Mon.Not.R.Astron.Soc.000,1–20(2005) Printed2February2008 (MNLATEXstylefilev2.2) Downsizing by Shutdown in Red Galaxies A. Cattaneo1⋆, A. Dekel2,†, S. M. Faber3, B. Guiderdoni4 1Astrophysikalisches Institut Potsdam, an der Sternwarte 16, 14482 Potsdam, Germany 2Racah Institute of Physics, HebrewUniversity of Jerusalem, 91904 Jerusalem, Israel 3UCO/Lick Observatory, Universityof California, USA 4Centre de Recherche Astrophysique de Lyon, France 8 ⋆acattaneo@aip.de, †dekel@phys.huji.ac.il 0 0 2 2February2008 n a J ABSTRACT 0 1 We addressthe originofthe ‘downsizing’ofellipticalgalaxies,accordingtowhich the starsinmoremassivegalaxiesformedearlierandoverashorterperiodthanthose ] h in less massive galaxies. We show that this could be the natural result of a shutdown p of star formation in dark matter haloes above a critical mass of ∼ 1012M . This is ⊙ - demonstratedusingasemi-analyticsimulationofgalaxyformationwithinthestandard o hierarchicalscenarioofstructureformation.Theassumedthresholdmassismotivated r t by the prediction of stable shock heating above this mass and the finding that such a s a shutdown reproduces the observed distribution of galaxies in luminosity and colour. [ The shutdown at a critical halo mass introduces a characteristic stellar mass for the transitionof galaxiesinto the ‘red sequence’of the galaxycolour-magnitudediagram. 1 Centralgalaxies of haloes that are more massive today have reachedthis mass earlier v andcanthereforegrowfurtheralongtheredsequencebydrymergers,endingupmore 3 massive and containing older stars.Small galaxies formed in haloes below the critical 7 6 masscanshutdownlate,whentheyfallintohaloesabovethecriticalmassandbecome 1 satellites. While our semi-analytic simulation that incorporates an explicit shutdown . reproduces downsizing as inferred from the stellar ages of ellipticals, we explain why 1 it is much harder to detect downsizing using the mass functions of different galaxy 0 types. 8 0 Key words: galaxies:clusters—galaxies:ellipticals—galaxies:evolution—galax- : v ies: formation — galaxies: haloes i X r a 1 INTRODUCTION 2003; Uedaet al. 2003; Heckman et al. 2004; Barger et al. 2005; Hasinger et al. 2005). Another form of downsizing, termed ‘archaeological The term ‘downsizing’ was coined by Cowie et al. (1996) downsizing’ (Thomas et al. 2005), is inferred from the to describe the decline with time of the K-band rest- stellar populations of today’s galaxies. Star formation frame luminosity of the galaxies with the highest spe- cific star formation rate M˙ /M (SFR) as ob- histories derived from observed line indices and abun- star star dance ratios using stellar evolution models reveal a strong served in the redshift interval 0.2 < z < 1.7. correlation between mean stellar age and galactic stel- This ‘downsizing in time’ has been confirmed by later lar mass both in elliptical galaxies (Nelan et al. 2005; studies (Guzman et al. 1997; Brinchmann & Ellis 2000; Thomas et al. 2005; Graves et al. 2007) and in the gen- Kodama et al. 2004; Juneau et al. 2005; Bell et al. 2005; eral population of galaxies from the large Sloan Digital Noeske et al. 2007). It can be viewed as part of a more SkySurvey(SDSS;Heavenset al.2004;Jimenez et al.2005; general phenomenon valid robustly across the Hubble se- Panteret al.2006).Inthecurrentstudywefocusonarchae- quence of galaxy types, in the sense that galaxies of later ological downsizing, as we address red galaxies that show type, which are typically less massive, are known to have only little active star formation at present. formed their stars most efficiently at later times and over longer periods (Searle et al. 1973; Tinsley 1973; Sandage Atafirstglance,theobserveddownsizingseemstobein 1986). A possibly related downsizing is evident in the ac- conflict with the standard wisdom of hierarchical structure cretion histories of supermassive black holes (Steffen et al. formation, according to which smaller objects collapse ear- (cid:13)c 2005RAS 2 A. Cattaneo, A. Dekel, S. M. Faber, B. Guiderdoni lierandgradually assembleintomoremassiveobjects. This plications of such a scenario have been studied using semi- apparent conflict is relaxed when realizing that star forma- analyticsimulationsbyCattaneo et al.(2006),Croton et al. tion and gravitational assembly are two distinct processes. (2006)andBower et al.(2006),eachapplyingaslightlydif- Inparticular,starscanformfirstinthesmallbuildingblocks ferentshutdownproceduredrivenbyhalomass(plus,some- of today’s massive galaxies without violating the assembly times,bulgemassorcentralblackholemass).Theformation hierarchyofeachgalaxy.Infact,ifgasprocesseslimitgalaxy of the red sequence through the quenching and reddening formation to dark matter haloes above a minimum mass, a of blue galaxies has also been studied by Bell et al. (2004) certain downsizing trend arises naturally from the hierar- and Faber et al. (2007). Here we highlight a particular as- chical dark matter assembly process itself (Neistein et al. pect of the quenching mechanism, associated with the fact 2006). Still, the origin of downsizing as observed requires a thatthecriticalmassforquenchingisroughlyconstantafter more quantitativetheoretical understanding. z∼2−3. Recent developments in the modelling of galaxy Inthisarticlewedemonstratethattheshutdownofstar formation (e.g. Cattaneo et al. 2006; Bower et al. 2006; formationaboveacriticalhalomassMcrit ∼Mshockatz<3 Croton et al.2006)havebeendrivenbytherealization that accounts for downsizing in the red galaxy population. The galaxies are divided into two major distinct types: blue keyideaisthatcentralgalaxiesstopmakingstarsandenter star-forminglate-typegalaxiesinlow-densityenvironments, the red sequence at a critical stellar mass Mcrit of the or- star red and dead early-type galaxies in groups and clusters derofthebaryonicmassinahaloofmass M .Galaxies shock (Lin et al. 1997, 1999; Im et al. 2001; Stratevaet al. 2001; with higher final stellar mass reach Mcrit earlier and there- star Kauffmann et al. 2003; Baldry et al. 2004; Balogh et al. fore have more time to grow through dissipationless (‘dry’) 2004; Bell et al. 2004; Hogg et al. 2004; Weineret al. 2005; mergers along thered sequence. seeDekel & Birnboim2006forasummaryofthebimodality There are three complications to this simple picture, phenomenon).Combinedwiththefactthatbluegalaxiesare whichwediscussinthisarticle.First,satellitegalaxies shut confinedbelowacriticalstellarmassofMsctraitr ∼3×1010M⊙ down earlier than central galaxies with thesame mass, and while the population above this mass is dominated by red theyoftendoitbeforetheyhavereachedMcrit (e.g.because star galaxies, the colour bimodality itself is evidence for down- theirhalohasmergedintoanotheronewithmass>M ). shock sizing. It indicates that the most massive galaxies, the red Second, the expected penetration of narrow cold streams ones,haveconvertedtheirgasintostarsseveralbillionyears through the hot media of massive high-redshift haloes ele- ago, while less massive galaxies, which are mostly blue, are vates the effective M to values above M at z > 3 crit shock still making stars. (Dekel& Birnboim 2006; Cattaneo et al. 2006). Third, ad- Downsizing is not only a reflection of the galaxy bi- ditionalshutdown mechanismsmay beat work, e.g. theex- modality. It is also valid separately within each of the two haustion of gas after major mergers and/or feedback from populations, the red one (Nelan et al. 2005; Thomas et al. the central black hole. We have attempted to mimick these 2005; Graves et al. 2007) and the blue one (Drory et al. effects by intoducing a further shutdown criterion related 2006; Noeske et al. 2007). Less massive galaxies contain to the bulge-to-disc ratio. The inclusion of a bulge-to-disc youngerstarsevenwithinthesamespectraltype.Neverthe- ratio criterion as a sufficient condition for quenchingin ad- less, we are tempted to consider the possibility that down- ditiontothehalo-masscriterionimprovesthefittothejoint sizing and bimodality originate from the same underlying colour-magnitude distribution of galaxies by accounting for physics. the presence of red galaxies in haloes below Mcrit, but its The existence of a characteristic mass for mas- overall effect is fairly minor (Cattaneo et al. 2006, Fig. 9). sive galaxies emerges from the the competition be- Downsizing has also been involved to explain the way tween the gravitational dynamical time and the radia- the stellar-mass functions of galaxies of different colors or tive cooling time (Rees & Ostriker 1977; Binney 1977; morphological types evolve with time. In particular, while Silk 1977; White & Rees 1978; Blumenthal et al. 1984). the comoving number density of blue galaxies has not Birnboim & Dekel (2003) and Dekel & Birnboim (2006) changed much since z ∼ 1, the number of red galaxies showed that a stable shock can expand to the virial ra- has seemingly grown by a larger factor at the faint end dius and be supported against gravity only in haloes above thanatthebrightend(Rudnicket al.2003;Bell et al.2004; a critical mass of Mshock ∼ 1012M⊙, producing a hot Drory et al. 2004; Bundyet al. 2005; Drory et al. 2005; medium at the virial temperature of T > 106K. In smaller Borch et al. 2006; Pannella et al. 2006; Faberet al. 2007). haloes, efficient cooling does not allow an extended sta- We argue below that the interpretation of this behavior as ble shock, so the accreting gas flows cold into the cen- downsizing is hampered by severe measurement uncertain- tre, leading to the buildup of discs and efficient star for- ties (see theAppendix)and conceptual misunderstandings. mation. This phenomenon was detected in parallel in cos- The paper outline is as follows. In § 2, we describe our mological simulations (Kereˇs et al. 2005; Birnboim et al. model of galaxy formation explored by means of a semi- 2007; Cattaneo et al. 2007), confirming the existence of analytic modelling technique applied to merger trees from a threshold mass that is quite independent of redshift. acosmological N-bodysimulation,followingCattaneo et al. Dekel& Birnboim (2006) argued that the transition from (2006). In § 3, we elaborate on how the shutdown of star cold flows to the shutdown of gas supply and star forma- formation leads to downsizing. In § 4, we show how the tion at M , which is predicted to be more pronounced shutdownproducesdownsizinginthebuildupoftheredse- shock after z ∼ 2−3, naturally leads to many of the observed quence, in the sense that the high-mass end is populated features associated with the galaxy bimodality. In partic- at earlier times. In § 5, we perform a comparison with the ular, the bimodality scale Mcrit is the typical stellar mass archeological downsizinginferredfromthestellaragesinel- star of the central galaxy in a halo with mass M . The im- liptical galaxies (Thomas et al. 2005). In § 6, we consider shock (cid:13)c 2005RAS,MNRAS000,1–20 Downsizing by Shutdown in Red Galaxies 3 thecharacteristictimesofgalaxyformation intermsofstar a ‘new’ model, which differ in the way gas from the halo formation history and mass assembly history, and use this accretes onto the central galaxy. analysistoaddresstheapparentconflictbetweendownsizing In the ‘standard’ model, the initial gas distribution andthehierarchicalmodel.In§7,weexplainhowdownsiz- is a singular isothermal sphere, at the virial temperature, inginstarformationandupsizinginmassassemblycombine truncated at the virial radius. The cooling time of the hot to produce the evolution of the mass functions of red and gas is computed using the radiative cooling function of blue galaxies, and why it is hard to detect downsizing us- Sutherland& Dopita (1993). The gas for which both the ing the mass functions of different galaxy types. In § 8, we cooling time and the free fall time are shorter than the summarizetheconclusionsofthearticle.Thedownsizingin timestep∆tbetweentwoN-bodysnapshotsisaccretedonto bluegalaxies will beaddressed in a separate publication. thecentralgalaxyduringthattimeinterval.Thetransferof baryons from the halo to the galaxy is accompanied by an inflowofhotgastokeepthehotgasdistributionatruncated singularisothermalsphere.Thenumericalaccuracyandthe 2 THE GALAXY FORMATION MODEL self-consistency of this cooling algorithm havebeen verified GalICS (Galaxies In Cosmological Simulations; by comparison with a cosmological hydrodynamic simula- Hatton et al.2003)isamethodtosimulatetheformationof tion based on the same physics and the same dark-matter galaxies in a ΛCDM Universe. It combines high-resolution realization (Cattaneo et al. 2007). cosmological N-body simulations of the gravitational In the ‘new’ model, we introduce the proposed clustering of the dark matter with a semi-analytic (SAM) quenching above a threshold halo mass, following approach to the physics of the baryons (gas accretion, Dekel& Birnboim (2006). Once a halo grows above galaxy mergers, star formation and feedback). The version Mshock ∼ 1012M⊙, the halo gas is assumed to be shock- of GalICS used here, as well as the adopted values of the heated to the virial temperature. Unlike previous models, parameters, are the same as described in Cattaneo et al. onceheated,thehotgasiskepthotforever.Thiscanbedue (2006, and references therein). We summarize here the to several different long-term quenching mechanisms, such relevant issues. as self-regulated radio-AGN feedback (e.g. Croton et al. 2006; Cattaneo & Teyssier 2007, and references therein), shocked accretion (Birnboim et al. 2007), or gravitational 2.1 Dark-matter simulation quenching by clumpy accretion (Dekel& Birnboim 2007; Khochfar & Ostriker2007).Thecriticalmassforquenching ThecosmologicalN-bodysimulationthatfollowsthehierar- is assumed to be chicalclusteringofthedark-mattercomponenthasbeencar- riedoutwiththeparalleltreecode.Theassumedcosmologi- Mcrit =Mshock×max{1, 101.3(z−zc)} , (1) cstaalnmtoodfeΩlΛis=a0fl.a6t6Λ7,CaDHMubUbnleivceornssetwanitthofaHco0s=mo6l6o.g7ickaml cso−n1-, twehrmere∝M1s0h1o.c3kz∼ac1c0o1u2nMts⊙foirs tthhee spheoncekt-rhaetiaotninogfsccoallde astnrdeatmhes andaΛCDMpowerspectrumofinitialfluctuationsnormal- in massive haloes at high redshift (Dekel & Birnboim 2006, ized to σ = 0.88. The computational volume is a cube of 8 Fig. 7). In Cattaneo et al. (2006), we set the parameters to side (150Mpc)3 with 2563 particles of 8.3 ×109M⊙ each Mshock =2×1012M⊙andzc=3.2byoptimizingthewaythe and a smoothing length of 29.3kpc. The simulation pro- new model fits the colour-magnitude distribution at z ≃ 0 duced 100 output snapshots spaced logarithmically in the and theLyman-break galaxy luminosity function at z≃3. expansion factor (1+z)−1 from z=35.59 to z=0. Inthestandardmodel,thereisnoexplicitshutdownof Wehaveanalysedeachsnapshotwithafriend-of-friend cooling, and the mass and luminosity of the central galaxy algorithm (Daviset al. 1985) to identify virialized haloes grow roughly linearly with halo mass over the entire range containingmorethan20particles.Theminimumhalomass resolved by the N-body simulation. Shutting down the hot is thus 1.65×1011M⊙. The three global properties charac- accretion modewhen M >M introducesacharacter- halo crit terizingeachhalotobeusedintheSAMarethevirialmass, isticmass(Fig.1)andluminosity,whichmarktheseparation thevirial density,and thespin parameter. Merger trees are between blue and red galaxies. constructedbylinkingthehaloesidentifiedineachsnapshot Initially, all galaxies are assumed toform at a distance with their progenitors in the previous snapshot, that is, all r = 0 from the centre of their halo. When two or more i predecessors from which thehalo hasinherited oneormore haloes merge, their galaxies are repositioned at a distance particles. We do not use substructure information from the r from the centre of the new halo, determined such that f N-bodysimulation. Instead, oncea halobecomes asubhalo r → r for M /M → 1 and r → r for M /M → ∞ f i f i f vir f i ofanotherhalo, weswitch from following itsevolution with (where M and M are the halo mass before and after the i f the N-body integrator to an approximate treatment based mergerandr isthevirialradiusofthemergedhalo.Halo vir on semi-analytic prescriptions. mergers rapidly create haloes with more than one galaxy, which we identify as galaxy groups and clusters. However, only the central galaxy is allowed to accrete gas from the 2.2 Semi-analytic modeling of gas processes halo (prior to quenching). A newly identified halo is assigned a gas mass based on a universal baryon fraction Ω /Ω = 0.135. The conditions b 0 2.3 Morphologies for the formation of a galaxy at its centreare that the halo is gravitationally bound and that its angular momentum GalICS models a galaxy with three components: a disc, a parameter is λ < 0.5. We have simulated a ‘standard’ and bulge and a transitional ‘starburst’ component. Each com- (cid:13)c 2005RAS,MNRAS000,1–20 4 A. Cattaneo, A. Dekel, S. M. Faber, B. Guiderdoni Figure 1. Galaxy stellar mass versus halo mass in the standard model (left) and the new model with shutdown (right). In the new model,thegeneral growthofMstar withMhalo breaksoffatMhalo∼Mshock∼2×1012M⊙.DifferencesatMhalo20m cm−2(m isthepro- gas p p timescale decreases by a factor of ten with respect to that tonmass).Furthermore,byimposingaminimumhalomass of the bulge (Section 2.4). Stars formed in the starburst ofMhalo =1.65×1011M⊙ duetotheN-bodyresolution,we are moved to the bulge after they have reached an age of effectively assume that there is no star formation in haloes 100Myr.Theonlygasinthebulgeisthatfromstellarmass below this mass, potentially mimicking the effects of more loss (§2.4). aggressive supernova feedback in small haloes (see below). The disc profile is assumed to be exponential, with its Moreover,inthenewmodelweassumeacompleteshutdown radius determined by conservation of angular momentum. of star formation in haloes with mass > M by removing crit ThebulgeisassumedtohaveaHernquist(1990)profileand all the cold present in any component of these galaxies and its radius is determined based on an energy conservation bymoving this gas tothe halo’s hot component. argument. The star formation efficiency parameter is assumed to We now elaborate on the two mechanisms for trans- be β∗ = 50 (Guiderdoniet al. 1998), the same for all com- ferring baryons from the disc to the spheroid. First, disc ponents.Wehaveα∗ =0inthestandardGalICSmodelbut instabilities transfer matter from the disc to the spheroid allow an enhanced star-formation rate at high redshift by (stars to the bulge, gas to the starburst) until the bulge adoptingα∗ =0.6inthenewmodel,tomimictherapidac- is massive enough to stabilize the disc. The stability cri- cretionbycoldflows.Thisimprovesthefittotheluminosity terion is v < 0.7v , where v and v are the disc’s ro- rot c rot c function of Lyman-break galaxies (Cattaneo et al. 2006). tation and circular velocity at the disc’s half mass radius Gas in transit from the disc to the bulge, whether (van den Bosch1998).Second,dynamicalfriction,modelled by mergers or disc instabilities, passes through a starburst as in Hatton et al. (2003), drives galaxies to the centre of phaseinwhichtheSFRgrowsbyafactorof10basedonthe their dark matter halo and is thedominant cause of galaxy dynamical time of the bulge. This high SFR is obtained by merging, althoughwealso includesatellite-satellite encoun- assumingthatthestarburstradiusistentimessmallerthan ters.Thefractionofthediscthatistransferredtothebulge the final bulge radius (see the hydrodynamic simulation in inamergergrowswiththemassratioofthemerginggalax- Cattaneo et al.2005).Asweanticipatedwhenwedescribed ies. It ranges from zero for a very minor merger to unity the different components of a galaxy, the stars formed in for an equal mass merger. This simplified picture of the the starburst component stay in the starburst component dynamicsof morphological transformations providesresults for 100Myr and then are moved to the bulge. The proper- consistent with the key observational constraints such as ties of low redshift galaxies are insensitive to the starburst the Faber-Jackson relation and the Fundamental Plane of star formation timescale as long as it is much shorter than spheroids (Hatton et al. 2003). theHubbletime. We assume a Kennicutt (1983) initial mass function. Stars are evolved between snapshots using substeps of at most 1Myr. During each sub-step, stars release mass and 2.4 Star formation and feedback energyintotheinterstellarmedium.Mostofthemasscomes The star formation law is thesame for all components: from the red giant and the asymptotic giant branches of (cid:13)c 2005RAS,MNRAS000,1–20 Downsizing by Shutdown in Red Galaxies 5 Figure2.Thetheu−rcolourdistributioninr-bandmagnitudebinsfortheSDSSdata(Baldryetal.2004;blacksmoothedhistogram) andforthreedifferentversionsofourSAM(redcurves). Left:thestandardmodelwithoutanexplicitshutdownofcentral galaxiesbut withastandardshutdownofgasaccretionontosatellites.Middle:AmodelwithshutdownofstarformationonceMhalo>Mcrit.Right: Sameasinthemiddle,withtheadditionalshutdownwhenMbulge>Mstar/2(reproducedfromCattaneo etal.2006). stellarevolution,whilemostoftheenergycomesfromshocks relationbetweenbolometricluminosityandinfraredcolours duetosupernovaexplosions.Theenrichedmaterialreleased observed locally in IRAS galaxies. In GalICS we only con- in thelatestages of stellar evolution is mixed with thecold sider each component’s self-absorption, e.g. the dust in a phase,whiletheenergyreleased from supernovaeisusedto starburst only obscures the starburst’s light, not the old reheat the cold gas and to return it to thehot phase in the bulge stellar population. halo. Reheated gas is ejected from the halo if the potential isshallowenough.Therateofmasslossthroughsupernova- driven winds M˙ is determined by theequation w 3 SHUTDOWN AND DOWNSIZING 1 2M˙wve2sc =ǫSNηSNESNM˙star, (3) In the new model, the accretion of gas onto the central galaxy is shut down once M > M . Both in the stan- halo crit where ESN = 1051erg is the energy of a supernova, ηSN = dard and the new model, as common in other SAMs, the 0.0093isthenumberofsupernovaefor1M⊙ ofstarsformed accretion of gas onto satellite galaxies is not allowed.1 Fig- and vesc is the escape velocity (Dekel& Silk 1986). In Gal- ure 1 shows that the stellar mass keeps pace with the halo ICS, we use vesc ≃1.84vc for discs and vesc =2σ for bulges mass up to Mcrit and then breaks off in the new model. It andstarbursts.ThesupernovaefficiencyǫSN ≃0.2issimilar also showstheeffect ofpreventingtheaccretion ofgas onto tothosecommonlyadoptedinSAMs(Somerville & Primack satellitegalaxies,whichareshownbythepointcloudsinthe 1999;Cole et al. 2000). lower right part of the diagrams. In order to maximize the quenching effect, whenever the shutdown criteria are satisfied we actually shut down 2.5 Stardust star formation altogether, that is, in addition tohaving the halogasshockheatedandtokeepingithot,weassumethat TheSTARDUSTmodel(Devriendtet al.1999)providesthe thecoldgasisremovedfromthegalaxiesandthatitisadded spectrum of a stellar population as a function of age and tothe hot halo. This can beachieved in central galaxies by metallicity and includes a phenomenological treatment of thermal evaporation (Nipoti & Binney 2007), and in satel- thereprocessingofstellarlightbydust.GalICSusesSTAR- lite galaxies by ram-pressure stripping (e.g. Bahcall 1977; DUST to compute the spectrum of each component and to Gallagher 1978). Cattaneo et al. (2006) demonstrated that output galaxy magnitudes. this robust shutdown leads to a good fit to the observed Dust absorption is computed with a phenomenological extinction law that depends on the column density of neu- tralhydrogen,themetallicity oftheobscuringmaterial and 1 Admittedly, this procedure may be too strict and should be therandomlyselectedinclinationangle(forspirals).There- revised, especially in small haloes with no hot medium, where emittedspectrumisthesumoffourtemplates(bigandsmall anyway it may be hard to distinguish between central galaxies carbon grains, silicates, and polycyclic aromatic hydrocar- andsatellites(e.g.Cattaneo etal.2007;alsoseeMcCarthyetal. bons). Their relative weights are chosen to reproduce the 2007). (cid:13)c 2005RAS,MNRAS000,1–20 6 A. Cattaneo, A. Dekel, S. M. Faber, B. Guiderdoni Figure 3.Colour-massdiagramforthe new model withshutdown. The‘greenvalley’separating the redsequence fromthe bluecloud is marked by the black line. Blue symbols mark galaxies in which the SFR has not been explicitly shut down. Red symbols denote central galaxies inwhich the SFRhas been shutdown because their halohas grownabove thecritical mass.Orangesymbols show the populationofsatellitegalaxiesinhaloesabovethecriticalmass.GreensymbolsarecentralgalaxiesofhaloeswithMhalo Mstar/2 (see Section 2.3). This ad- arises from the absence of quenched central galaxies with ditional quenching criterion slightly improves the fit to the Mstar ∼< 1 − 2 × 1011, since their haloes are below the SDSS colour-magnitude distribution near Mr ≃−21.5 (the shock-heating scale. This is the range where the ellip- ‘newmodel’inFig.2).Notethatthecoldgasisnotremoved tical population is dominated by rather discy configura- when a galaxy is quenched by this criterion alone. While tions, which do not show X-ray emission in excess of this is clearly a simplified ad hoc implementation of quasar the contribution of discrete sources (Bender et al. 1989). feedback, it has negligible effects at the bright end and at These galaxies could have been possibly quenched by the faint end, and it hardly affects the main results of our another mechanism, such as quasar feedback after gas- current analysis. rich mergers (Springel et al. 2005a; Hopkinset al. 2007), Onecouldconceiveanalternativescenariowherequasar following the notion that discy ellipticals emerge from feedback after galaxy mergers is the main shutdown mech- wet mergers (e.g. Cox et al. 2006), which also trigger anism (e.g. Hopkinset al. 2007), although it would have a quasar activity (Toomre & Toomre 1972; Cattaneo et al. hardtimeexplainingthelong-term maintenanceof quench- 1999;Kauffmann & Haehnelt2000;Cattaneo et al.2005a,b; ing.Thereissomeobservationalevidenceforsuchamecha- (cid:13)c 2005RAS,MNRAS000,1–20 Downsizing by Shutdown in Red Galaxies 7 Figure 4. Growth of halo mass (top) and stellar mass (bottom) for 24 galaxies randomly sampled from the four mass bins indicated (see Fig.3).The growth curves referto the mostmassiveprogenitors. Thebold blacklineintheupper panels isMcrit(z) above which coolingandstar formationareshut down(Eq. 1). Afterz∼3, Mcrit ∼Mshock ∼2×1012M⊙. AfterMhalo has crossedthis threshold, the central galaxy ceases to form stars and passively turns red and dead. Growth of the stellar mass after this point occurs only via mergers. The sudden jumps in Mhalo occur when a galaxy becomes a satellite in a larger halo. The passive fading of giant ellipticals afterz∼3−4iswelldescribedbythesimplerelationMB ∼−21.5−z±0.5(solidlinebetween thetwodotted linescorrespondingto ±0.5mag) . (cid:13)c 2005RAS,MNRAS000,1–20 8 A. Cattaneo, A. Dekel, S. M. Faber, B. Guiderdoni nism in action (Schawinski et al. 2007). Modelling this spe- 24 galaxies, the transition from blue to red coincides with cificscenarioisbeyondthescopeofthepresentpaper,where thetimewhenthehalomasscrossesM .Aslightdecrease crit we focus on the effect of halo quenchingon downsizing. of the stellar mass in the passive phase is due to the death In summary, the new model stops the accretion of gas of old stars not being replaced bynewones. Growth in this onto a galaxy when at least one of the following three con- phaseisbydrymergersonly,seen assuddenupwardsturns ditions is satisfied: (a) Mhalo > Mcrit, given by Eq. 1, or after Mstar(z) has flattened (Fig. 4), in contrast with the (b) Mbulge > Mstar/2, (c) the galaxy has become a satel- smoother growth of Mstar dueto star formation. lite.Whenthequenchingisbycondition(a),thecoldgasis The most massive galaxies have final stellar masses in explicitly removed, but even in the other cases the starved the range 1011.7M⊙ ∼< Mstar ∼< 1011.9M⊙. In these galaxies, galaxies rapidly exhaust their gas and stop making stars. Mstar ≫ Msctraitr because their haloes started forming very Fig. 3illustrates viadifferentcolours theroleof thesethree early and crossed Mcrit when the entry mass was larger different mechanisms in producing the galaxy bimodality. than Msctraitr ∼ 1011M⊙. The upturn of Mcrit(z) at z > 3 Weseethathalo-massquenching(a)isthemainmechanism causesmost ofthesegiant galaxies tobecome red-and-dead forMstar ∼> 2×1011M⊙,andthatthebulgequenchingcrite- almost simultaneously at z ≃3.5−4.Their post-quenching rion (b) plays a role near Mstar ∼ 1011M⊙, while most low luminosityevolutionisreasonablywelldescribedbyasimple massgalaxiesarebothquenchedbyhalomass(a)andsatel- relation of theform lites (c). Only 3% of the red sequence at Mstar > 1010M⊙ M ∼−21.5−z±0.5 (4) ismadeofgalaxiesthatarequenchedonlybecausetheyare B satellites(c).Although57%oftheredsequenceiscomposed (diagonal solid line and ±0.5mag dotted lines in Fig. 4). of galaxies with Mbulge>Mstar/2, only 24% of red galaxies Thehaloesofthesegalaxiescorrespondtothesitesofgalaxy are quenched by criterion (b) only; ∼ 10% of the galax- clusters at low redshifts. ies quenched by criterion (b) only are red because they are Frequent mergers inside massive haloes provide an ad- dusty.These galaxies are remnants of recent gas-rich merg- ditional mechanism for the growth of giant galaxies that ers. They haveceased toaccrete gas, but they havenot yet can raise their mass up to Mstar ∼ 1012M⊙. Indeed, five ceased to makestars. They account for ∼2% of the red se- out of our six massive galaxies grow by a factor of ∼ 2-3 quence at Mstar > 1010M⊙. About 8% of the red sequence through dry mergers after entering the red sequence. This at Mstar > 1010M⊙ is made of galaxies that have not been latemergingagreeswithsemianalyticmodellingcalculations explicitly quenched by any of the three mechanisms above byDeLucia et al.(2006)andDeLucia & Blaizot(2007).A (blue points in Fig. 3). The breakdown of this 8% is as fol- note of caution regarding the comparison of these predic- lows. About 7% are spiral galaxies that have naturally run tions to observations is that the light associated with the outofgaswithoutanobviousexternaltrigger,andtheother growing stellar mass at the centres of galaxy clusters may 1%areredbecausetheyaredusty.Inconclusion,3% ofthe be spread out across a non-negligible fraction of the clus- red sequence, a rather low fraction, is red because of dust. ter volume. Combined with observational limitations, this The shutdown of star formation when the halo mass may lead to an underestimate of the stellar mass in bright- grows above Mcrit introduces the notion of an ‘entry mass’ estclustergalaxiesatthecentersofclusters(Gonzalez et al. totheredsequence,Msctraitr,thatisthetypicalstellarmassof 2005; Lauer et al. 2007; Faber et al. 2007). thecentral galaxy of an Mcrit halo (Faberet al. 2007). The Theupper-intermediatemassbininFig.4(1011.2M⊙ < entrymassispredictedtobeconstantafterz∼2andhigher Mstar <1011.3M⊙)ispopulatedbycentralgalaxiesinwhich at higher redshifts (Dekel& Birnboim 2006). Its value at Mhalo has crossed Mcrit at z∼< 3, where Mcrit = Mshock z∼< 2 is under 10% of Mshock ∼ 1012M⊙, given the univer- (Eq. 1). All of these galaxies enter the red sequence with sal baryonic fraction of ∼ 0.15 and assuming that at least a same stellar mass of Msctraitr ∼ 1011M⊙. In both the high halfofthegasispreventedfrom makingstarsduetostellar and the upper-intermediate mass bin there is a strong cor- feedback. relation between the final stellar mass and the redshift at We illustrate the connection between shutdown, entry which the galaxies become red. Galaxies that enter the red massanddownsizingbycomparingthehaloandstellarmass sequence earlier end up being more massive at z ∼ 0, even growthhistoriesofgalaxieswithdifferentfinalstellarmasses whentheentrymassissimilar,becausetheyhavemoretime (Fig.4).Weconsiderfourmassbinsalongtheredsequence to grow through drymergers along thered sequence. in the colour-mass diagram (corresponding to the four red In contrast, the two lower mass bins (1010.7M⊙ < parallelograms in Fig. 3) and select six galaxies at random Mstar < 1010.8M⊙ and 1010.2M⊙ < Mstar < 1010.3M⊙) are fromeachbin.Themassintervalscorrespondingtothefour dominated by satellite galaxies, identified in Fig. 4 by an bins covera factor of forty in stellar mass, from ∼0.2Mcrit abruptbigrise in their halomass growth as theyfall intoa star to ∼8Mcrit. massive host halo. As satellites, they have a lower merging star All galaxies display an initial phase, in which the stel- rate,withthegrowthbydrymergersalongtheredsequence lar mass grows rapidly,followed by shutdownand a passive playingaroleonlyinacoupleofthelow-intermediatemass phase,inwhichthestellarmassremainsessentiallyconstant galaxies, and in none of the low-mass galaxies. For most of (Fig.4).Thetransitionbetweenthetwophasesisaccompa- the low-mass galaxies, the transition to the red sequence niedbyaveryfastreddeningoftheU−Bgalaxycolour.This corresponds to a merger of their dark matter halo into a reddeningisrecognizable asaverticaljumpupwardinadi- halo more massive than M , causing them to shut down crit agram ofcolourvs.stellarmass(Fig.5,leftcolumn).Itcan assatellites. Asthetimingsoftheseeventsarenot strongly also be seen in the galaxies’ evolutionary colour-magnitude correlated with thehalo massbefore merging,thelow-mass tracks(Fig. 5,right column), asit correspondsto thepoint galaxiesdisplayawidespreadinquenchingtimes,whichare where the galaxies start fading and reddening. In 23 out of not directly related to final mass. (cid:13)c 2005RAS,MNRAS000,1–20 Downsizing by Shutdown in Red Galaxies 9 Figure 5.Timeevolutioninthecolour-massdiagramforgalaxiesthat arecurrentlyinfourdifferentmassbinsalongtheredsequence, whicharethesameasinFig.3andFig.4.Thehistorytracksrefertothemostmassiveprogenitors.Thecolourassignedtoeachgalaxy isthe same as inFig.4. The greendashed linemarks the green valleythat separates the redsequence fromthe bluecloud at z ∼1in our model (see Fig. 6). The symbols refer to two different redshifts,as indicated, and show the pace at which galaxies move along the colour-mass tracks. Ignoring bursts of star formation, galaxies get steadily more massive and redder until they turn much redder in a shorttimeonce theyarequenched. Smallsatellitesarequenched andthenkeep afixedmass.Massivegalaxiescontinue togrowbydry mergers after they are quenched. The massive galaxies with Mstar∼>1011.7M⊙ have already been quenched by z =3. Dry merging is not apparent at Mstar ∼<1011M⊙. It becomes an important growth mechanism above this mass. We have plotted this figure assuming thatallgalacticdiscsareobservedface-on. (cid:13)c 2005RAS,MNRAS000,1–20 10 A. Cattaneo, A. Dekel, S. M. Faber, B. Guiderdoni Onelower-intermediatemassgalaxy(lightblue)resides 1996;Tremblay & Merritt1996;Gebhardt et al.1996).The in a halo less massive than M (and thus appears as one transition from wet to dry mergers may also be related to crit ofthe7%bluesymbolsinFig.3).Thisgalaxyhasnotbeen thedivisionofellipticalsaccordingtotheirinnerdensitypro- quenchedbyanyofthethreeexplicitmechanisms,butrather files,wheregiantellipticalsshowcoresandlessmassiveones ran out of gas by continuousstar formation. show power-law cusps, possibly reflecting gas-rich mergers Oneofthelow-massgalaxies(fuchsia)hasbeenthecen- (Faberet al. 1997;Lauer et al. 2007).This transition is ob- tral galaxy of a halo that reached nearly 1013M⊙ before it served at MV ≃ −20.5, which is ∼ 1010.8M⊙ (assuming crossedMcrit atz∼> 3.However,thisgalaxyremainedsmall M/LV ≃6×10−0.092(MV+22)M⊙/L⊙ basedontheM/Les- because it was quenched before it had time to convert into timates of Gebhardt et al. (2003)). This is indeed close to stars the gas that had accreted and was accreting onto it. our estimated entry mass of Msctraitr ∼1011M⊙, below which To conclude, Fig. 4 demonstrates that shutdown at a thegrowth is mainly by wet mergers. constant critical halo massintroducesaratherconstant en- Thesametransitionmassistypicallytheminimumen- try mass for central galaxies into the red sequence. Central try mass for central galaxies. It is also comparable to the galaxiesthatentertheredsequenceearlierendupmoremas- brightedgeofthebluecloud.Thefact thatthisbrightedge sivebecausetheyhavemoretimefor subsequentgrowth by is constant with time reflects the fact that the entry mass drymerging.NotethatthedownsizingofM athighred- for central galaxies is roughly constant after z∼2. crit shiftpredictedbyDekel & Birnboim(2006)initselfinduces Thelow-massbinandthelowerintermediatemassbins, a downsizing in the entry mass, which enhances the effect whicharedominated bysatellites, aremainlypopulated af- ofarchaeological downsizingintoday’sgiantellipticals.Dry ter z ∼ 1. Low mass galaxies make an abrupt transition merging is important in the growth of massive red galax- from blue to red at masses lower than the minimum entry ies with Mstar > 1011M⊙. Galaxies that become satellites massfor centralgalaxies. This isconsistent with thenotion enter the red sequence with masses lower than the charac- thattheyarequenchedwhentheyfallintolargerhaloesand teristic entry mass, and they dominate today’s population become members of groups or clusters. at Mstar ≪1011M⊙. We notice that at z ∼ 2 the red sequence has a rather constantcolourindependentofmass,andthatatiltdevelops gradually in time. The origin of this effect, and its relation to downsizing, will beaddressed elsewhere. 4 DOWNSIZING IN THE ASSEMBLY OF THE RED SEQUENCE In this section, we show that the shutdown above a critical 5 ARCHAEOLOGICAL DOWNSIZING IN halomassproducesdownsizinginthebuildupoftheredse- STELLAR AGES quence,in thesensethatthehigh-mass endispopulatedat earlier times.Forthispurpose,weconsiderin Fig.6alarge Perhaps the most useful way to measure downsizing is by randomly selected sample of 8,000 galaxies, except that all comparing thedistribution of stellar ages in galaxies of dif- the giant galaxies with Mstar > 1011.5M⊙ are included for ferent masses. Thomas et al. (2005) deduced stellar ages better statistics. We plot a series of colour-mass diagrams, from the absorption line indices Hβ, Mg b and for a whichshowthesegalaxiesatz=0,andtheirmainprogeni- sample of 124 early-type red sequence galaxies. They fitted torsathigherredshifts.Theredsymbolshighlightthegalax- the distribution of stellar ages in galaxies of a given stellar iesthatendupontheredsequenceinfourdistinctmassin- mass using a Gaussian, with the mean time and standard tervals,LogM =[10,10.5], [10.5,11], [11,11.5], [11.5,12]. deviation as free parameters. Their main finding, as read star Theoverallpopulationexhibitsthesamebehaviourseen from their Fig. 10, is that the mean stellar age is increas- inFig.4.Thedistinctionbetweenabluecloudandaredse- ing with mass, while the scatter is decreasing with mass. quenceisalreadypresentatz∼> 2(inagreementwithFIRES They also find that the mean stellar age is increasing with observations; Giallongo et al. 2005), with about 60% of the environmentdensityat agiven stellarmass. Itisimportant most massive galaxies already on the red sequence at that to realize that the measured age spreads are inferred from redshift. Upper intermediate mass galaxies grow along the [α/Fe] and not from detailed modelling of galaxy spectra. blue cloud until they reach the entry mass, near the upper Moreover,thespreadinthetimesatwhichdifferentgalaxies masslimitforthebluecloud,wheretheyturnred.Themost attain their peak SFR may be significantly larger than the massive galaxies climb up to the top of the blue sequence, age spread in each galaxy, which is what [α/Fe] measures. turn red, then continue their growth by dry merging along Takingthese differences intoaccount is important when we thered sequence. compare the age spread estimated by Thomas et al. (2005) Themassgrowthduetodrymergersisafactorof∼2.5 with those obtained from themean star formation histories inthehighestmassbinand∼1.7intheupper-intermediate in our model. mass bin. It becomes negligible below 1011M⊙. This tran- TocompareourmodelwiththeresultsbyThomas et al. sition from wet to dry mergers may be related to the ob- (2005), we should consider all the stars that end up in a served division of elliptical galaxies into two major types, givenredgalaxy,andnotjustthosethatformed initsmost giant boxy non-rotating ellipticals versus the smaller discy massiveprogenitor.Fig.7plotsthepredictionsofourmodel rotatingellipticals. Indeed,theorigin ofthisdistinctionhas forthedistributionofstellar agesin thespheroidsofbulge- been proposed to be the difference between dry merging dominatedgalaxies.Wecomparetheresultsforthestandard along the red sequence and recent wet mergers along the model(noshutdown,exceptinsatellites)andthenewmodel bluecloud (Bender et al. 1988, 1989; Nieto & Bender 1989; (shutdown of star formation in satellites, in massive haloes Nieto et al. 1991; Bender et al. 1992; Kormendy & Bender and in bulge-dominated galaxies). Once again, we split the (cid:13)c 2005RAS,MNRAS000,1–20

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