A Research Note on the Implementation of Star Formation and Stellar Feedback in Semi-Analytic Models

0.77 MB·English

by  Fabio Fontanot

A Research Note on the Implementation of Star Formation and
Stellar Feedback in Semi-Analytic Models
FabioFontanot1, GabriellaDeLucia2, AndrewJ. Benson3, PierluigiMonaco4, andMichael
3 Boylan-Kolchin5
1
0 1HITS-Heidelberger Institutfu¨rTheoretischeStudien,Schloss-Wolfsbrunnenweg35,69118,
2
Heidelberg,Germany
n
a 1Institutfu¨rTheoretischePhysikder Universita¨tHeidelberg,Philosophenweg,16,69120,
J Heidelberg,Germany

7 2INAF-OsservatorioAstronomicodiTrieste, ViaTiepolo11,I-34143,Trieste,Italy
1
3CarnegieObservatories,813 SantaBarbaraStreet,Pasadena,California,91101USA

] 4DipartimentodiFisica,sez. Astronomia,Universita´ diTrieste,via G.B. Tiepolo11, I-34143,
O
Trieste,Italy
C
5Center forCosmology,DepartmentofPhysicsand Astronomy,4129Reines Hall,Universityof
.
h
California,Irvine, CA 92697,USA
p
-
o
r January 21,2013
t
s
a
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Abstract

1
v
Westudythe impact of starformationand stellarfeedback prescriptions ongalaxy propertiespredicted by means
0
of “stripped-down” versions of independently developed semi-analytic models (SAMs). These include cooling, star
2
2 formation,feedbackfromsupernovae(SNe)andsimplifiedprescriptionsforgalaxymerging,butnochemicalevolution,
4 discinstabilitiesorAGNfeedback. Weruntheseversionson identicalsamplesofdarkmatter(DM)haloesextracted
. fromhigh-resolutionN-bodysimulationsinordertoperformbothstatisticalanalysisandobject-by-objectcomparisons.
1
Wecompare our resultswith previous work based on stripped-down versions of the same SAMs including only gas
0
cooling,andshowthatallfeedbackmodelsprovidecoherentmodificationsinthedistributionofbaryonsbetweenthe
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1 variousgasphases.Inparticular,wefindthatthepredictedhotgasfractionsareconsiderablyincreasedbyuptoafactor
: ofthree,whilethecorrespondingcoldgasfractionsarecorrespondinglydecreased,andasignificantamountofmassis
v
ejectedfromtheDMhalo. Nonetheless,wealsofindrelevantdifferencesinthepredictedpropertiesofmodelgalaxies
i
X amongthethreeSAMs: thesedeviationsaremorerelevantatmassscalescomparabletothatofourownGalaxy,and
arereducedatlargermasses,confirmingthevaryingimpactofstellarfeedbackatdifferentmassscales. Wealsocheck
r
a theeffectofenhancedstarformationevents(i.e.starburstsmodes),definedinconnectionwithgalaxymergers.Wefind
that,ingeneral,theseepisodeshavealimitedimpactintheoverallstarformationhistoriesofmodelgalaxies,evenin
massiveDMhaloswheremerger-drivenstarformationhasoftenbeenconsideredveryimportant.
Keywords:galaxies:formation-galaxies:evolution-galaxies:fundamentalproperties
email:[email protected]
1
1 Introduction
those of our own Milky-Way (MW). In the other hand,
for larger masses, corresponding to those of clusters at
Inordertounderstandthecomplexprocessofgalaxyfor- z = 0,wefoundsignificantlydifferentresultsinthepre-
mation over the entire cosmic history of the Universe, dictedamountofcoldgas,largelyduetothedifferentas-
many different physical processes need to be taken into sumptionsforthe hotgasdistributioninside DMHs, and
account. Theseprocessesactondifferentscalesandtheir todifferenttreatmentsofthe“rapidcooling”regime.
interplayappearscriticalforanappropriatedescriptionof In DL10, we also compared the different treatment
thechainofeventsleadingtothebuildupofpresent-day for the dynamical evolution of substructures and galaxy
galaxy population. However, our comprehension of the mergers, based either on fitting formulae derived from
physicalprocessesactingonthebaryoniccomponentsof numericalsimulationsoranalytic modelsaccountingfor
thesehaloesisstilllimited. dynamical friction, tidal stripping and tidal shocks. We
Anumberoftheoreticalmethodshavebeenintroduced, showed thatthese differentassumptionsresultin signifi-
trying to get a better understanding of galaxy forma- cantdifferencesinthetimingsofmergers,withimportant
tionandevolution: amongthesedifferentmethodssemi- consequencesfortheformationandevolutionofmassive
analytic models(hereafterSAMs - fora review, see e.g. galaxies.
Baugh2006)ofgalaxyformationandevolutionhavebe- Inthisresearchnote,weextendtheanalysisofDL10to
come a widely used tool, thanks to their flexibility and investigatetheinfluenceofdifferentprescriptionsadopted
(relatively)lowcomputationalcosts. Inthesemodels,rel- for the physical mechanisms of star formation and SN
evantphysicalprocessesareincludedbyassumingempir- feedback in both “quiescent” and “starburst” modes,
ically and/or theoretically motivated prescriptions, cou- avoidingtoconsiderotherprocesseslikemetalevolution,
pled through a set of differentialequations that describe AGNfeedbackanddiscinstabilitiesandusingsimplified
the mass and energy flows between the different galac- treatment of galaxy mergings. We stress that, given our
tic components (i.e. halo, bulge and disc) and baryonic limited understanding of the physical processes consid-
phases(i.e. stars,hotandcoldgas). ered,alltheprescriptionswewilldiscussinthefollowing
A number of competing models have been proposed, areequallyplausible,soouranalysisisnotaimedatiden-
assumingdifferent(butequallyplausible)descriptionsof tifyingthe“best”modelforstarformationandfeedback.
therelevantprocesses. Althoughtheanalysisofdiscrep- Rather,theouraimistoanalysetheinfluenceofdifferent
anciesandsimilaritiesbetweenpredictionsfromindepen- modelingredients(andofthevariousmodellingthatcan
dently developed SAMs has been the subject of a num- beadoptedforspecificprocesses)onthepredictedproper-
berofrecentstudies(seee.g. Fontanotetal.2009,2011; tiesofgalaxiesandtheirredshiftevolution. AsinDL10,
DeLuciaetal. 2011 and discussions therein), the role we run our models on the same sets of merger trees ex-
playedby the overallSAM “architecture”(i.e. the more tractedfromnumericalsimulations.Resultsfromourpre-
technical details of the construction of the models, and viousstudyallowustocontrolresidualdifferencesdueto
theinterplayoftheirdifferentassumptions)hasnotbeen adifferentmodelforgascoolingandgalaxymergers.
analysedindetail. Inthisworkweusestripped-downversionsoftheMu-
AfirststepinthisdirectionwasgiveninDeLuciaetal. nichmodelbyDeLucia&Blaizot(2007),theGALACTI-
(2010,hereafterDL10). Inthisstudy,weused“stripped- CUS modelofBenson(2012)asanextensionofDurham
down”versionsof three independentlydevelopedSAMs modelof Boweretal. (2006), and the MORGANA model
includingonlygascoolingandgalaxymergers.Themod- ofMonacoetal.(2007). Inallmodelsweimplementra-
els were run on identical sets of merger trees extracted diativecoolingofagaswithprimordialcomposition,star
fromN-bodysimulations,soastoremoveanysystematic formationandSNfeedbackin“quiescent”and“starburst”
effect due to the adopted description of the dark matter regimes,includingmodelsof“super-wind”ejectionfrom
evolution. Wefoundareasonablelevelofagreementbe- theDMhalosandlaterre-accretions,andsimplifiedpre-
tweenpredictionsfromthethreemodels,forthephysical scriptions for galaxy mergers. We do not modify the
processesconsidered.Inparticular,theagreementisvery choice of parameter values with respect to the original
goodatdarkmatterhaloes(DMHs)scalescomparableto calibrations:wedonotthenexpectpredictionsfromthese
2
stripped-downversionstobeinanywayrepresentativeof 2.1 The Simulationsand MergerTrees
realgalaxies,sincetheymisssomekeyphysicalprocesses
In this work we take advantage of merger trees ex-
by construction,namelyAGN feedback,metalevolution
tractedfromtwolarge,high-resolutioncosmologicalsim-
anddiscinstabilities. Ontheotherhand,someoftheex-
ulations, namely the Millennium Simulation (MS here-
cludedphysicalmechanismsare knownto have a strong
after, Springeletal. 2005) and the Millennium-II Simu-
impactonpredictedgalaxyproperties: sinceeachmodel
lation (MSII hereafter,Boylan-Kolchinetal. 2009). The
fine-tuningisdoneonversionsincludingtheseadditional
processes, theycouldmask orreduceanydifferencedue MSfollowsN =21603particlesofmass8.6 108M⊙/h
×
within a comoving box of size 500Mpc/h on a side.
totheprocessesconsideredhere.
The MS-II follows the evolution of the same number of
particles in a volume that is 125 times smaller than for
the MS (100Mpc/h on a side), with a correspondingly
2 Models smaller particle mass (6.9 106M⊙/h). For both sim-
×
ulations, the cosmological model adopted is a Λ cold
dark matter (CDM) with Ω = 0.25, Ω = 0.045,
m b
Inthefollowing,webrieflyreviewthemergertreesused h = 0.73,Ω = 0.75, n = 1, andσ = 0.9. TheHub-
Λ 8
and describe the main ingredients of the semi-analytic ble constantis parametrisedas H = 100hkm/s/Mpc.
0
models focusing on the physical processes considered. Group catalogues were constructed using the standard
Wereferthereadertotheoriginalpapersformoredetailed friend-of-friend(FoF)algorithm,andeachgroupwasthen
descriptions;thenot-interestedreadermayskipdirectlyto processed using the algorithm SUBFIND (Springeletal.,
sec.3. 2001)toidentifyself-boundsubstructures.
It is worth stressing, that we make no effortto reduce We then considerthe FoF mergertrees constructed as
the differences between the “cooling only” realizations detailedin DL10, andthe sametwo sets oftreesconsid-
showninDL10.Thischoiceallowsustokeepourpredic- ered there. A first sample (the “MW-like” sample) has
tionsascloseaspossibletotheoriginalformulationofthe beenconstructedbyselectingfromtheMS-II100haloes
three SAMs under investigation. However, we consider with log10(M200/M⊙) between11.5and12.5atz = 0.
two different sets of predictions relative to the Durham Here,M isdefinedasthemasswithinasphereofden-
200
model,byconsideringbothanisothermalandacoredpro- sity 200 times the critical density of the Universe at the
file for the hot halo. This choice allows us to compare corresponding redshift. A second sample of 100 haloes
predictions of the fiducial Durham model with those of was selected from the MS by taking haloes that have a
a model that gives results closer to those obtained using numberdensityof10−5h3Mpc−3 atz 2,andthatend
∼
thefiducialcoolingmodelsinMORGANAandtheMunich upinmassivegroups/clustersatz =0.Theadoptednum-
SAM. Moreover, in order to exclude differences due to ber density has been chosen to be comparable to that of
mergertimes(t )assignedtosatellitegalaxies,wefo- submillimetre galaxies at z 2 (Chapmanetal., 2004,
mrg ∼
cusona“no-merger”realizationassumingt = for see e.g.,). We thusreferto this sample as the “SCUBA-
mrg
∞
all satellites. We also consider “instantaneous merger” like”sample.
realizations(t =0),andwewillcommentonthepre-
mrg
dictionsofthesemodelswheneverappropriate.
2.2 The Munichmodel
We choosethe same ChabrierIMF forall modelsand
weswitchoffmetalproductioninourmodelrealizations The stripped-downversionof the Munichmodelused in
(i.e. primordialcompositionisassumedduringtheentire thisworkisbuiltupontheDeLucia&Blaizot(2007)im-
evolution of our model galaxies). As a check, we have plementation and uses prescriptions for the star forma-
rerunourrealizationsallowingmetalenrichment: there- tion and feedback that have been described in detail in
sultspresentedinSection3 aremodifiedinthe expected Crotonetal. (2006). Cold gas is associated only to the
direction(e.g.,coolingratesaresystematicallyincreased), disc component of model galaxies, and both a “quies-
butourmainconclusionsremainvalid. cent” and a “starburst” mode forstar formationare con-
3
sidered. Cold gas surface densities higher than a given of Coxetal. (2004). Mergersalso involve mass transfer
thresholdΣ arerequiredforquiescentstarformationto between the disc and bulge components of the remnant
crit
takeplace. Thiscriticalvaluemaybeexpressedinterms galaxy. A detailed description on how galaxy mergers
of the galactocentricdistance (R) and the virial velocity affect galaxy morphologyis presented in DeLuciaetal.
ofthehosthalo(V ,Kauffmann1996): (2011) and Fontanotetal. (2011). For the purposes of
vir
this work we do not distinguish between bulge and disc
V /200kms−1
Σcrit =120 vir M⊙pc−2, (1) componentsofmodelgalaxies,andfocusontheirglobal
× R/kpc properties.
As for stellar feedback, the Munich model links the
whichcanbetranslatedintoacriticalmass,assumingthe
amountofcoldgasreheatedbySNe(∆Mmun)inagiven
cold gas is uniformly distributed over a disc with outer rht
timeintervaltothemassofstarsformedinthesametime-
radiusr . Thediscscalelength(r )iscomputedusing
disc s
step(∆M ):
resultsfromthemodelbyMoetal.(1998),andtheouter sf
radiusof the disc is assumed to be r = 3 r . The
disc × s ∆Mmun =ǫ ∆M , (5)
criticalgasmassforquiescentstarformationtotakeplace rht rht sf
is: where ǫ = 3.5. The energyreleasedin thesame time
rht
Mcrit =3.8×109200Vkvmirs−110rdKispccM⊙. (2) interval(∆ESN)canbewrittenas:
∆E =0.5V2 η ∆M , (6)
SN SN SN sf
Thestarformationrate(SFRhereafter)ϕisthenassumed
where 0.5V2 represents the mean energyin SNe ejecta
tooccurattherate: SN
per unitmass of stars formed(V = 630kms−1 based
SN
M M
ϕ =α cold− crit , (3) onstandardSNetheoryandaChabrierIMF),andηSN =
mun mun τmun 0.35parametrisesitsefficiencyinreheatingthedisccold
dyn,D
gas.
wherethestarformationefficiencyissettoα =0.07,
mun Addingthereheatedgastothehothalowithoutchang-
andτmun = r /V isthediscdynamicaltime. The
dyn,D disc vir ing its specific energy leads to the total thermal energy
adopted modelling leads to episodic star formation self-
change(∆E ):
regulatingtomaintainalevelclosetothatcorresponding hot
tothecriticalsurfacedensity.
∆E =0.5V2 ∆Mmun. (7)
In addition to the quiescent mode, the model also al- hot SN× rht
lows for a “collisional starburst” mode of star forma- It is then possible to define an excess energy E =
exc
tion (Somervilleetal., 2001), triggered by galaxy merg- ∆E ∆E . If E < 0, all reheated gas is con-
SN hot exc
−
ers. Theamountofcoldgasconvertedintostarsthrough finedwithinthehalo,otherwiseafraction∆Mmunofhot
eje
thismodedependsonthebaryonic(gas+stars)massratio gasmass(M )isejectedfromtheparenthalothrougha
hot
of the mergingobjects. If it is largerthan 0.3, the event “super-wind”:
isclassifiedasa“major”merger,andallcoldgaspresent
in the two merging galaxies is converted into stars. In
E V2
thecase ofaminormerger,themodelassumesthatonly ∆Mmun = excM = η SN ǫ ∆M ,
a fraction fbrs of all available cold gas is convertedinto eje Ehot hot (cid:18) SNVv2ir − rht(cid:19) sf
(8)
stars:
where E = 0.5V2 M represents the total ther-
hot vir hot
M abrs mal energy of the hot gas. The ejected material may be
f =e 1 , (4)
brs brs reincorporated at later times as the parent DMH grows
M
(cid:18) 2(cid:19) (DeLucia,Kauffmann&White,2004):
whereM /M representsthebaryonicmassratio(M >
1 2 2
3M ), and a = 0.7 and b = 0.56 have been cho- M
1 brs brs M˙ mun =ηmun eje , (9)
sen to provide a good fit to the numerical simulations rei rei τ
dyn,H
4
where ηmun = 0.5 is a free parameter which controls fortheequilibriumradiusatwhichrotationsupportsthem
rei
the amount of reincorporation per halo dynamical time, againstgravityinthecombinedpotentialofdisc,spheroid
τ = R /V (R being the virial radius of the and NFW dark matterhalo (includingthe effects of adi-
dyn,H vir vir vir
parenthalo). abatic contraction). When spheroidsare formedthrough
majormergers(seebelow)theirradiiarecomputedbyas-
sumingconservationof(internalplusorbital)energy.Full
2.3 GALACTICUS
detailsaregiveninColeetal.(2000).
IntheSAMcomparisonwepresentedinDL10wemade Star formation is assumed to occur in galactic discs,
useofastripped-downversionoftheBoweretal.(2006) their cold gas reservoirs being depleted at a rate deter-
implementation of the Durham model. There we tested minedbythestarformationtimescaleτdur:
sf
two versions of the Durham model, the difference lying
intheassumptionsmadefortheprofileofthehotgasdis- ϕdur =Mcold/τsdfur. (10)
tribution: wedefineda“standard”modelwithaβ-profile
The star formation timescale is a function of the disc
(as used by Boweretal. 2006) and a “modified”version circularvelocityVHRtakenatthehalf-massradiusrHR:
usinganisothermalprofile. disc disc
Inthiswork,wetakeadvantageofthenew GALACTI- VHR βdur
CUS code (Benson, 2012) to recreate the stripped-down τsdfur =α−du1rτddyunr,D 200kdmiscs−1 , (11)
versionsof the Durham modelsof DL10. GALACTICUS (cid:18) (cid:19)
is designed to be highly modular to facilitate the explo- whereτdur =rHR/VHRrepresentsthedynamicaltime
dyn,D disc disc
ration of different descriptions of key physical ingredi-
of the disc, while α = 0.0029 and β = 1.5 are
dur dur
ents. We set-up GALACTICUS to run with the same as- freeparameters. −
sumptions1 regarding gas cooling and gas profiles as in
When two galaxies merge, the merger is deemed to
the standard and modified versions of the Durham code
be “major” if the less massive of the galaxies is at least
used in DL10. In the following, we will refer to these
30% of the mass of the more massive galaxy. In such
realizationsas GALACTICUS-CP (fortheβ orcoredpro- cases, the stars of both galaxies are redistributed into a
file)andGALACTICUS-IP(fortheisothermalprofile).We spheroid. Majormergersalways triggera starburst. Mi-
explicitly check that the “cooling only” stripped down
normergersmayalsotriggerastarburstifthegasfraction
versions of GALACTICUS reproduce with good approx- in the more massive galaxy exceeds 10%. In starbursts,
imation the predictions of the “cooling only” Durham
thegascontentofthemerginggalaxiesisplacedintothe
model presented in DL10. We then include the same
spheroidcomponentofthemergerremnant,whereitpro-
treatment for star formation and stellar feedback as de-
ceeds to form stars on a timescale given by eq. 11 but
picted in Coleetal. (2000) and Bensonetal. (2003, see
with α = 0.5, β = 0, and with a dynamicaltime
dur dur
alsoBoweretal.2006),inordertocreateanequivalentof
andvelocitycomputedforthespheroid,usingthemethod
theDurhammodelneededforouranalysis.Notethatboth
describedbyColeetal.(2000).
theGALACTICUS-CPandGALACTICUS-IPmodelsdiffer Stellarfeedbackismodelledbyassumingthattherate
significantlyfromthedefaultmodelinthe GALACTICUS atwhichcoldgasisreheated(M˙ dur)isdirectlyrelatedto
rht
toolkit.
theSFR:
Galaxy sizes play a key role in this model since they
determine dynamical times and rotation speeds in discs VHR −γ
and spheroids. Given the angularmomentumof cooling M˙rdhutr = Vdisc ϕdur, (12)
gas, the radii of galactic discs are computed by solving (cid:18) hot (cid:19)
where V = 485kms−1 andγ = 3.2 arefree parame-
hot
1Inthe GALACTICUSrealization used in this work, all other rele- ters. The reheated gasis not instantaneouslyreturnedto
vantassumptions,includingthedefinitionofformationtimes,DMpro- the hot phase, but it is stored into a separated reservoir,
filesandconcentrations, mergertimecalculation, galaxysizecalcula-
M . Thismaterialisthenaddedbacktothehotphaseat
tions,andmajormergerdefinitionsaretreatedasintheoriginalDurham rsv
model. arateequalto:
5
ϕ
M˙ dur =ηdur Mrsv , (13) E˙hw,D =fth,DESN mor,D . (17)
rei rei τ mSN
dyn,H
wherem representsthemassofnewlyformedstarsper
where ηmun = 1.26andτ isthedynamicaltimeof SN
rei dyn,H SN. A furtherenergycontributionis added by assuming
thedarkmatterhalo. Itis worthnotingthatthereheated
that one type Ia SN per year explodeseach 1012 M⊙ of
materialin GALACTICUS behavesastheejectedmaterial
stellarmass. Thisrathercrudeimplementationofenergy
intheMunichmodel,i.e. asaseparatedgasphase,which
fromSNeIadoesnotinfluencemuchmodelresults.
doesnottakepartintheexchangeofenergyandmassin-
Cold gas flows into the bulge component either by
sidetheparentDMH,andwhichisslowlyreincorporated
mergers or by disc instabilities. Moreover, a fraction of
into the hot phase. For a sake of simplicity, in the fol-
thecoolingflowisallowedtofalldirectlyintothebulge.
lowing, we will then refer to this component as ejected
Star formation in bulges is assumed to take place in a
material:
“thick” regime, where SN energy is effectively trapped
withintheISM.Inthiscase,SFR isassumedtofollowa
M˙ dur =M˙ dur. (14)
eje rht Schmidt-Kennicuttrelation,withatimescale:
−0.4
2.4 MORGANA τmor =4 Σcold,B Gyr. (18)
sf,B × M⊙pc−2
The MOdel for the Rise of GAlaxies aNd Agns (MOR- (cid:18) (cid:19)
The size of the starburst, necessary to compute the gas
GANA) was first presented in Monacoetal. (2007). The
surface density, is estimated as follows. Gas is assumed
treatment of star formation and stellar feedback in this
to havenoangularmomentum,andthusto besupported
code follows the results of the multiphase modelfor the
by turbulence generatedby SNe. Undervery simple as-
ISM by Monaco (2004). For the purposes of this work
sumptions (LoFaroetal., 2009), the velocity dispersion
weconsiderthecombinationofparametervaluesadopted
inthiscasecanbewrittenas:
whenusingaChabrierIMF(LoFaroetal.,2009).
Discsaretreatedas“thin”systems: SNremnantsblow τmor −1/3
outofthediscsoonaftertheyformandmostoftheSNe σ =σ sf , (19)
cold 0
Gyr
energy is injected into the halo hot gas, and only a few (cid:18) (cid:19)
percentofSNeenergyinjectedintotheISM.Thestarfor- whereσ0 =60kms−1istreatedasafreeparameter.Itis
mationtimescaleisoftheform: thenassumedthatthesize ofthe starburstregionis such
thatσ equatestherotationcurveofthebulge,assumed
cold
tobeflat(seeLoFaroetal.2009fordetails).
−0.73 0.45
Σ f Therateatwhichhotgasisejectedfromabulgetothe
τmor =9.1 cold,D cold,D Gyr,
sf,D 1M⊙pc−2 0.1 hosthaloisassumedtobe:
(cid:18) (cid:19) (cid:18) (cid:19)
(15)
wheref representsthecoldgasfraction(inthedisc
componceonldt),.DGasre-heatedbystellarfeedbackisejected M˙hw,B = √VVh2ohto−tVB2 ϕmor,B ifVB <Vhot (20)
fromthedisctotheanexternalreservoirofbaryons(i.e. ( 0 ifVB Vhot
≥
the “halo” component) still bound to the host DM halo,
Thisisdonetotakeintoaccounttheabilityofthepoten-
ata“hotwind”rateM˙ assumedtobeequaltothestar
hw tialwellofamassivebulgetokeephotgasconfined;the
formationrate:
parameter V is chosen to be 300 km/s, corresponding
hot
to the typical thermal velocity of a 107 K hot phase.
M˙ =ϕ . (16) ∼
hw,D mor,D Thecorrespondingenergycarriedbythehotwindis:
Afractionf =0.32ofSNenergyE iscarriedaway
th,D SN
whoitthwtihnidsteojetchteedthmeramtearliaeln,esrogythoefctohnethriobtuhtiaolnoEgahswiso:fthe E˙hw,B =fth,BESN Vh2ot−VB2 ϕmor,B , (21)
V m
p hot SN
6
wherewe use f = 0.1 forthe fractionof SN energy make different assumptions for the timescale of conver-
th,B
carriedaway. sion. In the Munich model, the star formation proceeds
A bulge also ejects cold gas into the halo, due to the onatimescaledirectlyproportionaltothedynamicaltime
same SN-driven turbulence that sets the starburst size of the disc, while in Durham-like models the timescale
(Eq. 19). This “cold wind” from the bulge to the halo ofstarformationisrescaledwithsomepowerofthecir-
componentisassumedtooccuratarate: cular velocity of the disc. Finally, MORGANA assumes
a star formation timescale consistent with the Schmidt
M P v
M˙ = cold,B ub ub , (22) law. The Munichmodelexplicitlyaccountsfora critical
cw,B
RB mass threshold for star formation, while MORGANA and
whereRB isthehalf-massradiusofthebulge,whilePub Durham-likemodelsdonot.
andvub representtheprobabilitythatacoldcloudisun- Besides a quiescent mode of star formation, both the
bound (i.e. it has a velocity larger than the escape ve- Munich and GALACTICUS-CP models assume an en-
locity of the bulge VB) and the average velocity of un- hanced star formation regime occurring during galaxy
boundclouds(bothprobabilitiesare computedassuming mergers,withafractionofthetotalcoldgasavailablebe-
aMaxwelliandistributionofvelocitieswithrmsσcold). ingturnedintostarsinaveryshorttimescale(thatofthe
The hot and cold halo gas components keep track of modelintegration). In MORGANA, coldgasisassociated
both the mass and the energyreceivedrespectivelyfrom also to the bulge component. Because of the complete
hot winds from discs and bulges and from cold winds lossofangularmomentum,gasinbulgesisconcentrated
frombulges. Thehaloreceiveswindsbothfromthecen- to very small sizes. Then the higher gas surface densi-
tralgalaxyandfromsatellites. Wheneverthegasphases ties force the Schmidt-Kennicutt relation to give much
of the halo component are too energetic to be bound to higher SFRs and shorter star formation timescales than
theDMhalo,theyareallowedtoescapetotheIGMasa thosecorrespondingtostarformationindiscs. Inourref-
galaxy“superwind”.Inparticular,iftheenergyEhot,Hof erenceruns,weexplicitlyexcludemergereventsandthe
thehalohotgasmassMhot,H overtakesthevirialenergy enhanced SFR by setting tmrg = . We will discuss
∞
Evirbymorethanafactorfwind =2,asuperwindoccurs the impact of the “starburst” mode on the predicted star
atarate: formationhistories by consideringthe predictionsof the
instantaneous-mergerrunsinsection3.2.
f E c M InMORGANAtheamountofdiscgasreheatedviastel-
M˙emjeo,rH = 1− wEind vir sRhot,H , (23) larfeedback(Mrht)equalstheSFR(ϕ),whileintheMu-
(cid:18) hot,H (cid:19) vir nichmodelthese two quantitiesare proportional,viathe
wherecsrepresentsthesoundvelocityinthehalo.Asim- parameter ǫrht > 1. This implies that the amountof re-
ilarformuladeterminestheejectionofcoldsuperwinds: heatedgasperunitstarformationis alwayslargerin the
Munich model than in MORGANA . A slightly different
M˙emjeo,rC = 1− fwinσdH2Vd2isp!σHMRvciorld,H . (24) tichsheoaaidcmdeiothiuaonsntabolelfeyrneamhsesauadtmeedeidngatthoserseGcmAalaLeiAnasCspTarIoCppUooSwrtmieorondoaeflltstoh,ewϕ,hdbeisurcet
A fraction (f = 0.5) of the mass ejected by the velocity.
back
DM halo is later re-incorporated(i.e. added to infalling An important quantity in the balance of the baryonic
IGM),whentheparentDMhaloreachesanescapeveloc- contentofeachDMHisgivenbytheamountofbaryons
itylargerthanthe(thermalorkinetic)velocitythegashad ejected. In both Durham-like and Munich models, the
whenitwasejected. fraction of ejected mass is directly proportional to the
mass of stars formed in the same time interval, while in
2.5 Comparisonbetween the models MORGANA thedependencyoftheejectionrateonstellar
feedbackismediatedviatheestimate ofthe thermal(ki-
All three models considered relate the SFR in the disc netic) energyof the hot(cold)gashalo phase. Allmod-
componenttotheamountofcoldgasthereavailable,but elsassumethatthisejectedmaterialisreincorporatedinto
7
thehaloatlatertimes,withdifferentassumptionsforthe Figures 1 and 2 show the redshift evolution of the
reincorporationrates. In Durham-likeand Munichmod- different baryonic componentsin the haloes considered:
els,thisismodelledasacontinuousprocessfollowingthe from top to bottom, we show the cold gas fractionasso-
DMHgrowth,whileinMORGANAonlyhalfofthemate- ciated with thecentralgalaxy,the hotgasfractionin the
rialconnectedtoeachejectioneventisre-acquiredinstan- halo, thenetcoolingrate (m˙ ; see below),thestellar
NCR
taneouslywhentheDMHhasgrownenoughtoovercome massofthecentralgalaxyandthemassejectedfromthe
itsescapevelocity. DMH.Inthethreeupperpanels,wecomparethepredic-
Durham-likeandMunich modelsemploya verysimi- tionsofthemodelsincludingstarformationandfeedback
larschemeformodelingtheejected component. In both (darkercolours-solidlines)withpreviousresultsforthe
casessomeofthefeedbackreheatedmaterialisexcluded “only cooling” realizations considered in DL10 (lighter
from the mass/energy flows between the cold and hot colours-longdashedlines).
gas phases: but while this is only a fraction in the Mu- Wedefinem˙ asthenetrateatwhichcoldgasand
NCR
nichmodel(theremainingbeinginstantaneouslyaddedto starsaredepositedintothegalaxy:
the hot phase), all reheated material is consideredin the
Durham-like models. The same reincorporationscheme m˙ = Mcold(t2)+Mstar(t2) Mcold(t1)+Mstar(t1),
NCR t2−t1 − t2−t1
isassumed,butwithafasterrateintheDurham-likemod-
elsthanintheMunichmodel. where t and t are the cosmic epochs correspondingto
1 2
Inthefollowing,wechoosetoavoidthecomplications two consecutive snapshots. The net cooling rate differs
arisingformdiscinstabilities2byswitchingthemoff. fromtheintrinsiccoolingrate,sinceittakesintoaccount
both the effect of feedback in removingpart of the cold
gas from the system and the effect of star formation in
3 Results lockingsomematerialinlonglivedstars.Forthestripped-
downSAMversionsconsideredinDL10thesetwoquan-
3.1 Test cases titiescoincidebyconstruction.
Theinclusionoffeedbackfromstarformationhasthe
Westartbyconsideringtheevolutionofthedifferentbary- net effect of reducing the amount of cold gas available
oniccomponentsinafewtestcases. Forconsistencywith inMW-haloes(figure1,thisholdsalsoforinstantaneous
DL10,wefocusonthesame4representativeDMHs(their merger realizations) and increasing the hot gas fraction
fig. 1 and 4). These have been chosen among the 100 withrespecttothe“coolingonly”runs.IntheMWhaloes,
MW-likeandthe100scuba-like(twoforeachsample)as this increase is particularly relevant in the Durham-like
representativeofaquietmassaccretionhistoriesandofa models,thatpredictshigherhotgasfractionwithrespect
large numberof mergerevents. In the following, when- to the other two models. This shows that the feedback
everwe referto“centralgalaxy”forourDMHs, wewill scheme implemented in the Durham-like models is the
refer to the central galaxy of the main progenitor at the mostefficient(amongthoseconsideredhere)inreheating
correspondingredshift. Allothergalaxieswillbedefined the coldgasin thehaloesatthese massscales. Thecold
as “satellites”. For the sake of simplicity, in this section gasfractionassociatedwith thecentralgalaxyischarac-
wewillshowresultsonlyforthe2haloeswithquietmass terizedbyamarkeddeclineatlowerredshift,andpredic-
accretionhistories. The othertwo haloesgiveconsistent tions from the three models considered are more differ-
results,andareshownforcompletenessinappendixA. entthaninthe“coolingonly”realizations. Inourmodels
there are two competing effects able to deplete the cold
2Inparticular,discinstabilitieshavenodirecteffectontheSFRpre-
gas reservoir: the formation of long lived stars and cold
dictedbytheMunichmodel,sinceonlyenoughstellarmassisremoved
fromthedisctothebulgetorestorestability. IntheDurhammodel,at gas removalby stellar feedback. In orderto disentangle
eachinstabilityevent,thewholediscisdestroyedandallitsbaryonsare thesetwoeffectsweconsidertheevolutionoftheoverall
giventothespheroidalcomponent,withanycoldgaspresentassumed cold gas plus stars and still find a decrease with respect
toundergoastarburst. InMORGANAadifferentchoicehasbeenmade,
to the predictions of DL10 for the cold gas component.
bymovingawelldefinedfractionofdiscstarsandcoldgastothebulge,
whereitformsstarsonaτmortimescale. These findings show that the inclusion of a strong stel-
sf,B
8
Figure1: Redshiftevolutionofthe baryoniccontentfora MW-likerepresentativeDMH (with quietmassaccretion
history;fig.1rightpanelsinDeLuciaetal.2010). Upperrow: coldgasfractionsassociatedwiththecentralgalaxy;
second row: hot gasfractions; third row: net cooling rates. Blue, red, yellow and green lines refer to MORGANA ,
GALACTICUS-CP , GALACTICUS-IP and the Munichmodel. Dark solid lines referto the modelsconsideredin this
work,whiledashedlinesrefertothe“coolingonly”models(DeLuciaetal.,2010). Lowerrow: stellarmasses(blue
dashedlines)andejectedmasses(redsolidlines). Inallmodelsweassumet = (seetextformoredetails).
mrg
∞
9
Figure2:RedshiftevolutionofthebaryoniccontentforaSCUBA-likerepresentativeDMH(withquietmassaccretion
history;fig.4rightpanelsinDeLuciaetal.2010).Symbols,linestyles,andcolourshavethesamemeaningasinfig.1.
10