Gas cooling in semi-analytic models and SPH simulations: are results consistent?

2.6 MB·English

by  A. Saro

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed18January2010 (MNLATEXstylefilev2.2)
Gas cooling in semi-analytic models and SPH simulations: are
results consistent?
A. Saro1,2, G. De Lucia3, S. Borgani1,2,3 & K. Dolag4
0 1DipartimentodiAstronomiadell’Universita`diTrieste,viaTiepolo11,I-34131Trieste,Italy(saro,[email protected])
1 2INFN–NationalInstituteforNuclearPhysics,Trieste,Italy
0 3INAF,OsservatorioAstronomicodiTrieste,viaTiepolo11,I-34131Trieste,Italy([email protected])
2 4Max-Planck-Institutfu¨rAstrophysik,Karl-SchwarzschildStr.1,D-85748,GarchingbeiMu¨nchen,Germany([email protected])

n
a
J
Accepted???.Received???;inoriginalform???
8
1

] ABSTRACT
O We present a detailed comparison between the galaxy populations within a massive cluster,
C as predicted by hydrodynamical SPH simulations and by a semi-analytic model (SAM) of
galaxyformation.Bothmodelsincludegascoolingandasimpleprescriptionofstarforma-
.
h tion, which consists in transforming instantaneously any cold gas available into stars, while
p neglecting any source of energy feedback. This simplified comparison is thus not meant to
-
o be compared with observational data, but is aimed at understanding the level of agreement,
r atthestripped-downlevelconsidered,betweentwotechniquesthatarewidelyusedtomodel
t galaxyformationinacosmologicalframeworkandwhichpresentcomplementaryadvantages
s
a and disadvantages. We find that, in general, galaxy populations from SAMs and SPH have
[ similarstatisticalproperties,inagreementwithpreviousstudies.However,whencomparing

galaxiesonanobject-by-objectbasis,wefindanumberofinterestingdifferences:a)thestar
1
v formationhistoriesofthebrightestclustergalaxies(BCGs)fromSAMandSPHmodelsdif-
5 fersignificantly,withtheSPHBCGexhibitingalowerlevelofstarformationactivityatlow
1 redshift,andamoreintenseandshorterinitialburstofstarformationwithrespecttoitsSAM
1 counterpart;b)whileallstarsassociatedwiththeBCGwereformedinitsprogenitorsinthe
3 semi-analytic model used here, this holds true only for half of the final BCG stellar mass
1. in the SPH simulation, the remaining half being contributed by tidal stripping of stars from
0 the diffuse stellar component associated with galaxies accreted on the cluster halo; c) SPH
0 satellitescanlooseupto90percentoftheirstellarmassatthetimeofaccretion,duetotidal
1 stripping,aprocessnotincludedinthesemi-analyticmodelusedinthisstudy;d)intheSPH
: simulation,significantcoolingoccursonthemostmassivesatellitegalaxiesandthislastsfor
v
upto1Gyrafteraccretion.Thisphysicalprocessisnotincludedinthesemi-analyticmodel
i
X usedinourstudy,aswellasinmostofthemodelsdiscussedintherecentliterature.Ourre-
r sultsidentifyspecificdirectionsofimprovementsforourmethodstostudygalaxyformation
a inahierarchicalUniverse.
Keywords: Cosmology:theory–galaxies:clusters–methods:N-bodysimulations,numer-
ical–hydrodynamics
1 INTRODUCTION understood and complicated by gas-dynamical and radiative pro-
cessesthatcanbetreatedonlytosomeextentusingdirecthydro-
Inthecurrentstandardcosmologicalscenario,galaxiesformwhen dynamicalsimulations.
gasthathasbeentrappedinthepotentialwellsofdarkmatterhaloes
Infact,lackinga‘completetheory’ofstarformation(aswell
and has been shock heated to high temperatures, cools and con-
asofalmostallthephysicalprocessesatplay),wearecurrentlynot
densesatthecentreofthehaloes.Thedynamicalevolutionofdark
inthepositiontomodelgalaxyformationfromfirstprinciples.
matterhaloesisgovernedbygravityaloneandcanbestudiedus-
ingeitheranalytictechniques(i.e.thePress–Schechtertheoryand Differentmethodshavebeendevelopedtomodelgalaxyfor-
its extensions; Press & Schechter 1974; Bond et al. 1991; Lacey mation in a cosmological context. Among these, semi-analytic
& Cole 1993) or N-body simulations (e.g. Boylan-Kolchin et al. models (SAMs) have developed into a flexible and widely used
2009, to mention just the most recent cosmological simulation). technique to make detailed predictions of galaxy properties. In
Theevolutionofthebaryoniccomponentis,incontrast,lesswell thesemodels,thephysicalprocessesdrivinggalaxyformationand
(cid:13)c 0000RAS
2 A.Saro,etal.
evolutionareapproximatedusingphysicallyand/orobservationally odsprovideresultsthatarestatisticallyconsistent,wewillhighlight
motivatedanalyticlaws(forareview,seeBaugh2006).Computa- that significant differences arise when focusing on an object-by-
tionalcostsarelimitedsothatthisapproachallowsanefficientin- objectcomparison,particularlyinthehigh-densityenvironmentof
vestigationoftheparameterspaceandoftheinfluenceofdifferent galaxyclusters.Aswewilldiscussbelow,someofthediscrepan-
physicalassumptions.Modernrenditionsofthesemodelsarecou- cieshighlightedinthisworkhavebeenalreadynotedinprevious
pledtoN-bodysimulations,thusremovinguncertaintiesofthean- studies, although the general consensus is that the cooling model
alyticapproach(Bensonetal.2005;Lietal.2007;Coleetal.2008) usually employed in SAMs is in good agreement with hydrody-
andprovidingconsistentdynamicalinformationformodelgalax- namicalsimulationsthatadoptthesamephysics.
ies(e.g.Kauffmannetal.1999;Bensonetal.2000;Springeletal. The layout of the paper is as follows. In Sec. 2 we describe
2001).AnotherapproachconsistsincarryingoutN-body+hydro- the cluster simulation used in this study, while in Sec. 3 we pro-
dynamicalsimulationsthatincludebothgasanddarkmatter(e.g. videabriefdescriptionoftheadoptedSAM.InSec.4wepresent
Katzetal.1996;Pearceetal.2001;Whiteetal.2001).Thesesim- astatisticalcomparisonbetweentheclustergalaxypopulationpre-
ulationsprovideanexplicitdescriptionofgasdynamics,butthey dictedbythetwomethods,whileinSec.5wefocusonadetailed
arestilllimitedbyrelativelylowmassandspatialresolutionandby comparison of a sample of galaxies which have been matched in
computationalcoststhatbecomehighlyprohibitiveforsimulations thedifferentruns.Finally,wediscussourresultsandgiveourcon-
of galaxies within large cosmological volumes. Recent work has clusionsinSections6and7.
analysedthepropertiesofgalaxiesinhydrodynamicalsimulations
(e.g.Frenketal.1996;Pearceetal.1999;Nagamineetal.2005;
Nagai&Kravtsov2005;Romeoetal.2005;Saroetal.2006;Op-
2 THESIMULATION
penheimer&Dave´ 2006;Simhaetal.2008),butsomedifficulties
arepersistent.Albeitsomerecentprogress(e.g.,Mayeretal.2008), Inthisstudy,weuseare-simulationofamassiveisolatedgalaxy
itremainsdifficultforexampletoproducerealisticandrapidlyro- cluster with M 1 (cid:39) 1.14 × 1015h−1M and r (cid:39) 1.7
200 (cid:12) 200
tatingdisksfromcosmologicalinitialconditions(e.g.Scannapieco h−1Mpc,atz = 0(seealsoclusterg51fromDolagetal.2009).
etal.2009). ThetargetclusterwasidentifiedinaDMonlysimulationthatfol-
In this paper, we will carry out a comparison between pre- lowedtheevolutionof5123 DMparticles(withaparticlemassof
dictionsofSAMsandofSPHhydrodynamicalsimulationsforthe 7×1010h−1M )inacomovingboxofsize479h−1Mpconaside
(cid:12)
propertiesofgalaxiesinsideandaroundgalaxyclusters.Inorderto (Yoshidaetal.2001).Thesimulationwascarriedoutassuminga
minimizetheuncertaintiesrelatedtodifferenttreatmentsofener- flatΛCDMcosmologywithparameters:Ω = 0.3,h = 0.7,
m 100
geticfeedbackprocessesfromsupernovaeandAGN,wehavecon- σ = 0.9, and Ω = 0.039. All particles in the target cluster
8 b
sideredonlyradiativegascooling,andassumedthatcooledgasis anditsimmediatesurroundingswerethentracedbacktotheirLa-
instantaneouslytransformedintostars.Itisimportanttostressthat grangianpositionsandre-simulatedusingtheZoomedInitialCon-
already at this basic level, the different ways in which cooling is dition(ZIC)techniquebyTormenetal.(1997),increasingtheforce
treatedbySAMsandhydrodynamicalsimulationcodesmaylead andmassresolutionintheregionofinterest.Inthehigh-resolution
inprincipletonon-negligibledifferences(e.g.,Violaetal.2008). region,eachDMparticlehasamassm (cid:39)1.13×109h−1M ,
DM (cid:12)
Semi-analytic models assume that the haloes are spherically whilegasparticleshavemassm (cid:39)1.7×108h−1M toaccount
gas (cid:12)
symmetricandthatthegasisefficientlyshockheatedtothe‘virial forthecosmicbaryonfraction.
temperature’ of the halo. Hydrodynamical simulations do not re- ThesimulationwascarriedoutusingtheTreePM–SPHcode
quireanyspecificassumptiononhalogeometry,andsolveexplic- GADGET-2 (Springel 2005), and includes gravitational dynamics,
itlythehydrodynamicequationsdescribingtheevolutionofthegas gas cooling, and a simple scheme of star formation, in which all
thatis,however,representedbyadiscretenumberoffluidelements. gasparticlescolderthan105Kanddenserthan4×10−27gcm−3
Is is difficult, given these limitations, to understand which of the (correspondington =0.1cm−3foragasofprimordialcomposi-
H
two techniques gives the correct answer. While a comparison of tion)areimmediatelyturnedintostarparticles.Thesimulationdoes
the‘fullsemi-analyticmodel’withsimulationsthatattempttoin- notincludeamodelforsupernovaandactivegalacticnuclei(AGN)
cludeallphysicalprocessesatplaywouldbeofinterest,acorrect feedback.ThePlummer–equivalentsofteninglengthforthegravi-
interpretationoftheresultsofsuchacomparisonwillnecessarily tationalforcewassetto(cid:15)=5h−1kpcinphysicalunitsfromz=5
requireagoodunderstandingofanydiscrepancyinducedbyadif- to z = 0, while at higher redshifts it was set to (cid:15) = 30h−1kpc
ferenttreatmentofgascooling.Inaddition,itwouldbeverydiffi- incomovingunits.Thesmallestvalueassumedforthesmoothing
culttounderstandtheoriginofanysimilarityordifferencebetween lengthoftheSPHkernelishalfthegravitationalsoftening.
resultsfromnonstripped-downversionsofSAMsandsimulations, Simulation data were stored in 93 outputs that are approxi-
asmostofthephysicalprocessesonewouldneedtoconsider(e.g. mately logarithmically spaced in time down to z ∼ 1, and ap-
feedback)arenecessarilyincludedusingquitedifferent‘recipes’. proximatelylinearlyspacedintimethereafter.Foreachsnapshot,
Previousstudies(e.g.Bensonetal.2001;Yoshidaetal.2002; wehaverunastandardfriends-of-friends(FOF)algorithmwitha
Helly et al. 2003; Cattaneo et al. 2007) have compared numeri- linkinglengthof0.2inunitsofthemeanparticleseparation.Each
calpredictionsfromstripped-downversionsofsemi-analyticmod- FOF group was then decomposed into a set of disjoint substruc-
elswiththosefromhydrodynamicalsimulationstoverifywhether tures, identified by the SUBFIND algorithm (Springel et al. 2001)
thesemethodsprovideconsistentpredictionsintheidealizedcase aslocallyover-denseregionsinthedensityfieldofthebackground
inwhichonlygascoolingisincluded. mainhalo.Foroursimulation,wehaveusedaslightmodification
In this study, we will present both a statistical comparison oftheSUBFINDalgorithm(fordetails,seeDolagetal.2009)which
and an object-by-object comparison between the two techniques.
To this aim we use a simulation of a massive cluster, and calcu-
latethemergertreesdirectlyfromthesimulation.Whileourresults 1 WedefineM200asthemasscontainedwithinaradiusencompassinga
agreewiththoseofpreviousstudiesinshowingthatthetwometh- meandensityequalto200timesthecriticaldensityoftheUniverse.
(cid:13)c 0000RAS,MNRAS000,000–000
Gascoolinginsemi-analyticmodelsandSPHsimulations 3
linkstogetherallhigh-resolutionparticles(DM,gas,andstarpar- however,hasbeenshowntoproduceresultsthatareingoodagree-
ticles). Only subhalos that retain at least 20 bound DM particles, mentwithN–body+hydrodynamicalsimulationsthatadoptthe
afteragravitationalunbindingprocedure,areconsidered‘genuine samephysics(Yoshidaetal.2002).Inaddition,itprovideresults
substructures’.WenotethatSUBFINDclassifiesallparticlesinside thatareinquitegoodagreementwithothersemi-analyticmodels
aFOFgroupeitherasbelongingtoaboundsubstructureorasbe- whichadoptsmorerealisticassumptionsaboutthehotgasprofile
ing ‘unbound’. The self-bound part of the FOF group itself will (DeLuciaetal.,inpreparation).
then also appear in the substructure list, and represents what we Tosimplifyourcomparisonwithsimulationresults,wehave
willrefertobelowasthe‘mainhalo’.Thisparticularsubhalocon- also adopted a simplified star formation recipe: all gas that con-
tainstypically∼ 90percentofthemassoftheFOFgroup(e.g. denses onto central objects via radiative cooling is immediately
Springel et al. 2001). The group catalogues were finally used to (rather than on a disk dynamical timescale) turned into stars. No
construct merger histories of all gravitationally self-bound struc- other physical process (e.g. supernova and AGN feedback, gas
tures using the software originally developed for the Millennium and/ormetalrecycling)isconsidered.
Simulationproject2.We refertoSpringelet al.(2005)andto De Werecallthatthesemi-analyticmodeladoptedinthisstudy
Lucia & Blaizot (2007) for a detailed description of the merger includes explicitly dark matter substructures: the haloes within
tree construction algorithm. These merger trees represent the ba- whichgalaxiesformarestilltracedevenwhenaccretedontolarger
sicinputneededbythesemi-analyticmodelusedinourstudy(see systems.AsexplainedinSpringeletal.(2001)andDeLuciaetal.
Section3).Inthefollowing,wewillrefertoallquantitiesrelated (2004),theadoptionofthisparticularschemeleadstothedefini-
tothesimulationusingthelabelSPH. tionofthreedifferent‘types’ofgalaxies.EachFOFgrouphostsa
‘Type-0’galaxy,thatislocatedatthepositionofthemostbound
particle of the main halo, and is the only galaxy fed by radiative
cooling from the surrounding hot halo medium. All galaxies at-
3 THESEMI-ANALYTICMODEL
tachedtodistinctdarkmattersubstructuresarereferredtoas‘Type-
We use a stripped-down version of the semi-analytic model de- 1’. These galaxies were previously central galaxy of a halo that
scribed by De Lucia & Blaizot (2007), which builds upon the latermergedontothelargersysteminwhichtheycurrentlyreside.
methodology originally introduced by Kauffmann et al. (1999), Positions of these galaxies are given by those of the most bound
Springeletal.(2001),andDeLucia,Kauffmann&White(2004). particlesofthesubalostracingthesurvivingcoresoftheaccreted
In order to carry out a fair comparison with the simulation de- haloes,whilevelocitiesarethemassweightedmeanvelocitiesof
scribed above, all physical processes in the semi-analytic model alltheselfboundparticles.Thehotreservoirthatisoriginallyas-
havebeenswitchedoff,withtheexclusionofgascoolingandstar sociatedwiththemerginggalaxy,isassumedtobekinematically
formation. strippedatthetimeofaccretionandisaddedtothehotcomponent
GascoolingismodelledfollowingWhite&Frenk(1991).The oftheremnanthalo.Tidaltruncationandstrippingrapidlyreduce
hotgaswithindarkmatterhaloesisassumedtofollowanisother- the mass of dark matter substructures below the resolution limit
malprofile: of the simulation (De Lucia et al. 2004; Gao et al. 2004). When
thishappens,weestimatearesidualsurvivingtimeforthesatellite
M
ρ (r)= hot galaxies,usingtheclassicaldynamicalfrictionformulabyChan-
g 4πR r2
200 drasekhar(1943)(seealsoSaroetal.2008).Thepositionsandve-
FollowingDeLuciaetal.(2004),wedefineacoolingradiusasthe locities of these galaxies are followed by tracing the most bound
radiusatwhichthelocalcoolingtimeisequaltothehalodynamical particlesofthesubhalosatthelasttimetheywereidentified,be-
time3.Whenthecoolingradiuslieswithinthevirialradius,thegas fore being disrupted. Galaxies no longer associated with distinct
isassumedtocoolquasi-staticallyandthecoolingrateismodelled darkmattersubstructuresarereferredtoas‘Type-2’galaxies,and
byasimpleinflowequation: theirstellarmassisassumednottobeaffectedbythetidalstripping
thatreducesthemassoftheirparenthaloes.
dM dr
dctool =4πρg(rcool)rc2ool dctool Wenotethat,byconstruction,themergertreesextractedfrom
oursimulationwillnotincludeanyType-2galaxy(onlysubhalos
Atearlytimesandforlow-masshaloes,theformalcoolingradius
with more than 20 DM particles are retained). In order to show
is larger than the virial radius. In these conditions, the hot gas is
howthesemi-analyticresultsareaffectedbytheinclusionofady-
neverexpectedtobeinhydrostaticequilibriumandthecoolingrate
namical friction time-scale, we will analyse in the following two
isessentiallylimitedbythegasaccretionrate.Inthis‘rapidcool-
differentruns.WewillusethelabelSAMtorefertoaruninwhich,
ing regime’, we assume that all new diffuse gas that is added to
whenever a subhalo falls below the resolution limit, its galaxy is
thehalo,isaccretedimmediatelyontothecentralobjectofthehalo
assumed to merge instantaneously with the galaxy sitting at the
underconsideration.Wenotethatdifferentassumptionsaremade
centre of the main halo. This SAM run allows us to carry out a
in other published semi-analytic models (e.g. a cored gas profile
fair object-by-object comparison between the simulation and the
profile, and the inclusion of a free-fall time for gas to be incor-
semi-analyticresults.Wewillalsoshowresultsfromamodelthat
porated into the model galaxies). The model used in this paper,
includesthedynamicalfrictionformulationdescribedinDeLucia
&Blaizot(2007)andSaroetal.(2008).Theseresultswillbeindi-
catedusingthelabelSAM2.WenotethattheSAM2runshouldbe
2 http://www.mpa-garching.mpg.de/galform/virgo/millennium/
comparedwiththeSAMrun,ratherthanwiththeSPHsimulation.
3 WenotethatWhite&Frenk(1991)definedthecoolingradiusequating
Toillustratehowresultsfromthehydrodynamicalsimulation
thecoolingtimetotheageoftheUniverse,whichisaboutoneorderof
and from the semi-analytic model used in this study compare to
magnitudelargerthanthehalodynamicaltime.AsexplainedinDeLucia
etal.(2004),thisparticularchoicewasrequiredbythesignificantenhance- eachother,weshowinFigure1themergertreeofthesixthmost
mentofcoolingratesingalaxy-sizehaloeswhenadoptingmetaldependent massivesatellitegalaxywithinr200atz =0.Theupperleftpanel
coolingfunctions. correspondstothemergertreeextractedfromtheSPHsimulation,
(cid:13)c 0000RAS,MNRAS000,000–000
4 A.Saro,etal.
Figure1.Galaxymergertreeofthesixthmostmassivesatellitegalaxyfoundinthesimulationwithinr200atz =0.Theupperleftpanelshowsthegalaxy
mergertreeextractedfromtheSPHsimulation.TheupperrightpanelandlowerleftpanelshowthecorrespondingmergertreesfromtheSAMandSAM2runs
(seetextfordetails).Thesizeofthesymbolsscalesasthesquarerootofthegalaxystellarmass,whiledifferentcoloursareusedfordifferentgalaxytypes
(blackforType-0,greenforType-1,andredforType-2galaxies-thelatterexistonlyintheSAM2run).Thefinalstellarmassofthegalaxyineachrunis
givenintheupperleftcornerofeachpanel.
while the corresponding trees from the SAM and SAM2 runs are their‘appearance’andpresent,andarethereforenotincludedinthe
shownintheupperrightandinthelowerleftpanel,respectively. mergertreeshowninthebottompanelofFigure1.
Inthisfigure,thesizeofthesymbolsscalesasthesquarerootof The figure shows that in the SAM and SAM2 runs, galaxies
thegalaxystellarmass,anddifferentcolourscorrespondtodiffer- increase their stellar mass mostly while they are Type-0 central
entgalaxyTypes(blackforType-0,greenforType-1,andredfor galaxies and gas is allowed to radiatively cool towards their cen-
Type-2galaxies).Werecallthatbyconstruction,theSPHsimula- trestoformstars.SatelliteType-1galaxiescanincreasetheirstel-
tionandtheSAMrundonotcontainType-2galaxies.Thisgalaxy larmassonlyviamerging.Inthesemi-analyticmodel,theirstellar
populationisonlypresentintheSAM2run. massneverdecreasesasstellarstrippingisnotmodelled.Incon-
trast,intheSPHsimulation,satelliteType-1galaxiescontinuously
The final stellar masses of the SAM and SAM2 galaxies are loose mass because of tidal interactions with the main halo. The
M (cid:39) 1012h−1M andM (cid:39) 8×1011h−1M ,respectively. stellarmaterialthatislostisdepositedinadiffusestellarcompo-
∗ (cid:12) ∗ (cid:12)
TheSPHgalaxyhasastellarmassofM (cid:39) 2.1×1011h−1M , nentthatisassociatedwiththecentralgalaxyofthemainhaloby
∗ (cid:12)
lowerthanthecorrespondingSAMandSAM2valuebyafactorfive SUBFIND.BythetimesatellitegalaxiesmergeinSPHsimulation,
andfour,respectively.Figure1showsthattheSAM2mergertree theirstellarmassesaresignificantlyreduced.Wewillcomebackto
has fewer branches than the corresponding SPH and SAM trees. thisissueinSections4and5.
This happens because of the large number of surviving Type-2 Figure2showsthestellarmassdensitywithinaboxof2 r
200
galaxieswhichareprogenitorsofthefinalgalaxyintheSPHand onaside,centredonthemainhaloofthecluster.Superimposedon
SAMrunsaswesetthemergingtimesequaltozerooncetheparent eachmaparethepositionsofallthesatellitegalaxieswithstellar
substructurefallsbelowthe20DMparticleslimit.IntheSAM2run, mass larger than 2×1011h−1M . Each satellite galaxy is indi-
(cid:12)
thesegalaxiesareassignedaresidualmergingtimewhichislonger catedbyanopencirclewhoseradiusscaleswiththegalaxystellar
thanthetimeintervalbetweenthelookbacktimecorrespondingto mass.Eachpanelcorrespondstoadifferentrun(lefttoSPH,cen-
(cid:13)c 0000RAS,MNRAS000,000–000
Gascoolinginsemi-analyticmodelsandSPHsimulations 5
Figure2.Stellardensitymapsofaboxcentredonthemainhalooftheclusterusedinthisstudyandofsize2r200 onaside.Thepositionsofallthe
satellitegalaxieswithstellarmasslargerthan2×1011h−1M(cid:12)aremarkedbycircles,withlargerradiicorrespondingtolargerstellarmasses.Theleftpanel
correspondstotheSPHrun,thecentralpanelisfortheSAMrun,andtherightpanelisfortheSAM2run.Differentcoloursareusedfordifferentgalaxytypes:
blackforType-1andgreenforType-2galaxies(onlypresentintheSAM2run).Positionofthesixthmostmassivesatellitegalaxyinthesimulationshownin
Fig.1ishighlightedwithacross.
traltoSAM,andrighttoSAM2).OnlyoneType-2galaxyisfound reconstructionalgorithm.Inordertomaximizethealgorithmper-
inthisregionintheSAM2run,andismarkedwithagreencircle. formanceforhaloesthatareclosetothe20particleslimit,when-
Positionofthesixthmostmassivegalaxyinthesimulationshown ever a descendant of a halo under consideration is not found in
inFig.1ismarkedwithacross.Thefigureshowsthatthesatellite thenextsimulationsnapshot,thealgorithmalsosearchesforade-
galaxies in the SPH run are significantly less massive than those scendantinthesubsequentsnapshot.Closetotheresolutionlimit,
in the SAM and SAM2 run, because of the tidal stripping of stars however,thereareafewhaloesthatdisappearformorethantwo
discussed above. As a consequence, semi-analytic runs contain a contiguoussnapshots.Theseareidentifiedatalatertimeassatel-
largernumberofmassivegalaxieswithinthevirialradius. litegalaxieswithanon-zerostellarmassinthesimulation.Inthe
semi-analyticmodel,gasisallowedtocoolonlyoncentralgalax-
iesof‘mainhaloes’.Sincethesestructuresappearas‘subhalos’,no
newgalaxyisformedwithinthem.Therewillbe,however,atype
4 ASTATISTICALCOMPARISON 2galaxyassociatedwiththe(erroneously)lostType-1galaxy.We
haveverifiedthatthis‘failure’isactuallyoccurringforallType-2
InthisSection,wewillcarryoutastatisticalcomparisonbetween
galaxiesintheSAM2runwhoseassociatedmergingtimesarelarge
thepropertiesofgalaxiesfromtheSPHsimulationandthosefrom
enoughtoletthemsurviveasdistinctgalaxiesdowntoz =0.The
theSAMandSAM2runs.Inparticular,wewillfocusontheradial
positionsassignedtotheType-2galaxiescoincidewiththoseofthe
density distribution and on the stellar mass function. In the next
Type-1SPHgalaxieswhichareerroneouslyidentifiedasnew.
section, we will then carry out a more detailed object-by-object
Figure4showsthestellarmassfunctionofallgalaxiesidenti-
comparison.
fiedwithin1.5r atz=0.Thedifferentialandcumulativemass
Figure 3 shows the radial density distribution of all galax- 200
functions are shown in left and right panel, respectively. Dotted
ies lying within 1.5r at z = 0. The dotted black line shows
200
blacklinesrepresentthestellarmassfunctionofgalaxiesidentified
thedistributionofgalaxiesidentifiedintheSPHsimulation,while
intheSPHrun,whileredandgreenlinescorrespondtotheSAM
thedashedredandsolidgreenlinescorrespondstotheSAMand
and SAM2 runs, respectively. The solid vertical blue lines in the
SAM2runsrespectively.Thedot-dashedbluelineshowsthetotal
two panels mark the mass corresponding to the cosmic baryonic
massdensityprofile,normalisedtomatchtheradialnumberden-
fractionmultipliedbythemassof20DMparticles,andtherefore
sityofgalaxiesintheSAM2runat0.5r .AsshownbyGaoetal.
200
roughlycorrespondstotheresolutionlimitofthesimulation.
(2004),arunthatincludesType-2galaxiestracesbetterthemass
densityprofile,whilethecorrespondingdistributionsfromtheSPH The figure shows that the stellar mass of the SAM BCG is
andSAMrunsareanti-biasedwithrespecttothematterdistribution largerthanthecorrespondingvalueintheSAM2run,butsmaller
intheinnerregions,asthesubhaloprofiles(DeLuciaetal.2004; than the corresponding value in the SPH run. We recall that the
Gao et al. 2004). Interestingly, the contribution from the Type-2 lattervalueincludestheintra-clusterlight.Thedifferencebetween
populationintheSAM2runremainssignificantalsoatlargeradii, the SAM and SAM2 BCGs is mainly due to the lower number of
andevenbeyondtheclustervirialradius. progenitorsoftheSAM2BCG(seeFigure1),whichtranslatesin
Figure 3 indicates a small excess of SPH satellites with re- amuchlarger(byabout50percent)numberofgalaxiesatz = 0
specttotheSAMresults,intheinnercentralbin.Wehaveverified withrespecttotheSAM(andSPH)run,asclearlyshownbythecu-
that this small excess is due to galaxies which do not have any mulativemassfunctions.Asexplainedabove,therearemoremas-
counter-partintheSAMrunbecauseofafailureofthemergertree sivegalaxiesintheSAMrunthanintheSPHsimulation.Aswewill
(cid:13)c 0000RAS,MNRAS000,000–000
6 A.Saro,etal.
We note, however, that the SPH BCG has a stellar mass that is
∼ 20 and ∼ 65 per cent larger than the corresponding values in
theSAMandSAM2runs,respectively.Inthenextsection,wewill
showthatthesedifferencesaremainlyduetotidalstrippingofstars
from satellite galaxies in the SPH simulation. At larger distances
fromtheclustercentre,theimportanceoftidalstrippingdecreases
andtheagreementbetweentheSPHandthesemi-analyticrunsim-
proves.
5.2 EvolutionoftheBrightestClusterGalaxies
As discussed above, the SPH simulation predicts for the BCG a
stellar mass that is larger than the corresponding values found in
theSAMandSAM2runs.Inthissection,wediscussinmoredetail
theoriginofthisdifferences.Asexplainedabove,theBCGmass
intheSPHsimulationincludesthediffusestellarcomponent.The
semi-analyticmodelusedheredoesnotaccountfortidalstripping
of stars from satellite galaxies and does not model explicitly the
formationoftheICL.However,Muranteetal.(2007)haveshown
Figure3.Radialdensitydistributionofallgalaxiesidentifiedatz = 0 thatmostofthediffusestellarcomponentdoesnotcomefromtidal
within1.5r200.Thedottedblacklineshowsthedistributionofgalaxies strippingbutoriginatesfrommergersassociatedwiththeformation
identifiedintheSPHsimulation,whiletheredandgreenlinesshowthe
oftheBCG.ThustheSAMBCGwillalsoincludetheICL,withthe
correspondingresultsfromtheSAMandSAM2runs.Thedot-dashedblue
exclusion of the (small) contribution of stellar material that was
lineshowsthetotalmatterdensityprofile,normalisedtomatchtheradial
tidallystrippedfromsatellitegalaxies.
numberdensityofgalaxiesintheSAM2runat0.5r200.
In Figure 6, we show the mass accretion and star formation
history of the BCG as predicted by the SPH simulation (black
seeinthefollowing,thedifferencesbetweentheSPHandthesemi- lines), by the SAM run (red lines) and by the SAM2 run (green
analyticrunscanbeexplainedasacombinationoftidalstripping lines). The upper left panel shows the number of progenitors of
ofstarsfromtheSPHsatellitegalaxies,andtodifferentpredicted theBCGasafunctionoflookbacktimeforthethreeruns.Asex-
starformationhistoriesfortheBCGs. plainedinSection3,thenumberofprogenitorsintheSPHsimu-
lationandintheSAMrunislargerthanintheSAM2run.Thisdif-
ferenceisduetotheType-2galaxies,whichmaintaintheiridentity
5 ANOBJECT-BY-OBJECTCOMPARISON downtoz = 0intheSAM2run.Byconstruction,thispopulation
ofgalaxiesdoesnotexistinboththedirectsimulationandinthe
ThedynamicalevolutionofcentralgalaxiesandofsatelliteType-1 SAMgalaxycatalogue,whicharebasedonequivalentmergertrees.
galaxiesinthesemi-analyticmodelisbasedonmergertreesthatare Intheseruns,wheneverasubstructure‘merge’(i.e.fallsbelowthe
equivalenttothoseextractedfromtheSPHsimulation.Thisallows resolutionlimitofthesimulation),theassociatedgalaxyisassumed
ustoidentifyasampleofgalaxieswhichincludesallthoseatz=0 tomergeinstantaneouslywiththecentralgalaxyofitshalo.Thus,
thathavethesamepositionsinallthreeruns.Thissampleincludes thenumberofprogenitorsishigherinthesetworuns.Themerg-
allcentralType-0galaxiesandallsatellitesType-1galaxies,with ingrate(thederivativeofthecurveshowninthetopleftpanelof
the exception of those Type-1 satellites in the SPH run which do Figure6)predictedbytheSPHandbytheSAMrunslooksquite
nothaveacounterpartintheSAMandSAM2runsasdescribedin differentfromtheonepredictedbytheSAM2run.Inparticular,the
Section4. mergingrateisalmostlinearalongthewholegalaxyhistoryinthe
SAM2 run, while in the SPH simulation and in the SAM run it is
characterisedbyaphaseofhighmergingactivitybeforelookback
5.1 Generalbehaviour
time∼7Gyrs,followedbyashallowdeclinewhichlastsdownto
Figure5showsthestellarmassofmatchedgalaxiesatz=0aspre- alookbacktime∼2Gyrs,andthenanotherphaseofhighmerging
dictedbytheSPHsimulation(x-axis),bytheSAMrun(y-axis,left activityinthepast2Gyrs.
panels),andbytheSAM2run(y-axis,rightpanels).Type-0central The upper right panel of Figure 6 shows the star formation
galaxiesareshownasblackcrosses,whileType-1satellitegalaxies history of the BCG (obtained by summing up the star formation
areshownasredcirclesfortheSAMrunandasgreencirclesforthe histories of all its progenitors). The star formation histories pre-
SAM2run.Thedottedlineineachpanelrepresentstheone-to-one dictedbythethreemodelsdiffersignificantly.TheSPHBCGex-
relation.Differentpanelscorrespondtodifferentradialbins,with hibits an intense initial burst of star formation at lookback time
cluster-centricdistanceincreasingfromtoptobottompanels. ∼ 12Gyrs,followedbyasharpdecline.Afterlookbacktime∼ 8
In the innermost region of the cluster (upper panels), corre- Gyrs, the star formation rate associated with the BCG is roughly
sponding to galaxies at distances smaller than 0.5r , there is constantatavalueof∼450h−1M yr−1.Thecorrespondingstar
200 (cid:12)
only one Type-0 central galaxy, which is the BCG itself. On av- formationhistoriesfromthesemi-analyticmodellookverydiffer-
erage,satellitegalaxiesintheSAMandSAM2runstendtobemore ent.AsfortheSPHBCG,theSAMrunexhibitsaninitialburstof
massivethanintheSPHsimulation,evenbymorethanoneorderof star formation at early times. This burst is, however, less intense
magnitude.Thescatterabovetheone-to-onerelationisalsolarger andbroaderthantheonepredictedbytheSPHsimulation.Thedif-
intheinnermostradialbin.ForcentralType-0galaxies,theagree- ferentintensityoftheinitialburstofstarformationmightbedue
mentbetweenthesimulationandthesemi-analyticrunsisbetter. toinaccurate/simplifiedtreatmentofthe‘rapidcoolingregime’.In
(cid:13)c 0000RAS,MNRAS000,000–000
Gascoolinginsemi-analyticmodelsandSPHsimulations 7
Figure4.Differential(leftpanel)andcumulative(rightpanel)stellarmassfunctionsforallgalaxiesz=0within1.5r200ofthesimulatedclusterusedinour
study,aspredictedbytheSPHsimulation(blackdottedlines),bytheSAMrun(reddashedlines)andbytheSAM2run(greensolidlines).Thesolidvertical
bluelinesmarktheresolutionlimitofthesimulation.
the semi-analytic model used in this study, all hot gas associated line), while the outer regions are dominated by DM (black solid
with the main halo is assumed to condense instantaneously onto line).Satellitegalaxiesandthediffuseintra-clusterlightassociated
the central galaxy when the formal cooling radius is larger than withtheBCGmakethestellarcomponentcontributingmorethan
r (seeSection3).Thissimpleimplementationdoesnotseemto thegascomponentatr ∼ 0.1r .Atlargerradii,thegascom-
200 200
describeaccuratelythedepositionofcoldgasalongfilamentsthat ponent represents the dominant baryonic component. The dotted
penetrate the virial radius without being heated to the virial tem- bluelineinFigure7representstheresultinggasprofileassumedto
perature(Dekeletal.2008andreferencestherein). computethegascoolingrateintheSAMruns.Atthevirialradius
r ,thegasmassmeasuredfromtheSPHsimulationagreesvery
Inthelast∼ 10Gyrs,thestarformationhistoryoftheSAM 200
wellwiththegasmasspredictedbytheSAMrun.Forradiismaller
BCGisroughlyconstantwithanaveragestarformationrateof∼
2000h−1M yr−1.FortheSAM2BCG,thestarformationhistory than∼ 0.2r200,thegasdistributionassumedinthesemi-analytic
(cid:12)
model differs significantly from the actual gas distribution in the
appearsroughlyconstantalongthewholehistoryofthegalaxywith
anaveragevalueof∼2000h−1M yr−1.Itisclosetothevalues simulation.Here,coolingathighredshifthasalreadyremovedlow
(cid:12)
entropy gas, leaving only a small amount of gas able to cool at
predictedintheSAMruninthelast∼10Gyrs,butissignificantly
lowerredshift.Atz =0,oursemi-analyticcodecomputesacool-
lowerthanthecorrespondingvaluespredictedintheSAMrunand
ing radius for the main cluster of ∼ 40h−1kpc. Figure 7 shows
SPHsimulationatearlytimes.Thisdifferencecanbeascribedto
that,withinthisradius(markedbyaverticaldottedline),thetotal
the lower number of progenitors of the SAM2 BCG, as shown in
gasmassassumedbythesemi-analyticmodelisaboutafactorfour
theupperleftpanel.Indeed,theType-2galaxypopulation,which
larger than the gas mass present in the SPH simulation. The pre-
ispresentintheSAM2run,hasformeditsstellarmassatveryearly
dictedcoolingrateatz=0,andthereforethepredictedstarforma-
times.
tionrateintheSAMrun,willbeaboutafactorfourlargerthaninthe
As explained above, our comparison is based on a stripped-
SPHrun,asshownintheupperrightpanelofFig.6.Wenotethat
down version of the semi-analytic model and on a simulation in
not all semi-analytic models (e.g. Cole et al. 2000 and derivative
whichstarformationistreatedinaverysimilarway.Hence,any
papers) use this approximation. The different behaviour between
difference in the predicted star formation histories reflects a dif-
semi-analyticmodelsandhydrodynamicalsimulations,however,is
ference in the amount of gas that cools in the model and in the
exacerbatedinrunswithoutfeedback,likethoseconsideredinour
simulation. The ‘bursty’ behaviour of the star formation histories
analyses.Whenamodelforefficientsupernovaeand/orAGNfeed-
predictedintheSAMandSAM2runsisthereforeduetodifferences
back is included, a larger amount of gas is allowed to remain in
inthepredictedcoolingrates,andnottoburstsinducedbymergers.
the hot phase in the central regions, thus possibly alleviating the
AsexplainedinSection3,theamountofgasthatcools(M )in
cool disagreementshowninFigure7.
thesemi-analyticmodelisproportionaltothemassofgasenclosed
withinthecoolingradius(r ).Thehotgasisassumedtofollow The lower left panel of Figure 6 shows the total mass in all
cool
anisothermalprofile,sothedensityofgasataradiusr scalesas BCGprogenitors,inthethreerunsconsideredinourstudy.Inthe
r−2. Therefore, the total mass of gas within a certain radius r is SPHsimulation,thereisafirstphase(atlookbacktimelargerthan
M (< r) ∝ r.Inabsenceofanyfeedback,gasparticlesinthe 9 Gyrs) characterized by a steep increase in mass, which corre-
gas
SPHsimulationassumearadialprofilethatisnotwelldescribedby sponds to the initial intense burst of star formation shown in the
anisothermaldistribution(seeBorganietal.2006).Figure7shows toprightpanel.Thestellarmassstaysalmostconstantbetween8
theDM,starandgasmassenclosedwithinagivenradiusasafunc- and6Gyrsago,andthenincreasesrapidlydowntopresenttime.
tionofcluster-centricdistance.Theinnermostregionsofthecluster This behaviour is in quite good agreement with predictions from
(r∼<0.01r200)aredominatedbythestellarcomponent(dashedred theSAMrun.Incontrast,theSAM2runexhibitsanapproximately
(cid:13)c 0000RAS,MNRAS000,000–000
8 A.Saro,etal.
Figure5.StellarmassofmodelgalaxiesfromtheSAM(leftpanels)andSAM2(rightpanels)runsasafunctionofthecorrespondingstellarmassasmeasured
fromtheSPHsimulation.Panelsfromtoptobottomshowbinsofincreasingcluster-centricdistance.CentralType-0galaxiesareshownasblackcrosses,
whileredandgreencirclesrepresentsatelliteType-1galaxiesintheSAMandSAM2runs,respectively.Thedottedlineineachpanelrepresentstheone-to-one
relationandisshowntoguidetheeye.
(cid:13)c 0000RAS,MNRAS000,000–000
Gascoolinginsemi-analyticmodelsandSPHsimulations 9
linearaccretionhistory,consistentwiththeapproximatelyconstant
star formation history shown in the top right panel. These accre-
tion histories are shown again in the lower right panel, together
withtheintegralsofthestarformationhistoriesshowninthetop
rightpanel.FortheSAMandSAM2runs,thetotalmassinprogeni-
torsmatchestheintegralsofthestarformationhistories(dottedand
solidlinesoverlapperfectly).Indeed,allthestarsthatareassoci-
atedwiththeBCGatpresentintheseruns,wereformedinBCG
progenitors.ThisisnotthecaseintheSPHsimulation,wherethe
two curves start diverging below lookback time ∼ 10 Gyrs. By
z = 0,theintegralofthestarformationrateofallBCGprogeni-
torsisresponsibleforonlyabouthalfofthefinalstellarmass.In-
terestingly,evenifthestarformationhistoriesofBCGspredicted
by the simulation and the semi-analytic runs differ significantly,
theirintegralsagreewithin∼ 20percentfortheSPHandSAM2
run.FortheSAMrun,theintegralofthestarformationhistoryis
aboutafactortwolargerthanthatmeasuredfromtheSPHsimu-
lationandfromtheSAM2run.Atz =0,theintegratedtotalmass
oftheBCGis(cid:39) 1.7×1013h−1M ,(cid:39) 2.1×1013h−1M and
(cid:12) (cid:12)
(cid:39)3.2×1013h−1M(cid:12)fortheSPH,SAM,andSAM2,respectively. Figure7.Totalmassofdarkmatter(blacksolidline),gas(dottedblueline),
Part of the excess mass associated with the SPH BCG and andstars(dashedredline)enclosedwithinagivenradiusintheSPHsimu-
not formed in its progenitors, comes from diffuse star formation lation,atz =0.Thedot-dashedgreenlineshowsthegasprofileassumed
occurringinunresolvedgalaxieswhicheventuallymergewiththe bytheSAMadoptedinthisstudy.Theverticaldottedlinemarksthecooling
radiusassumedintheSAMatthisredshift(seetextfordetails).
BCG by redshift z = 0 (see also Saro et al. 2009). To compute
thestarformationrateassociatedwitheachSPHgalaxy,wehave
summedallthestarparticlesinthegalaxyunderconsiderationwith
formationtimelowerthanthetime-intervalbetweentwoadjacent distancebetweenthemainprogenitorofthegalaxyandthecluster
snapshots.Galaxiesthatareformallyunresolvedandthatformout- centre varies as a function of lookback time. The vertical line in
sidetheFOFgroupofthemainhalo,willnotappearinthegalaxy this(andinalltheotherpanels)marksthetime whenthegalaxy
mergertree.Therefore,theircontributionisnottakenintoaccount becomesasatellite.Thisparticulargalaxyhasbeenorbitingaround
whencomputingthestarformationhistoryshowninthetopright theclustercentreinthelast∼8.5Gyrsandiscurrentlylocatedata
panel of Figure 6. Their stellar mass, however, contributes to the distanceof∼0.3r fromtheclustercentre.Byz=0,thegalaxy
200
total masses shown in the bottom left panel, once these galaxies hascompletedsixorbitsandbothitsapocentricdistanceandorbital
mergewiththeBCG. periodhavedecreasedasaconsequenceofdynamicalfriction.The
Thelargestcontributiontotheexcessstellarmassnotformed upperrightpanelofFigure8showsthenumberofprogenitorsin
in the SPH BCG progenitors, however, comes from stars that the three runs analysed in our study (as we did in Figure 6, for
formedinType-1satellitesandthatweretidallystrippedandadded theBCG).ThefigureshowsthatbothintheSPHandintheSAM
to the diffuse ICL associated with the main cluster. We note that run,thereisonlyonemergingepisodeafterthegalaxyhasbecome
SUBFIND does not separate the stars bound to the BCG from the a satellite: it happens only ∼ 0.5 Gyrs after the satellite galaxy
diffuse stellar component (e.g., Murante et al. 2007), so that the crossedr .IntheSAM2run,thenumberofprogenitorsdecreases
200
BCG ‘stellar mass’ will include this component. To quantify the moregraduallythanintheothertworuns,asaconsequenceofthe
contribution due to the diffuse stars, we have identified all satel- continuousaccretionofType-2galaxies.
lite galaxies of the SPH BCG and traced them back in time un- Themid-leftpanelofFigure8showsthestarformationhistory
til their stellar mass reaches a maximum. This time corresponds ofthegalaxyunderconsideration.Allthreerunsarecharacterised
approximatelytothelasttimethegalaxywasacentralgalaxyof byanintenseburstofstarformationatearlytimes,andnostarfor-
itsownhalo.Wethensumupthedifferencesbetweentheirmax- mationinthelast∼7Gyrs.AsfortheBCGs,however,theSAM2
imummassesandtheirmassesatz = 0,andobtainatotalmass galaxyischaracterizedbyalessintenseandbroaderinitialburst,
of ∼ 1.6×1013h−1M(cid:12). Interestingly, this amount corresponds comparedtoitsSPHandSAMcounterparts.Interestingly,thestar
almostexactlytothedifferencebetweenthefinalstellarmassas- formationassociatedwiththeSPHsimulatedgalaxy,lastsfor∼1
sociated with the SPH BCG at z = 0 and the integral of its star Gyrsafterthegalaxyhasbecameasatellite.Sinceallavailablecold
formationhistory.Wecaution,however,thatSPHgalaxiesmaybe gasisinstantaneouslyturnedintostars,newfreshmaterialforstar
toofragile(Saroetal.2006),boostingthesignificanceofthisef- formationmustcomefromcoolingonsatellitegalaxiesoccurring
fect.Inparticular,thelargerfractionofstellarmassformedatearly intheSPHsimulation.IntheSAMandSAM2runs,nocoolingis
timesinabsenceofanyregulatingfeedbackmechanism,isenhanc- allowedonsatellitegalaxiesandallgasavailableisinstantaneously
ingthiseffect,thusover-predictingtheamountofICL. turnedintostars.So,byconstruction,nostarformationoccursafter
thegalaxyisaccretedontoalargerstructure.
The mid-right panel of Figure 8 shows the total mass in all
5.3 Evolutionofsatellitegalaxies
theprogenitorsofthegalaxyunderconsideration,asafunctionof
Figure 8 shows the evolution of the sixth most massive satellite lookbacktime.ThedipinthetotalstellarmassoftheSAMgalaxy
galaxy found in the SPH simulation at z = 0, within r . The atthepositionoftheverticallineisduetotheadoptedmergertree
200
mergertreesofthissamegalaxyinthethreerunsanalysedinthis construction algorithm. As explained in Section 4, the algorithm
paperwereshowninFigure1.Theupperleftpanelshowshowthe looksforadescendantofeachhalointhetwofollowingsnapshots
(cid:13)c 0000RAS,MNRAS000,000–000
10 A.Saro,etal.
Figure6.Topleftpanel:numberofBCGprogenitors(galaxiesthatmergewiththeBCGbyz = 0)atdifferentlookbacktimes.Toprightpanel:star
formationhistoryoftheBCGsineachoftherunsanalysedinthisstudy,obtainedincludingthecontributionfromeachBCGprogenitor.Lowerleftpanel:
totalstellarmassinallBCGprogenitorsasafunctionoflookbacktime.Lowerrightpanel:samequantitiesshowninthelowerleftpanelarecompared
withtheintegralsofthestarformationhistoriesshowninthetoprightpanel.DottedandsolidlinesfortheSAMandSAM2runsoverlap.Differentcolours
correspondtodifferentrunsasindicatedineachpanel.
sothatinthedarkmattermergertrees,haloesareallowedtoskip lossofstellarmaterialfromtheSPHsatellitegalaxy,wedefineat
a snapshot. This also happens for the galaxy that is sitting at the each snapshot a representative ‘stripping radius’. This quantity is
centreofthisstructure,asinFigure8.Inthelowerleftpanel,the defined,ateachsnapshot,astheminimumcluster-centricdistance
totalmassinallprogenitorsiscomparedtotheintegralsofthestar reachedbytheorbitingsatellitegalaxybythetimecorresponding
formationhistories,aswedidfortheBCGsinthelowerrightpanel totheanalysedsnapshot.Thissimpleestimateofthestrippingra-
ofFigure6.AsfortheBCGs,thetotalmassfortheSAMandSAM2 diusisshownbyareddashedlineinthelowerrightpanelofFigure
galaxiesoverlapperfectlytheintegralofthecorrespondingstarfor- 8,togetherwiththepredictedenclosedmass,asafunctionoflook-
mation history, confirming that all stars in the final galaxy have back time. The figure shows that the galaxy suffers a significant
beenformedinitsprogenitors.ThebehaviouroftheSPHgalaxyis lossofstellarmassduringthefirstorbit,followedbysmootherbut
morecomplicated,andwecanidentifytwodifferentregimes: constant stripping down to z = 0. Our estimate of the stripping
radius is clearly simplified, but it captures well the evolution of
• atearlytimes,beforethegalaxyisaccretedontoalargerstruc-
the bound stellar mass as measured from the SPH simulation. At
ture,itsstellarmassfollowscloselytheintegralofthestarforma-
pericentres,SUBFINDtendstounder-predicttheboundstellarmass
tionhistory.
withrespecttotheestimateobtainedusingthestrippingradiusde-
• asthegalaxycrossesthevirialradiusandbecomesasatellite,
fined above. This bias is intrinsic in the SUBFIND algorithm, but
itstartsloosingstellarmassbecauseoftidalinteractionswiththe
cannotaccountforthetotalamountofstellarmasslossattheapoc-
clusterhalo.
entre,asdiscussedinNatarajanetal.(2007)andMaciejewskietal.
To better understand the mechanism which causes the measured (2009)andproducesanartificialdecreaseinmasswhenagalaxy
(cid:13)c 0000RAS,MNRAS000,000–000