Downsizing by Shutdown in Red Galaxies

1.1 MB·English

by  A. Cattaneo

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
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⋆[email protected], †[email protected]
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2February2008
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ABSTRACT
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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⊙.DifferencesatMhalo<Mshock aredueto
the additional shutdown of accretion onto the galaxies that have become bulge-dominated. Objects with high Mhalo but low Mgal are
mostlysatellitesthathavefallenintolargerhaloes.
ponent may contain stars and cold gas, while the hot gas M˙ = Mcold (1+z)α∗ . (2)
is treated as a component of the halo. Only the disc of the star β∗tdyn
central galaxy accretes gas from the halo. The bulge grows
Themassofcoldgas,M ,referstothecomponentinques-
cold
by mergers and by disc instabilities. While stars are tras-
tion,andt isthedynamicaltime(correspondingtohalfa
dyn
ferred directly from thedisc tothebulge, thegas in transit
rotationfordiscsandhalfacrossingtimeforbulges).Inthe
from the disc to the bulge is assumed to pass through an
standard GalICS model, star formation is activated when
intermediatestarburstcomponent,whereitsstarformation thegassurfacedensityisΣ >20m 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<Mcrit,where
theformationofstarshasbeenshutdownbecausethebulgehasbecomethedominantcomponent.Blacksymbolsrefertogalaxiesthat
donotaccretegassimplybecausetheyaresatellites.Inthisdiagramgalaxieshavebeencolouredaccordingtotheirstatusatz=0,and
not according to the first mechanism that has intervened and caused the shutdown of star formation in the history of a given galaxy.
TheredparallelogramsshowthefourbinsalongtheredsequencefromwhichwehaveselectedthegalaxiesforFigs.4and5.
colour-magnitude distribution (Fig. 2, centre). In the ab- Springel et al. 2005b; Hopkinset al. 2005). We do not at-
senceof suchan explicit shutdownthestandardmodel pre- tempt here to model quasar feedback in detail. We simply
dicts too many luminous and bluegalaxies (Fig. 2, left). mimic its effect by stopping the accretion onto a galaxy
whenever it is dominated by its bulge component, even if
The only slight disagreement between the predictions
it is still in a halo with M <M . This can occur only
of the simple model of shutdown by halo mass (red curves halo crit
after a major merger or a sequence of minor mergers since
in the panel marked ‘no additional bulge mass crite-
rion’) and the SDSS data (black smoothed histograms) the disc instability criterion does not permit the growth of
is a small excess of blue galaxies at −22.25∼< Mr, which bulges with Mbulge > 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 <Fe> 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