofthe lisetal.1997,Stanfordetal.1998,vanDokkumetal.1998a).
sample. In general, the observedevolution of the mean lumi- Theredshiftrange2–3isofinterestbecauseitisobservation-
nosity and color of early-typegalaxies is slower than the true allyaccessible. Inparticular,ourresultsareconsistentwiththe
evolutionofallprogenitorsofearly-typegalaxies,andthescat- ideathat(some)Ly-breakgalaxiesarethestarformingbuilding
terinluminosityandcolorissmaller. Ifmorphologicalevolu- blocksofpresent-dayearly-typegalaxiesinclusters(Baughet
tionisstrongtheobservedmeanevolutionissimilartothatof al.1998).
asingleagestellarpopulationformedatz=∞,andthescatter In our main analysis we treated the evolution of early-type
is approximately constant with redshift. These results can be galaxiesasoneclass,butwealsoexploredamodelwhichsep-
derivedanalytically(cf.AppendixA). aratesthetwoclasses. Inourmodel,onlytheS0galaxiesevolve
Intraditionalmodelsitisdifficulttoexplainthelownumber morphologicallyfromspiralgalaxies,asadvocatedbyDressler
fractionsofearly-typegalaxiesindistantclustersandthehomo- etal.(1997). ThemodelpredictsthatcolorsandM⁄Lratiosof
geneityandslowevolutionoftheirstellarpopulationssimulta- luminousS0galaxiesinnearbyclustersaresystematicallyoff-
neously. We have shown that the observed constantscatter in setfromthoseofellipticalgalaxies,in thesensethatelliptical
theCMrelationandtheFPandtheslowevolutionofthemean galaxiesareredderandhavehigherM⁄Lratios.Thisresultisin
M⁄Lratioarenaturalconsequencesofmorphologicalevolution. conflict with studies of brightearly-type galaxies in the cores
Observationsofearly-typegalaxiesinclustersat0<z<1are of rich clusters, which generallyfind very little differencebe-
wellfittedbyourmodels,andwecanconstrainthemorphologi- tweenellipticalandS0 galaxies(e.g., Bower etal. 1992,Ellis
caltransformationrateandthestarformationhistoriesofgalax- et al. 1997). There are several ways to resolve this conflict:
iespriortotransformationfromthefits.Theobservedevolution star formationmayhavestarted later in the ellipticalgalaxies,
of the early-typegalaxyfractionconstrainsthe transformation ormostofthestarformationinellipticalandS0galaxiesmust
rate,theevolutionofthemeanM⁄Lratioconstrainsthetimeof have occurred at very early times, long before morphological
onsetofstar formation,andthe scatter inthe color-magnitude transformationtoearly-typegalaxy. Alternatively,theremight
relation and the Fundamental Plane constrain the star forma- beaconspiracybetweenageandmetallicity(e.g.,Trageretal.
tion historiesofgalaxiespriorto transformation. The bestfits 2000)such thatS0 galaxieshave systematically highermetal-
are obtained if approximately 50% of present-day early-type licities than elliptical galaxies of the same luminosity. This
galaxies were transformed from other morphologicaltypes at