嶺嶺 嶺 嶺嶺 嶺 ( ( 嶺嶺 嶺嶺嶺 ・ 嶺嶺 嶺嶺嶺 ・ ) ) Black hole formation Black hole formation 1. 1. Astrophysical black holes Astrophysical black holes 2. 2. Formation of black holes Formation of black holes 3. 3. Evolution of black holes Evolution of black holes Ref: Proc. Carnegie sympo. on coevolution of black holes Ref: Proc. Carnegie sympo. on coevolution of black holes and galaxies (2003) and galaxies (2003) http://www.ociw.edu/ociw/symposia/ser http://www.ociw.edu/ociw/symposia/ser
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嶺重 慎 ( 京大・基礎研 ) Black hole formation 1. Astrophysical black holes 2. Formation of black holes 3. Evolution of black holes Ref: Proc. Carnegie sympo. on.
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嶺重 慎 嶺重 慎 (( 京大・基礎研京大・基礎研 ))
Black hole formationBlack hole formation
1.1. Astrophysical black holesAstrophysical black holes2.2. Formation of black holesFormation of black holes3.3. Evolution of black holesEvolution of black holes
Ref: Proc. Carnegie sympo. on coevolution of black holes and galaxies (2003) Ref: Proc. Carnegie sympo. on coevolution of black holes and galaxies (2003) http://www.ociw.edu/ociw/symposia/series/symposium1/proceedings.htmlhttp://www.ociw.edu/ociw/symposia/series/symposium1/proceedings.html
What are NLS1s? Narrow “broad lines” (< 2000 km s-1) Sy 1 type X-ray features Extreme soft excess Extreme variability
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⇒
Boller et al. (NewA 44, 2000)
Intermediate-Mass Black Holes (IMBHIntermediate-Mass Black Holes (IMBHs) s) van der Marel (Carnegie sympo., 2003)
Ultra Luminous X-ray sources (ULXs) 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)
IMBHs through grav. microlensing No IMBH MACHOs in LMC. Some of Galactic bulge MACHOs could be IMBHs, since
Primordial black holes (PBHs) 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)
⇒
sunH s
Mt
G
tcM
1105
3
yrg
3
evap
1510
4
32
1010
M
c
MGt
-1/2
PBH g
1518
1010
Mγ emission
ΩPBH < 1
2. Formation of BHs:2. Formation of BHs: Stellar-mass to massive BHsStellar-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 End product of stars
Present-day stars Massive stars shed most of their mass through wind. Massive stars leave compact remnants with M < 15 M sun
The minimum initial mass to produce a BH is 20-25 M sun
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 Star evolution: remnant massmass
Heger & Woosely (ApJ 591, 288, 2003)
remnant mass (Msun)
BHNSWD
BH
1 9 28 140 260 initial mass (Msun)
1
3
1
0
3
0
1
00
30
0
How massive single stars end their lifHow massive single stars end their life? e? Heger et al. (ApJ 591, 288, 2003)
Fate of a massive star is governed by
(1) its mass,
(2) chemical composition,
(3) mass loss.
9 25 40 60 100 140 260
initial mass (Msun)
met
al p
oor
so
lar
Rees diagram - hoRees diagram - how to make a maw to make a ma
ssive BHs?ssive BHs? (Rees ARA&A 22, 471, 1984)
collapse of a massive objector
mergers in a cluster
Direct collapse of a gas cloudDirect 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.
(a) No spin, with UV (b) With spin (λ=0.05) & UV (c) No spin, no UV
2640 /R GM c
rigid rotation mass-shedding limit unstable at
stable
unstable
critical point
うめ
General Relativistic Instability
Baumgarte & Shapiro 1999, ApJ, 526, 941
Rapidly rotating supermassive star in equilibrium
massive objects → Prad > Pgas
→ γ ~ 4/3 → instability
GR: unstable even if γ> 4/3
Dynamical Collapse (Full General Relativity)
Dynamical collapse Apparent Horizon
Kerr parameter 0.75 (Kerr BH)
(Shibata & Shapiro 2002, ApJ, 572, L39)
うめ
~
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.)
BH formation in dense clustersBH formation in dense clusters (van der Marel 2003)
Conditions for runaway collapseConditions 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 & McMillan 2002).
From IMBHs to SMBHs 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).
Inter-mediate mass BHs to SupermInter-mediate mass BHs to Supermassive BHsassive BHs (coutesy of T. Tsuru)
Status at the End of Starburst Star Clusters with IMBH Sink of Star Clusters with IMBHs
into Galaxy CenterMerge of Star Clusters and
Sink of IMBHs into Galaxy Center
Merge of IMBHs into a Super Massive BH by Radiation of Gravitational Wave
67
8
9
GlobularCluster
BulgeSuper MassiveBlack Hole
Jet, Radiation
Formation of Bulge, Globular Clusters and AGN
10 QSO in Early Universe
3. Evolution of BHs: 3. Evolution of BHs: Quasar LFs & BH mass densityQuasar 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?
If some fraction of AGN are obscured, energy conversion efficiency is smaller ⇒ BH density should be higher.
BH mass density (2).BH mass density (2).From galaxy velocity-disp.From galaxy velocity-disp.
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; …)
Yu & Tremaine (MN 335, 965, 2002)
Theoretical models of quasar lum. fuTheoretical models of quasar lum. func.nc. (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 on MBH, but spectra do,
since the BBB peak frequency, νpeak ∝ MBH-1/4
Calculated quasar LFs at zCalculated quasar LFs at z ~~ 33 Hosokawa 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.
(199
8); B: Pei (19
95)
Which model is correct?Which model is correct? Hosokawa (ApJ 576, 75, 200
2) Model A: MBH ∝ Mhalo
5/3 (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
log(MBH/Msun)
log(
dΨ
/dlo
g M
BH)
present-day BH mass func.model Bmodel A
Silk-Rees picture for Silk-Rees picture for quasar-galaxy connectionquasar-galaxy connection
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
if Mσ2 < L ~ LEdd no further BH growth
This condition gives maximum BH mass;
MBH < σ5κ/G 2c ~ 8×108 (σ/500 km s-1)5 Msun
Silk & Rees (A&A 331, L1, 1998)
.
.
2rad * * *0.14e l t m c
Radiation drag model for Radiation drag model for quasar BH formationquasar BH formation
mass accretion rate (τ=1 limit)
accretion time
radiation energy from stars
massive dark object2
MDO 0 0/
t tM Mdt L c dt
1 12 227
drag kpc128.6 10 yr
10
c R L Zt R
L L Z¤ ¤
~
MDO
bulge
0.14 0.002 M
M
( = 0.007 : H He nuclear fusion energy conversion efficiency)
sun
BHEdd
sun
*1-sun
* yr.M
MM
L
LM
c
LM
8122 101010
~~
Umemura (ApJ 520, L29, 2001)
MBH – sigma relation
Semi-analytical model (1)Semi-analytical model (1) Kauffmann & Haehnelt (M
N 311, 576, 2000) Merging trees of dark halos
+ gas cooling, star formation, SN, feedback, …
SMBHs form from cold gas in major mergers.
Quasar evolution and galaxy Quasar evolution and galaxy evolutionevolution
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. emissivity of high luminosity quasars
Franceschini et al. (MN 310, L5, 1999)
Quasar density vs. star-formation rate (SFR)
z
Semi-analytical model (2) EvolutionSemi-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.
quasar density evolution SFR evolution z z
Semi-analytical model (3) Assemby hiSemi-analytical model (3) Assemby historystory 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 How can we make a massive BH at z ~~ 5.85.8 Haiman & Loeb (ApJ 552, 459, 2001)
Salpeter timescale (e-fold time): Mc2/LEdd~ 4×107 yr
Growth time for a 10 MsunBH to 3.4×109 Msun via a
ccretion ~ 7×108 (ε/0.1)η-1 yr ~ age of universe at z = 5.8
Lensing? Super-critical accretion??
SDSS 1044-0125 at z ~ 5.80 (Fan et al. 2000) MBH ~ 3.4×109 Msun
minimum η≡ L/LEdd vs. ε≡L/Mc2.
L = LEddrequired
Open questionsOpen questions (Haehnelt 2003)
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: Summary: possible BH formation possible BH formation paths paths