Black hole formation 嶺重 慎 (京大・基礎研) 1.Astrophysical black holes 2.Formation of black holes 3.Evolution of black holes Ref: Proc. Carnegie sympo. on coevolution of black holes and galaxies (2003) http://www.ociw.edu/ociw/symposia/series/symposium1/proceedings.html
Introduction: Astrophysical BH formation z～20 : first objects (?) z～6 : first quasar (observed) z～2 : peak quasar density z = 0 : many, many BHs BLACK HOLE Key words: • Co-evolution (with galaxies) • Feedback (to form structure)
Astrophysical black holes: Observational facts Key questions: • What kinds of astrophysical black holes are there? • What are recent topics about black holes? • Do they share common properties or not? • What is known about galaxy-BH connection?
108 106 104 102 100 Black Hole Candidates before 〜1995 after〜1995 galactic nuclei (quasars) mass (solar mass) (NLS1s) SgrA* (unknown populations??) intermediate-mass BHs (ULXs) gamma-ray bursts (?) stellar-mass BHs Our Galaxy nearby galaxies distant galaxies early universe BHs can be found in many places and seem to have had great influence on the evolution of the universe. (c) K. Makishima
Black-Hole Objects (1)Stellar-mass BHs (in binaries) • Constitute X-ray binaries with normal companions. • ～10 stellar-mass BHs in our Galaxy.(Brown & Bethe 1994) • Binary separation 7-9
Two spectral states (Galactic BH candidates) soft logfν hard log hν hard (low) state power-law,fν ∝ν-α with α～0.7 cutoff at ～102keV soft (high) state blackbody spec. withkT～1keV
X-ray variability (Cyg X-1) in low/hard stateNegoro (1995) X-ray light curve (left) and PSD (below) log PSD 1/f1.1 1/f1.5 log f
BH mass estimation: Stellar-mass BHs in binaries Observe orbital motion of optical companion M1 = compact star mass, M2 = companion mass, i = inclination, P = period observable M1 lower limit radial velocity Case of GRS 1915+105 (Greiner et al. 2001) orbital phase
Black-Hole Objects (2)Massive BHs in galactic nuclei • Supermassive BHs seem to lie at the center of (active) galaxies. HST image of gas (dust) disk surrounding a central black hole. • Occasionally associated with jet(s).
Spectra of Sy 1 typeAGNs logνfν BBB power law + exp. cutoff log hν Big Blue Bump (UV) blackbody with Teff～ 105K (10 eV) power law (radio ～γ) fν∝ν-α with α～ 0.7 cutoff at ～100-200keV How do we understand such SED by disk models?
BH mass estimation: Massive BHs in galactic nuclei • Stellar kinematics • Detect proper motions of individual stars (Galactic center) • Stellar absorption-line kinematics (galaxies with distances, d < 20 Mpc) • Optical emission-line gas • Distances of up to d < 100 Mpc, BH mass of MBH>107Msun • H2O Masers • Line width & radius → MBH～(1-40)×106Msun; up to d～70 Mpc. • Reverberation (echo) mapping • Cont.-line time delay, Δt → rBLR =cΔt (= distance to BLR) • BLR line width ～ (GMBH/rBLR)1/2 → MBH • X-ray variability scaling(timescale ∝ MBH) ～
BH-host galaxy correlations MBH – Mbulge relations (normal gal.) MBH /Mbulge 0.005 (Kormendy & Richstone 1995;Magorrian et al. 1998…) MBH /Mbulge 0.001 (Kormendy 2000; Merritt & Ferrarese 2001) MBHMbulge1.53; MBH /Mbulge 0.005 (MV-22)～0.0005 (MV-18) (Laor 2001) MBH – Mbulge relations (AGN) MBH /Mbulge 0.005 in QSOs (Laor 1998) MBH /Mbulge 0.0005 in Sy 1s (Wandel 1999; Gebhardt et al. 2000; Nelson 2000) MBH – σ(velocity dispersion) relation MBH, =4.72 (Ferrarese & Merritt 2000; Merrit & Ferrarese 2000) MBH, =3.75 (Gebhardt et al. 2000)
うめ BH to bulge mass ratio Magorrian (1998) MBH[M ] Seyfert Merritt & Ferrarese (2001)
Other BH-host galaxy correlations • Cusp slope – absolute magnitude(Gebhardt et al. 2000) • Sersic index - vel. dispersion - BH mass(Erwin et al. 2003) • Bulge light profile ∝r1/n; n = Sersic index cusp density slope Brighter galaxies have flatter density slopes absolute magnitude
Narrow-Line Seyfert 1 galaxies (NLS1s) Boller et al. (NewA 44, 2000) • What are NLS1s? • Narrow “broad lines” (< 2000kms-1) • Sy 1 type X-ray features • Extremesoft excess • Extremevariability • Spectral features resemble GBHCs’ • Seem to contain less massive BHs • High Tbb(∝MBH-1/4) ⇒ large soft excess • Small (GMBH/RBLR)1/2⇒ narrow line width
Intermediate-Mass Black Holes (IMBHs) van der Marel (Carnegie sympo., 2003) • Ultra Luminous X-ray sources (ULXs) • Successively discovered with X-rays in nearby galaxies • Luminosity isLX > 1039 erg s-1> (LEof a neutron star) • QSS (=quasi-soft source) may be low luminosity IMBHs (?) (Kong & Di Stefano 2003) • IMBHs through grav. microlensing • No IMBH MACHOs in LMC. • Some of Galactic bulge MACHOs could be IMBHs, since microlens timescale, ～ 130(M/Msun)1/2 d, exceeds 130d. • IMBH in globular clusters(?) • Still controversial. Needs confirmation.
(c) A. Kubota X-ray spectra of ULXs • MCD (multi-color disk) type • PL (power-law) type • Transition between MCD⇔PL Alike Galactic BHCs IC342 galaxy
Black hole accretion in GRBs(?)(Narayan, Paczynski & Piran 1992; Narayan, Piran & Kumar 2001) • Central engine of GRBs? • NS-NS/BH-NS merger • BH-He core merger • failed supernovae (collapsar) • magnetar • Two basic timescales: • dynamical t.s. = (rS3/GM)1/2 < 0.1 sec • viscoust.s. = (r/H)2(rtorus3/GM)1/2～1-100 sec massive torus around a BH: Mtorus=0.01～1 Msun MBH= 3～10(?) Msun
Primordial black holes (PBHs) (Carr 2003, astro-ph/0310838) Primordial density perturbations may lead to grav. collapse (Zel’dovich & Novikov 1967; Hawking 1971) Small BHs should have evaporated already Constraints for β(fraction of regions of mass M which collapse) ⇒ ΩPBH < 1 γ emission
2. Formation of BHs:Stellar-mass to massive BHs Key questions: • How do massive stars end their lives? • How can supermassive BHs be formed, Collapse or mergers? • How are quasar formation related to galaxy formation? Which are the first objects, stars (galaxies) or BHs?
End product of stars • Present-day stars • Massive stars shed most of their mass through wind. • Massive stars leave compact remnants with M < 15 Msun • The minimum initial mass to produce a BH is 20-25 Msun • Metal-free (Pop. III) stars • Typical mass is ～ 100 Msun • Stars with M < 140 Msun probably evolve into BHs. • Stars with M = 140～260 Msun leaves nothing (pair instability). • Stars with M > 260 Msun directly collapse to IMBHs.
Star evolution: remnant mass Heger & Woosely (ApJ 591, 288, 2003) 1 3 10 30 100 300 remnant mass (Msun) WD NS BH BH initial mass (Msun) 1 9 28 140 260
How massive single stars end their life? Heger et al. (ApJ 591, 288, 2003) Fate of a massive star is governed by (1) its mass, (2) chemical composition, (3) mass loss. metal poor solar initial mass (Msun) 9 25 40 60 100 140 260
Rees diagram - how to make a massive BHs?(Rees ARA&A 22, 471, 1984) collapse of a massive object or mergers in a cluster
(a) No spin, with UV (b) With spin (λ=0.05) & UV (c) No spin, no UV Direct collapse of a gas cloud Bromm & Loeb (ApJ 596, 34, 2003) Basic scenario: a metal-free primordial clouds of 108Msun → condensations of ～ 5×106Msun → collapse to a BH A cloud avoids fragmentation into stars by background UV radiation.
うめ General Relativistic Instability Baumgarte & Shapiro 1999, ApJ, 526, 941 Rapidly rotating supermassive star in equilibrium critical point stable unstable rigid rotation mass-shedding limit unstable at massive objects → Prad > Pgas → γ～4/3 → instability GR: unstable even if γ> 4/3
うめ Dynamical Collapse (Full General Relativity) (Shibata & Shapiro 2002, ApJ, 572, L39) Dynamical collapse Apparent Horizon Kerr parameter 0.75 (Kerr BH) ～
BH formation in dense clusters (van der Marel 2003) • Basic idea • Self-gravity gives negative heat capacity → gravo-thermal catastrophe → formation of high density core → BH • Runaway merging occurs in dense clusters (ρ> 106Msun pc-3) of many stars (N > 107) (Lee 1987, Quinlan & Shapiro 1990).→IMBH → (accretion) →SMBH • Problem • Formation of an BH does not occur in clusters with N <107 because binary heating halts core collapse (Hut et al. 1992). (Three-body interactions between binaries and single stars add energy to the cluster.)
Conditions for runaway collapse (Rasio et al. Carnegie sympo. 2003) Solution: mass segregation Heaviest starts undergo core collapse independently of the other cluster stars → runaway collapse → formation of an IMBH ifcore collapse time< main-sequence lifetime (Pontegies Zwart & McMillan 2002).
From IMBHs to SMBHs (van der Marel 2003) • Merging • Pop. III stars → IMBHs → IMBHs sink to the center of proto-galaxies → SMBH (Schneider et al. 2002; Velonteri et al. 2003). • SMBHs that grow through mergers generally have little spin, difficult to power radio jets (Hughes & Blandford 2003). • Accretion • Collapse of a proto-galaxy onto a BH (Adams et al. 2001) • Accretion of material shed by stars (Murphy et al. 1991). • Feedback from energy release near the center may limit growth of the BH and of galaxy (Haehnelt et al. 1998; Silk & Rees 1998). • Feedback from star formation may also (Burkert & Silk 2001).
3. Evolution of BHs: Quasar LFs & BH mass density Key questions: • What do we learn from the observed QSO luminosity functions (LFs)? • What do we know about current BH density? Any useful constraints on BH accretion? • How can we model QSO formation scenarios?
Quasar (BH) evolution (Rees 1990) Quasars co-moving density reached its maximum at z ～ 2.
Evolution of Quasar Luminosity Functions (LFs) QSO LFs from 2dF QSO redshift survey (0<z<2.3; Boyle et al. 2000) High z QSO LFs from SDSS (z~4.3; Fan et al. 2001)
Cosmological evolution of AGN spatial density Ueda et al. (ApJ, 2003) Number density of higher luminosity AGNs peaked at higher redshifts. Similar evolutions are found for star-formation rates.
BH mass density (1).From quasar luminosity func. Yu & Tremaine (MN 335, 965, 2002) • 2dF redshift survey(Boyle et al. 2000) ρBH(z)～∫(dt/dz)dz∫Lbol (1-ε)/(εc2) Ψ(L,z)dL ρBH(0)～ (2-4)×105 h0.652 Msun Mpc-3(for ε～ 0.1) Hosokawa (2002)
Obscured BH accretion (Haehnelt 2003) If some fraction of AGN are obscured, energy conversion efficiency is smaller ⇒ BH density should be higher.
BH mass density (2).From galaxy velocity-disp. Yu & Tremaine (MN 335, 965, 2002) • Sloan Digital Sky Survey σ= velocity dispersion (early type gal.) MBH～ (1.5±0.2)×108 Msun (σ/200 km s-1)4±0.3 ρBH～ (2.5±0.4)×105 h0.652 Msun Mpc-3 • Consistent with the previous estimates, if ε～ 0.2 (Soltan 1982; Choksi & Turner 1992; Small & Blandford 1992; …)
Theoretical models of quasar lum. func.(Haehnelt et al. 1998; Haiman & Loeb 1998) • Model assumptions (previous models): • Press-Schechter formalism Mhalo distribution • Black holes immediately merge when two halos merge. • Empirical Mhalo- MBH relation MBH [ratio=parameter] • Simple light variation: L = LE exp(-t/te) [te =parameter] • Simple spectrum LFs at optical/X-rays • Our model(Hosokawa et al. 2001, PASJ 53, 861) • Realistic quasar model spectra + absorption • Disk luminosities do not depend onMBH, but spectra do, since the BBB peak frequency,νpeak∝ MBH-1/4
Calculated quasar LFs at z～3Hosokawa et al.(PASJ 53, 861, 2001) • X-ray & B band LFs are well reproduced simultaneously. • IR band LFs are sensitive to spectral shape (thus MBH). Data from: X: Miyaji et al. (1998); B: Pei (1995)
Which model is correct?Hosokawa(ApJ 576, 75, 2002) Model A: MBH∝ Mhalo5/3 (Haehnelt et al. 1998) Model B: MBH∝ Mhalo (Haiman & Loeb 1998) life-time MBH /Mhalo Model A 107-8 yr～10-4.5 Model B 105-6 yr ～10-3.5 • Model B over-predicts current BH mass density. • Quasar life-time estimates by Yu & Tremaine also support Model A. Mean life time ～ (3-13)×107 yr present-day BH mass func. model B model A log(dΨ/dlog MBH) log(MBH/Msun)
Silk-Rees picture for quasar-galaxy connection Silk & Rees (A&A 331, L1, 1998) • Which are firstly formed, stars or BHs? • If BHs are first, significant effects from BHs to star formation. (quasar peak at z >2, while galaxy formation at z～1.5). • Then, there exists maximum BH mass • Maximum feeding rate towards the center M～ρ(σtff)3/tff =σ3/G • A quasar expels all this gas from the galactic potential well on a dynamical timescale ifMσ2<L～ LEdd no further BH growth • This condition gives maximum BH mass; MBH <σ5κ/G2c ～ 8×108(σ/500 km s-1)5Msun . .
Radiation drag model for quasar BH formation Umemura (ApJ 520, L29, 2001) • mass accretion rate (τ=1 limit) • accretion time • radiation energy from stars • massive dark object ～ ( = 0.007 : H He nuclear fusion energy conversion efficiency) ～ ～
Semi-analytical model (1)Kauffmann & Haehnelt (MN 311, 576, 2000) MBH – sigma relation Merging trees of dark halos + gas cooling, star formation, SN, feedback, … SMBHs form from cold gas in major mergers.
Quasar evolution and galaxy evolution Franceschini et al. (MN 310, L5, 1999) Quasar density vs. star-formation rate (SFR) • Opt-UV observations of field galaxies star-formation rate (SFR) • Same but for field elliptical galaxies star-formation rate (SFR) • ROSAT (soft-X) survey 0.5-2 keV vol. emissivityofhigh luminosity quasars z
Semi-analytical model (2) EvolutionKauffmann & Haehnelt (MN 311, 576, 2000) Rapid declne in quasar # density from z～2 to z=0 is due to (1) less frequent mergers, (2) depletion of cold (accretion) gas, and (3) incrase in accretion timescale. z z quasar density evolution SFR evolution
Semi-analytical model (3) Assemby historyHaehnelt (2003) BH growth: Build up starts at z～6-8 and grow to ～109 Msun Occasionally super-critical accretion appears. bright bulge faint bulge
How can we make a massive BH at z ～5.8Haiman & Loeb (ApJ 552, 459, 2001) SDSS 1044-0125 at z～5.80(Fan et al. 2000) MBH～3.4×109Msun • Salpeter timescale (e-fold time): Mc2/LEdd～4×107yr • Growth time for a 10MsunBH to 3.4×109Msun via accretion ～ 7×108(ε/0.1)η-1 yr ～ age of universe at z=5.8 • Lensing? Super-critical accretion?? required L=LEdd . minimum η≡ L/LEdd vs.ε≡L/Mc2