Growth of Intermediate Massive Black Holes in the Hierarchical Formation of Small Spiral Ga

APreprinttypesetusingLTEXstyleemulateapjv.11/12/01

GROWTHOFINTERMEDIATEMASSIVEBLACKHOLESINTHEHIERARCHICALFORMATIONOFSMALLSPIRALGALAXIESINTHEHIGH-ZUNIVERSE

NOZOMUKAWAKATU

InternationalSchoolforAdvancedStudies(SISSA/ISAS),ViaBeirut2-4,34014Trieste,Italy

kawakatu@sissa.it

NationalAstronomicalObservatoryofJapan,Mitaka,Tokyo181-8588,Japan

saitoh.takayuki@nao.ac.jp

TAKAYUKIR.SAITOH

and

arXiv:astro-ph/0504202v1 8 Apr 2005NationalAstronomicalObservatoryofJapan,Mitaka,Tokyo181-8588,Japan

wada.keiichi@nao.ac.jpDraftversionFebruary2,2008

KEIICHIWADA1

ABSTRACT

Combiningatheoreticalmodelofmassaccretionontoagalacticcenterwithahigh-resolutionN-body/SPHsimulation,weinvestigatetheformationofanintermediatemassiveblackhole(IMBH)duringthehierarchicalformationofasmallspiralgalaxy(withatotalmassof1010M⊙)inthehigh-zuniverse.Wefoundthattherateofaveragemassaccretiontothenucleusduetotheradiationdragexertedbynewlyformedstarsintheforminggalaxyis≈10−5M⊙yr−1.Asaresultofthisaccretion,anIMBHwith≈104M⊙canbeformedinthecenterofthespiralgalaxyatz∼4.WefoundthatacentralBHcoevolveswiththedarkmatterhalofromz∼15toz∼2.ThemassratiooftheBHtothedarkmatterhaloisnearlyconstant≈(1−3)×10−6fromz∼10toz∼2.Thisisbecausethatchangeinthedarkmatterpotentialenhancesstarformationinthecentralpartofthegalaxy,andasaresulttheBHevolvesduetomassaccretionviatheradiationdrag.Therefore,ourmodelnaturallypredictsacorrelationbetweenmassiveBHsanddarkmatterhalos.Moreover,itisfoundthatthefinalBH-to-bulgemassratio(≈5×10−5)inasmallspiralgalaxyathigh-zismuchsmallerthanthatinthelargegalaxies(≈10−3).OurresultsalsosuggestthatthescatterintheobservedscalingrelationsbetweenthebulgemassandblackholemassarecausedbyatimelagbetweenBHgrowthandgrowthofbulge.WealsopredictthattheX-rayluminosityofAGNispositivelycorrelatedwiththeCOluminosityinthecentralregion.BycomparingourresultswiththepropertiesofLymanbreakgalaxies(LBGs),itispredictedthatsomeLBGshavemassiveBHsof≈106−107M⊙.

Subjectheadings:blackholephysics–galaxies:nuclei,starburst–hydrodynamics–radiation

mechanisms:general–method:numerical

1.introduction

Recentcompilationofthekinematicaldataongalacticcentershasrevealedthatacentral“massivedarkobject”(MDO),whichisacandidateforasupermassiveblackhole(BH),tightlycorrelateswiththemassofagalacticbulge;theBH-to-bulgemassratiois≈0.001asamedianvalue(e.g.,Kormendy&Richstone1995;Magorrianetal.1998;Merritt&Ferrarese2001;McLure&Dunlop2002;Mar-coni&Hunt2003).Therehavebeenanumberoftheoret-icaleffortstoclarifytheoriginofthisrelation(e.g.,Silk&Rees1998:Ostriker2000;Adams,Graff&Richstone2001).However,littlehasbeenelucidatedregardingthephysicsontheangularmomentumtransferinaspheroidalsystem(abulge),whichisinevitableforformationofBHs.Recently,Ferrarese(2002)andBaesetal.(2003)havear-guedthattheBHmassinspiralgalaxiesisrelatedtothedarkmatterhalomass.Thiscorrelationsuggeststhatfor-mationofsupermassiveBHsisphysicallyconnectednotonlywithformationofgalacticbulges,butalsowithas-semblyprocessesofdarkmatterhalosingalaxyformation.Sincemergingofproto-galaxiestriggersactivestarforma-1

tion,aphysicallinkbetweenstarformationandmassac-cretiontowardthecentralBHisexpected.

Umemura(2001)hasconsideredtheeffectsofradiationdragasamechanismforremovingtheangularmomen-tumofthegasintheactivegalacticnuclei.Theradia-tiondraginthesolarsystemisknownasthePoynting-Robertsoneffect.Notethat,intheearlyuniverse,Comp-tondragforcehasasimilareffectonformationofmassiveBHs(Umemura,Loeb,&Turner1997).Therateofan-gularmomentumlossduetoradiationdragisgivenbydlnJ/dt≃−χdE/c,whereJisthetotalangularmomen-tumofthegaseouscomponent,Eistheenergydensityoftheuniformspheroidalsystem,andχdisthemassextinc-tioncoefficientwhichisgivenbyχd=ndσd/ρgaswiththenumberdensitynd,cross-sectionσdandgasdensityρgas.Theexactexpressionsfortheradiationdragaregivenintheliterature(e.g.,Umemura,Fukue,&Mineshige1997;Fukue,Umemura,&Mineshige1997).

Inanopticallythinregime,dlnJ/dt≃−(τL∗/c2Mgas),whereτisthetotalopticaldepthofthesystem,L∗isthetotalluminosityofthespheroidalsystem,andMgasisthetotalmassofgas.Inanopticallythickregime,the1

DepartmentofAstronomicalScience,TheGraduateUniversityforAdvancedStudies,Osawa2-21-1,Mitaka,Tokyo181-8588,Japan

2Kawakatuetal.

radiationdragefficiencyissaturatedduetoconservationofthephotonnumber(Tsuribe&Umemura1997).Thus,anexpressionoftheangularmomentumlossratesuitableforbothregimescanbedlnJ/dt≃−(L∗Themass˙/c2Mg)(1−e−τ).

=−M(LgdlnJ/dt=∗/c2accretion)(1−e−τ

rateisthereforeM

).InansimplyM

˙opticallythickregime,thisgives

=L∗/c2(Umemura2001).Thus,theto-talmassaccretedontotheMDO,MMFormorerealisticMDO,ismaximallyMDO≃󰀃L∗/c2

dt.cases,weshouldtakeintoaccountinhomogeneityoftheinterstellarmatter(ISM).Inactivestar-forminggalaxies,theISMisobservedtobehighlyinhomogeneous(Sandersetal.1988;Gor-don,Calzetti&Witt1997).Inaddition,highresolutionthree-dimensionalhydrodynamicsimulationshaveshownthatmultiplesupernovae(SNe)inagalacticcenterformaquasi-stableinhomogeneoustorusaroundasupermassiveblackhole(Wada&Norman2002).Insuchinhomoge-neousISM,opticallythinsurfacelayersofopticallythickclumpycloudslosetheirangularmomentumduetoradia-tiondrag,andeventuallytheyaccretetowardthegalacticcenter(Satoetal.2004).Kawakatu&Umemura(2002)haveshownthattheinhomogeneityofISMplaysanimpor-tantroleintheradiationdragattainingmaximalefficiency.Basedontheradiationdragmodel,Kawakatu,Umemura,&Mori(2003)predictthatamassratiobetweentheblackholemassandthebulgemass,MisdeterminedbytheenergyconversionBH/Mbulgeefficiency≃0.001,ofwhichnu-clearfusionfromhydrogentohelium,i.e.,0.007(Umemura2001).Inthesepreviousstudies,galaxiesaretreatedasaone-zonemodel,thereforethegrowthofsupermassiveBHshasnotbeenrevealedinamorerealisticsituation,namelythatofthehierarchicalformationofgalaxies.Granatoetal.(2004)presentedasemi-analyticmodelingoftheearlyevolutionofmassivespheroidalgalaxiesandAGNswithinthedarkmatterhalo,includingtheangularmomentumtransferviaradiationdrag.TheyclaimedthefeedbackfromsupernovaeandfromAGNsdeterminestherelationbetweentheBHmass,thebulgemassandthedarkmatterhalomass(seealsoBukert&Silk2001).

DiMatteoetal.(2003)followedtheevolutionofthegas,stars,andthedarkmatterinforminggalaxies,andtheyfoundthattheobservedBHmass-to-stellarvelocitydispersionofabulgeisreproducedifthegasmassinthebulgeislinearlyproportionaltotheblackholemass.How-ever,itisimpossibletoresolvethestructureofthecentralsub-kpcregionorthebulgecomponentofhostgalaxiesbe-causeofthelimitationontheirnumericalresolution(massresolutionsare107−108M⊙andgravitationalsofteninglengthsis4-9kpc).Recently,usinghigh-resolutioncos-mologicalN-body/SPHsimulationswith2×106particles(oneSPHparticlehas103M⊙andagravitationalsoften-inglengthof∼50pc),Saitoh&Wada(2004)investigatedstellarandgaseouscoresonasub-kpcscaleduringthehierarchicalformationofasmallspiralgalaxy(withato-talmassof1010M⊙),andfoundthatthegalacticcore(dragoriginatinginthenuclearstarburst(e.g.,Umemura2001),ortheBHs-BHsmerger(e.g.,Haehnelt2004).

Herewefocusontheradiationdragasoneofthepos-sibleprocessesofmassaccretionontoaBHduringhi-erarchicalformationofagalaxy.TheobservedAGN-starburstconnectioninnearbygalaxies(Heckmanetal.1989;Kauffmanetal.2003;Imanishi&Wada2004;Jahnkeetal.2004)suggeststhatstarformationplaysanimportantroleinthemassaccretion.Weexpectacor-relationbetweenBHsandbulgesasanaturalresultofgalaxyformation,iftheradiationdragworks.Inthispa-per,wequantitativelyestimateevolutionofablackholemassinaforminggalaxy,combiningN-body/SPHsimu-lationsofcosmologicalgalaxyformationdonebySaitoh&Wada(2004)withananalyticmodelofangularmomen-tumtransferduetotheradiationdrag.

Thispaperisorganizedasfollows:InSection2,webrieflydescribethesimulationofgalaxyformation.OurmodelforthegrowthofamassiveBHviatheradiation-hydrodynamicprocessisalsoexplained.Basedonthismodel,inSection3,weshowthehistoryofaccretiontoaBHinaspiralgalaxy.Wealsodiscussthemutualrela-tionshipsbetweenamassiveBH,agalacticbulge,andadarkmatterhalo.Finally,wediscusscorrelationbetweenAGNactivitiesandthepropertiesofbulges.InSection4,wecompareourpredictionswithobservationalscalingrelations,andwediscusstheLymanbreakgalaxies,ascan-didatesforthesmallspiralgalaxiesthatwedemonstratehere.Section5isdevotedtoconclusions.

2.models

2.1.Simulationsofgalaxyformation

ThenumericalsimulationsusedherearebasedonSaitoh&Wada(2004)andSaitohetal.(inpreparation).WemodeltheformationandevolutionofgalaxiesintheCDMuniverse,adoptingatop-hatinitialconditionwithanopenboundaryforasinglegalactichalo(Mourmodelhaloare∼Ω1010M⊙).Thecosmologicalparametersin1,h=H0=1.0,Ωλ=0.0,Ω0.63.Theb=0.collapseepochof0/km/s/Mpc=0.5,andσ8=thehaloissetatzanditsspinparameteris0.05(Barns&Efstathiouc1987;∼3Heavens&Peacock1988).

Sincethetotalmassoftheobjectinoursimulationissmall(1010M⊙),evolutionofthesystemandthereforetheconclusioninthispaperdonodependontheemployedcosmology.Thecollapseepochoftheobjectinoursim-ulationiszaffectedbycthe∼Λ3,term.forwhichThistheisinevolutioncontrastistonotmuchstronglylargersystems,suchasclustersofgalaxies.

Thenumberofbaryon(SPH)anddarkmatterparti-clesinthesphericalregionisNThemassresolutionsofbaryonSPH=N(gasandDM=1005600.starsconvertedfromthegas)andDMparticlesare1.1×103M⊙and1.0×104M⊙,respectively.Thegravitationalsofteninglengthsare52pcforbaryonparticlesand108pcforDMparticles.Theinitialdistributionoftheparticlesisgen-eratedbyCOSMICS(Bertschinger2001).Wediscusstheevolutionofgalaxiesuntilz=2,becausetheassemblyhistoryfortheboundaryconditionswouldnotberealisticmuchlaterthanthecollapseepoch,zc.But,z∼zofthesimulatedgalaxyfinishes,sothatthectheassemblymassofthegalaxyatz=0wouldbeequaltothatatz=2.

IMBHsinSpirals

ThenumericaltechniqueweemploytorepresenttheevolutionofgalaxiesisastandardhybridN-body/hydrodynamiccodeforgalaxyformation.Thecodeincludesboththeradiativecoolingandstarformation.However,thedynamicalandradiativefeedbackprocessesfromstarformationandsupernovaexplosionsarenotex-plicitlytakenintoaccount.ThelengthoftheinteractionlistofeachSPHparticleisNNB=50.IntheSPHsim-ulations,theJeansinstabilitycanberesolvedcorrectlyformasseslargerthan2NNBmSPH(Bate&Burkert1997),wheremSPHismassofanSPHparticle.Inthesimulation,wecanresolvegravitationalinstabilityofacloudwhosemassislargerthan1.1×105M⊙.Inordertomodelthemultiphasenatureoftheinterstellarmedium(e.g.,Wada&Norman2001),wesolvetheenergyequationwiththeradiativecoolingunder104KandtheinverseComptoncooling.Weassumethatthegashasaprimordialabun-danceofX=0.76andY=0.24andweassumeanidealgaswithγ=5/3.Themeanmolecularweightofgas,µ,issetto0.59.

ThestarformationalgorithmissimilartotheonebyKatz(1992).IfanSPHparticlesatisfiesallthefol-lowingconditions:(1)theregionsareinvirializedhalos(ρSPH>200ρBG),whereρBGisthebackgrounddensity,(2)lowtemperature(T<3×104K),and(3)collapsingregions(∇·v<0),thenitisconvertedintoacollision-lessstarparticleinheritingthevelocityandthemassofthegasparticle.Thelocalstarformationrate,SFR,isassumed√tobeSFR=c∗mSPH/τffwithc∗=1/30,whereτff=1/

3

3πrbulge

3

isthenum-berdensityofgasclouds.Inthispaper,weassumethat

¯int≈O(1),thecloudcoveringfactorisorderunity,i.e.N

accordingtothepreviousanalysis.AdifferentlevelofISMclumpinesscanreducetheradiationdragefficiencybyafactorof2(Kawakatu&Umemura2002).Wealsoconfirmthattheopticaldepthinaclumpymediaisanorderofunity,usinga3-Dhydrodynamicsimulations(seeFig.1inWada&Norman2002).Evenifthesystemisextremelygas-rich(Mgas=108M⊙inthecentral100pc),wefoundthattheopticaldepthforthediskplanefromvariousdi-rectionsisdistributedbetween0.5and1.2,assumingthesamegas/dustratioanddustopacityintheanalysishere.Finally,usingMgas=Ncmgasthetotalopticaldepthofthebulgecanbere-writtentobe

¯int≃3χdτbulge(t)=τ¯(t)N,(1)2rbulge(t)

whererbulge(t)andMgas(t)arethesizeandthegasmassofthebulge.4

Theradiationdrag,whichdrivesthemassaccretion,originatesintherelativisticeffectinabsorptionandsubse-quentre-emissionoftheradiation.Thiseffectisnaturallyinvolvedinrelativisticradiationhydrodynamicequations(Umemura,Fukue,&Mineshige1997;Fukue,Umemura,&Mineshige1997).Theangularmomentumtransferinradiationhydrodynamicsisgivenbytheazimuthalequa-tionofmotionincylindricalcoordinates,

1χd

=dt

(3)

c2

whereLbulge(t)andτbulge(t)arethetotalluminosityandthetime-dependenttotalopticaldepthofthebulge.Kawakatu&Umemura(2002)foundthattheefficiencyηdragismaximally0.34intheopticallythickregime.

Theradiationenergyemittedbyamainsequencestaris0.14ǫtotherestmassenergyofthestar,whereǫistheen-ergyconversionefficiencyofthenuclearfusionfromhydro-gentohelium,whichis0.007.Thus,theluminosityofthe

ItisnotedthatsimulationswithathreetimeslargernumberofcloudsdidnotleadtoanyfundamentaldifferenceforfinalBHmass,althoughatleast104cloudsarenecessarytotreattheradiationtransfereffectproperlyinclumpyISM.Thetotalopticaldepth,τbulge,isnotalsosignificantlyaffectedbychangingthecloudsize,rc.

3WeshouldkeepinmindthatrecentobservationssuggestthatthemetallicityofthegasintheAGNscanbesuper-solarZ>Z⊙(e.g.,Ohtaetal.1996;Dietrich&Wilhelm-Erkens2000;Maiolinoetal.2003).Ifthisisthecase,theopticaldepthofagascloudcanbeenhancedbyafactorof3-4.

4Inthepresentpaper,weidentifya‘bulge’asaspheroidalstar-formingregionwheretheaveragenumberdensityofthegas,n,islargerthan

H

0.1cm−3inaspiralgalaxy.Thiscriterioncorrespondstothedensitycriterionofthestar-formingregion.

2

󰀇󰀆

−τbulge(t)

,1−e

4Kawakatuetal.

3.results

bulgeatopticalandUVbandsissimplyapproximatedby

˙bulge(t)c2,whereM˙bulge(t)istheSFRLbulge(t)≃0.14ǫM

inthebulge.Here,weemployastellarinitialmassfunc-tion(IMF)suchasφ=dn/dlogm∗=A(m∗/M⊙)−αforamassrangeof[ml,mu],wherem∗,ml,andmuarethestellarmass,thelowermass,andtheuppermass,respec-tively.Weassumeml=0.1M⊙andmu=60M⊙,andtheindexαis1.355.Theaccretionrate,equation(3),istherefore

˙bulge(t)(1−e−τbulge(t)),(4)˙drag≃1.2×10−3ηdragMM

Onthebasisofthecoevolutionmodeldescribedinthe

previoussection,weestimatethemassaccretiondrivenbytheradiationdragduringhierarchicalgalaxyforma-tion.Next,werevealtherelationshipbetweenthegrowthofaBHandthatofadarkmatterhalo.Finally,wediscusstherelationbetweenAGNactivityandthepropertiesofthebulges.

3.1.Massaccretionrateviaradiationdrag

EvolutionoftheSFRandtheopticaldepthofbulge(∼1kpc)areshowninFigure1.Beforez∼4,theSFRandtheopticaldepthincrease,whiletheydecreaserapidlyforz<4.Thiscanbeunderstoodasfollows:Athigh-z(z>4),supplyofthegasduetomergersofsmallerproto-galaxiesandconsumptionofthegasinthecentralpartofthegalaxy(bulge)arealmostbalanced.Thus,boththeSFRandtheopticaldepthareenhanced.Atlow-z(z<4),accretionofthegastothebulgeassociatedwithmergereventsisdecreased.Thegasinthebulgeisconsumedbythestarformation.Asaresult,itmakesthegasofbulgepoor.AsseeninFigure1,wefoundthattheevolutionoftheSFRandtheopticaldeptharenotsmooth,butepisodic.Thisepisodicgrowthcorrespondstothephaseofthehighmassaccretionontothebulgecomponenttrig-geredbymajormergerswithsometimedelays,whicharetypically107yrs(seeSaitoh&Wada2004indetails).

1

1

HereweignoretheinfraredluminosityfromtheevolvedstarsbecausethedustopacityfortheinfraredbandismuchsmallerthanthatfortheopticalandUVbands.˙bulgeandτ(t)aredirectlygivenfromthenumericalsim-M

ulations.ThetotalmassofdustyISMaccretedtothecentralmassivedarkobject(MDO),MMDO(t),isobtainedby

󰀅t

˙dragdt.MMDO(t)=M(5)

0

(6)

wheret0is0.1Gyr(z∼25)whichcorrespondstotheepochwedetecttheprogenitorofgalaxyfirstly,andt0is2.6Gyr(z∼2).Thecorrespondancebetweentimeandredshiftisbasedonthecosmologicalmodelweadopted.Inthismodel,weshoulddistinguishtheBHmassfromthatofanMDO,althoughthemassofanMDOisof-tenregardedasBHmassfromanobservationalpointofview.Theradiationdragisnotlikelytoremovethean-gularmomentumthoroughly,andthussomeresidualan-gularmomentumwillterminatetheradialcontractionoftheaccretedgas(Satoetal.2004).Hence,thedustyISMprobablyformsacompactrotatingtorus.Inthisnucleartorus,wesupposethatthemassaccretionontotheBHhorizonisdeterminedbytheEddingtonrate,andthattheBHmassgrowsaccordingto

MBH(t)=M0et/tEdd,

(7)

Asseeninequation(3),(4)and(5),thelinearrelationbetweentheMDOmassandthebulgemassisadirectre-sultoftheradiationdragmechanism.Thepossiblemassaccretedbytheradiationdragintheopticallythicklimitisgivenby

󰀅t1

Lbulge/c2dt≃5×10−3Mbulge,MMDO,max=ηdrag

t0

10

-1

SFR

0.5

SFR[M /yr]τbulge10

-2

0.25

τbulge

10

-3

0.125

10

-4

0510

z

152025

Fig.1.—Redshiftevolutionofthestarformationrate(inunits

ofM⊙yr−1)andtotalopticaldepth(τbulge)ofthebulgeatredshift(z).Atz>4,boththeSFRandtheopticaldepthincreasewithtime,whiletheydecreaseatlow-z(z<4).

wheretEddistheEddingtontimescale,tEdd=ηBHMBHc2/LEdd,withtheenergyconversionefficiency,ηBH,andtheEddingtonluminosity,LEdd.Unlessother-wisestated,ηBHisassumedtobe0.42,whichistheconver-sionefficiencyofanextremeKerrBH.Recently,Shibata(2004)hasfoundthatarigidlyrotatingverymassivestar(VMS)withseveral100M⊙canbeunstableforasofterequationofstate,andeventuallyitformsaBH.Inaddi-tion,thetheoryofstellarevolutionrevealsthatthenuclearburninginVMSsabove260M⊙isunabletohaltgravita-tionalcollapse(e.g.,Hegeretal.2003).Thus,theVMSsinevitablyevolveintomassiveBHswithoutsupernovaex-plosions.Here,weassume260M⊙asthemassoftheseedblackholeM0.

5

Figure2isevolutionofthemassaccretionratedue

˙drag),therateofmassaccretiontotheradiationdrag(M

˙BH),andtheEddingtonmassaccretionrateontoaBH(M

˙Edd).ItisclearthatM˙dragisalsoepisodic,reflecting(M

theevolutionoftheSFRandopticaldepth(Figure1andeq.[4]).Wehavealsofoundthattheaveragedmassaccre-tionrateis≈10−5M⊙yr−1.ThisrateiscomparabletotheEddingtonmassaccretionrateforablackholemasswith104M⊙,thatis,

󰀄󰀆η1BH−5−1˙Edd=M.≈10M⊙yr

c2104M⊙

(8)

AsfortheeffectofIMF,IftheslopeandthemassrangeofIMFarechangedtosatisfythespectrophotometricpropertiesofgalacticbulges,thentheradiationdragefficiencyisalteredbyafactorof±50%(Kawakatu&Umemura2004).

IMBHsinSpirals

5

InFigure2,theislargerthanM

˙Eddingtonmassaccretionrate(eq.[8])

dragafterz∼5.SincetheBHmassequalsthemassofMDOatz≈4(seeFigure3),themassac-cretionontotheBHsafterz∼4wouldbecontrolledbythemassaccretiontotheMDOviatheradiationdrag,

i.e.M

˙BH=M˙drag.Figure2showsthatM˙.8(theshadedareaBH>M˙aperiodof4.22 4 6 8 10 12 14

1010

MhaloFig.3.—SameasFig.1,butformassesofthedarkhalo(M,gas(MEvolutionofthemassofblackhalo)gas),andbulge(Mholebulge).Themass(BH)ofandthetheseedmassiveblackholedarkisassumedobject(MDO)tobeMarealsoplotted.0=260M⊙(seeeq.[7]).MDOandMbulgeMandMgas,respectively,ofthemassivewhileBH.MMDOItshowsisthethatmasstheofMDOBHisthemasstheMDOmassmassisproportionalatz≈4.

tothebulgemass.TheBHmassreachesoitar ssaM 2 4

6 8 10

z

6Kawakatuetal.

donotsignificantlychangewithMMBH/MbulgeBH/Mthehaloscatter≈3in×the10−6.Therefore,we≈would5×10−5andpre-dictthatscalingrelationislargerintheBH-growingobjectsathigh-zthaninnearbywell-evolvedgalaxies.

InFigure5,weplotmassoftheMDOandtheBHagainstthehalomass.ThisrevealsthattheMDOandtheBHcoevolvewiththedarkmatterhalofromz∼10toz∼2.ThemassesoftheMDOandtheBHincreasewiththedevelopmentofthedarkhalo.Themassratioofthe−6BHtothehalo6(MfromBH/Mz∼7DM)increasesgraduallyfrom10to3×10−toz∼2(seealsoFigure4).Fromthesearguments,theMcatesthatvariationofthedarkBH-Mmatterhalocorrelationindi-halopotentialas-sociatedwithmergingprocessespositivelylinkswiththemassaccretiontowardthegalacticcenterviatheradiationdrag.OurmodelsuggeststhataBHmassismutuallyre-latedtothemassofabulgeandthatofadarkmatterhalothroughoutthehistoryofthegalaxyformation.Compar-isonwithobservationsisdiscussedin§4.

105104MMDO] M[ 103sMBHsaM102z=3.5z=12z=10z=7.6z=5.0101081091010Mhalo [M ]Fig.5.—MassesoftheBH(thickline)andMDO(thinline)aremassesplottedoftheagainstdarkmasshaloatoflabeledthedarkredshifts.halo.TheItarrowsshowsthatindicatethetheBHcoevolveswiththedarkmatterhalofromz∼10toz∼2.

3.3.AGNactivity-hostrelation

Inthissection,weexaminetherelationbetweentheAGNactivitiesandthepropertiesofbulgecomponents.Evolutionofthebulgeluminosity(Lbulge)atopticalandUV-bandandtheAGNluminosity(Lz>4,theAGNluminosityAGN)areplottedinFigure6.Duringincreaseswiththetime,becausethemassaccretionisdeterminedbytheEddingtonlimitedbyM

˙rate.Afterz∼4,theAGNluminosityis

drag(seeFigure3).Thus,theAGNluminos-ityexhibitsapeakaroundz∼4,whenMthisfigure,theAGNluminosityisMDOalways∼MsmallerBH.Asseeninthanthebulgeluminosity;inotherwords,noquasarphase,i.e.AGNluminositydominantphase,appears.However,theluminosityratiooftheAGNtothebulgeexhibitsthemaximalvalue(LThissuggeststhatsomesmallAGN/Lspiralbulgegalaxies≈0.1)atathigh-z∼4.zcouldshowthesameleveloftypicallowluminosityAGNsinthelocaluniverse.

Figure7showstherelationbetweentheX-raylumi-nosity,LX,oftheAGNandtheCOluminosity,Lofthebulge.Here,theX-rayluminosityLCO,Xisesti-

matedassumingLemittingefficiency,X=ǫwhichXLAGN,whereǫissupposedXistheX-raytobe0.1.TheCOluminosityisderivedfromthegaseousmassassumingaconversionfactor,X4.6Mkms−1pc2(deBreucketCO=Mal.2003).gas/LWeCO=⊙/KfoundthattheX-rayluminosityispositivelylinkedwiththeCOluminosityforawiderangeofluminosities,i.e.L1038(ergss−1)(LXFigure7,weCO/Kkms−1kpc2)2.

∼Inalsofindthatsomepointsobviouslyde-viatefromthelinearrelation.ThesepointscorrespondtotheBH-growingphase(4.21044

1043

Lbulge]s/gre[ ytis1042

onimuL1041

LAGN

1040

0

2

4

68

10

12

14

z

IMBHsinSpirals

7

thatLymanbreakgalaxies(LBGs),whicharestarburstgalaxiesathigh-z,maybeintheformingphaseofagalac-ticbulge(Friaca&Terlevich1999;Matteucci&Pipino2002).TheSFRintheLBGsis∼3−300M⊙yr−1.LBGshaveatypicalluminosity∼1010−1011L⊙,astellarmass∼1010−1011M⊙,andtheyareobservedtobeopticallythin(e.g.,Shapleyetal.2001).Theyalsoexhibitstrongclusteringatz∼3,suggestingthathierarchicalclusteringison-going.Inaddition,theChandraX-rayobservatoryhasdetectedthehardX-rayofLBGsatz=2−4withtheluminosityof∼108L⊙althoughitisstilluncertainwhethertheX-rayemissionarisesfromAGNs(Brandtetal.2001).ComparingthesepropertiesofLBGswithourpredictions(i.e.(1)-(6)),thesmallspiralgalaxy(withatotalmassof1010M⊙)intheBH-growingphasemaycor-respondtolow-masscounterpartsoftheLBGs.Extrapo-latingthescalingrelationthatwefoundtotheobservedLBGs,theywouldhavetheMBHswith≈106torecentobservations,only3%ofLBGs−107M⊙.AccordingshowAGNactivityintherest-framehardX-rayband(Nam-draetal.2002)andopticalband(Shapleyetal.2001).However,ithasnotbeenclearthatthis3%fractionre-flectsthedutycycleofmassaccretiontoBHs(seeShap-leyetal.2001indetails)orthepossibilitythattheLBGshavemassiveBHs.Hosokawa(2004)claimed,assumingMhaveBH/Mamassivebulge≈0BH.001,withthat∼∼1010%7M⊙oftoLBGsreproduceatz∼the3canlo-calmassfunctionofSMBHs(Saluccietal.1999;Yu&Tremaine2002;Aller&Richstone2002;Shankaretal.2004).

4.2.MBH−MbulgeandMBH(2004)suggested−thatMhalorelations

Barthetal.thecorrelationbetweenBHmassandstellarvelocitydispersion(theMBHBHwith−σrelation)≈104−10holds6M⊙on.Inamassaddition,scaleofBaesanintermediateetal.(2003)foundacorrelationbetweentheBHmass27andhalomass,i.e.MBH/108M⊙∼0.11(Mhalo/1012M⊙)1.,byusingtheMBH−σrelation.ThisrelationgivesMBH=3×104M⊙forMhalo=1010M⊙,whichiscomparabletoourpredic-tion(MBH≈3×104M⊙atz∼2).However,itshouldbenotedthattherearelargeuncertaintiesintheempiricallaws,asmentionedbyFerrarese(2002).

Inourmodel,−5thefinalBHmass-to-bulgemassratiois≈5×10,whichismuchsmallerthantheobservedvalue(≈10−3)innearbylargegalaxies.Thus,ifoursce-natioiscorrect,itisexpectedthatsmallspiralgalaxiesathigh-z,whicharenotdirectcounterpartsofthedwarfgalaxiesatlow-z,couldhavetheIMBHsandthesmallerBHmass-to-bulgemassratios.Currently,itisdifficulttodetecttheIMBHsinsmallgalaxiesathigh-z,andthere-forewecannotdirectlyproveourprediction,namelythesmallBHmass-to-bulgemassratio.Moreover,thereisalsoaroominthetheoreticalmodel,especiallyoneffectsofmechanical,radiativeandchemicalfeedbackprocessesfromstarformation.Forinstance,itisnottrivialwhetherthestellarfeedbackaffectsontheSFRpositivelyorneg-atively.Therefore,itisultimatelynecessarytoperformhigh-resolutionradiativehydrodynamicalsimulationsforgalaxyformationtakingintoaccounttheseeffectsexplic-itly.

Inthispaper,wefocusontheformationofaMBHdue

totheradiationdraginasmallspiralgalaxy.However,theprocessdiscussedherecouldbeappliedtomoremassivegalaxiesbecausethetransferoftheangularmomentumviatheradiationdragisindependentofthemassscaleofthegalaxies.ByusingtheBHmass-to-halomassrelationforasmallspiralgalaxy(MthemassivespiralBH/Mgalaxieshalowith≈10−6),wecanpre-dictthatM−107Mhalo=1012M⊙haveMBHswith106⊙.Inaddition,theobserva-tionshavesuggestedtheSFRsofthemassivegalaxiesathigh-zare10-100timeshigherthanthoseofsmallgalaxiesliketheoneconsideredhere.Thus,thefinalBHsmightachieve≈108M⊙becausetheeffectoftheradiationdragislinearlyproportionaltotheSFR(eq.[4]).Ifthisisthecase,hostgalaxiesoftheluminousquasarsathighred-shiftwouldbestar-formingorpost-starburstgalaxies.Ontheotherhand,weshouldnotethatthemassofaBHwoulddependonthemorphologyofthegalaxiesevenifthemassofthedarkhaloisthesame.ThisisbecausetherateofmassaccretionontotheBHsisnotdeterminedbythediskcomponents,butbythebulgecomponentsinthehostgalaxies,duetotheeffectsofgeometricaldilu-tionandopacity(seeKawakatu&Umemura2004inde-tails).Therefore,themorphologydifferencesofhostgalax-ieswouldcausethelargescatterinthemassrelationoftheBHstothehalosinspiralgalaxies.Infact,someauthorsclaimthattheMBH−MhalorelationismuchweakerthantheM2000;BHZasov−Metbulgerelationinspiralgalaxies(Saluccietal.al.2004).

z=4.441

z=4.2z=4.8]s/gre[ xL goL40

39

0.60.81.01.21.4Log Lco [K km/s Kpc2]

Fig.7.—TherelationbetweentheCOluminosity(LtheX-rayluminosity(LCOBH)andX)duringtheevolutionoftheandtheThegalaxy.X-rayluminosityThefillediscirclespositivelyshowcorrelatedtimeevolutionwiththeinCOourluminos-model.ity.Thethinlinerepresentsthiscorrelation,i.e.logLX(erg/s)∼38+2BHgrowinglogLCOphase(Kkm(4s−1.24.3.LXIn§3.3,wepredictedthat−LCOrelation

theX-rayluminosityofAGNsispositivelycorrelatedwiththeCOluminosityofbulgesfromz∼10toz∼2.Thiscorrelation(i.e.L1038(ergss−1)

X∼(LCO/Kkms−1kpc2)2),ifweextrapolateittoAGNswithhigherluminosity,isconsistentwiththeLtionfoundinthelowredshiftSeyfertgalaxiesX−andLCOrela-quasars(Yamada1994).TheobservedLX−LCOrelationshowsascatterofaboutoneorderofmagnitude.Supposeall

8Kawakatuetal.

BH-to-bulgemassratioisabout5×10−5inasmallspi-ralgalaxy,whichismuchsmallerthantheobservedvalue(≈10−3)inthelargegalaxiesduetotheopacityeffect,althoughthestellarfeedbackwouldaffectontheresult.Moreover,thetime-lagbetweentheBHgrowthandthegrowthofthebulge(halo)wouldcausethescatteroftheobservedscalingrelation.

IntermsofrelationshipbetweentheAGNactivityandthepropertiesofhostgalaxies,wefoundthatevenasmallspiralgalaxycouldshowthesamelevelofthetypicallowluminosityAGNswithLAGN/Lbulge≈0.1atz≈4.OurmodelshowsthattheX-rayluminosityoftheAGNispositivelycorrelatedwiththeCOluminosity(thegaseousmass)ofthebulgeverywell.Furthermore,ourresultpre-dictsthattheBH-growingobjectsdeviatefromthisscalingrelation.BycomparingourresultswiththepropertiesoftheLBGs,wepredictthattheLBGscouldharbormassiveBHswith106−107M⊙.

Theauthorsthanktheanonymousrefereeforhis/herfruitfulcommentsandsuggestions.NKacknowledgesItal-ianMIURandINAFfinancialsupport.Numericalcompu-tationswerecarriedoutonGRAPEclusters(MUV)andFujitsuVPP5000atNAOJ(MUVProjectIDg04a07,VPPProjectIDrkw20a).TheauthorsaresupportedbyGrants-in-AidforScientificResearch(no.15684003(KW)andno.16204012(TS))ofJSPS.

galaxiesfollowthesameLX−LCOrelationthatwefoundhere,wesuspectthatthelargescatterintheobservedscalingrelationwascausedwhentheBHswereintheirgrowingphases.SubmillimeterobservationsbyALMAforluminoushigh-zquasarswillbehelpfultoinvestigatetheconnectionbetweentheblackholemassandthehostprop-erties.

5.conclusions

Combiningatheoreticalmodelofthemassaccretionontoagalacticcenterduetotheradiationdragwithhigh-resolutionN-body/SPHsimulations(2×106particles,oneSPHparticlehas103M⊙andasofteninglengthof∼50pc),wedemonstrategrowthandformationofamassiveBHduringhierarchicalformationofasmallspiralgalaxy(withatotalmassof1010M⊙).Wefoundthattheaver-agerateofthemassaccretionduetotheradiationdragis≈10−5M⊙yr−1.Finally,asmallspiralgalaxycanhaveanIMBHwith104−105M⊙atz∼4.

OurmodelsuggeststhatthegrowthofthemassiveBHscorrelatesnotonlywiththatofthegalacticbulges,butalsowiththatofthedarkmatterhalosinthehierarchicalformationofspiralgalaxies.ThemassiveBHscoevolvewiththedarkmatterhalofromz∼15toz∼2.ThismeansthatthechangeinthedarkmatterpotentialcloselycorrelateswiththerateofthemassaccretionontoaseedBHwiththehelpoftheradiationdrag.Thefinalmassra-tiooftheBH-to-darkmatterhalois≈10−6andthefinal

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