The Building Up of the Black Hole Mass - Stellar Mass Relation

0.86 MB·English

by  Alessandra Lamastra

Mon.Not.R.Astron.Soc.000,??–??() Printed29January2010 (MNLATEXstylefilev2.2)
The Building Up of the Black Hole Mass - Stellar Mass Relation
A. Lamastra1(cid:63), N. Menci1, R. Maiolino1, F. Fiore1, A. Merloni2
1INAF-OsservatorioAstronomicodiRoma,viadiFrascati33,I-00040Monteporzio,Italy
2Max-Planck-Institutfu¨rExtraterrestrischePhysik,Giessenbachstrasse,D-85741Garching,Germany
0
1
0 Submitted:
2

n
a ABSTRACT
J WederivethegrowthofSMBHsrelativetothestellarcontentoftheirhostgalaxypredicted
9 undertheassumptionofBHaccretiontriggeredbygalaxyencountersoccurringduringtheir
2 merging histories. The latter are described through Monte Carlo realizations, and are con-
nected to gas processes, star formation and BH accretion using a semi-analytic model of

] galaxyformationinacosmologicalframework.Thisallowsustoconnectthestarformation
O
processinthehostgalaxiestothegrowthofSupermassiveBlackHoles.Weshowthat,within
C thisframework,theratioΓ ≡ (M /M )(z)/(M /M )(z = 0)betweentheBlackHolemass
BH ∗ BH ∗
. and the galactic stellar mass (normalized to the local value) depends on both BH mass and
h redshift.WhiletheaveragevalueandthespreadofΓ(z)increasewithz,suchaneffectislarger
p
for massive BHs, reaching values Γ ≈ 5 for massive Black Holes (M ≥ 109 M ) at z (cid:38) 4,
- (cid:12)
o inagreementwithrecentobservationsofhigh-redshiftQSOs;thisisduetothetheeffective-
r nessofinteractionsintriggeringBHaccretioninhigh-densityenvironments(wheremassive
t
s haloesform)athighredshifts.
a ToinvestigatehowdifferentobservationsofΓ(z)fitwithinourframework,weworkedout
[
specificpredictionsforsub-samplesofthesimulatedgalaxiescorrespondingtothedifferent
1 observational samples for which measurements of Γ have been obtained. We found that for
v BroadLineAGNsatintermediateredshifts1(cid:46)z(cid:46)2valuesofΓ≈2areexpected,withamild
7 trend toward larger value for increasing BH mass. Instead, when we select from our Monte
0 Carlosimulationsonlyextremelygasrich,rapidlystarforminggalaxiesattheepochofpeak
4 inthecosmicstarformation(2 ≤ z ≤ 3),wefindlowvalues0.3 ≤ Γ ≤ 1.5,consistentwith
5
recentobservationalfindingsonsamplesofsub-mmgalaxies;intheframeworkofourmodel,
.
1 theseobjectsendupatz=0inlow-to-intermediatemassBHs(M ≤109 M ),andtheydonot
(cid:12)
0 representtypicalpathsleadingtolocalmassivegalaxies.Thelatterhaveformedpreferentially
0 throughpaths(intheM −M plane)passingabovethelocalM −M relation.Wediscuss
∗ BH ∗ BH
1
how the global picture emerging from the model is consistent with a downsizing scenario,
:
v wheremassiveBHsaccretealargerfractionoftheirfinalmassathighredshiftsz≥4
i
X Keywords: galaxies:active—galaxies:formation—galaxies:evolution
r
a
1 INTRODUCTION in the past, and that a strong physical connection exists between
galaxyformationandthegrowthofSMBHs.
ThediscoveryoftightlocalcorrelationsbetweenthemassM of
BH
Understanding the mechanisms responsible for such a con-
SupermassiveBlackHoles(SMBHs)andglobalpropertiesoftheir
nection, and establishing the relative time scales for star forma-
hostgalaxies,likethestellarmassM orthevelocitydispersionσ ,
∗ ∗ tion/assembly and for SMBHs growth, requires the measurement
(Kormendy & Richstone 1995; Magorrian et al. 1998; Ho 1999;
oftheabovecorrelationsathigherredshifts.Forsuchascope,the
Gebhardtetal.2000;Ferrarese&Merritt2000;Marconi&Hunt
moststraightforwardcorrelationtostudyistheM −M relation,
2003;Ha¨ring&Rix2004;Kormendy&Bender2009)constitutes BH ∗
sincetheotherfundamentalrelation M −σ wouldrequirethe
an important breakthrough in the understanding of galaxy evolu- BH ∗
measurementofstellarvelocitydispersionswhichareverydifficult
tion.IfthegrowthofSMBHsisconsiderablycontributedbyaccre-
toachieveatz(cid:38)1innormalgalaxies.
tionovercosmologicaltimes(Soltan1982;Yu&Tremaine2002;
Marconietal.2004;Merloni&Heinz2008)thisimpliesthatmost, TheMBH−M∗relationinthelocalUniversehasbeenwidely
ifnotall,galaxieshavehostedanActiveGalacticNucleus(AGN) investigatedintheliterature.Magorrianetal.(1998)werethefirst
to find a correlation between the black hole mass and the stellar
mass, however they found a very large scatter (∼0.51 dex). This
relation was then re-examined using more reliable M and M
BH ∗
(cid:63) E-mail:[email protected] measurements(Merritt&Ferrarese2001,Marconi&Hunt2003,
(cid:13)c RAS
2 Lamastraetal.
Ha¨ring & Rix 2004); these studies showed that the scatter in the thecorrelationbetweenstarformationrateandstellarmass,such
M − M relation is comparable to the scatter in the M −σ observationstendtobebiasedtowardsmassivestellarhosts.
BH ∗ BH ∗
relation(∼0.3dex,seeHa¨ring&Rix2004).Itisalsoworthnoting Attemptstoderivetheevolutionoftheglobal(cid:104)Γ(z)(cid:105)averaged
that the relation is BH mass dependent (Ha¨ring & Rix 2004), overforwholeAGNpopulationrequiresadifferentapproach,based
although the mean value of the MBH/M∗ ratio obtained from the onintegratedobservables.Bycomparingtheredshiftevolutionof
Ha¨ring&Rix(2004)sample:(cid:104)log(MBH/M∗)(cid:105) (cid:39)-2.8,isconsistent theintegratedBHandofthestellarmassdensitiesMerloni,Rud-
withthosederivedbyMerritt&Ferrarese(2001)andMarconi& nick&DiMatteo(2004)foundthat(cid:104)Γ(cid:105) ≈ (1+z)α withα (cid:39)0.5.
Hunt(2003)whenthelatterisloweredbyafactorof5/3toaccount Sucharesultsisconsistentwiththeupperlimitsontheevolution
formorerecentestimatesofthebulgevirialmasses(seeMaiolino of(cid:104)Γ(cid:105)derivedbyHopkinsetal.(2006)forz(cid:46)2.
etal.2007). Thus,amajorchallengefornextstudiesofAGNandgalaxy
formationisunderstandingwhichoftheaboveclassesofpathsΓ(z)
TheSMBHmassesatz (cid:38) 0.5aregenerallyestimatedinlu- isthedominantoneinthecosmologicalevolutionofgalaxiesand
minoustype1AGNslikequasars(QSOs)andradiogalaxies;for SMBHs, and what are the physical mechanisms determining the
example, virial BH mass estimators are based on the assumption particularpathfollowedbyagalaxyasafunctionofitsproperties
thatthebroad-lineregionoftheAGNsaredominatedbythegrav- in different cosmic epochs. While on the observational side such
ityoftheSMBH(see,e.g.,Peterson&Wandel2000),andprovide a task would require a large, unbiased sample of AGNs, a com-
massestimatesofSMBHsathigherredshifts(seeWandel,Peterson plementaryapproachistoconsidercosmologicalmodelsofgalaxy
&Malkan1999;Kaspietal.2000;McLure&Dunlop2002,Mer- and SMBH evolution which assume a given physical mechanism
lonietal.2009),extendingouttoz ≈ 6(e.g.,Willott,McLure& fortheAGNfeedingandforitsconnectionswiththeevolutionof
Jarvis2003;McLure&Dunlop2004;Vestergaardetal.2004;Wal- the host galaxy; then, comparing the predictions of such models
teretal.2004;Riechersetal.2008).TheevolutionoftheMBH/M∗ forspecificclassesofobjectswithdifferentexistingobservations
ratio from the local value is generally quantified in terms of the would constitute a powerful probe for the proposed physical link
parameter: betweengalaxiesandSMBHs.
Indeed,intherecentyears,significantsstepsforwardhadbeen
Γ≡(MBH/M∗)(z)/(MBH/M∗)(z=0). (1) taken toward the modelling of the cosmological co-evolution of
galaxies and AGNs, starting from the seminal papers by Silk &
AlthoughtheAGNactivitymakesitdifficulttoderivestellar Rees(1998);Fabian(1999);Cavaliere&Vittorini(2000);Wyithe
masses for the host galaxies at z (cid:38) 1.5, several observational &Loeb(2003).Ontheonehand,recenthigh-resolutionhydrody-
works suggest that at such redshifts the mean MBH/M∗ ratio is namicN-bodysimulations(see,e.g.,DiMatteo,Springel&Hern-
significantlyhigherthanthepresentvalue,correspondingtoΓ>1. quist 2005, Springel 2005; Hopkins 2005, 2006) have shown the
importanceofgalaxymergersastriggersforAGNaccretion,and
Peng et al. (2006), applying the virial method on a sample theroleoftheAGNenergyfeedbackinthesubsequentevolution
of 31 gravitationally lensed AGNs and 20 non-lensed AGN and of the host galaxy. However, such simulations are affected by a
derivingthehostgalaxystellarmassfromtheR-bandluminosity, limitedexplorationofthesub-gridprescriptionsforthephysicsof
found the M /M ratio to be higher than the present value by a SMBHs;mostimportant,theynecessarelyfocusonspecificgalaxy
BH ∗
factorΓ≈2forAGNsat1≤z≤1.7andbyafactorofΓ≈4atz≥ systems,makingitdifficulttoassessthestatisticalrelevanceofa
1.7; analysing the hosts of 89 broad-line AGNs in the COSMOS particularpathinthebuildingupofthelocal M −M relation.
BH ∗
surveyMerlonietal.(2009)deriveapositiveevolutionfittedwith Ontheotherhand,semi-analyticmodels(SAMs,Monaco,Salucci
Γ ≈ (1+z)0.74 intheredshiftrange1 ≤ z ≤ 2.2;exploitingradio- &Danese2000,Kauffmann&Haenhelt2000;Volonteri,Haardt&
loud unification McLure et al. (2006) obtained virial (linewidth) Madau2003;Granatoetal.2004;Mencietal.2006;Crotonetal.
BHmassestimatesfromthe3CRRquasars,andthestellarmass 2006;Boweretal.2006;Marullietal.2008)canprobethewhole
estimatesfromthe3CRRradiogalaxies,therebyprovidingblack setofpossiblepathsfollowedbygalaxiesinthe M −M plane
BH ∗
holeandstellarmassestimatesforasinglepopulationofearly-type during their evolution. Since their results depend on the mecha-
galaxies, finding Γ ≈ (1+z)2 for z (cid:46) 2; at even higher redshifts nisms assumed for the trigger of the AGN accretion and for the
z≥4,measurementsofthedynamicalmassfromtheCOemission AGN energy feedback, SAMs are suitable to probe the statistical
ofmoleculargasinthehostsofhigh-redshiftQSOs(Walteretal. outcomesprovidedbytheimplementedphysicalprocesseslinking
2004;Riechersetal.2008)yieldlargevaluesofΓ=5−10. SMBHswiththeirhostgalaxy.
While the above studies indicate that the growth of SMBHs Here we adopt a state-of-the-art SAM (Menci et al. 2006,
is faster than the stellar mass assembly, they all focus on lumi- 2008) which implements a specific, physical model for the BH
nousAGNs,andarethusbiasedtowardsselectingthemostmas- accretionbasedoninteractionsastriggersforboththefuelingof
sive SMBHs (see Lauer et al. 2007). In contrast to the above re- SMBHsandthestarbursts.Inturn,theinteractionrate,theamount
sults, from the analysis of a sample of sub-mm selected galaxies ofgasavailableforBHaccretion,andthestellarcontentofgalax-
(SMGs) Borys et al. (2005) find Γ to decrease with redshift for ies are computed from Monte Carlo realizations of galaxy merg-
z(cid:46)2;morerecently,Alexanderetal.(2008)foundΓ(z=2)=0.3 ingtrees,enablingustofollowtheevolutionarypathsofgalaxies
forSMGsatz ≈ 2,indicatingthatforsuchobjectsthegrowthof andoftheirSMBHsovercosmologicaltimes,fromthecollapseof
SMBHsactuallylagsthatofthehoststellarmass.Theselatterstud- their progenitors from the primordial density field to the present.
iesareaffectedbyadifferentbias,inthattheyselectultra-luminous Based on such a model we derive the evolutionary paths for the
(L(cid:38)1012L ),gas-richgalaxies(withgasfractionrelativetobary- growthofSMBHsrelativetothatofthestellarmassoftheirhost
(cid:12)
onicmass f (cid:38) 0.6,seeGreveetal.2005;Tacconietal.2008), galaxies,toinvestigatewhicharethedominantpathsfollowedby
gas
characterizedbytheconversionofasignificantfractionoftheirini- differentgalaxypopulationsinbuildingupthelocalM −M re-
BH ∗
tialgasreservoirof1010−1011 M intostarsinashorttimesscale lationinascenariocharacterizedbyAGNfuelingdrivenbygalaxy
(cid:12)
ofafew108 yrs(seeTacconi2008andreferencestherein);given interactions.Wethencomparedifferentmodelpredictionsforthe
(cid:13)c RAS,MNRAS000,??–??
TheBuildingUpoftheBlackHoleMass-StellarMassRelation 3
M /M ratioofluminousintermediate-andhigh-redshiftgalax- inducinglossafangularmomentum.Therateofsuchinteractions
BH ∗
ies,andforintermediateredshiftSMGswithexistingobservations, is
anddiscussthephysicaloriginofthedifferentpathsΓ(z)followed
τ−1=n Σ(r,v,V )V . (2)
by galaxies and SMBHs during their evolution. Finally, we shall r T t rel rel
providespecificpredictionstypicalofthescenariocharacterizedby Heren isthenumberdensityofgalaxiesinthesamehalo,V is
T rel
interaction-drivenAGNfueling,tobetestedwithnextexperiments. theirrelativevelocity,andΣisthecrosssectionforsuchencoun-
terswhichisgivenbySaslaw(1985)intermsofthetidalradiusr
t
associatedtoagalaxywithgivencircularvelocityv(seeMenciet
al.2003,2004).
2 THEMODEL
ThefractionofcoldgasaccretedbytheBHinaninteraction
Weusethesemi-analyticmodelasisdescribedindetailsinMenci eventiscomputedintermsthevariation∆jofthespecificangular
et al. (2005, 2006, 2008); this connects, within a cosmological momentum j≈Gm/v ofthegastoread(Mencietal.2003)
d
framework,theaccretionontoSMBHsandtheensuingAGNactiv- (cid:12)(cid:12)∆j(cid:12)(cid:12) (cid:28)m(cid:48) r v (cid:29)
itieswiththeevolutionofgalaxies.Herewerecallthebasicpoints. facc≈10−1(cid:12)(cid:12)(cid:12) j (cid:12)(cid:12)(cid:12)=10−1 m bd Vd . (3)
rel
Herebistheimpactparameter,evaluatedastheaveragedistanceof
2.1 HierarchicalGalaxyEvolution thegalaxiesinthehalo.Also,m(cid:48)isthemassofthepartnergalaxy
intheinteraction,andtheaveragerunsovertheprobabilityoffind-
Galaxy formation and evolution is driven by the collapse and
ingsuchagalaxyinthesamehalowherethegalaxywithmassmis
growth of dark matter (DM) haloes, which originate by gravita-
located.Thevaluesofthequantitiesinvolvedintheaverageyield
tionalinstabilityofoverdenseregionsintheprimordialDMden-
values of f (cid:46) 10−2. For minor merging events and for the en-
sityfield.Thisistakentobearandom,Gaussiandensityfieldwith acc
countersamonggalaxieswithveryunequalmassratiosm(cid:48) (cid:28) m,
ColdDarkMatter(CDM)powerspectrumwithinthe”concordance
dominating the statistics in all hierarchical models of galaxy for-
cosmology”(Spergeletal.2007)forwhichweadoptroundparam-
etersΩΛ =0.7,Ω0 =0.3,baryonicdensityΩb =0.04andHubble mation,theaccretedfractiontakesvalues10−3(cid:46) facc(cid:46)10−2.
constant(inunitsof100km/s/Mpc)h=0.7.Thenormalizationof Theaverageamountofcoldgasaccretedduringanaccretion
thespectrumistakentobeσ =0.9intermsofthevarianceofthe episode is thus ∆macc = faccmc, and the duration of an accretion
8
fieldsmoothedoverregionsof8h−1Mpc. episode, i.e., the timescale for the QSO or AGN to shine, is as-
sumedtobethecrossingtimeτ = r /v forthedestabilizedcold
ThemergingratesoftheDMhaloesareprovidedbytheEx- d d
gascomponent.
tendedPress&Schechterformalism(seeBondetal.1991;Lacey
The time-averaged bolometric luminosity so produced by a
& Cole 1993). The clumps included into larger DM haloes may
QSOhostedinagivengalaxyisthenprovidedby
surviveassatellites,ormergetoformlargergalaxiesduetobinary
aggregations,orcoalesceintothecentraldominantgalaxydueto ηc2∆m
dynamicalfriction;theseprocessestakeplaceovertimescalesthat L= acc . (4)
τ
growlongerovercosmictime,sothenumberofsatellitegalaxies
We adopt an energy-conversion efficiency η = 0.1 (see Yu &
increasesastheDMhosthaloesgrowfromgroupstoclusters(see
Tremaine 2002), and derive the X-ray luminosities L in the 2-
Mencietal.2005,2006). X
10 keV band from the bolometric corrections given in Marconi
The processes connecting the baryonic components to the
etal.(2004).TheSMBHmassm growsmainlythroughaccre-
growing DM haloes (with mass m) are described in our previous BH
tion episodes as described above, besides coalescence with other
papers(e.g.,Mencietal.2005).Thegasatvirialequilibriumwith
SMBHs during galaxy merging. As initial condition, we assume
theDMpotentialwellsundergoesradiativecooling.Thecooledgas
smallseedBHsofmass102M (Madau&Rees2001)tobeini-
mass m settles into a rotationally supported disc with radius r (cid:12)
c d
tiallypresentinallgalaxyprogenitors;ourresultsareinsensitiveto
(typicallyrangingfrom1to5kpc),rotationvelocityv anddynam-
icaltimet = r /v .Twochannelsofstarformationdmayconvert thespecificvalueaslongasitissmallerthansome105M(cid:12).
d d d
partofsuchagasintostars:
i)quiescentstarformation,correspondingtothegradualconversion
intostarsataratem˙ ∝m /t 2.3 AGNfeedback
∗ c d
ii)starburststriggeredbyinteractions,whichdestabilizepartofthe
Finally,ourSAMmodelincludesadetailedtreatmentofAGNfeed-
cold gas available by inducing loss of angular momentum. Note
back.Thisisassumedtostemfromthefastwindswithvelocityup
thatgalaxyinteractions(amonggalaxieswithrelativevelocityV )
rel to10−1cobservedinthecentralregionsofAGNs(Weymann,Car-
includenotonlymergingbutalsofly-byevents.Partofenergyre-
swell&Smith1981;Turnsheketal.1988;Crenshawetal.2003;
leasedbySNaefollowingstarformationisfedbackontothegalac-
Chartasetal.2002;Poundsetal.2003,2006;Risalitietal.2005);
ticgas,thusreturningpartofthecooledgastothehotgasphase
theseareusuallythoughtooriginatefromtheaccelerationofdisc
outflowsduetotheAGNradiationfield(Proga2007andreferences
therein,Begelman2004).Thesesupersonicoutflowscompressthe
2.2 AccretionontoSMBHsandAGNemission
gas into a blast wave terminated by a leading shock front, which
ThemodelalsoincludesatreatmentofSMBHsgrowingatthecen- movesoutwardswithalowerbutstillsupersonicspeedandsweeps
treofgalaxiesbyinteraction-triggeredinflowofcoldgas,follow- outthesurroundingmedium.Eventually,thismediumisexpelled
ing the physical model proposed by Cavaliere & Vittorini (2000) fromthegalaxy.
and implemented in Menci et al. (2006, 2008). The accretion of Quantitatively,theenergyinjectedintothegalacticgasinsuch
cold gas is triggered by galaxy encounters (both of fly-by and of innerregionsistakentobeproportionaltotheenergyradiatedby
mergingkind),whichdestabilizepartofthecoldgasavailableby theAGN,∆E =(cid:15) ηc2∆m .Thevalueoftheenergyfeedback
AGN acc
(cid:13)c RAS,MNRAS000,??–??
4 Lamastraetal.
Figure1. LeftPanel:ThelocalpredictedMBH−M∗relationiscomparedwithdatabyHa¨ringandRix(2004,diamonds),andMarconi&Hunt(2003,squares,
hereM∗isderivedusingthebest-fittingvirialrelationofCappellarietal.2006);thecolourcoderepresentsthedensity(perMpc3)ofBHsinagivenMBH−M∗
bin,asindicatedbytheuppercolourbar.Thecontourplotallowstoshowhowthepredictedbehaviourofthescatter(growingwithdecreasingstellarmass)is
consistentwiththeobservedscatterofthedatapoints.
CentralPanel:ThepredictedMBH−M∗relationatz=4(colourcodedasabove)iscomparedwithdatacorrespondingtoobservationsofbroad-lineAGNs
andhostgalaxiesintherange4≤z≤6;detailsonthedataandcorrespondingreferencesareprovidedintheAppendixA.Wealsoshowasasolidlinethe
predictedmedianlocalvalue,correspondingtothemedianlocalvalueofMBHformodelgalaxieswithgivenM∗.
RightPanel:WeshowsomeofthepathsintheMBH(t)−M∗(t)planefollowed,duringtheirevolution,byBHs(andbytheirhostgalaxies)reachingafinal
massofMBH(z=0)≥1010M(cid:12).
efficiencyforcouplingwiththesurroundinggasistakenas(cid:15) = acterizesthemerginghistoriesofmassiveobjectsformedinbiased,
AGN
510−2(seeMencietal.2008). highdensityenvironments(seeMencietal.2008).
NotethattheM −M relationispredictedtoevolvewithz
BH ∗
asshownbythecentralpaneloffig.1,withthemassiveendofthe
distributionreachingtheregioncorrespondingtotheobservations
ofluminous,broad-lineAGNsatz≥4(seeAppendixAfordetails
3 RESULTS:OVERVIEWOFSMBHGROWTH
onthedata).Atypicalpredictionofourinteraction-drivenmodelis
AsafirststepinthestudyoftherelativegrowthofBHsandhost thattheevolutionoftheMBH−M∗relationincreasesforincreasing
galaxies, we show in fig. 1 the local (left panel) and the high- stellarorBHmass;indeed,whilelow-massBHsinmodelgalaxies
redshift (z = 4, central panel) MBH − M∗ relation that we obtain athighredshiftsarecharacterizedbyMBH/M∗ratiosclosetotheir
fromourmodel. localvalues(atleastforthemajorityofthem),forthemostmassive
The predicted local relation is consistent with observations, simulatedBHsthe MBH/M∗ issubstantiallylargerthanthemodel
andthedatalieonthepredictedconfidenceregionrepresentedby localvalues.Wecanquantifytheevolutionofthe MBH/M∗ inour
thecontourplot,althoughthepredicteddistributionshowsasmall modelthroughthequantityΓdefinedinSect.1(eq.1);sinceour
offsetfromtheobservedbest-fittingrelationsderivedbyMarconi model predicts a whole distribution of local MBH for each stellar
&Hunt(2003)andHa¨ring&Rix(2004).Although,inprinciple, mass M∗ (not justa simple power-law,as is generallyadopted to
the model parameters (like the AGN feedback efficiency (cid:15)AGN or fitthelocaldata),wecomputeΓasthedeviationofthe MBH/M∗
thenormalizationofthestarformationefficiency)couldbetuned ratioofeachmodelblackholefromitsownlocalvalue.Thenfor
to optimize the fitting to the observed local MBH − M∗ relation, galactic hosts with stellar mass M∗ ≈ 1011M(cid:12) the BH masses at
this would also affect the predicted properties of the galaxy pop- z ≥ 4 are typically MBH ≈ 109.6M(cid:12) (see central panel of fig. 1),
ulation (e.g., the evolution of the luminosity function, the colour moremassivethanthepredictedlocalvaluebyafactorΓ≈5.These
distributions,thelocalTully-Fisherrelation)atbothlowandhigh objects constitute the progenitors of the local extremely massive
redshifts.Sincethemodelisintendedtoprovideaunifieddescrip- BHs,andtheirgrowthwithtimeisrepresentedbythepathsshown
tion of AGNs and galaxy evolution, we chose to adopt the same intherightpaneloffig.1.Notehowsuchpathsarecharacterized
fiducial model adopted in our previous works since it provides a byanassemblyofBHmassesextremelyrapidintheearlyphases,
good match to a wide set of galactic properties (see Menci et al. which is faster than the stellar mass growth since they approach
2006,2008).Instead,arobustfeatureofthe MBH −M∗ isconsti- theirfinalpositioninthe MBH −M∗ planepassingabovethelocal
tutedbythebehaviourofthescatter,whichisalmostindependentof MBH−M∗relation.
themodelparametersandevenonthespecificmechanismassumed Thephysicaloriginoftheabovebehaviourcanbeunderstood
to trigger the AGN feeding. In fact, its decrease with increasing as follows: such high-redshift massive BHs (the counterpart of
M istypicalofhierarchicalscenarios,anditisduetotheearly thoseobservedbyWalteretal.2004;Maiolinoetal.2007;Riech-
BH
assemblyofprogenitorsintoauniquemainprogenitorwhichchar- ersetal.2008)areformedfromgalaxiescollapsedinbiased,high-
(cid:13)c RAS,MNRAS000,??–??
TheBuildingUpoftheBlackHoleMass-StellarMassRelation 5
Figure3. ThepredictedevolutionoftheBHtostellarmassratioΓ(nor-
malizedtothelocalvalue,seeeq.1),fortheevolutionofBHswithmasses
MBH≥109M(cid:12)atz≥4.The6filledcontourscorrespondtoequallyspaced
Figure2. TopPanel:Weshowthestarformationhistoriesforasubsetof valuesofthefractionofobjectswithagivenvalueofΓ(z)attheconsidered
modelgalaxies.Allhistorieshavebeennormalizedtounitywhenintegrated redshift:from0.01forthelightestfilledregionto0.1forthedarkest.For
overcosmictime,tomakeeasierthecomparison,suchanormalizationde- referencewedrawasadashedlinethelocalvalueΓ(0)=1.Thedatapoints
finestheunitsofthey-axis. representtheexcessΓderivedfromtheobservedBHmassesofthehigh-
BottomPanel:TheBHmassaccretionhistoriesforthesamemodelgalax- redshiftbroad-lineAGNfollowingtheproceduredescribedinAppendixA.
ies,normalizedasabove.ThechosensubsetofgalaxiesinourMonteCarlo
simulationisthesameadoptedtoillustratethepathsintheMBH−M∗plane
infig.1.
clumpsatlowz)characteristicofhierarchicalscenarios,asnotedby
severalauthors(e.g.,Zhao,Jing&Bo¨rner2003;Diemand,Kuhlen
densityregionsoftheprimordialdensityfieldwherethecollapse &Madau2007;Homanetal.2007;Ascasibar&Gottloeber2008);
andgrowthofgalactichostsisaccelerated.Thestarformationand 2)theinteraction-drivenscenarioforthetriggeringofAGNactiv-
BHaccretionhistoriesofsuchobjectsareshowninfig.2,andcan ity.
beschematicallydividedintwophases. In the above picture, we expect the paths with Γ(z) ≥ 1 to
At high redshifts z (cid:38) 3, the rapid interactions characteriz- dominatethegrowthhistoriesofmassiveobjects,formedinbiased
ingthedenseenvironmentofsuchgalaxiesareeffectiveinrapidly regionsofthedensityfieldwherehigh-redshiftinteractionsareex-
destabilizingthegalacticgasandinfeedingthecentralBHs.Infact, tremelyeffective,whileweexpectthehigh-redshiftvaluesofΓto
insuchenvironmentsandcosmictimes,boththeinteractionratein progressively lower when galaxies formed in less dense environ-
eq. (2) and the fraction of destabilized gas (eq. 3) are large; the ment(andhencewithalowermassonaverageatanygivenz)are
first,duetothelargedensities,andthesecondduetothelargeratio considered,duetotheprogressivelylowerefficiencyofinteractions
m(cid:48)/m≈1(i.e.,amassm(cid:48)ofthemergingpartnerclosetothemass intriggeringBHaccretionathigh-z.Indeed,thedependenceofthe
mofthemainprogenitor)characteristicofthisearlyphase(z(cid:38)3) aboveeffectonBHmassandonredshiftconstitutesatypicalsig-
whengalaxyinteractionsmainlyinvolvepartnerswithcomparable natureoftheaboveinteraction-drivenmodelforthegrowthofBHs
mass.Thefrequentstarburstsinstarformationandthecorrespond- ingalaxies.
ingepisodesofBHmassaccretionatthisearlycosmictimesare
showninfig.2.
Atlowerz,thedeclineoftheinteractionrateandofthedesta-
bilized fraction facc suppresses the growth of BHs which in our 4 RESULTS:THEEVOLUTIONOFMBH−M∗FOR
model is only due to galaxy interactions (see the drop in the BH DIFFERENTAGNPOPULATIONS
accretionepisodesinthebottompaneloffig.2),whilequiescent
4.1 TheEarlyBHGrowthandHigh-redshiftQSO
star formation still proceeds, as is shown by the smooth compo-
nentinthestarformationhistoriesinthetoppaneloffig.2.The Anefficientwaytotesttheabovescenarioistoinvestigatehowthe
latter,quiescentcomponentofstarformationcontinuestobuildup pathsfollowedbyBHsandbytheirhostgalaxiestoreachthelocal
stellar mass at z (cid:46) 2 (though at a milder rate), thus lowering the M −M relationdependontheirproperties(mass,gasfraction,
BH ∗
M /M ratio.Theoverallresultisthat,whentheM /M ratiois starformationrate),andtocomparesuchspecificpredictionswith
BH ∗ BH ∗
normalizedtothefinallocalvalue,theexcessΓ(z)increaseswith thecorrespondingavailableobservationsforwhichwewillusethe
redshift. meanlocalvalueoftheM /M ratioobtainedfromtheHa¨ring&
BH ∗
Notethattheaboveresultistheoutcomeoftwophysicalpro- Rix(2004)sampletocalculateΓ.Weshalldevotetothisthenext
cesses:1)theapproximativelytwo-phasegrowthofcosmicstruc- subsections.
tures(withmajormergingathighredshiftsandaccretionofsmall ToexploreindetailthegrowthofBHsingalaxieswithdiffer-
(cid:13)c RAS,MNRAS000,??–??
6 Lamastraetal.
Figure4. LeftPanel:ThepredictedevolutionoftheBHtostellarmassratioΓ(normalizedtothelocalvalue,seeeq.1),forAGNsselectedastohavea
bolometricluminosityL≥1044.5erg/sat1≤z≤2.The4filledcontourscorrespondtoequallyspacedvaluesofthefractionofobjectswithagivenvalueof
Γ(z)attheconsideredredshift:from0.01forthelightestfilledregionto0.1forthedarkest.ThedatapointsrepresenttheexcessΓderivedfromtheBHmasses
oftheCOSMOSbroad-lineAGNmeasuredbyMerlonietal.(2009).NotethatthebulkoftheBHbuildingupoccurredadhigherredshift,whenmostofthe
galaxyinteractionstriggeringtheBHaccretiontakeplace:theslowevolutionΓ(z)for1≤z≤2isdrivenbythegradualandmuchmildergrowthofthestellar
mass.
RightPanel:ThedistributionoflogΓforallgalaxiesintheredshiftrange1 ≤ z ≤ 2formodelgalaxies(solidline)iscomparedwiththecorresponding
observeddistribution(Merlonietal.2009,filledhistogram):thelatterhasbeenobtainedincludingthelowerlimitsshownintheleftpanel.Theaveragevalue
andthedispersionforlogΓshownonthetoprefertotheobserveddistribution,thesevaluesarenearlyinsensitivetotheexclusionofthelowerlimits.
entproperties,westartwiththemostextremeobjects,namely,the agreement with the observed distribution (see right panel in fig.
massiveBHalreadyinplaceathighredshifts. 4).Thisindeedconstituteanextremelyimportanttestformodels
Thetimeevolutionofthe M /M ratioofsuchextremeob- basedonthehierarchicalscenarios,sincethescatterisdirectlyre-
BH ∗
jectsisshowninfig.3intermsoftheexcessΓ(z)overtheirlocal latedbythespreadinthemerginghistoriesofthehostgalaxies,a
value for model BHs with masses M ≥ 109M at z ≥ 4. For specificpredictionofthesemodelswhichcannotbetunedthough
BH (cid:12)
such objects Γ(z) ≥ 1 holds at any time between z = 6 and the adjustablefreeparameters.
present, with Γ ≈ 5 holding at at z = 5−6. These Γ values are Note that the model predictions shown in fig. 4 refer to all
consistentwiththeobservationsofluminousQSOat3.6< z <6.4 AGNsintheredshiftandluminosityrangesspecifiedabove,while
(seeAppendixA). thedatawecomparewithincludeonlyunobscuredobjects.How-
ever,inourmodeltheobscurationpropertiesofAGNsdependonly
on the amount of gas swept by the blast wave originated by the
4.2 TheBHgrowthatIntermediate-redshiftandBLAGNs AGN at the time of observation (see Sect. 2.3), i.e., on the de-
tailed hydrodynamic of the interstellar medium during the last,
Now, we focus on BL AGNs at intermediate redshift 1 ≤ z ≤ 2 short (∆t (cid:46) 5107 yrs) AGN active phase. Since the Γ ratios of
and AGN bolometric luminosity L ≥ 1044.5 erg/s, for which the
modelBHsbasicallydependontheintegrated,pasthistoryofthe
modelresultscanbecomparedwithdetailedexistingobservations. simulated BHs and host galaxies, we expect distribution of Γ for
Suchobjectsareexpectedtoforminlessbiasedregionsofthepri-
obscured and unobscured AGNs to be similar. While we cannot
mordialdensityfieldcomparedtotheclassofhigh-redshiftQSO
performanexactinvestigationofthisissue(wedonotmodelthe
discussedintheprevioussection;infact,theyhaveacomparable nuclearobscurationofAGNs),afirst-orderestimateoftheeffectof
AGNluminositybutarefoundatalowerredshifts,andthusareex-
selecting only obscured objects can be performed by considering
pectedtooriginatefrommerginghistoriescharacterizedbyalower
inourmodelonlyAGNshostedingalaxieswithhighgassurface
rate of high-redshift encounters. Therefore, according to our pic- densities Σ ≥ 30M pc−2: evenin this casethe mean valueof
turediscussedattheendofSect.3,weexpectsuchobjectstoshow Γinthedisgtarsibutionin(cid:12)fig.4isonlydecreasedbyafactor≈ 1.2,
a lower excess Γ(z). This is indeed the case, as illustrated in fig.
leavingthescatterunchanged.
4,wherewecomparethemodelpredictionswithobservationsby
Merlonietal.(2009).
ThedistributionofΓforsuchintermediateobjectsisstilldom-
4.3 TheGrowthofBlackHolesinGas-RichGalaxies:
inatedbyΓ ≥ 1atanyrefdshift;themodelpredictstypicalvalues
ComparisonwithSubmillimiterEmittingGalaxies
Γ ≈ 1.5−2,smallerthanthoseattainedbythehigh-redshiftQSO
shown in fig. 3, and consistent with the observational range. Be- Inourmodel,acompletelydifferentsetofBHaccretionhistories
sidesprovidinganaverageΓclosetotheobservationalvalue,itis isthatcorrespondingtoAGNsinsub-mmgalaxies(SMGs).Their
interestingtonotehowthemodelpredictsascatterinremarkable largegasfractions(f (cid:38) 0.6relativetothetotalbaryonicmass)
gas
(cid:13)c RAS,MNRAS000,??–??
TheBuildingUpoftheBlackHoleMass-StellarMassRelation 7
Figure5.ThepredictedevolutionoftheBHtostellarmassratioΓ(normalizedtothelocalvalue,seeeq.1),isshowninPanelsAandBforAGNsinSMG-like
galaxiesselectedfromourMonteCarlosimulationaccordingtothecriteriai)-iii)(seetext).The5filledcontourscorrespondtoequallyspacedvaluesofthe
fractionofobjectswithagivenvalueofΓ(z)attheconsideredredshift:from0.01forthelightestfilledregionto0.1forthedarkest.PanelsAandBreferto
thedifferentselectioninX-rayluminosityoftheAGNsshownonthetopofthePanels.WecomparewithdataforSMGswithX-rayobscuredAGNs(Panel
A)andwithBLAGNs(PanelB)inthesameluminosityrangeadoptedfortheselectionofmodelgalaxies;thedatacorrespondtoindividualgalaxiesfor
whichbothBHandstellarordynamicalmassesmeasurementswereavailableintheliterature(seeAppendixB).TheerrorbarsinthePanelAshowonlythe
uncertaintiesinthedataduetotheadoptedEddingtonratioλ,whileerrorbarsonPanelBincludetheobservationaluncertaintiesinboththeBHandthestellar
massmeasurements.Wealsoshowasashadedareathe1−σuncertaintyregionaroundthevalueofΓobtainedbyAlexanderetal.(2008)fromaverage
BH(adoptingλ=0.2)andstellarmasses(obtainedfromnearIRluminosityandCOlinewidths)takenfromvarioussamples(seeAlexanderetal.2008and
referencestherein).Notethattheextremelygas-richgalaxiesselectedasSMGsrepresentrareevolutionarypaths(seetextforthecomputedandtheobserved
numberdensities)comparedtotypicalgalaxiesatsuchredshifts:thestatisticalfluctuationsassociatedwiththelownumberofselectedSMGsinourmodel
reflectsintheirregularcontoursandtheisolatedbinsshowninthefigure.
andstarformationrate(m˙ =100−1000M /yr,seeIntroduction) tiveburstsandBHaccretionepisodesattheseearlyepochs.Since
∗ (cid:12)
indicatethatthesegalaxiesoriginatefrommerginghistorieschar- inourmodelthehigh-redshiftinteractionsaretheonlytriggerfor
acterizedbylessprominenthigh-redshft(z(cid:38)4)starburstsandBH earlyBHgrowth,thisresultsinlowervaluesofΓ(z)atlatertimes
accretionepisodes,sothatalargefractionofgasisleftavailableat (z = 2−3). Such results do not depend on the details of the se-
lowerredshiftsz ≈ 2−3.Tocomputequantitativelythepredicted lectioncriteriai)-ii)thatweadoptedtoextractSMG-likegalaxies
M and M for such galaxies and to compare with existing ob- from our Monte Carlo simulations. Indeed, we have verified that
BH ∗
servations,weselectedfromourMonteCarlosimulationsgalaxies adoptingdifferentthresholdsforthegasfractions(f ≥ 0.6)and
gas
withi)gasfractions f ≥ 0.7,ii)starformationratesm˙ ≥ 100 starformationrates(upto400M /yr)thefractionofgalaxieswith
gas ∗ (cid:12)
M /yr;iii)AGNswithX-rayluminositiesL ≤ L ≤ L ,whereL Γ<1isalwaysdominant.
(cid:12) 1 2 1
andL havebeenchosenastomatchtheselectioncriteriaadopted It must be noted that the observed SMG at z=2 in the right
2
fortheobservationswecomparewith(Borysetal.2005;Alexander paneloffig.5hasaΓvaluemuchlowerthanthatpredictedbythe
etal.2008);theX-rayluminosities(intheband2−10keV)have modelatthesameredshift.Inviewoftheunavoidableuncertainties
beencomputedfromthebolometricluminositiesineq.(4)adopting affectingthepresentobservationaldata(discussedinAppendixB),
thebolometriccorrectionbyMarconietal.(2004). itwillbeimportanttoconfirmthereliabilityandthestatisticalsig-
Theresultingpredicteddistributionofthe M /M ratioare nificanceofsuchadatapointasamarkeroftheunobscuredAGNs
BH ∗
shown in figs. 5a and 5b for SMG with AGN luminosity in two inSMGs,sinceitwouldconstituteaseveretestforourmodelwhich
different ranges (see caption) as to compare with the Γ estimates predictsabasicallysimilarbehaviourofΓ(z)forobscuredandun-
ofsixX-rayobscuredandthreebroadline(BL)SMGsforwhich obscuredAGNs.Ontheotherhand,thepredicteddistributionofΓ
individual estimates of M and M were available in the litera- forSMG-likegalaxiesshowsamilddependencewiththeAGNlu-
BH ∗
ture(seetheAppendixBfordetailsontheadopteddata).Although minosity,beinglargerforluminousAGN.Althoughtheuncertain-
the comparison with observations results are still indicative (due tiesinpresentdatadonotallowyettomakeprecisecomparisons,
tothelargeuncertaintiesassociatedwiththeEddingtonratiosand thistrendconstitutesamodelpredictionwhichisatleastconsistent
with the measurements of both the BH and the stellar mass, see with estimates of Γ based on average values for M and M in
BH ∗
AppendixB),themodelpredictsforbulkoftheSMGpopulation SMGgalaxies(seetheshadedarea).
values of Γ ≤ 1, due to the slower growth of BHs at high red- Aninterestingfeatureofourinteraction-drivenmodelforBH
shifts.Thisisduetotheparticularmerginghistoriescorresponding accretionisthattheSMGsproducedbythemodelendupinlow-
toourselectioncriteria;largeresidualgasfractionsatz ≈ 2.5im- redshiftdescendantswhichliebelowthelocal M −M relation
BH ∗
plylessfrequenthigh-redshiftencountersatz ≥ 4andlesseffec- asshowninfig.6.Inotherwords,thelow-redshift(z≤2)descen-
(cid:13)c RAS,MNRAS000,??–??
8 Lamastraetal.
whichcontinuestobuildupstellarmassatz(cid:46)2,thoughatalower
rate(seefig.2a).IntermsoftheratioΓ(z)suchaglobalbehaviour
isrepresentedbyfig.7,wherethedistributionofΓisshownbythe
colouredcontoursasafunctionofredshiftfortheentire(i.e.,forall
galaxiescontainingBHwithmassesM ≥105M ).Astrikingfea-
(cid:12)
tureofsuchadistributionisthemodestincreaseofΓ(z)forz (cid:46) 3
asopposedtoitsrapidupturnathigherredshiftsz(cid:38)4;suchamild
increase of the global Γ at low-intermediate redshifts is in agree-
mentwiththatderivedbyMerlonietal.(2004)andHopkinsetal.
(2006)bycomparingtheobservedintegratedBHandstellarmass
densitiesatsuchredshifts.
Note that the overall predicted trend for larger values of Γ
with increasing redshift is associated to an increasing the spread
inthedistribution.Thisconstitutesaquantitativepredictionforthe
z-dependence of the Lauer et al. (2007) bias. In this respect, the
Γ distributions shown in fig. 3, 4, and 5 can be interpreted as a
Figure6.TypicalgrowthpathsforBHandstellarmassesforourmodel
quantitativeevaluationoftheincidenceofsuchabiasindifferently
SMG-likegalaxies.Thedotsrepresentthefinallocation(atz = 0)ofthe
selectedsamplesatdifferentredshifts.Infact,fig.7showsthatthe
descendentsofSMG-likegalaxiesselectedaccordingtoourcriteriai)-iii)
(seetext)intheredshiftrange2 ≤ z ≤ 3.Thedashedlinerepresentthe differentobservationswecomparedwithinthepreviousSections
medianvalueofthelocalMBH−M∗relationforallmodelgalaxiesatz=0. arenotfullyrepresentativeoftheglobalbehavioursincetheyre-
fer to specific populations selected according to different criteria
whichsampleonlyaportion(inthecaseofSMGactuallyaminor
dants of SMGs are predicted to have BHs with low-intermediate fraction)ofthewholegalaxypopulation.
masses M = 108 −109 M (see fig. 6), and the BHs in SMG-
BH (cid:12)
likegalaxiesat2 (cid:46) z (cid:46) 3areinanactivegrowingphase,asitis
showninfig.6bytheirsteeplyrisingpathsintheM −M plane. 5.2 Modelpredictionsanddownsizing
∗ BH
Conversely,wecomputedthatafraction≈ 10%oflocalgalaxies AmajorresultofourprevioussectionsisthattheevolutionofΓ(z)
withBHmassesintherangeM =108−109M hadaprogenitor
BH (cid:12) isastrongfunctionoftheBHmass.Suchastrongmassdependence
whichpassedthroughanSMG-phaseatsomeredshiftintherange ofΓ(z)isillustratedbyfig.8(leftpanel),whereweshowwiththe
2≤z≤3. contourstheaveragevaluesΓ(z)asafunctionofthefinal(z=0)BH
Suchapictureisinagreementwiththeindependentfindings
mass(representedinthey-axis)andofredshift;theaverageruns
ofAlexanderetal.(2008),basedonthelargernumberdensityof
overallpathsleadingtothefinalBHmass(andhenceoverallthe
SMGscomparedtothatoflocalgalaxieshostingBHswithmasses
possiblemainprogenitorsatagivenredshift).Thefigureillustrates
exceeding109 M .Tocheckforthefullconsistencyofourresults
(cid:12) that indeed for massive objects M ≥ 109M at high redshifts
BH (cid:12)
andofourinterpretationwiththeobservationsofSMGs,wehave z (cid:38) 4 large values of Γ > 3 are expected, since such BH form
compared the number densities of the model SMG galaxies with
inthemostbiasedregionsofthedensityfieldwherehigh-redshift
thenumberdensitiesρSMG (cid:39)2.5×10−5Mpc−3 measuredbySwin- interactionswerefavoured;valuesofΓ (cid:38) 1.5−2arealsonatural
bank et al. (2006) based on the redshift distribution obtained by
forBHatintermediateredshifts1 ≤ z ≤ 2,whilethelowvalues
Chapmanetal.(2005)forz=1-3.5SMGswithS850µm >5mJy.To ofΓobservedinSMGat2 ≤ z ≤ 3arenotrepresentativeofthe
performsuchacomparisonwefirstconvertedtheabovefluxlimit wholeAGNpopulationatsuchredhifts(theaverageΓrepresented
intermsofstarformationrate(usingtherelationsinSwinbanket
infig.8is≈1.5),butinsteadonlyapplytoapopulationoriginated
al.2008),sinceoursemi-analyticmodeldoesnotincludethesub-
bypeculiarstarformationhistories(seesection4.3).
mm emission from dust; for the model SMG galaxies above the
Animmediateimplicationoftheaboveisthatmassivelocal
resultingthresholdinstarformationratethepredictednumberden-
galaxies and their BHs have formed preferentially through paths
sityinthesameredshiftintervalisρ = 4.4×10−5Mpc−3 when
SMG (in the M − M plane) passing above the local M − M re-
SMGswith f ≥0.6areconsidered,andρ =1.9×10−5Mpc−3 ∗ BH ∗ BH
gas SMG lation;thisisillustratedinfig.8(rightpanel)whereweshowthe
forSMGswith fgas ≥ 0.7,fullyconsistentwiththeobservational fractionofpathscharacterizedbyagivenΓ(intworedshiftbins)
estimates.
leadingtolocalgalaxieswithmassM ≥1012M .Thepathswith
∗ (cid:12)
Γ>1dominatethestatisticsnotonlyathigh-redshiftz=4−5but
also-thoughtoalowerextent-atz = 1−3.Asaconsequence,in
5 DISCUSSION themerging-drivenscenarioSMGsdonotrepresenttypicalpaths
leadingtolocalmassivegalaxies,butrathercorrespondtopeculiar
5.1 ThegrowthofBHsfordifferentAGNpopulations
pathsinthetailofthedistribution,namelythoseselectedastolead
Theresultspresentedintheprevioussectionsleadtothefollowing to gas-rich galaxies at z = 1−3; this interpretation is supported
globalpictureofourcosmological,interaction-drivenmodelforthe bytheconsistencyofthepredictednumberdensityofsuchpecu-
BHaccretion.TherelativegrowthspeedofSMBHscomparedto liarpathswiththeobservednumberdensitiesofSMGs,shownand
thestellarmassischaracterizedbyalargespreadinthegalaxypop- discussedattheendofsect.4.3.
ulation,withanoveralltrendforafasterBHgrowthcomparedto TheabovemassdependenceofΓ(z)hasstraightforwardimpli-
galaxiesathighredshiftsz(cid:38)3;thisisbasicallyduetothefactthat cationsfortheso-calledAGNdownsizing,i.e.,thefasterbuilding-
BHgrowonlywheninteractionsareeffective,i.e.,athighredshifts upofluminousAGNscomparedwiththosewithlowerluminosities
z (cid:38) 3, while star formation proceeds not only through impulsive whichisindicatedbyobservations(see,e.g.,Marconietal.2004);
bursts(athighredshifts)butalsothroughquiescentstarformation suchadownsizingeffectisalsocharacterizingthefasterdrop(2.5
(cid:13)c RAS,MNRAS000,??–??
TheBuildingUpoftheBlackHoleMass-StellarMassRelation 9
Figure7.ThepredictedevolutionoftheBHtostellarmassratioΓforthewholegalaxypopulationinourMonteCarlosimulation;thecolourcoderepresents,
atanyredshiftz,thefractionofobjectswithexcessΓ(z).TheaveragevaluesofΓderivedfromobservationsofSMGs(Alexanderetal.2008),ofBLAGNs
(Merlonietal.2009)andhigh-redshiftQSOs(seeMaiolinoetal.2007andAppendixA)areshownasshadedareascoveringtheirobservedredshiftrangeand
observationaluncertainties.
Figure8.LeftPanel:TheaveragevaluesofΓatdifferentredshifts(x-axis)correspondingtoBHwithagivenfinalmass(y-axis)arerepresentedascontours.
TheaverageistakenoverallmainprogenitorsinourMonteCarlomerginghistoriesleadingtotheagivenfinalmass.
RightPanel:ThefractionofpathsleadingtolocalmassivegalaxieswithM∗≥1012M(cid:12)asafunctionoflogΓisshownfortworedshiftbins:4≤z≤5(shaded
region),and1≤z≤3(solidline).
dex)fromz≈2tothepresentofluminous(L ≥1045erg/s)AGNs Thisisillustratedbyfig.9(leftpanel),wherethecontoursrepresent
X
compared to the low-luminosity population (L ≤ 1043 erg/s), thefractionofBHmassformedatagivenredshift(inthex-axis),
X
which is observed to follow only a gradual decrease (less than 1 fordifferentvaluesoftheBHfinalmassinourmodel;anygiven
dexinthenumberdensity)fromz = 2toz = 0(see,e.g.,Fioreet fractionofthefinalmassisassembledatlowerredshiftfortheless
al.2003;Hasinger,Miyaji&Schmidt2005;LaFrancaetal.2005). massiveobjectswithM (cid:46)108M withrespecttomoremassive
BH (cid:12)
Infact,themassdependenceofΓ(z)representedinfig.8implies objects.Wealsoreproduceasasequenceofpointsasimilarcon-
thatthemassiveBHactuallygrowfasterthanthelow-massBHs. tourplotproducedbyMarconietal.(2004)basedontheobserved
(cid:13)c RAS,MNRAS000,??–??
10 Lamastraetal.
Figure9.LeftPanel:ThepredictedgrowthhistoriesofBHwithdifferentfinalmass.ForanyfinalBHmass(representedinthey-axis),the10filledcontours
correspondtodifferentvaluesoftheaveragefractionalmassMBH(z)/MBH(z=0)oftheprogenitorBH:MBH(z)/MBH(z=0)=0.05,0.1,0.2,0.3,0.4,0.5,0.6,
0.7,0.8,0.9,fromthelightesttothedarkestcontour.Wehavehighlightenedwiththickblackcontoursthelevelscorrespondingtovalues0.9,0.5,and0.05,
tocomparewithpointsobtainedbyMarconietal.(2004).ThesewereobtainedfromtheanalysisoftheevolutionoftheobservedAGNluminosityfunction
(Uedaetal.2003),undertheassumptionofconstantEddingtonratioλ=1.Forsuchobservationalpoints,thesymbolssquares,diamondsandcircles,mark
thecontourlevelscorrespondingtothegrowthof90%,50%,and5%ofthefinalBHmass,respectively.
RightPanel:WeplotascontinuouscontoursthesamegrowthhistoriesfromtheanalysisbyMerloni(2009,seetext),assumingthataccretionatlowm˙ tobe
radiativelyinefficient(RIAF).ThedashedcontoursshowthesamegrowthhistorybutassumingforallAGNsthesameradiativeefficiency(8%)independently
ofλ.
massandluminosityevolutionofAGNs,undertheassumptionof nosity functions. Thus, the discrepancy is likely to be due to the
fixedEddingtonratioλ=1,andthatgalaxymergingdoesnotaffect assumption(commontoalltheapproachesbasedontheobserved
thegrowthofSMBHs;althoughbothassumptionsnotholdinour luminosityfunctions)thattheBHgrowthisalwaysdominatedby
model,itisinterestingtonotethattherepresentationofdownsizing accretion,andthattheBHgrowthduetomergingisnegligibleat
naturallyarisingfromtheinteraction-drivenmodelresemblesthat anyz.
extrapolatedfromobservations. Thisconclusionisnotunexpectedwhenoneconsiderstheba-
sicfeaturesofthehierarchicalclusteringpicture.Indeed,inallap-
The general observed trend of larger assembled fraction for
proachedbasedonhierarchicalscenarios,themergingsectorofthe
increasingly massive BH is quite well accounted for by our
models predicts massive objects to form later; such a trend is in-
interaction-driven model, although the model seems to show a
bending in correspondence of the 50% contour level at z ≈ 1.5 vertedwhenoneconsiderhowandwhenbaryonsareconvertedinto
for masses above 109 M which is not present in the data; this starsoraccretedintoSMBHs.Theoveralldownsizingeffectinhi-
(cid:12)
erarchical models thus results from the balance between the two
might constitute a true model inadequacy, or simply result from
effects above; the downsizing trend resulting at low-intermediate
thesimpleassumptionsofconstantλadoptedinthederivationof
massesinourmodelmeansthataccretionlargelydominatesover
the data points by Marconi et al. (2004) from the analysis of the
merginguptoverylargefinalBHmassesM ≥109M .
local BH mass function and of the evolution of the AGN lumi- BH (cid:12)
WhilethecomparisonperformedinFig.9isjustafirststep
nosity functions. To clarify this issue we reproduce in fig. 9b the
toward a detailed observational testing of the downsizing proper-
results from an improved version (Merloni 2009, in prep.) of the
tiesofcosmologicalmodelsforthegrowthofSMBHs,theglobal
Merloni&Heinz(2008)analysis,basedonupdatedAGNluminos-
pictureemergingfromtheinteraction-drivenmodelforthegrowth
ityfunctions.Suchananalysisissimilarinmethodologytothatby
Marconietal.(2004),butavoidstheassumptionλ=1byderiving ofSMBHsseemstoconsistentlyaccountforawidesetofindepen-
dent observations concerning the growth of SMBHs; these range
phenomenological,physicallymotivatedrelationsbetweentheac-
fromthedistantQSOs,totheintermediate-zBLAGNs,totheex-
cretionrate,theBHmassandtheAGNluminosity,andsolvingfor
tremepopulationconstitutedbytheSMGsatz ≈2,totheaverage
acontinuityequationfortheSMBHmassfunctionevolution.Be-
growthhistoriesestimatedfromtheobservedluminosityfunctions,
yondthedetailsconcerningtheexactvaluesoftheassembledmass
extending over a wide range of redshifts 0 (cid:46) z (cid:46) 4 and of BH
fractionderivedfromtheobservedluminosityfunctions(whichis
stilllargelyaffectedbyuncertainties,asshownbythedifferences masses107(cid:46)MBH/M(cid:12)(cid:46)109.
among the results obtained under different assumptions, see cap-
tion to fig. 9), the comparison with the Merloni & Heinz (2008)
approach shows i) that the BH growth inferred from the evolu-
6 CONCLUSIONS
tion of the AGN luminosity functions generally yields a stronger
downsizing effect at large masses compared with our model, and We have investigated the growth of SMBHs relative to the stel-
ii)thatsuchaneffectisprobablynotduetotheassumptionsonλ larcontentofthehostgalaxyintheframeworkofaninteraction-
adoptedtoderivetheBHgrowthhistoriesfromtheobservedlumi- driven model for the feeding of BHs during the merging history
(cid:13)c RAS,MNRAS000,??–??