The cosmic evolution of massive black holes in the Horizon-AGN simulation

18 Pages·2016·9.67 MB·English

MNRAS460,2979–2996(2016) doi:10.1093/mnras/stw1123
AdvanceAccesspublication2016May12
The cosmic evolution of massive black holes in the Horizon-AGN
simulation
M. Volonteri,1‹ Y. Dubois,1 C. Pichon1 and J. Devriendt2,3
1Institutd’AstrophysiquedeParis,UPMCetCNRS,UMR7095,98bisbdArago,F-75014Paris,France
2Sub-departmentofAstrophysics,UniversityofOxford,KebleRoad,OxfordOX13RH,UK
3ObservatoiredeLyon,UMR5574,9avenueCharlesAndre´,SaintGenisLavalF-69561,France
Accepted2016May10.Received2016May9;inoriginalform2016February4
ABSTRACT
Weanalysethedemographicsofblackholes(BHs)inthelarge-volumecosmologicalhydro-
dynamical simulation Horizon-AGN. This simulation statistically models how much gas is
accretedontoBHs,tracestheenergydepositedintotheirenvironmentand,consequently,the
back-reactionoftheambientmediumonBHgrowth.ThesyntheticBHsreproduceavariety
ofobservationalconstraintssuchastheredshiftevolutionoftheBHmassdensityandthemass
function.Strongself-regulationviaAGNfeedback,weaksupernovafeedback,andunresolved
internalprocessesresultinatightBH–galaxymasscorrelation.Startingatz∼2,tidalstrip-
ping creates a small population of BHs over-massive with respect to the halo. The fraction
of galaxies hosting a central BH or an AGN increases with stellar mass. The AGN fraction
agreesbetterwithmulti-wavelengthstudies,thansingle-wavelengthones,unlessobscuration
istakenintoaccount.ThemostmassivehaloespresentBHmultiplicity,withadditionalBHs
gainedbyongoingorpastmergers.Insomecases,bothacentralandanoff-centreAGNshine
concurrently, producing a dual AGN. This dual AGN population dwindles with decreasing
redshift,asfoundinobservations.SpecificaccretionrateandEddingtonratiodistributionsare
ingoodagreementwithobservationalestimates.TheBHpopulationisdominatedinturnby
fast,slow,andveryslowaccretors,withtransitionsoccurringatz=3andz=2,respectively.
Keywords: methods:numerical–galaxies:active–galaxies:evolution.
signpostfortheunderlyingBHpopulation(e.g.Marconietal.2004;
1 INTRODUCTION
Merloni2004;Shankaretal.2004;Hopkinsetal.2006;Merloni
Compellingevidenceformassiveblackholes(BHs)existsforthe & Heinz 2008; Draper & Ballantyne 2012). Through a wealth of
nucleioftensofnearbygalaxies(e.g.Kormendy&Ho2013,and observationsweknowthatBHsarepartoftheevolutionofcosmic
referencestherein).Scalingrelationshavebeenidentifiedbetween structures,buthowtheyformed,grewandinteractedwiththeirhost
the BH masses and the large-scale properties of the host galaxy, galaxiesisstillunclear.
such as mass, luminosity, and velocity dispersion, pointing to a The joint evolution of BHs and galaxies within the evolving
co-evolution between BHs and galaxies (e.g. Heckman & Kauff- cosmoscanbestudied,theoretically,throughdifferenttechniques:
mann2011,andreferencestherein).Activegalacticnuclei(AGN), analytical,semi-analyticalandnumerical.Werecallherethesemi-
poweredbyaccretingBHs,havebeensuggestedtobethemain‘reg- nalpapersbye.g.Small&Blandford(1992),Silk&Rees(1998),
ulators’oftheBHgrowthitself,andalsoofthestarformationrate Haehnelt, Natarajan & Rees (1998), Haiman & Menou (2000),
intheirhostgalaxies,atleastinmassivesystems(e.g.Silk2011, Cavaliere & Vittorini (2000) that first suggested, through analyt-
andreferencestherein).TherelationshipbetweengalaxiesandBHs ical arguments, how BHs evolve cosmologically. Later on, semi-
hasbeensuggestedtoholdthekeytounderstandingmassivegalaxy analyticalmodelshavebeensuccessfulinmatchingtheevolution
evolution. of, e.g. the luminosity function (LF) of quasars (Kauffmann &
AGNarealso‘lighthouses’atearlycosmictimes:throughmulti- Haehnelt2000;Cattaneo2001;Volonteri,Haardt&Madau2003)
wavelength campaigns we can track the AGN population and its andthescalingbetweenBHmassandgalaxyproperties(Haehnelt
evolution (e.g. Hopkins, Richards & Hernquist 2007; Silverman & Kauffmann 2000; Monaco, Salucci & Danese 2000; Cattaneo
etal.2008;Rossetal.2013,andreferencestherein),anduseitasa etal.2005)andshowedhowtheinclusionofAGNfeedbackim-
provedthematchbetweenpredictedandobservedgalaxymassand
LFs(Boweretal.2006;Crotonetal.2006;Monaco,Fontanot&
(cid:2)E-mail:[email protected] Taffoni 2007; Hirschmann et al. 2012). We refer the reader to
(cid:3)C 2016TheAuthors
PublishedbyOxfordUniversityPressonbehalfoftheRoyalAstronomicalSociety
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2980 M.Volonterietal.
Fontanotetal.(2011)forareviewoftheresultsofsemi-analytical andhighlighthowBHsgothroughdifferentmodesofaccretionas
modelspertainingtoBHsandAGN. afunctionofcosmictime.InSection7wesummarizeourresults
More recently, hydrodynamical cosmological simulations have andconclude.
alsoincludedBHevolution.Self-consistentsimulationscapturethe
anisotropic gas accretion and how galaxies interact during merg-
2 THE HORIZON-AGN SIMULATION
ers,whichsemi-analyticalmodelscannotdo.Manystudies(Sijacki
etal.2007;DiMatteoetal.2008;Booth&Schaye2009;Dubois TheHorizon-AGNsimulationisdescribedindetailinotherpapers,
etal.2010,2012;Hirschmannetal.2014;Sijackietal.2015)have e.g. Dubois et al. (2014). We recall here the information relevant
shownthattheinclusionofBHsas‘sinkparticles’thatareallowed forBHphysics,andfortheanalysisweperformed.
toaccretegasfromtheirsurroundings,andproduceinturnenergy,a The Horizon-AGN simulation is run with the Adaptive Mesh
fractionofwhichisreleasedinthehosthalo,reproducestheglobal Refinement code RAMSES (Teyssier 2002). We adopt a standard
evolutionoftheBH+galaxypopulation.Thiscanappearsurprising, (cid:3)CDM cosmology with total matter density (cid:4) = 0.272, dark
m
ascosmologicalsimulationsarefarfrombeingabletoresolvethe energydensity(cid:4)(cid:3)=0.728,amplitudeofthematterpowerspec-
scales over which accretion on BHs take place. Nevertheless, the trum σ = 0.81, baryon density (cid:4) = 0.045, Hubble constant
8 b
statisticalpropertiesofAGNandBHsaresufficientlywellrepro- H =70.4kms−1Mpc−1, n = 0.967 compatible with Wilkinson
0 s
duced.ThismayperhapsreflectthatmostofthegrowthoftheBHs MicrowaveAnisotropyProbe-7cosmology(Komatsuetal.2011).
andtheeffectsontheirsurroundingsofAGNfeedbackarelinked ThesizeoftheboxisL =100h−1Mpcwith10243 DMparti-
box
toshortandintensephases,aspreviouslynotedinsemi-analytical cles,whichgivesaDMmassresolutionofMDM,res=8×107M(cid:4).
studies. Fromthelevel10coarsegrid,acellisrefined(orunrefined)upto
In this paper we analyse Horizon-AGN1 (Dubois et al. 2014), an effective resolution of (cid:6)x = 1 proper kpc (level 17 at z = 0)
a large-volume cosmological hydrodynamical simulation, with a whenthemassinacellismore(orless)thaneighttimesthatofthe
physicalresolutionof∼1kpc,runwiththeadaptivemeshrefine- initialmassresolution.Thesimulationincludesprescriptions,de-
ment(AMR)codeRAMSES(Teyssier2002).Comparedtomostex- scribedinmoredetailsinDuboisetal.(2014),forbackgroundUV
isting studies (e.g. Di Matteo et al. 2008; Booth & Schaye 2009; heating,gascoolingincludingthecontributionfrommetalsreleased
Sijackietal.2015),therearethreeaspectswheretheRAMSESim- bystellarfeedback,starformationfollowingaSchmidtlawwitha
plementationdiffers(butseeBellovaryetal.2010;Tremmeletal. 1percentefficiency(Rasera&Teyssier2006),andfeedbackfrom
2015),Theseare:(i)BHsarenotplacedinhaloesonlybasedon stellarwindsandTypeIaandTypeIIsupernovae(SNae)assuming
ahalomassthreshold,butonthepropertiesofgasingalaxies;(ii) a Salpeter initial mass function (Dubois & Teyssier 2008; Kimm
BH are not anchored to the centre of the host or advected when 2012).
farfromthecentre,(iii)BHfeedbackhasadualmode,thermalat BHsarecreatedincellswherethegasandstellardensityexceed
highaccretionratesandthroughacollimatedjetatlowaccretion the threshold for star formation, n =0.1Hcm−3, and where the
0
rates. These more realistic physical implementations allow us to stellar velocity dispersion, in that cell, is larger than 100kms−1,
push forward in the comparison between theoretical models and withaninitialseedmassof105M(cid:4).Inordertoavoidtheformation
observations,andmakeadditionalpredictionsonthelinkbetween ofmultipleBHsinthesamegalaxy,BHsarenotallowedtoform
BHsandtheirhosts. at distances smaller than 50 comoving kpc from any other BH
Aseriesofpapers(Duboisetal.inpreparation;Sugataetal.in particle.BHformationisstoppedatz=1.5.Allgalaxieswithmass
preparation)haveanalysedthegalaxypopulationinHorizon-AGN, >1010M(cid:4)atz=0havealreadyformedbythatpoint,i.e.theyhave
andshowedagoodagreementwithseveralobservables(mass/LFs, atleastoneprogenitorwhereaBHwouldhavebeenseeded.
morphological mix, galaxy sizes, etc.). In this paper we validate We use the same ‘canonical’ accretion and AGN feedback
theBHandAGNpopulationandtheBH–galaxycross-correlated modelling employed in Dubois et al. (2012). The accretion
properties (BH–galaxy scaling relations). A resolution study for rate on to BHs follows the Bondi–Hoyle–Lyttleton rate M˙ =
BH
thisimplementationhasbeendoneinDuboisetal.(2012),from0.5 4παG2M2 ρ¯/(c¯2+u¯2)3/2,whereM istheBHmass,ρ¯ istheav-
BH s BH
to4kpcvaryingthespatialresolution,anddarkmatter(DM)mass eragegasdensity,c¯ istheaveragesoundspeed,u¯istheaveragegas
s
resolutionaswell.BH–galaxyscalingrelationsweresimilarinslope velocityrelativetotheBHvelocity,andαisadimensionlessboost
andnormalization.However,atlowmasses,theBHpopulationwas factorwithα=(ρ/ρ )2whenρ>ρ andα=1otherwise(Booth
0 0
affected,andthereadershouldkeepthisinmind;wealsostressin &Schaye2009)inordertoaccountforourinabilitytocapturethe
thebodyofthepapertheinstanceswhereHorizon-AGNisaffected colderandhigherdensityregionsoftheISM.Theeffectiveaccre-
byresolutionissues.Wethenidentifythelimitswhereobservables tionrateontoBHsiscappedattheEddingtonluminositywithan
arewellreproducedandfurtherproposeadditionalpredictionsand assumedradiativeefficiencyof(cid:9) =0.1fortheShakura&Sunyaev
r
observationalcomparisons. (1973)accretionontoaSchwarzschildBH.
The outline of the paper is as follows. In Section 2 we briefly InordertoavoidspuriousoscillationsoftheBHinthegravita-
reviewtheBHandAGNimplementation.InSection3wevalidate tionalpotentialwellduetoexternalperturbationsandfiniteresolu-
thesimulationagainstseveralobservationalconstraints.InSection4 tioneffects,weintroduceadragforcethatmimicsthedynamical
weconsidertheconnectionbetweenBHs,galaxiesandDMhaloes, frictionexertedbythegasontoamassiveparticle.Thisdynamical
and instances where tidal stripping breaks the BH–host relations. frictionisproportionaltoF =f 4παρ(GM /c¯ )2,wheref
DF gas BH s gas
In Section 5 we discuss galaxies that host no BH, or more than isafudgefactorwhosevalueisbetween0and2andisafunctionof
oneBHorAGN.InSection6wefollowtheupsanddownsofBH themachnumberM=u¯/c¯ <1(Ostriker1999;Chapon,Mayer
s
growth over cosmic time, analysing the distribution of accretion &Teyssier2013),andwhereweintroducetheboostfactorαforthe
rates(inEddingtonunits,orperunitstellarmass),thedutycycle, samereasonsthanstatedabove.SeealsodiscussionsinTremmel
etal.(2015),Lupi,Haardt&Dotti(2015),Gaboretal.(2016)on
the limitations of gravity solvers for BH dynamics in AMR and
1http://www.horizon-simulation.org/about.html SPHsimulations.
MNRAS460,2979–2996(2016)
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BHsinHorizon-AGN 2981
TheAGNfeedbackisacombinationoftwodifferentmodes,the at the redshifts of interest falls between those proposed by Ueda
so-calledradiomodeoperatingwhenχ =M˙ /M˙ <0.01and et al. (2014) and Shankar et al. (2009), thus marking a ‘middle
BH Edd
thequasarmodeactiveotherwise.Thequasarmodecorrespondsto ground’.WealsoadoptthemostrecenthardX-rayLF(2–10keV;
anisotropicinjectionofthermalenergyintothegaswithinasphere Buchneretal.2015),whichincludesacorrectionforobscured(1022
of radius (cid:6)x, at an energy deposition rate: E˙ =(cid:9)(cid:9)M˙ c2, < N < 1024cm−2, where N is the equivalent neutral hydrogen
AGN f r BH H H
where (cid:9) = 0.15 for the quasar mode is a free parameter chosen columndensity)andComptonthickAGN(N >1024cm−2)–but
f H
to reproduce the correlations between BHs and galaxies and the estimatingthecontributionoftheelusiveComptonthickAGNre-
BHdensityinourlocalUniverse(seeDuboisetal.2012).Atlow mainschallenging.Fotopoulouetal.(2016),whoestimatetheLF
accretion rates, on the other hand, the radio mode deposits the at [5–10 keV], find no evidence of a rapid decline of the LF up
AGNfeedbackenergyintoabipolaroutflowwithajetvelocityof to redshift four, consistently with Buchner et al. (2015). For this
104kms−1 into a cylinder with a cross-section of radius (cid:6)x and comparisonweconvertbolometricluminositiestoX-rayusingthe
height2(cid:6)xfollowingOmmaetal.(2004)(moredetailsaboutthe bolometriccorrectionfromHopkinsetal.(2007)forconsistency.
jetimplementationaregiveninDuboisetal.2010).Theefficiency To give an idea of the current uncertainties, we also include, at
oftheradiomodeislarger,with(cid:9) =1. z(cid:2)2,theconversiontobolometricLFofthemid-infraredselected
f
WeidentifyDMhaloesandsub-haloesusingHaloMaker,which AGN LF proposed by Lacy et al. (2015), where they suggest a
uses AdaptaHOP (Aubert, Pichon & Colombi 2004; Tweed et al. largerpopulationoffaintAGNexists,whichcanbemissedatother
2009),astructurefinderbasedontheidentificationofsaddlepoints wavelengths.
inthe(smoothed)densityfield.Atotalof20neighboursareused TheresultingLFsatdifferentredshiftsareshowninFig.2.The
tocomputethelocaldensityofeachparticle,andwefixthedensity brightendoftheLFisgenerallyingoodagreementwithobserva-
thresholdat178timestheaveragetotalmatterdensity.Theforce tions,whilethefaintendisoverestimatedwhenincludingBHsinall
softening(minimumsizebelowwhichsubstructuresareconsidered haloesabovethenominalresolutionof8×1010M(cid:4),i.e.resolved
irrelevant)is∼2kpc.OnlyDMhaloesidentifiedwithmorethan bymorethan1000DMparticles(dashedcurves).Theoverestimate
50particlesareconsidered.Galaxiesareidentifiedusingthesame ofthefaintendoftheLFisacommonproblemincosmologicalsim-
methodandsameparametersbutusingthestellarparticledistribu- ulations;forinstanceSijackietal.(2015)findasimilarbehaviour
tioninsteadoftheDMone.BecauseofAGNfeedback,DMdensity intheIllustrissimulations.Theysuggestthatagoodagreementis
profilesflatteninthecentre,andmisidentificationofthehalocentre reachedwhenincludingonlyBHswithmass>5×107 M(cid:4),and
canoccurwhen itispurelydetermined bythedensestparticle in discussothersourcesofpossiblediscrepancywithdata.Wesuggest
thehalo(Peiranietal.,inpreparation):asmallcuspedsub-halocan that the main source of the overestimate is due to SN feedback.
beidentifiedasthecentreofthemainmoremassivecoredhalo.We Duboisetal.(2015)findthatstrongSNfeedback(usinga‘delayed
usetheshrinkingsphereapproachproposedbyPoweretal.(2003) cooling’prescriptionfromTeyssieretal.2013)inlow-massgalax-
togetthecorrecthalocentre.Fromafirstguessofthecentreusing ies(orhaloes)isabletolimitBHgrowthbySN-drivenoutflows,
thedensestparticle,werecursivelysearchthecentreofmasswithin whichdepletethecentralregionofthegalaxyofgas.Asthegalaxy
aradius10percentsmallerthantheradiusatthepreviousiteration anditshaloaccumulatemass,theybecomeabletoconfinenuclear
(startingfromthevirialradius).Weendthesearchwhenthesphere inflows and the BH can start to grow. If we included only BHs
hasasizesmallerthan2kpc,andtakethedensestparticlewithin withhalomass>5×1011M(cid:4)(solidcurves),whereBHsgrowthis
thatsphereasthenewhalocentre. unimpededbySNfeedback,theagreementgreatlyimproves.Sim-
In Horizon-AGN BHs are not anchored in the centre of DM ilarresultsareobtainedwithacutingalaxymass>3×1010M(cid:4)
haloes, therefore we have to assign BHs to their host haloes and atthethresholdwhere,intheirhigher-resolutionsimulationswith
galaxies.WeassignaBHtoahaloifitiswithin10percentofthe delayed coolingSNfeedback, Duboisetal.(2015)findthatBHs
virialradiusoftheDMhaloandtoahalo+galaxystructureiftheBH become unaffected by SN feedback. Using a minimum threshold
isalsowithintwicetheeffectiveradiusofthemostmassivegalaxy BHmassof>2–3×107M(cid:4)leadstoanalogousresultsfortheLF.
withinthathalo.IfmorethanoneBHmeetsthecriteria,themost A direct comparison of BH growth under the effect of SN feed-
massiveBHisdefinedasthecentralBH,andremovedfromthelist. backinacosmologicalvolumeissubjectofapaperinpreparation
Westartfrommainhaloesandproceedhierarchicallythroughsub- (Habouzitetal.,inpreparation),butwestressthatthemasslocked
haloes.SomeBHsarenotassignedtoanyhalo,subhalo,orgalaxy. in BHs hosted in low-mass haloes, <5 × 1011M(cid:4), is relatively
Thesearetreatedas‘off-centre’BHsanddescribedinSection5.In unimportantfromthecosmologicalpointofview,asshowninthe
Fig.1weshowamapofgasdensitywithBHpositionsoverlaid. followingsection.Additionally,simulationsmayoverproducethe
high-redshiftAGNLF,butgiventheratherpoorobservationalcon-
straintsathigh-zanduncertaintiesinthespectralenergydistribu-
3 COMPARISON WITH OBSERVATIONS
tion,thediscrepancymayeventuallybereducedordisappearwhen
Ourfirststepistovalidateoursimulation,i.e.todemonstratethat betterandmorecalibratedhigh-zLFsbecomeavailable.Thereis
itproducesapopulationofBHscompatiblewiththerealUniverse. alsoapossibleoverestimateofthehigh-luminosityendatz<1.5,
Forthischeck,weconsiderfourmaindiagnostics:theLFofAGN, butthestatisticsarepoor,andthisisseenonlyinthebolometricLF,
theBHmassfunction,theBHmassdensityversusredshiftandthe notinthehardX-rayLF.
relationbetweenBHandgalaxyproperties.
3.1 AGNluminosityfunction 3.2 BHmassdensityandmassfunction
WecomparethetheoreticalLF((cid:11))totheobservationaldetermina- The BH mass density and its evolution over cosmic time are im-
tionofthebolometricLF,ofwhichdifferentestimatesexist(Hop- portantobservationaldiagnostics.Thewaytheyarecalculatedob-
kinsetal.2007;Shankaretal.2009;Uedaetal.2014).Wechoose servationallyisworthadiscussionpriortothecomparisonwiththe
herethefunctionalformproposedbyHopkinsetal.(2007),which theoreticalresultsfromHorizon-AGN.
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2982 M.Volonterietal.
Figure1. ThepositionsofBHs,shownasdiffractionspikes,inasliceof200×142×50h−1Mpcareoverlaidonagasdensityandmetallicity(top)ordensity
andtemperature(bottom)mapinHorizon-AGNatz∼1.5.
Atz=0thetotalBHmassdensity,ρ ,isestimatedstartingfrom fraction)andtheprobabilitydistributionfunctionforthevelocity
BH
theempiricalcorrelationsbetweenBHmassandgalaxyproperties dispersion(Shankar2013,andreferencestherein).Inprinciple,this
(normally,thevelocitydispersion,thebulgemassandluminosity). BH mass density is driven by the correlations found on the local
TheBHmassdensityiscalculatedthroughtheconvolutionofthe sampleofquiescentBHs,lessthan150BHsatthetimeofwriting,
chosen correlation with the distribution function of galaxies as a then extrapolated to the global population, including AGN (see
functionofthatproperty(Yu&Tremaine2002).Thismeans,for Reines&Volonteri2015,andreferencestherein,foradiscussionon
instance,thegalaxymassfunctionandLFs(correctedforthebulge thecaseofactiveBHs).Theshape,normalizationandscatterinthe
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BHsinHorizon-AGN 2983
Figure 3. Total mass density locked in BHs (dark red), and BH mass
densityinactiveBHs(lightred),definedasthosewithbolometricluminosity
>1043ergs−1 versusredshift.Triangles:BHsinhaloeswithmass>8×
1010M(cid:4),squares:BHsinhaloeswithmass>5×1011M(cid:4)(seetextfor
details).ThegreenhatchedregionshowsthelimitsprovidedbySoltan’s
argument,asproposedbyBuchneretal.(2015)usingaradiativeefficiency
of0.1,andscalingtheradiativeefficiencybetween0.06and0.32(upper
andlowerhatchedregions,respectively).Theverticalbluelineindicatesthe
z=0BHmassdensityestimatedbyShankaretal.(2004),andcorrectingthe
BH-to-bulgerelationassuggestedbyKormendy&Ho(2013).Thelimits
atz>6arederivedfromstackedhigh-zgalaxies(Willott2011;Cowie,
Barger&Hasinger2012;Fioreetal.2012;Treisteretal.2013)orfrom
theintegratedX-raybackground(Salvaterraetal.2012);Comptonthick
sourcesarenotincludedintheselimits.
2012;Bongiornoetal.2014),andthereforelargeuncertaintiesexist.
Typically,Soltan’sargument(Soltan1982)anditsupdates(Fabian
&Iwasawa1999;Elvis,Risaliti&Zamorani2002;Yu&Tremaine
2002;Hopkins,Richards&Hernquist2007;Merloni2016)areused
insteadtoestimatetheBHmassdensity.TheLFofAGNisinte-
gratedovertime,startingfromagivencosmictimet fromwhich
max
theLFisknownsufficientlywell,andrescaledbya(fixed)radiative
efficiency,(cid:9),toobtainamassdensity,ρ (z)≤ρ (z),ofmass
BH,acc BH
accretedonBHsasafunctionofredshift:
(cid:2) (cid:2)
Freidgsuhrieft2s..TBheoldoamsheetrdiccu(brvluees)inanclduhdaeradllXB-Hrasyi(n2H–1o0rizkoeVn-,AreGdN)LinFhaatldoiefsfewreintht ρBH,acc(z)= 1(cid:9)−c2(cid:9) tt(z)dt dLL(cid:11)AGN(L,t). (1)
mass>8×1010M(cid:4),whilethesolidcurvesincludeonlyBHsinhaloeswith max
mass>5×1011M(cid:4),whereSNfeedbackshouldnotquenchBHgrowth In general, the population of BHs in Horizon-AGN is in good
(Dubois et al. 2015). The dotted light blue curve is the bolometric LF agreement with a variety of observations based on Soltan’s argu-
proposedbyHopkinsetal.(2007)(seealsoShankar,Weinberg&Miralda- ment,fromhighredshifttoz=0(Fig.3),butwecanalsoderive
Escude´2009;Uedaetal.2014).TheorangehatchedregionisthehardX-ray additional information and constraints. The density of mass ac-
LFbyBuchneretal.(2015)correctedforComptonthinandthickAGN.The cretedonBHsisobviouslyalowerlimittothetotalmassdensityin
greendottedcurveistheLFderivedfromaspectroscopicsurveyofAGN BHs,whichincludesquiescentonesandtheinitialmassin‘seeds’
selectedfromSpitzerSpaceTelescopeimagingsurveys(Lacyetal.2015). (seeVolonteri2010;Volonterietal.2013;Merloni2016),plusob-
scuredAGN(Merloni2016).ThisisexemplifiedinFig.3,where
relationshipsplayanimportantrole.Forinstance,Kormendy&Ho wedistinguishthetotalBHmassdensity(darkred)andthemass
(2013)suggestthattheratiobetweenBHandbulgemasspreviously densityinaccretingBHsintheAGNphase(bolometricluminosity
usedinbenchmarkcalculations(e.g.Marconietal.2004;Shankar >1043ergs−1,lightred).Thelatterquantityisthetruemassdensity
et al. 2004) should be increased, based on their updated sample, inaccretingBHsatagivenredshift,ratherthanthetotalluminos-
leadingtoatotalmassdensityhigherbyafactorofalmost2. ityrescaledbytheradiativeefficiency((cid:9) =0.1inHorizon-AGN)
Atz>0theshapeandnormalizationoftheBH–galaxycorrela- and the speed of light, integrated over time. This quantity allows
tionsaresubjectofdebate(e.g.Pengetal.2006;Jahnkeetal.2009; us to immediately see the relevance of the bright AGN phases in
Merloni 2010; Cisternas et al. 2011; Targett, Dunlop & McLure growing BHs. At high redshift, z > 2, most of the BH mass is
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2984 M.Volonterietal.
forbroad-linequasarsandAGN(Type1,Kellyetal.2010;Kelly
& Shen 2013; Schulze et al. 2015), which are only the subset of
quasars for which broad lines can be seen, i.e. with a favourable
viewing angle and unobscured. Obscuration may be produced by
the geometry of the torus, and depend only on viewing angle; in
thiscaseitseffectcanbeaccountedforstatistically.Obscuration,
however,mayalsobecausedbymaterialinthehostgalaxy,which
ishardertoaccountfor.WeincludeinFig.4,atz=1andz=2,the
estimatebySchulzeetal.(2015)atz=1.5basedonaconvolution
oftheobservationalstellarmassfunction(Ilbertetal.2013)with
theBH–bulgemassrelationofMcConnell&Ma(2013),without
applyinganybulge-totalmassconversion.Wealsoincludethemass
function proposed by Merloni & Heinz (2008) obtained by mod-
ellingtheBHpopulationthroughacontinuityequationderivedfrom
usingtheredshiftevolutionoftheLFandtheBHmassfunctionat
z=0asconstraints.Theagreementbetweenthesimulationandthe
observationsisgood;thedisagreementatlowBHmasses(<3×
107M(cid:4))atz=1–3issimilartowhatwefindfortheAGNLF.It
isusefultocontrasttheBHmassfunctiontothestellarmassfunc-
tioninhorizon-AGN(Kavirajetal.,inpreparation).Thesimulated
galaxiesreproducewelltheobservationalstellarmassfunctionat
z=0–5,withonlyanoverestimateof∼0.3dexforstellarmasses
Figure 4. Mass function of BHs in Horizon-AGN at different redshifts.
<3 × 1010M(cid:4). This overestimate is somewhat smaller than the
Weindicatewiththehatchedregionstherangeproposedbyestimatesat
z=0(Laueretal.2007b;Shankar2013,verticalanddiagonalhatching, onewefindintheBHmassfunctionatz=1–3atBHmasses<3×
respectively),and,athighredshift,therangeproposedatz=1.5bySchulze 107M(cid:4).
et al. (2015), shown as grey dashed curves at z = 1 and z = 2, and by FromFig.4wecanalsoaddressthequestionofdowntowhich
Merloni&Heinz(2008)atz=1–5,shownwithhorizontalblackhatching. BH mass the simulation is reliable. The closer the BH mass is
to the resolution, the more results are resolution dependent. One
growninluminousAGN,whileatlowerredshiftthemassgrowth approachistoproceedlikeinthecaseofgalaxiesandderivethe
isdrivenbyfaintAGN(bolometricluminosity<1043ergs−1).This minimalmassfromthecompletenessoftheBHmassfunction.The
figurealsoshowsthatBHsinlow-masshaloes(<5×1011M(cid:4))are argumentisasfollows:thereisnoexplicitscalebreakinginourBH
relativelyunimportantinthecosmicpictureasonecanseebycom- model,thereforethereisnoreasonforthenumberofBHsnottoin-
paringtrianglesandsquares,whichincludeBHsinhaloeswithmass creasewiththenumberofhostgalaxies/haloes.Consequently,any
>8×1010M(cid:4) or>5×1011M(cid:4),respectively.Finally,thetotal decreaseinthemassfunctionofBHatthelow-massendcouldbe
massdensityinseedsis(cid:2)103M(cid:4)Mpc−3,similartowhatispre- attributedtolackofresolutioninthesimulation.Applyingthisar-
dicted by analytical and semi-analytical models of BH formation gumenttheminimalBHmassis2×107M(cid:4).However,whilethere
(Volonteri 2010), which means that accretion accounted for basi- isnoexplicitscalebreakinginourBHmodel,thereisanimplicit
cally the whole mass density we find at z = 0, corresponding to threshold on the minimum gas density required for BH seeding,
∼8.3×105M(cid:4)Mpc−3. whichdisfavourslow-massgalaxies.Therefore,itdoesnotneces-
Horizon-AGNreproduceswelltheBHmassdensity,butthisdoes sarilyfollowthatweshouldnottrustBHwithmasses<107M(cid:4),
notnecessarilyensurethatitreproducestheBHmassfunction.The thisissayingthatthissampleisnotcompleteinthesimulationso
BHmassdensityistheintegraloftheBHmassfunction,anditis ourconclusionsmightbebiasedinthatregime.Wefurtherdiscuss
dominatedbyBHsatitsknee,thereforereproducingthemassden- therangeofvalidityofthesimulationinthenextsection.
sitydoesnotgiveinformationonlow-andhigh-massBHs.InFig.4
weshowtheBHmassfunction(reddots),andattemptacomparison
3.3 CorrelationsbetweenBHsandgalaxiesatz∼0
withobservationalestimates,bothatz=0andathighredshift.The
comparisoniscomplicatedbytryingtomatchthetheoreticalsample One of the most common ways to determine whether simulated
toobservations.We referthe reader tothecomprehensive review BHsarerealisticistocomparetheirmassestopropertiesofthehost
by Kelly & Merloni (2012) for a discussion on the difficulties in galaxiesthathavebeenshowntocorrelatewithBHmasses.Indeed,
determiningtheBHmassfunctionobservationally,andtherelated inmostcasestheparametersofBHaccretionandfeedbackaretuned
uncertainties. We discuss in the following the main problems of toreproducethesecorrelations(e.g.Sijackietal.2007;DiMatteo
relevance for our comparison here. Regarding the comparison at etal.2008;Booth&Schaye2009;Duboisetal.2012).Inreality,a
z = 0, we use the results from Lauer et al. (2007b) and Shankar ‘fair’comparisonisfarfromsimple.Ontheonehand,thesampleof
(2013)(seealsoShankaretal.2004).Asnotedpreviouslyforthe galaxieswithdynamicalBHmassmeasurementsisnotanunbiased
massdensity,theestimatesoftheBHmassfunctionhingeonacon- representation of the whole galaxy population. Most BH masses
volutionofthecorrelationsbetweenBHandgalaxypropertieswith pertain to massive, dense elliptical galaxies, while disc galaxies
thedistributionfunctionofgalaxiesasafunctionofthatproperty. andlow-velocitydispersiongalaxiesareunder-represented,aswell
Thefunctionalformandtherangeofvalidityofthesecorrelations as low-mass galaxies (van den Bosch et al. 2015), with the rare
are subject of debate, and therefore a source of uncertainty. For exception of megamasers (Greene et al. 2010). Additionally, the
instance,theslopeoftheBHmass–velocitydispersioncorrelation definitionofthegalaxypropertyofinterest(e.g.bulgemass,velocity
and the normalization of the BH–bulge mass one are still uncer- dispersion,galaxymass)isnotconsistentintheliterature,andthe
tain.Athigherredshift,themassfunctionhasbeenestimatedonly analysesareheterogeneous.
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BHsinHorizon-AGN 2985
themassesofsimulatedgalaxieshavebeenshiftedby−0.33dex
(seethediscussioninReines&Volonteri2015).Atthehigh-mass
end, M > 108 M(cid:4) and M > 1011 M(cid:4), simulations and ob-
BH gal
servationsareinrelativelygoodagreement,butlow-massBHsand
low-mass galaxies are more problematic. Specifically, BHs with
M <5×107 M(cid:4) inintermediate-massgalaxies(1010 M(cid:4) <
BH
M <1011 M(cid:4))arealmostabsent.AsdiscussedinSection3.1,
gal
thismaybecausedbythelackofstrongSNfeedbackinHorizon-
AGN,whichallowsBHsinlow-massgalaxiestogrowmoreeasily.
SNfeedbackwouldaffectonlyBHsinlow-massgalaxies.Oncea
galaxyreachesamassof∼1010 M(cid:4)thentheBHcangrowunim-
peded and self-regulation ensues, thus, for instance, in the simu-
lationsbyDuboisetal.(2015)thehostgalaxypropertiesdidnot
depend on SN feedback after z ∼ 3. In the presence of delayed
coolingSNfeedbackthebulgegrowthwassuppressedatz>3.Af-
terwards,whenthegalaxymassreachedafew×1010 M(cid:4)thepres-
enceoftheAGNregulatedthebulgemassindependentlyoftheSN
implementation.Inanalogywiththis,wearguethat,withsmaller
BHs, causing reduced AGN feedback in small and intermediate-
massgalaxies,thefractionofsimulatedbulge-dominatedgalaxies
at stellar mass (cid:2) 1011 M(cid:4) would decrease. This would improve
Figure5. BHversustotalstellarmassofthegalaxyfor10000random
thematchwiththeobservedmorphologicalmixinthatmassrange
gEadldaixnigestoantzra=tio0>(g0re.0y1)..DTahrekogrraenygsequlianreesm:BarHksswMiBthHL=bol2<×101404−e3rMggsa−l.1Tanhde (3D.2u,bboeilsowetBaHl.,minaspsreesp2ar×ati1o0n7).MA(cid:4)dd(ictioonnsaelqlyu,enastlyn,ogteadlaxinymSeacstsio(cid:2)n
blacklineisthebest-fittinglinearcorrelation.Thedarkergreenpentagons
1010M(cid:4))resolutioneffectsbecomeimportant.
arelow-luminosityAGNfromReines&Volonteri(2015),andthelighter
greentrianglesarethequiescentBHsfromtables2and3inKormendy&Ho In Fig. 6 we turn to BH mass versus bulge mass. This is one
(2013)withstellarmassesrevisedbyReines&Volonteri.Thestellarmasses of the ‘classical’ scalings that seem to have small scatter in the
ofHorizon-AGNgalaxieshavebeenshiftedby−0.33dextoaccountforthis observations(<0.3dex),atleastforclassicalbulges,andwhichis
correction.Ifweselectforlow-luminosityAGN,theirBHsoccupyaregion widelyextrapolated,alsoathigh-redshift,andalsowhenbulge/disc
inthelower-rightcorneroftheBH–galaxydistribution,reminiscentofthe decompositionsarenotavailable,tostudytheco-evolutionofBHs
regionwhereinobservationswetendtofindlow-luminosityAGN.However, and galaxies. We start by highlighting that indeed the measure-
thescatterinthesimulatedsampleismuchlessthanintheobservations(see
ment of a univocal bulge mass is tricky. In our simulations we
textfordetails).
candefineeitherakinematicalbulgemass,wherebulgeparticles
arethosewithatangentialvelocitycomponent(incylindricalco-
Westartwiththegalaxypropertythatiseasiertodefineandmea- ordinates with the spin of the galaxy as the axis of symmetry)
sureinbothsimulationsandobservations,thetotalstellarmassof smallerthanthenon-tangentialvelocitycomponent,orperforma
thegalaxy,althoughwhetherthetotalstellarmassisagoodpredictor bulge/discdecomposition,witheithertwoSe´rsicprofiles,onewith
oftheBHmass,andatightcorrelationcanbedefined,isamatterof n = 1 for the disc, and one with n = 4 for the bulge, or two
debate(Kormendy&Ho2013;La¨skeretal.2014).Recently,Reines Se´rsicprofiles,bothwithn=1,oronewithn=1,andonewith
&Volonteri(2015)re-analysedinasmuchconsistentawayaspos- n=[1,4],keepinginmindthatourphysicalresolution,1kpc,lim-
siblethesampleoflocalBHswithdynamicalmassmeasurements itsourabilitytoperformthedecompositioninsmallorlow-mass
(Kormendy&Ho2013),andalsoincludeBHsinAGNwithmass galaxies.
measuredthroughreverberationmapping(Bentz&Katz2015),as The difficulties of defining a bulge mass is apparent in Fig. 6
wellasasampleofbroad-lineAGNswithsingle-epochBHmass andtheyarealsodiscussedinappendixAofDuboisetal.(2012)
estimatesselectedfromtheNASA-SloanAtlas,whichisbasedon for simulations and by La¨sker et al. (2014) for observations (see
the Sloan Digital Sky Survey Data Release 8 spectroscopic cata- alsoLaskeretal.2015).Wenotethatthebulgemassesaretaken
logue(Aiharaetal.2011).TheyfoundthattherelationbetweenBH from Kormendy & Ho (2013), therefore, when the galaxy mass
andstellarmassdefinedbylocalmoderate-luminosityAGNinrel- corresponds to the bulge mass, they are larger by 0.33 dex than
ativelylow-massgalaxies(pentagonsinFig.5)hasanormalization the stellar masses shown in Fig. 5, because of the difference in
thatislowerbyapproximatelyanorderofmagnitudecomparedto zero-point described by Reines & Volonteri (2015). Despite the
theBH–bulgemassrelation,andtotherelationobtainedonmas- intrinsic difficulties, the match between Horizon-AGN BHs and
sive,bulge-dominatedgalaxies(trianglesinFig.5),whichappears the observational sample is good, where the comparison can be
alsotobesteeper. performedmeaningfully(thiswastobeexpected,aswereproduce
Wedefineasgalaxymassthetotalstellarmass.Thestellarmass correctlytheBHmassfunctionthatisobservationallydetermined
is the sum of all star particle masses within a region meeting a throughthiscorrelation,aswellasthestellarmassfunctions;see
densitythresholdcriterion,setat178timestheaveragetotalmat- Kavirajetal.,inpreparation).Thelogarithmicslopesforthevarious
ter density. Only galaxies identified with more than 50 particles fits,includingonlyobjectswithM >109M(cid:4),varyfrom1.05
bulge
are considered. (See Section 2 for details.) Fig. 5 reports 10 000 forthekinematicalbulgemass,0.75forthetwoSe´rsicprofileswith
randomBHs+galaxiesfromHorizon-AGNatz=0(squares).We n=1andn=4,1.0forboththetwoSe´rsicprofileswithn=1,
notethattheBHparametersinRAMSEShadbeenoriginallychosen andn=1andn=[1,4].
toreproduceolderdataandtrends(Duboisetal.2012),therefore,to In summary, the tighter BH–bulge mass relation is well re-
makethecomparisonwiththeobservationalsampleself-consistent, produced in Horizon-AGN, while the broader BH–stellar mass
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2986 M.Volonterietal.
the simulations to reproduce a correlation that is tight only for a
specificclassofgalaxies,thereistheriskoffailingtoobtainthe
fullviewoftheBH/galaxypopulation.Onewaytoseethisisthat
relativelylowmassBHsinintermediate-massgalaxiesthatarenot
bulge-dominated,high-velocitydispersiongalaxies,arenotpresent
inthesimulation.
Alternatively,wecouldseethisasaproblemwithgalaxyprop-
erties.Galaxieswithstellarmassessuchthattheyshouldtypically
host ∼107 M(cid:4) BHs instead harbour BHs with mass 10 times or
morelarger.Atthesametimethesimulationreproduces,however,
the observed BH mass versus bulge mass. The simulation may
therefore over-predict bulge masses and bulge-to-disc ratios. We
have compared our simulated galaxies to distributions of bulge-
to-total ratios, Krajnovic´ et al. (2013) for early-type galaxies and
Gadotti(2009)fordiscgalaxies,andBlucketal.(2014)foramor-
phologicalmix.Simulatedgalaxiesunder-estimatethefractionof
purebulges,butover-estimatebulge-to-totalratiosforgalaxieswith
mass1010(cid:2)M (cid:2)1011M(cid:4).Westress,however,thatthisshould
gal
beconsideredaqualitativecomparison,asobservationalbulge–disc
decompositionssufferfromthesameproblemsthatweencountered
indefininguniquelyabulgemass,plusissuesrelatedtoinclination,
surfacebrightnesslimits,spatialresolutionandsignal-to-noiseratio
(seee.g.thediscussioninSimardetal.2011).
Althoughmergerhistoriesandenvironmentaleffectsinducesome
scatter in mock BH–galaxy relations, internal galactic processes,
such as gas turbulence, variation in the compactness, which are
notcapturedbecauseoflimitedresolution,mayalsoinfluencethe
scatter.Thescattergivenbydifferentmergerhistoriesarisingfrom
cosmological initial conditions appears insufficient to explain the
observational scatter, especially in M at fixed M , therefore
BH gal
these unresolved internal processes are likely to be an important
contributiontothescatter.Asimilarbehaviourcanbeseeninother
cosmologicalhydrodynamicalsimulations(figs4and10inSijacki
etal.2015;Schayeetal.2015,respectively).
We end by studying the BH mass versus stellar velocity dis-
persion, σ, in Fig. 7. This is also a benchmark scaling, and it is
consideredtobeoneofthebestpredictorsforBHmasses,i.e.to
haveasmallintrinsicscatter(<0.3dex).Thisisperhapsthemost
problematicforHorizon-AGN.Ifwefitasinglelogarithmicslope
totheBHmassversusstellarvelocitydispersion,wefindavalue
of4.02forgalaxieswithσ >60kms−1,comparedto4.38found
byKormendy&Hoonaculledsubsampleofthegalaxiesshown
inFig.7.Themainreasonisthatvelocitydispersionsinthesimu-
Figure6. BHversusbulgemassfor10000randomgalaxiesatz=0(grey). lationareunderestimatedatMbulge <1011M(cid:4) (σ <200kms−1),
Thebulgemassismeasuredeitherkinematicallyorthroughabulge/disc andoverestimatedabove,whencomparingtotheobservedFaber–
decompositionwithtwoSe´rsicprofiles,eitherbothwithn=1,oronewith Jackson relation (Bernardi et al. 2003). The dearth of BHs with
n=1,andonewithn=4,oronewithn=1,andonewithn=[1,4].We M <5×107 M(cid:4) inintermediate-massgalaxieshighlightedin
BH
reportalsoallBHsfromtables2and3inKormendy&Ho(2013),using thediscussionofFig.5alsocontributes,butgiventhegoodagree-
bluesymbolsforthesubsetusedforfittingtheBHmassversusbulgemass mentintheM versusM relation,itisaminorcontribution,
BH bulge
relation.
for this specific comparison. One contribution to the discrepancy
isthatgalaxysizesinthesimulationarelargerthanforobserved
scaling(s) are in worse agreement. The light green triangles in galaxies with mass (cid:2) 1011M(cid:4). In fact, the galaxy sizes are in
Fig. 5 are almost entirely the same points that appear in Fig. 6. goodagreementwithobservedlow-masslate-typegalaxies,butare
If we had restricted our analysis to this subsample, composed of larger, by a factor of ∼ 3–4, than observed low-mass early-type
galaxies with dynamically measured BH mass, which tend to be galaxies(Duboisetal.,inpreparation).Sincethecompletesample
denseandbulgedominated,wewouldhaveagoodmatchbetween isamixoflate-andearly-typegalaxies,thereapp√earstobeanover-
simulationandobservationsalsoinFig.5,i.e.inBH–galaxymass. allmismatchatσ <200kms−1ofafactorof∼ 2inthevelocity
Infact,oursimulationandallothersimilarsimulationshavebeen dispersion (roughly corresponding to an average overestimate of
tunedtomatchtheBH–stellar(bulge)masscorrelationforthesub- the galaxy size of a factor of 2). The velocity dispersion is also
sampleofgalaxiesthatworkswell(greentrianglesinFig.5,blue sensitivetotheDMhalocentralprofile,whichdependsnotonlyon
symbolsinFig.6).Suchgalaxies,however,areabiasedsubsam- DMhalomassbutalsoonasubtleinterplaywiththebaryonsand
ple of the real universe (see also Shankar et al. 2016). By tuning AGNfeedback.Indeed,thecentralDMdensitiesinHorizon-AGN
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BHsinHorizon-AGN 2987
Figure 7. BH mass versus bulge velocity dispersion at z = 0 for non-
interactinggalaxies(grey).Only10000randomgalaxiesareshown.We
reportalsoallBHsfromtables2and3inKormendy&Ho(2013),using
bluesymbolsforthesubsetusedbytheauthorsforestablishingtheBHmass
versusbulgevelocitydispersionrelation.Low-massearly-typegalaxiesin
Horizon-AGNtendtohavelargersizethanrealones,thereforethevelocity
dispersionisunderestimatedforthesegalaxies.
are lower than for the Horizon-noAGN simulation, which differs
only in that AGN are not included in the latter. We defer a more
detailed study quantifying the exact contribution of this effect as
a function of galaxy mass and assembly history to another paper
(Peiranietal.,inpreparation).
4 BHS IN HALOES AND SUBHALOES: THE
EFFECT OF STRIPPING
SomeBHsinlocalgalaxiesappeartohavemassesmuchlargerthan
expectedonthebasisofthestellarorbulgemass(e.g.NGC4486B,
NGC1277,M60-UCD1,NGC4342,NGC4291),andapossibility
isthatthehostgalaxywasoriginallymoremassiveandlostsomeof
itsmassbecauseofstripping(Volonteri,Haardt&Gu¨ltekin2008b;
Sethetal.2014),althoughthisisunlikelyatleastforsomecases
(NGC4342,NGC4291;Bogda´netal.2012). Figure8. BHmassversushalomass(top)andversusgalaxymass(bottom)
Weinvestigateherehowstrippinginsub-haloesaffectsthecon- atz=0.Red:mainhaloes;orange:sub-haloes.Contoursarebasedon10
equallyspacedlogarithmiclevels,droppingthefivelowestlevelsforclarity.
nectionwithDMhaloesandstellarmasses.InthetoppanelofFig.8
AtlatecosmictimesapopulationofBHsinstrippedsub-haloesemerges,
weshowhowsub-haloestendtohostlargerBHs(atfixedDMhalo
wheretheBHisover-massiveatagivenhalomass.Inreality,thehalois
mass)comparedtohaloesatz=0.Thisisaneffectthat,although
under-massive,havinglostpartofitsmass.Stripping,however,isseldom
presentalsoearlier,buildsupwithcosmictime.Onlyveryseldom,
effectiveallthewaytothestellardistributionofgalaxies.Wehighlightwith
however,strippingiseffectiveallthewayintothestellardistribution greensquaresthefewgalaxieswheretheBHmassis>0.01×Mgal.All
andcreatesover-massiveBHs(atfixedstellarmass).Normally,the suchgalaxiesresideinsub-haloes.
ratiobetweentheBHandgalaxymassisbetween0.002and0.005
forellipticalgalaxiesandbulges(Marconi&Hunt2003;Ha¨ring& >0.01×M ,andthisfractionincreasesonlybyafactorof3ifwe
gal
Rix2004;Kormendy&Ho2013),andcanbe20–60timeslower restrictthesampletogalaxieslocatedwithinsub-haloes.Athigher
formoreactiveormorediscygalaxies(Greeneetal.2010;Reines redshift,over-massiveBHsare0.10percentofthefullpopulation
&Volonteri2015).WedefineaBHtobeover-massiveifitsmass atz=3andz=2,and0.07percentatz=1.Restrictingthesample
is>0.01×M . tosubhaloes,thepercentageschangeto0.08,0.11and0.17atthe
gal
The few subhaloes with over-massive BHs are shown as green threeredshifts.Atearlytimesmostover-massiveBHsarehostedin
squares. Although we note that there are no main haloes hosting normalhaloes:BHsandgalaxiesarestillgrowing–andnotalways
over-massive BHs based on the definition given above, the cases exactlyatthesamepace.
wheretheBHisover-massivebecauseofstrippingarefew.Only This is short by an order of magnitude compared with obser-
0.2percentoftheentiregalaxypopulationhaveaBHwithmass vations, where out of ∼ 135 galaxies with dynamical BH mass
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2988 M.Volonterietal.
measurements,approximatelyeightgalaxieshavebeensuggested
to be over-massive at 3 − σ above the BH–bulge mass correla-
tion(Ferre´-Mateuetal.2015,butseeSavorgnan&Graham2016).
Bogda´n et al. (2012) proposed that over-massive BHs where the
hosthasnotbeenstrippedcanbeexplainedbynon-standardpaths
of BH–galaxy co-evolution (see also Fabian et al. 2013; Trujillo
etal.2014;Ferre´-Mateuetal.2015).Someoftheproposedpaths
includeasequenceofaccretioneventsdominatedbylowangular
momentum gas, boosting BH growth, and causing star formation
tooccurinacompactconfiguration.OncetheBHhasgrownsuffi-
ciently,AGNfeedbackpreventedadditionalBHandgalaxygrowth.
Ina similarvein, thesegalaxies andtheirBHssimplydonotex-
perienceanygrowthbymergersafterz∼3,remainingstructurally
untouchedandwithoutfurthermassandsizeincrease,butrecord-
ingatimewhen,statistically,theratiobetweenBHandbulgemass
waslargerthantoday.Keepinginmindthatscatterinthesimulated
BH–galaxyrelationsislessthaninobservations,wehavelooked
forBHsthatare‘almost’over-massive,>0.004×M ,andindeed
gal
foundsomecaseswheretheBHisnothostedinasub-halo,andthe
galaxygrowthhasnearlystoppedatz∼2–3.Thesecasesremain
veryfew,at10percentofthe‘almost’over-massiveBHs,whichin
Figure 9. Occupation fraction of BHs as a function of halo mass at
turnrepresentthe2.5percentofthefullpopulation. z = 0 (top) and z = 3 (bottom). We separate main haloes (red, thin
Insummary,averysmallfractionofBHsappearover-massive
curves)andsub-haloes(orange,thickcurves).Solidlinesrepresentcentral
withrespecttothestellarmassoftheirhostbecausethelatterhas BHs, i.e. BHs located within 10 per cent of the virial radius. The occu-
beenstripped,beingasub-haloofalargerhalo.However,allthe pationfractionofcentralBHsreachesunityathalomasses∼1010M(cid:4)at
BHs with M > 0.01 × M we identified in our simulation at z=3and∼1011M(cid:4) atz=0,thustracingthemassgrowthofhaloes.
BH gal
z = 0 are in sub-haloes (see also Barber et al. 2016). If we are Theoccupationfractionofsubhaloes,atagivenmass,ishigherthanthat
moregenerousinourdefinitionofover-massive,>0.004×M , ofhaloesbecauseofstripping:theinitialhalomasswaslargerthanatthe
gal
thenalargerpopulationemerges,includingalsosomecaseswhere presenttime,thereforetheOFtracestheinitialhaloproperties(cf.Fig.8).
Dashedlinesrepresentoff-centreBHswhicharelocatedwithinthevirial
tidal stripping is not the culprit. To put in context the fraction of
radiusofagivenhaloandarenotassociatedwithanysub-halo.Tensof
over-massiveBHsinthesimulationandinobservations,itisalso
off-centreBHscanbefoundinthemostmassivehaloes.
importanttoremarkthatmany(ifnotmost)galaxiesforwhichdy-
namicalBHmassmeasurementsexistarelocatedingalaxyclusters
wheretidalstrippingandgalaxy–galaxyinteractionsareexpected theexpectationthatlow-massgalaxieshavemoretroubleforming
tobemore important(especially inthe centre ofgalaxy clusters) andkeepingBHs,andfeedingthem.
thaninasimulationspanningawiderangeofenvironmentssuchas The OF of BHs as a function of halo mass is shown at two
theonepresentedhere. differentredshifts(z=0andz=3)inFig.9.Allhaloeswithmass
>1011M(cid:4)atz=0and>3×1010M(cid:4)atz=3hostacentralBH.
TheOFishigheratlowhalomassforsub-haloesforreasonssimilar
5 THE OCCUPATION FRACTION OF
tothosediscussedintheprevioussection.Beforethehalobecame
CENTRAL AND OFF-CENTRE BHS
a substructure, it was more massive, and this is the information
InmassivegalaxieswhereaBHhasbeenlookedfor,onewasfound. recordedbytheOF.
However, the situation differs for low-mass galaxies. Faint AGN Therearealsohaloesthathostoff-centreBHs.Tofindoff-centre
arenowbeingfoundinmanylow-massgalaxies(Reines,Greene& BHs, we first assign all the central BHs, within 0.1 × R , and
vir
Geha2013;Lemonsetal.2015;Milleretal.2015;Paggietal.2015; remove them from the list. We then consider the BHs which do
Trump et al. 2015; Mezcua et al. 2016), but there are only upper notbelongascentralstoanyhalo,andassignanoff-centreBHto
limits for BHs in NGC 205 (Valluri et al. 2005), M33 (Gebhardt ahaloifitiswithinR .Westartfromsubstructuresandproceed
vir
et al. 2001), Fornax (Jardel & Gebhardt 2012). The fraction of thentomainhaloes.Theseoff-centreBHsaregeneratedbymergers
haloes or galaxies hosting BHs as a function of galaxy mass and duringthehierarchicalassemblyofhaloes.Someofthemarethe
properties(BHoccupationfraction,OF)isanimportantdiagnostic resultofarecentmerger,andtheyareontheirwaytojoiningand
tolearnaboutthefirstBHs,inawaysimilartonear-fieldcosmology coalescingwiththecentralBH,andmayhaveveryhighluminosity,
and the first galaxies (Volonteri, Lodato & Natarajan 2008a; van throughmerger-drivengasinflows.Inhaloeswithmasses3×1012
Wassenhoveetal.2010).ThefractionofgalaxieshostingAGNasa < M < 3 × 1013M(cid:4) these merger-driven off-centre AGN are
h
functionofgalaxymassandpropertiesisalower-limittotheBHOF, locatedwithin10kpcfromthehalocentre,andhaveluminosities
andadditionallyprovidesinformationonAGNfuelling.InHorizon- ∼1043 − 1047 erg s−1. Other off-centre BHs are stranded in the
AGNBHseedinghasbeenperformedinarelativelysimpleway,not outerpartsofhaloesandhaveverylowluminosities.Inhaloeswith
directlybasedonmodelsofBHformationintheearlyUniverse,and masses3×1012 <M <3×1013M(cid:4) mostoff-centreBHsare
h
ithasbeenstoppedatz=1.5.ThechoiceofhaltingBHformation located at ∼100 kpc from the halo centre and have luminosities
atthisredshiftdoesnotaffectourconclusions,asallwell-resolved of∼1036ergs−1.TheluminositiesarelowbecausetheseBHsare
galaxiesattheendofthesimulationshaveatleastoneprogenitor surrounded by hot, low-density gas. By z = 0 the most massive
atz=1.5.AlthoughwecannotderiveconstraintsonBHformation haloescanhosttensoftheseBHs,asshownwithdashedlinesin
scenarios,wecantestqualitativelythetrendswithgalaxymass,i.e. Fig.9.
MNRAS460,2979–2996(2016)
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