Black hole formation 1 Astrophysical black holes 2

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/symposium 1/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 Key words: n Co-evolution (with galaxies) Feedback (to form structure) n BLACK HOLE

1. Astrophysical black holes: Observational facts Key questions: n What kinds of astrophysical black holes are there? n What are recent topics about black holes? n Do they share common properties or not? n What is known about galaxy-BH connection?

Black Hole Candidates before 〜 1995 after〜 1995 (quasars) 108 mass (solar mass) galactic nuclei 106 (NLS 1 s) Sgr A* (unknown populations? ? ) 104 intermediate-mass BHs (ULXs) 102 100 stellar-mass BHs Our Galaxy nearby galaxies gamma-ray bursts (? ) 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) n n Constitute X-ray binaries with normal companions. 7 -9 ～ 10 stellar-mass BHs in our Galaxy. (Brown & Bethe 1994) n Binary separation

Two spectral states (Galactic BH candidates) log fν soft hard log hν soft (high) state blackbody spec. with k. T ～ 1 ke. V hard (low) state power-law, fν ∝ν-α with α～ 0. 7 cutoff at ～ 102 ke. V

X-ray variability (Cyg X-1) in low/hard state Negoro (1995) X-ray light curve (left) and PSD (below) log PSD 1/f 1. 1 1/f 1. 5 log f

BH mass estimation: Stellar-mass BHs in binaries Observe orbital motion of optical companion M 1 = compact star mass, M 2 = companion mass, i = inclination, P = period observable M 1 lower limit radial velocity Case of GRS 1915+105 (Greiner et al. 2001) orbital phase

Black-Hole Objects (2) Massive BHs in galactic nuclei n Supermassive BHs seem to lie at the center of (active) galaxies. HST image of gas (dust) disk surrounding a central black hole. n Occasionally associated with jet(s).

Spectra of Sy 1 type AGNs logνfν BBB power law + exp. cutoff log hν Big Blue Bump (UV) blackbody with Teff～ 105 K (10 e. V) power law (radio ～γ) fν∝ν-α with α～ 0. 7 cutoff at ～ 100 -200 ke. V How do we understand such SED by disk models?

BH mass estimation: Massive BHs in galactic nuclei n Stellar kinematics n n n Optical emission-line gas n n Line width & radius → MBH～ (1 -40)× 106 Msun; up to d ～ 70 Mpc. Reverberation (echo) mapping n n n Distances of up to d < 100 Mpc, BH mass of MBH ～ > 107 Msun H 2 O Masers n n Detect proper motions of individual stars (Galactic center) Stellar absorption-line kinematics (galaxies with distances, d < 20 Mpc) Cont. -line time delay, Δt → r. BLR = cΔt (= distance to BLR) BLR line width ～ (GMBH/r. BLR)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) 　 MBH Mbulge 1. 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 1 s (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)

MBH[M ] BH to bulge mass ratio Magorrian (1998) Seyfert Merritt & Ferrarese (2001) うめ

Other BH-host galaxy correlations n Cusp slope – absolute magnitude (Gebhardt et al. 2000) cusp density slope Brighter galaxies have flatter density slopes absolute magnitude n Sersic index - vel. dispersion - BH mass (Erwin et al. 2003) n Bulge light profile ∝r 1/n; n = Sersic index

Narrow-Line Seyfert 1 galaxies (NLS 1 s) Boller et al. (New. A 44, 2000) n What are NLS 1 s? n n n Narrow “broad lines” (< 2000 km s-1) Sy 1 type X-ray features Extreme soft excess Extreme variability Spectral features resemble GBHCs’ n Seem to contain less massive BHs High Tbb (∝MBH-1/4) ⇒ large soft excess n Small (GMBH/RBLR)1/2 ⇒ narrow line width n

Intermediate-Mass Black Holes (IMBHs) van der Marel (Carnegie sympo. , 2003) n Ultra Luminous X-ray sources (ULXs) n n n Successively discovered with X-rays in nearby galaxies Luminosity is LX > 1039 erg s-1 > (LE of a neutron star) QSS (=quasi-soft source) may be low luminosity IMBHs (? ) (Kong & Di Stefano 2003) n IMBHs through grav. microlensing n n n No IMBH MACHOs in LMC. Some of Galactic bulge MACHOs could be IMBHs, since microlens timescale, ～ 130 (M/Msun)1/2 d, exceeds 130 d. IMBH in globular clusters(? ) n 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 IC 342 galaxy

Black hole accretion in GRBs(? ) (Narayan, Paczynski & Piran 1992; Narayan, Piran & Kumar 2001) n Central engine of GRBs? 　 n NS-NS/BH-NS merger n BH-He core merger n n n failed supernovae (collapsar) massive torus around a BH: Mtorus=0. 01～ 1 Msun MBH= 3～ 10(? ) Msun magnetar Two basic timescales: n n dynamical t. s. = (r. S 3/GM)1/2 < 0. 1 sec viscous t. s. = (r/H)2(rtorus 3/GM)1/2 ～ 1 -100 sec

Primordial black holes (PBHs) (Carr 2003, astroph/0310838) Primordial density perturbations may lead to grav. collapse (Zel’dovich & Novikov 1967; Hawking 1971) Small BHs should have evaporated already ΩPBH < 1 Constraints for β (fraction of regions of mass M which collapse) ⇒ γ emission

2. Formation of BHs: 　　　 Stellar-mass to massive BHs Key questions: n How do massive stars end their lives? n How can supermassive BHs be formed, 　　　　　 Collapse or mergers? n How are quasar formation related to galaxy 　 formation? Which are the first objects, 　　　 stars (galaxies) or BHs?

End product of stars n Present-day stars n n 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 n n 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 (Msun) 3 10 30 100 300 Heger & Woosely (Ap. J 591, 288, 2003) 1 WD NS 1 9 BH 28 BH 140 260 initial mass (Msun)

How massive single stars end their life? Heger et al. (Ap. J 591, 288, 2003) solar Fate of a massive star is governed by 　(1) its mass, 　(2) chemical 　　　 metal poor composition, 　(3) mass loss. 9 25 40 60 100 140 260 initial mass (Msun)

Rees diagram how to make a massive BHs? (Rees ARA&A 22, 471, 1984) collapse of a massive object or mergers in a cluster

Direct collapse of a gas cloud Bromm & Loeb (Ap. J 596, 34, 2003) Basic scenario: a metal-free primordial clouds of 108 Msun → condensations of ～ 5× 106 Msun → collapse to a BH A cloud avoids fragmentation into stars by background UV radiation. (a) No spin, with UV (b) With spin (λ=0. 05) & UV (c) No spin, no UV

General Relativistic Instability Baumgarte & Shapiro 1999, Ap. J, 526, 941 stable critical point Rapidly rotating supermassive star in equilibrium 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, Ap. J, 572, L 39) Dynamical collapse Apparent Horizon ～ 0. 75 (Kerr BH) Kerr parameter うめ

BH formation in dense clusters (van der Marel 2003) n Basic idea n n n Self-gravity gives negative heat capacity → gravo-thermal catastrophe → formation of high density core → BH Runaway merging occurs in dense clusters (ρ> 106 Msun pc-3) of many stars (N > 107) (Lee 1987, Quinlan & Shapiro 1990). 　 → IMBH → (accretion) → SMBH Problem n 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 　　 　if core collapse time　　　　　　 < main-sequence lifetime (Pontegies Zwart & Mc. Millan 2002).

From IMBHs to SMBHs (van der Marel 2003) n Merging n n n Pop. III stars → 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 n n 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).

Inter-mediate mass BHs to Supermassive BHs (coutesy of T. Tsuru)

3. Evolution of BHs: Quasar LFs & BH mass density Key questions: n What do we learn from the observed 　　　　　　　 QSO luminosity functions (LFs)? n What do we know about current BH density? 　 Any useful constraints on BH accretion? n 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 2 d. F 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. (Ap. J, 2003) Number density of higher luminosity AGNs peaked at higher redshifts. Similar evolutions are found for starformation rates.

BH mass density (1). From quasar luminosity func. Yu & Tremaine (MN 335, 965, 2002) n 2 d. F redshift survey (Boyle et al. 2000) ρBH(z) ～∫(dt/dz)dz∫Lbol (1 -ε)/(εc 2) Ψ(L, z)d. L ρBH(0)～ (2 -4)× 105 h 0. 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) n 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 h 0. 652 Msun Mpc-3 n 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) n Model assumptions (previous models): n n n 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 n Disk luminosities do not depend on MBH, but spectra do, 　　　 since the BBB peak frequency, νpeak∝ MBH-1/4 n

Calculated quasar LFs at z～ 3 　　　　　 Hosoka wa et al. (PASJ 53, 861, 2001) n n 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 (Ap. J 576, 75, 2002) Model A: MBH∝ Mhalo 5/3 (Haehnelt et al. 1998) mo Model B: MBH∝ Mhalo (Haiman & Loeb n n 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. log(dΨ/dlog MBH) 1998) Quasar life-time estimates by Yu & Tremaine also support Model A. 　　　 mo de del present-day BH mass func. l. B A log(MBH/Msun)

Silk-Rees picture for quasargalaxy connection Silk & Rees (A&A 331, L 1, 1998) n Which are firstly formed, stars or BHs? n n 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 n n n . 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 if Mσ2 < L～ LEdd no further BH growth This condition gives maximum BH mass; MBH < σ5κ/G 2 c ～ 8× 108 (σ/500 km s-1)5 Msun

Radiation drag model for quasar BH formation n mass accretion rate (τ=1 limit) n accretion time n radiation energy from stars Umemura (Ap. J 520, L 29, 2001) ～ ( = 0. 007 : H He nuclear fusion energy conversion efficiency) n massive dark object ～ ～

Semi-analytical model (1) Kauffmann & Haehnelt (MN 311, 576, 2000) Merging trees of dark halos + gas cooling, star formation, SN, feedback, … SMBHs form from cold gas in major mergers. MBH – sigma relation

Quasar evolution and galaxy evolution Franceschini et al. (MN 310, L 5, 1999) Quasar density vs. star-formation rate (SFR) n Opt-UV observations of field galaxies star-formation rate (SFR) n Same but for field elliptical galaxies star-formation rate (SFR) n ROSAT (soft-X) survey 0. 5 -2 ke. V vol. emissivity of high luminosity quasars 　 z

Semi-analytical model (2) Evolution Kauffmann & 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 quasar density evolution z SFR evolution

Semi-analytical model (3) Assemby history Haehnelt (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. 8 Haiman & Loeb (Ap. J 552, 459, 2001) SDSS 1044 -0125 at z ～ 5. 80 (Fan et al. 2000) MBH～ 3. 4× 109 Msun n Salpeter timescale (e-fold time): L = LEdd Mc 2/LEdd～ 4× 107 yr Growth time for a 10 Msun. BH to 3. 4× 109 Msun via accretion ～ 7× 108 (ε/0. 1)η-1 yr ～ age of universe at z = 5. 8 Lensing? Super-critical accretion? ? d e r i equ r 　 minimum η≡ L/LEdd vs. ε≡L/Mc 2 .

Open questions (Haehnelt 2003) n n n Is AGN activity triggered by mergers? What is the timescale of QSO activity and what determines it? Why is it apparently shorter than the merger timescale of galaxies? How much room is there for dark or obscured accretion? 　 Can the accretion rate exceed the Eddington limit? What is the physical origin of the MBH-σ relation? Does it evolve with redshift? What role do SMBHs play in galaxy formation and in defining the Hubble sequence of galaxies? Are supermassive binary BHs common? On which timescale do they merge? Do IMBHs form in shallow potential wells? Does the MBH-σ relation extend to smaller BH masses?

Summary: possible BH formation paths PBH stars evaporation Pop. III star cluster stellarmass BH merger/ accretion ? ? stellar-mass BH IMBH runaway collapse IMBH merger/ accretion interaction with galaxies SMBH