Forming supermassive black holes by accreting dark and baryon matter

a r X i v :a s t r o -p h /0510222v 1 7 O c t 2005

Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 5February 2008

(MN L A T E X style ?le v2.2)

Forming supermassive black holes by

accreting dark and baryon matter

Jian Hu 1,Yue Shen 1,5,Yu-Qing Lou 1,2,3,4,and Shuangnan Zhang 1,6,7,8

1

Physics Department and Tsinghua Center for Astrophysics (THCA),Tsinghua University,Beijing 100084,China;hujian98@https://www.sodocs.net/doc/6512191829.html,;yshen@https://www.sodocs.net/doc/6512191829.html,;louyq@https://www.sodocs.net/doc/6512191829.html,;zhangsn@https://www.sodocs.net/doc/6512191829.html, 2Centre de Physique des Particules de Marseille (CPPM)/Centre National de la Recherche Scienti?que (CNRS)

/Institut National de Physique Nucl′e aire et de Physique des Particules (IN2P3)et Universit′e de la M′e diterran′e e Aix-Marseille II,163,Avenue de Luminy Case 902F-13288Marseille,Cedex 09,France;

3Department of Astronomy and Astrophysics,The University of Chicago,5640South Ellis Avenue,Chicago,IL 60637USA;4National Astronomical Observatories of China,Chinese Academy of Sciences,A20,Datun Road,Beijing 100012,China;5Department of Astrophysical Sciences,Peyton Hall,Princeton University,Princeton,NJ 08544USA;6Department of Physics,University of Alabama in Huntsville,Huntsville,AL 35899USA;

7National Space Science and Technology Center,320Sparkman Drive,SD50,Huntsville,AL 35805USA;8Institute of High Energy Physics,Chinese Academy of Sciences,P.O.Box 918-3,Beijing 100039,China.

Accepted .Received ;in original form

ABSTRACT

Given a large-scale mixture of self-interacting dark matter (SIDM)particles and baryon matter distributed in the early Universe,we advance here a two-phase accretion scenario for forming supermassive black holes (SMBHs)with masses around ～109M ⊙at high redshifts z (>～6).The ?rst phase is conceived to involve a rapid quasi-spherical and quasi-steady Bondi accretion of mainly SIDM particles embedded with baryon matter onto seed black holes (BHs)created at redshifts z <～30by the ?rst generation of massive Population III stars;this earlier phase rapidly gives birth to signi?cantly enlarged seed BH masses of M BH ,t 1?1.4×106M ⊙σ0/(1cm 2g ?1)(C s /30km s ?1)4during z ～20?15,where σ0is the cross section per unit mass of SIDM particles and C s is the velocity dispersion in the SIDM halo referred to as an e?ective “sound speed”.The second phase of BH mass growth is envisaged to proceed primarily via baryon accretion,eventually leading to SMBH masses of M BH ～109M ⊙;such SMBHs may form either by z ～6for a sustained accretion at the Eddington limit or later at lower z for sub-Eddington mean accretion rates.In between these two phases,there is a transitional yet sustained di?usively limited accretion of SIDM particles which in an eventual steady state would be much lower than the accretion rates of the two main phases.We intend to account for the reported detections of a few SMBHs at early epochs,e.g.,SDSS 1148+5251and so forth,without necessarily resorting to ei-ther super-Eddington baryon accretion or very frequent BH merging processes.Only extremely massive dark SIDM halos associated with rare peaks of density ?uctuations in the early Universe may harbour such early SMBHs or quasars.Observational con-sequences are discussed.During the ?nal stage of accumulating a SMBH mass,violent feedback in circumnuclear environs of a galactic nucleus leads to the central bulge for-mation and gives rise to the familiar empirical M BH ?σb correlation inferred for nearby normal galaxies with σb being the stellar velocity dispersion in the galactic bulge;in our scenario,the central SMBH formation precedes that of the galactic bulge.Key words:accretion,accretion discs –black hole physics –cosmology:theory –dark matter –galaxies:formation –quasars:general

1INTRODUCTION

On the basis of various observational diagnostics and nu-merous case studies,supermassive black holes (SMBHs)are now widely believed to be ubiquitous,particularly at the nu-

clei of both normal and active galaxies (e.g.,Kormendy &Richstone 1995;Haehnelt 2004).As the central gravitational engines to power most energetic activities of quasi-stellar objects (QSOs)or quasars (e.g.,Salpeter 1964;Lynden-Bell 1969;Bardeen 1970),SMBHs dynamically impact the for-

2Hu,Shen,Lou,Zhang

mation and evolution of host galaxies(e.g.,Silk&Rees1998; Page,Stevens,Mittaz&Carrera2001;King2003;Murray, Quartaert&Thompson2005).Their most tantalizing man-ifestations are the observed M BH?M bulge correlation(e.g., Magorrian et al.1998;Laor2001;H¨a ring&Rix2004)and its tighter version—the M BH∝σ4.2b correlation for both active and normal galaxies(e.g.,Gebhardt et al.2000;Fer-rarese&Merritt2000;Tremaine et al.2002),where M BH is the black hole mass,M bulge is the galactic central bulge mass andσb is the stellar velocity dispersion in the galactic bulge.

Given substantial progresses in probing and under-standing the basic physics of SMBHs as well as galaxy forma-tion and evolution over past several decades(e.g.,Lynden-Bell1969),much still remain to be learned and explored because of the somewhat speculative nature of the subject to a certain extent.During the extensive Sloan Digital Sky Survey(SDSS),the newly reported SMBH with a mass of M BH～3×109M⊙in the quasar SDSS1148+5251(Fan et al.2003;Willott et al.2003)at a high redshift z=6.43 particularly highlights the outstanding mystery of the rapid BH mass growth in the early Universe and reveals inconsis-tency with the local M BH?σb relation(e.g.,Walter et al. 2004).1

For a sustained Eddington accretion of baryon matter, the mass growth rate˙M BH of a BH is presumed to be pro-portional to the black hole mass M BH,namely

˙M

BH=M BH/t Sal,(1) where t Sal is the so-called Salpeter timescale(Salpeter1964)

t Sal≡?M BH c2

0.1(1??)L

with c,L,L Edd and?being the speed of light,the luminos-ity,the Eddington luminosity and the radiative e?ciency, respectively.For constant?and L/L Edd parameters,the BH mass grows exponentially in the form of

M BH(t)=M0exp[(t?t0)/t Sal],(2) where M0is the seed BH mass and t0is the initial time of accretion.Recent observations suggest L/L Edd<～1(e.g., Vestergaard2004;McLure&Dunlop2004)and? 0.1?0.2 (e.g.,Yu&Tremaine2002;Elvis et al.2002;Marconi et al.2004).The latest magnetohydrodynamic(MHD)simu-lations for disc accretion indicate an?higher than the oft-quoted value of～0.1(e.g.,Gammie,Shapiro&McKinney 2004).A higher value of?tends to increase the Salpeter timescale t Sal and thus makes the mass growth of a SMBH via gas accretion more di?cult within a short time(e.g., Shapiro2005).Given an estimated age of～0.9Gyr for the quasar SDSS1148+5251at z=6.43,it would not be easy to assemble a SMBH of mass～3×109M⊙from a ～10?100M⊙seed BH(e.g.,the remnant of an imploding core of a massive Population III star;Arnett1996;Heger &Woosley2002)even for a sustained accretion of baryon matter at the Eddington limit all the time.

While speculative to various extents,possible theoret-ical resolutions to this dilemma of rapid SMBH growth in

1In this context,we note in passing the recent detection of a gamma-ray burst afterglow with a high redshift z>～6.the early Universe include:(1)more massive seed BHs either from collapses of supermassive stars(e.g.,Shapiro2004)or from accretion of low angular momentum baryon materials in the early Universe(e.g.,Koushiappas,Bullock&Dekel 2004);(2)more frequent BH merging processes(e.g.,Yoo& Miralda-Escud′e2004;Shapiro2005;but see Haiman2004);

(3)rapid mass growths via a sustained super-Eddington ac-cretion(e.g.,Ruszkowski&Begelman2003;Volonteri& Rees2005).All these proposals with various assumptions might produce the required mass>～109M⊙of a SMBH at z=6.43through a baryon accretion alone.

Alternatively,a sustained accretion of self-interacting dark matter(SIDM)particles(e.g.,Spergel&Steinhardt 2000)onto a seed BH have been modelled to reproduce the observed M BH?σb relation(Ostriker2000;Hennawi&Os-triker2002;cf.MacMillan&Henriksen2002for an alter-native approach).As a di?erent application of these ideas and as a theoretical contest,here we entertain the possibil-ity that a proper combination of SIDM and baryon accretion at distinct stages might lead to desired features of forming SMBHs in the early Universe.It is natural and sensible to imagine that on large scales,SIDM particles and baryons are intermingled and mediated by gravitational interactions through?uctuations in the early Universe.Based on the the-oretical knowledge of accreting baryon matter,we therefore advance in this paper a two-phase scenario involving accre-tion of both quasi-spherical SIDMs and baryon matter.In §2,we describe and elaborate our two-phase accretion model scenario in speci?cs.Summary and discussion are contained in§3.

2THE TWO-PHASE ACCRETION SCENARIO In our two-phase accretion model for SMBH formation,the ?rst phase is featured by a sustained,rapid quasi-spherical and quasi-steady Bondi accretion of mainly SIDM particles (a small fraction of baryon matter mixed therein)onto a seed BH created at z<～30presumably by a core implosion inside a?rst-generation massive star of Pop III until reach-ing a BH mass of M BH～106M⊙during the redshift range of z～20?15.The second phase of subsequent BH mass growth is primarily characterized by a baryon accretion to eventually assemble a SMBH of mass M BH～109M⊙;such SMBHs may form either around z～6for a sustained baryon accretion at the Eddington limit or later at lower z for aver-age accretion rates below the Eddington limit.For concep-tual clarity,we consider these two major phases separately. On the theoretical ground,the?rst phase should gradually evolve into a di?usively limited accretion of SIDM parti-cles continuing towards the BH.As time goes on,the initial mixture of SIDM particles and baryon matter will eventually become more or less separated during the accretion process in the sense that radiative baryon matter gradually?atten to a disc accretion which eventually overwhelms the steady accretion of SIDM particles fading into the di?usively lim-ited process.

Two-Phase Formation of SMBHs3 2.1Phase I:a sustained spherical accretion of

mainly SIDM particles onto a seed black hole

We presume that the initial seed BHs were created by core

implosions of massive Pop III stars with typical remnant BH

masses of M0～10?100M⊙in the redshift range z～30?10

[e.g.,Wilkinson Microwave Anisotropy Probe(WMAP)ob-

servations for the excess power in cosmic microwave back-

ground provide tantalizing evidence for the reionization era;

see Kogut et al.2003];frequent coalescences of such seed

BHs might possibly happen to produce more massive seed

BHs around the same epoch or shortly thereafter.When

such a seed BH happens to immerse in a dark matter(DM)

halo of low angular momentum,it accretes SIDMs together

with a small fraction of baryon matter mixed therein.As an

optimistic approximation,such a SIDM accretion is envis-

aged as grossly spherically symmetric by an e?ective trans-

port of angular momentum outward in the ensemble of

SIDM particles(Ostriker2000).We de?ne the speci?c cross

section asσ0≡σx/m x for an SIDM particle with a mass

m x and a cross sectionσx;the mean free path is therefore

λ=1/(ρσ0)withρbeing the mass density of the SIDM in-

cluding a small mass fraction of baryon matter.For regions

within the radial range r>～λ,the SIDM is su?ciently dense

and may be grossly perceived as a‘?uid’(e.g.,Peebles2000;

Subramanian2000;Moore et al.2000;Hennawi&Ostriker

2002).

As a classical reference of estimates,we begin with

the well-known stationary Bondi(1952)accretion.Given

a singular isothermal sphere(SIS)mass density pro?le2

ρ=C2s/(2πGr2)for a SIDM halo,the mass growth with

time of a BH embedded in a quasi-spherical SIDM halo is

M BH(t)=2C3s t/G,where G is the gravitational constant

and C s is the SIDM halo“sound speed”(Ostriker2000).

Here the“sound speed”is essentially the local velocity dis-

persion of SIDM particles and is equal to the virial velocity

for the SIS case.A quantitative comparison of the Bondi

accretion with the Eddington accretion is given by the ratio

˙M

Bon

0.1 C s106M⊙ ?1,(3)

where˙M Bon and˙M Edd are the Bondi and Eddington mass ac-cretion rates,respectively.Apparently,given a seed BH mass and a typical halo sound speed(see below),the Bondi mass accretion rate˙M Bon dominates over the Eddington mass ac-cretion rate˙M Edd.As SIDM particles do not radiate,this super-Eddington accretion will proceed without impedence. For sustained isothermal spherical self-similar collapses or accretion(e.g.,Lou&Shen2004;Shen&Lou2004),the maximum mass growth rate remains in the same order of magnitude as that of the steady Bondi accretion.We em-phasize that in the presence of accretion shocks,the central 2While being highly speculative for a SIDM halo,the SIS density pro?le for SIDM and gas was also considered earlier by Ostriker (2000)and King(2003).Ostriker discussed consequences of other density pro?les of r?1(e.g.,Navarro,Frenk,&White1995)and r?3/2(e.g.,Jing&Suto2000;Subramanian,Cen,&Ostriker 2000;Lou&Shen2004;Bian&Lou2005;Yu&Lou2005). There are other cusped power-law density pro?les available in the so-called hypervirial family(e.g.,Evans&An2005).

Figure1.The mass growth history of a black hole in the SIDM halo mixed with a fraction of baryon matter.The upper and lower panels are for the histories of mass accretion rate dM/dt and of black hole mass M BH growth,respectively.The thin solid line before t1represents the Phase I steady Bondi accretion of SIDM particles,while the other thin lines are the di?usive limited SIDM accretion after t1.The curves of thicker(boldface)linetypes are the Phase II baryon accretion at the Eddington rate:here,we consider three di?erent cases of the moment that Phase II accre-tion begins,that is,before(dotted),at(dash-dotted)and after (dashed)t1,respectively.Please note that the dash-dotted line and dotted line almost coincide to the right side of t1.The initial seed black hole mass due to a Pop III star is30M⊙at z=20. The input parameters are C s=30km s?1,σ0=1.0cm2g?1 and?=0.15.

mass accretion rate should be modi?ed(Shen&Lou2004; Bian&Lou2005).

This SIDM accretion phase continues until the mean free pathλbecomes comparable to the accretion radius r A with a corresponding timescale t1=σ0C s/(4πG),a BH mass M BH(t1)=σ0C4s/(2πG2)and a transitional accretion radius r A(t1)=σ0C2s/(2πG).For typical parameters,we have the following quantitative estimates

t1?1.1×105yr(C s/30km s?1)σ0/(1cm2g?1),

M BH,t

1

?1.4×106M⊙(C s/30km s?1)4σ0/(1cm2g?1),

r A,t

1

?7pc(C s/30km s?1)2σ0/(1cm2g?1).

(4)

For a virialized SIDM halo at high z,the typical halo virial velocity or local velocity dispersion of SIDM particles

4Hu,Shen,Lou,Zhang

(mimicked as a‘sound speed’)may be estimated by

C s=8.2(M/109M⊙)1/3(1+z)1/2km s?1(5) (e.g.,Barkana&Loeb2001).Therefore,an estimate of C s～30km s?1for a virilized SIDM halo of mass M～109M⊙during z～20?15appears plausible.The comoving halo number density n(M,z)with mass M at a given z can be calculated from the standard hierarchical structure forma-tion model.We adopt an input power spectrum computed by Eisenstein&Hu(1999).For cosmological parameters,we take?m=0.3,?Λ=0.7,?b=0.045,h0=0.7,σ8=0.9 and n=1in our model calculations.

Estimated constraints onσ0from both observations and theories are brie?y summarized at this point.Wandelt et al. (2000)evaluated the constraints onσ0and found aσ0range of～0.5?6cm2g?1.Yoshida et al.(2000)numerically simu-lated the evolution of a galaxy cluster forσ0=10,1,and0.1 cm2g?1,and obtained corresponding radial mass pro?les. Using the high-resolution X-ray data of Chandra satellite and the assumption of a hydrostatic equilibrium,Arabadjis et al.(2002)derived a mass pro?le for the galaxy cluster MS 1358+62that peaks strongly in the central region.From a comparison with the result of Yoshida et al.(2000),they concluded thatσ0<～0.1cm2g?1.However,Markevitch et al.(2004)pointed out that there are certain di?culties with this stringent limit and they provided a less stringent limit ofσ0<～1cm2g?1.

In general,σ0may well depend on relative velocity v of SIDM particles(e.g.,Firmani et al.2000).Here,we tenta-tively adopt aσ0in the form of

σ0= 30km s?1

˙M

Edd =3.4×10?5

?

1cm2g?1 C s106M⊙

?2.

(7)

For order-of-magnitude estimates,we may safely ignore the SIDM accretion more or less after the formation of a signi?-cantly enlarged seed BH around the end of Phase I accretion. In this sense and in reference to the very initial seed BH,we regard it as a‘secondary seed BH’for the Phase II accretion of baryon matter.In Figure1,we have explored three di?er-ent onset times for the Eddington accretion rate of baryon matter for comparison.Within our scenario,it is more sen-sible to have the baryon accretion all along with the SIDM accretion,roughly corresponding to the heavy dotted curve.2.2Phase II:a disk accretion of baryon matter

In contrast to baryon matter accretion at the Eddington limit as estimated by equation(2),a rapid quasi-spherical accretion of SIDM particles during Phase I dominated dur-ing the?rst～105yr or so and the BH mass rapidly grows to M BH,t

1

～106M⊙to become a secondary seed BH for the subsequent baryon matter accretion.After this almost in-stantaneous Phase-I accretion in reference to the Salpeter timescale t Sal,the accumulation of SIDMs proceeds at a much slower pace with an ine?cient loss cone accretion(Os-triker2000;Hennawi&Ostriker2002).With favourable en-virons or sustained reservoirs of fuels,accretion of baryon matter gradually become dominant to increase the BH mass by a factor of～103within subsequent several Salpeter times [see equation(2)]at the Eddington accretion rate.It is this subsequent accretion of baryon matter that eventually as-sembles most of the SMBH mass,consistent with observa-tions that the BH mass densities in nearby galactic bulges and in active SMBHs are comparable to the mass density accreted during the optically bright/obscured QSO phase (e.g.,Yu&Tremaine2002;Fabian2004;Haehnelt2004). Based on the explorations in Figure1,it would not matter that much as for the exact moment when the Phase II Ed-dington baryon accretion sets in.In fact,it may begin at any moment(either before or after t1).However,the Phase I SIDM accretion can produce a massive enough seed BH for the Phase II baryon accretion.

Figure1illustrates a black hole growth history includ-ing the two phases.The Phase I SIDM accretion increases the black hole mass substantially,and then the Phase II baryon accretion enhance the enlarged seed black hole fur-ther.The accretion due to SIDM particles after t1peters out rapidly into the di?usively limited regime.

2.3Model applications to high-z quasars

Figure2shows the mass range of forming high?z SMBHs, where we take on three observed SDSS high?z quasars with reported SMBH masses(Fan et al.2001,2003;Willott et al. 2003;Vestergaard2004):J114816.64+525150.3(z=6.43, M BH～3×109M⊙),J103027.10+052455.0(z=6.28, M BH～3.6×109M⊙),and J130608.26+035626.3(z=5.99, M BH～2.4×109M⊙)distinguished by dashed,dotted,and dash-dotted curves,respectively.Based on our model sce-nario,we trace BH masses back to higher z,assuming a sustained baryon Eddington accretion and three di?erent ra-diative e?ciencies?=0.1,0.15,0.2to compute the required minimum BH mass of the phase-I accretion as a function of redshift z.We plot the actual?nal BH mass M BH,t

1

of the phase-I accretion(light solid curves in Fig.2)in DM halos with4-σand5-σ?uctuations at a given z,using equation (4)and C s given by equation(5).As an exploration,we also calculate M BH,t

1

with C s～100km s?1yet with a smaller speci?c cross sectionσ0=0.02cm2g?1shown by the heavy dashed line in Fig.2.

As shown in Fig.2,our model(i.e.,light solid curves) can readily account for the three high?z SMBHs for?=0.1 and0.15,without invoking either super-Eddington baryon accretion or numerous BH merging processes.For a higher ?=0.2,it is unnatural to explain the presence of high-z SMBHs with4-σ?uctuations.For5?σ?uctuations,the

Two-Phase Formation of SMBHs5

Figure2.Three sets of dashed,dotted,dash-dotted curves with

radiative e?ciency?=0.2,0.15,0.1respectively are the required

minimum BH masses for10

cretion,with distinct line types referring to three reported high?z

quasars(SMBHs).The heavy solid lines show the virialized dark

matter halo mass M vir(z)with4σand5σ?uctuations at di?erent

z values.The light solid lines show the secondary seed BH mass

M BH,t

1created by the?rst rapid accretion phase at various z for

C s andσ0according to equations(5)and(6).The heavy dashed

line shows M BH,t

1with a constant sound speed C s=100km s?1

and a smaller cross sectionσ0=0.02cm2g?1.

mass requirement can be just met.It is clear that only un-der rare circumstances,extremely massive SIDM halos may give birth to seed BHs with required Phase-I masses in our scenario.

There are fundamental di?erences between the two main accretion phases,among which the most important one is that baryon accretion produces strong detectable feedback (e.g.,intense radiations and out?ows or jets etc)into sur-roundings.Reviving some ideas of Silk&Rees(1998),King (2003)found a simple yet remarkable association between accretion and out?ows which plausibly leads to the local M BH?σb relation(e.g.,Tremaine et al.2002)at the termi-nation of accreting a SMBH.The phase-II accretion in our scenario involves processes largely similar to those outlined by King(2003),including Eddington luminosity,baryon ac-cretion,intense out?ows,and so forth;an M BH?σb relation (see equation15of King2003)can be established as the baryon accretion goes on and the SMBH is continuously as-sembled.As described,such an M BH?σb relation may not emerge before ending the phase-I accretion.To be speci?c, we combine equations(14)and(7)of King(2003)as

M BH=κf gσ4b

σb 2?1.5×108σ4b200(v m/σb)2M⊙,(8)

whereκis the electron scattering opacity,f g?0.16is the gas fraction,v m is the mass shell velocity driven by out?ows andσb200is the bulge stellar velocity dispersionσb in unit of 200km s?1.Potentially,it would also be very important to incorporate e?ects of magnetic?eld in the baryon accretion phase(Yu&Lou2005;Wang&Lou2005in preparation). During the accretion phase,v m<σb at?rst and gradu-ally v m approaches～σb as the accretion diminishes;mean-while,the M BH?σb relation appears.During the QSO/AGN phase,BH masses may drop below the M BHu?σb relation for normal galaxies,as indicated by some results of narrow-line Seyfert1galaxies(e.g.,Bian&Zhao2004;Grupe&Mathur 2004).Further observations and data analysis of BH masses versus velocity dispersions are needed to explore these as-pects.

On the basis of our scenario,we may accommodate the high?z and low?z quasars in a uni?ed framework:There ex-ists a distribution of baryon accretion rates onto secondary seed BHs of～106M⊙produced between z～20?15by rapidly accreting SIDMs during Phase I.Given speci?c sit-uations,such secondary seed BHs may continue to accrete baryon matter with high rates until they run out of fuels or the accretion rate becomes considerably lower than the Eddington limit;this then gives rise to high?z SMBHs of ～108?9M⊙.Those secondary seed BHs with lower rates of accreting baryon matter will evolve into SMBHs much later as already discussed above.Given the paucity of high?z quasars detected so far,our scenario implies that BH sys-tems with high accretion rates should be extremely rare.

3SUMMARY AND DISCUSSION

We summarize the two-phase accretion model of SMBH for-mation in the early Universe below and discuss a few obser-vational implications.

Phase I involves a rapid quasi-spherical accretion of mainly SIDM particles mixed with a small fraction of baryon matter onto an initial seed BH created by a Pop III star. Such a BH grows rapidly to～106M⊙within a fairly short timescale of～105yr.

Phase II involves an accretion of primarily baryon mat-ter(initially mixed with SIDM particles)at the Eddington limit to accumulate most of the BH mass.Since the BH mass is su?ciently massive at the beginning of this phase II,it takes only several Salpeter e?folding times to grow a BH mass of～109M⊙according to the estimate of an exponential growth by equation(2).

The transition from Phase I to the much slower dif-fusion limited accretion of SIDM particles goes on concur-rently with the gradual dominance of baryon accretion at the Eddington limit in Phase II.

The Phase-I accretion of SIDMs is crucial to produce a su?ciently massive secondary seed BH for further growth by accreting baryon matter.In this scenario,the reported high?z SMBHs of～109M⊙can be produced,without in-voking the hypotheses of either super-Eddington baryon ac-cretion or extremely frequent BH merging processes.Based on a sample of six quasars with z>5.7observed by the SDSS,Fan et al.(2003)estimated a comoving density of such luminous quasars at z～6and found these quasars showing a～5σpeak in the density?eld.This inference may be readily accounted for by our cosmological model re-sults shown in Fig.2.We attempt to combine the models of quasi-spherical and quasi-steady SIDM accretion with a baryon accretion to give more plausible schemes of accretion leading to early formation of SMBHs with masses～109M⊙at high redshifts of z>～5?6.

We now elaborate on consequences of this two-phase scenario.If most SMBHs form by this two-phase accretion with fairly rare BH mergers,the currently observed upper

6Hu,Shen,Lou,Zhang

mass limit for a SMBH<～1010M⊙constrains the combina-tion of the speci?c SIDM cross sectionσ0and the e?ective baryon accretion time t2(cf.equation4),such that

σ0

100km s?1

4exp(t2/t Sal)<～60,(9)

where the Eddington luminosity is adopted.3For SIDM ha-los formed at low z,they may become massive enough to make the virialized velocity dispersion or‘sound speed’of the order of C s～100km s?1.So the baryon accretion time t2cannot exceed～5t Sal for low?z QSOs.For typi-cal parameters of?=0.1and L=L Edd,it would require a t2<2×108yr,consistent with the observational QSO lifetime of t Q?107?108yr estimated for low?z QSO populations(e.g.,Yu&Tremaine2002;McLure&Dunlop 2004).

If we take on reference values of equation(4)for the particular z=6.43SMBH withσ0=1cm2g?1and C s=30km s?1,it would have accreted baryon matter over～8t Sal(～3×108yr)for?=0.1and L=L Edd, in the absence of accretions at super-Eddington rates and of BH merging processes.Such a Phase II accretion time is much longer than the low?z QSO lifetime,but accounts for only～1/3of ages for these quasars.We speculate that high?z quasars may have longer e?ective accretion times than low?z quasars as the former might have more abun-dant fuel supplies.The plausible physical reasons include: (1)gas materials in galaxies have been much consumed by star formation activities in the low?z quasars;(2)interac-tions among galaxies might have been more frequent in the early Universe,that may trigger high accretion activities.In-su?cient or interrupted baryon accretion would very likely leave behind less massive SMBHs with masses well below the M BH?σb relation curve.

We note that the Phase I accretion will not a?ect ob-servations at low?z galaxies.First,the Phase I SIDM Bondi accretion is more dominant than the Eddington accretion of baryons only for very early(z>10)SIDM halos,as such ha-los tend to have a high‘sound speed’C s(cf.equations3?5). Secondly,the phase-I accretion might be severely limited by the inner density pro?le of the SIDM halo.We have used a SIS mass density pro?leρ∝r?2.For a self-similar accretion at a given time t,one would haveρ∝r?3/2(e.g.,Jing& Suto2000;Lou&Shen2004;Bian&Lou2005;Yu&Lou 2005).Numerical N-body simulations(e.g.,Navarro et al. 1997)indicate an innerρ∝r?1,i.e.the NFW pro?le(see discussions of Ostriker2000).For the more inclusive family of the hypervirial models,we haveρ∝r?(2?p)with the in-dex p falling in the range of0

A shallower pro?le may lead to a less e?cient accretion of SIDMs(e.g.,Hennawi&Ostriker2002).Observations?nd that the inner density pro?les(e.g.,aρ∝r?0.5)of dark matter halo of nearby galaxies are shallower than both the SIS and NFW density pro?les,and therefore the resulting secondary seed BH mass M BH,t

1

may be expected to be smaller.

3Should we take into account of BH merging processes by a sig-ni?cant mass ampli?cation factor of～104(e.g.,Yoo&Miralda-Escud′e2004),then this upper limit would be reduced by a factor of～104accordingly.

Speci?c to our Milky Way galaxy,the central black hole has been inferred to possess a mass of～4×106M⊙by stellar dynamic diagnostics.For such a less massive SMBH,there are many possible ways to assemble such a BH and it is not necessary to invoke our two-phase scenario.

Finally,we note possible observational signatures and consequences of the two-phase scenario envisaged in this pa-per.If some large regions in the early Universe were some-how distributed with considerable less baryon matter(e.g., the gravitational potential well of the halo may not be deep enough to bind the high speed baryons due to supernova or hypernova feedbacks),then we may?nd some DM halos with BHs at their centres but without forming host galaxies. In other words,these BHs grow entirely by Phase I SIDM quasi-spherical Bondi accretions ended with di?usively lim-ited phase,and the baryon accretion has never occurred in a signi?cant manner.Such unsual systems of DM halo-BHs might be revealed directly by chance through gravitational lensing e?ects.

Very recently,Magain et al.(2005)reported the discov-ery of a bright quasar HE0450-2958yet without a massive host galaxy.The black hole of HE0450-2958may well be em-bedded within a dark matter halo(‘dark galaxy’),constitut-ing a DM halo-BH system.Ambient interactions with such a massive object could more readily explain the ring-like star-burst in the neighbouring galaxy as well as the capture of gas materials,leading to the eventual onset of quasar ac-tivities we observe.Our model can readily account for such kind of phenomena.The phase I SIDM accretion in the dark matter halo produced a seed black hole with a mass range of～106?107M⊙,but the phase II baryon accretion has never occurred due to the absence of a host baryon galaxy. As such a massive seed black hole travelled across a neigh-bouring disc galaxy,it began to induce baryon accretion activities violently to give rise to a bright quasar.We will further develop models on the basis of such a scenario in a separate paper.

Another interesting piece of observational evidence comes from the galaxy NGC4395(Peterson et al.2005).

A very‘small’low-luminosity SMBH(～3×105M⊙)re-sides in the bulgeless galaxy NGC4395,implying that the stellar bulge is not a necessary prerequisite for a black hole in the nucleus of a galaxy.Our model can provide a plausible explanation in the sense that a relatively small SMBH is the product of the phase I SIDM accretion,while the phase II baryon accretion at the Eddington rate is almost absent in a bulgeless galaxy(of course,a very low rate baryon accretion might take place).

ACKNOWLEDGMENTS

For JH and YS,this research was inspired by Black Hole Accretion lectures by J.F.Lu in December2004.For YQL, this research was supported in part by the ASCI Cen-ter for Astrophysical Thermonuclear Flashes at the Univ. Chicago under Department of Energy contract B341495, by the Special Funds for Major State Basic Science Re-search Projects of China,by the THCA,by the Collabora-tive Research Fund from the National Natural Science Foun-dation of China(NSFC)for Young Outstanding Overseas Chinese Scholars(NSFC10028306)at the National Astro-

Two-Phase Formation of SMBHs7

nomical Observatories of China,Chinese Academy of Sci-ences,by NSFC grants10373009and10533020(YQL)at Tsinghua University,and by the Yangtze Endowment from the Ministry of Education at Tsinghua University.The hos-pitality and support of the Mullard Space Science Labo-ratory at University College London,U.K.,of School of Physics and Astronomy,University of St Andrews,Scotland, U.K.,and of Centre de Physique des Particules de Marseille (CPPM/IN2P3/CNRS)et Universit′e de la M′e diterran′e e Aix-Marseille II,France are also gratefully acknowledged. A?liated institutions of YQL share this contribution.SNZ acknowledges support by NSFC grant10233030and by NASA’s Marshall Space Flight Center and through NASA’s Long Term Space Astrophysics Program.

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