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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 (?)
BLACK
z ～ 6 : first quasar (observed)
z ～ 2 : peak quasar density
z = 0 : many, many BHs
Key words:

Co-evolution (with galaxies)
Feedback (to form
structure)

HOLE
1. 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?
Black Hole Candidates
before 〜1995
108
after〜1995
(quasars)
mass (solar mass)
galactic nuclei
106
(NLS1s)
Sgr A*
(unknown populations??)
104
intermediate-mass
BHs (ULXs)
102
100
stellar-mass BHs
Our Galaxy
gamma-ray
bursts (?)
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.
7-9
～10 stellar-mass
BHs in our Galaxy.
(Brown & Bethe 1994)

Binary separation
13
 M1
M2 
11


a  3  10 (cm) 

 M sun M sun 
4 Rsun
 P 


 day 
23
Two spectral states
(Galactic BH candidates)
log fν
soft
hard
log hν
soft (high) state
hard (low) state
blackbody spec.
with kT ～ 1 keV
power-law, fν ∝ν-α
with α～ 0.7
cutoff at ～ 102 keV
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
M1 = compact star mass, M2 = companion mass, i = inclination, P = period
K  r2 sin i , r2 
M1
r,
M1  M 2

2
G ( M1  M 2 )

P
r3
4 2 K 3
M1 sin3 i

 f ( M1 , M 2 )  M1
2
2
GP
( M1  M 2 )
3

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 type AGNs
logνfν
BBB
power law + exp. cutoff
log hν
Big Blue Bump (UV)
blackbody with
Teff～ 105 K (10 eV)
power law (radio ～γ)
fν∝ν-α with α～ 0.7
cutoff at ～100-200 keV
How do we understand such SED by disk models?
BH mass estimation:
Massive BHs in galactic nuclei

Stellar kinematics



Optical emission-line gas


Line width & radius → MBH～ (1-40)×106Msun; up to d ～ 70 Mpc.
Reverberation (echo) mapping



Distances of up to d < 100 Mpc, BH mass of MBH ～
> 107 Msun
H2O Masers


Detect proper motions of individual stars (Galactic center)
Stellar absorption-line kinematics (galaxies with distances, d < 20 Mpc)
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)
 MBH Mbulge1.53; 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)
BH to bulge mass ratio
1011
1010
109
108
Magorrian (1998)
107
106
10
Seyfert
5
Merritt & Ferrarese (2001)
10 4 8
10
109
1010
M bulge  M
1011

1012
1013
うめ
Other BH-host galaxy correlations

Cusp slope – absolute magnitude (Gebhardt et al. 2000)
cusp
density
slope
Brighter
galaxies have
flatter
density slopes
absolute magnitude

Sersic index - vel. dispersion - BH mass (Erwin et al. 2003)

Bulge light profile ∝r1/n; n = Sersic index
Narrow-Line Seyfert 1 galaxies
(NLS1s)
Boller et al. (NewA 44,
2000)

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

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 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
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)

massive torus
around a BH:
Mtorus=0.01～1 Msun
MBH= 3～10(?) Msun
magnetar
  102 M / R3 GM  1028 g/s  L / c2
M
sun
sun
sun
E

Two basic timescales:


dynamical t.s. = (rS3/GM)1/2 < 0.1 sec
viscous t.s. = (r/H)2(rtorus3/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
c 3t
 t 
1971)
MH 
 105   Msun
G
1s 
Small BHs should have
evaporated already
tevap 
3
G M
10  M 

10
 15  yr
4
c
 10 g 
2
3
ΩPBH < 1
Constraints for β (fraction of
regions of mass M which collapse)
-1/2
18  M 


10
  15 
PBH
⇒
 10 g 
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
remnant
mass
(Msun)
3
10
30
100
300
Heger & Woosely
(ApJ 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. (ApJ 591, 288, 2003)
solar
Fate of a massive
star is governed
by
(1) its mass,
(2) chemical
composition,
metal poor
(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 (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
General Relativistic Instability
Baumgarte & Shapiro 1999, ApJ, 526, 941
stable
critical point
Rapidly rotating supermassive star
in equilibrium
unstable
 rigid rotation
 mass-shedding limit
 unstable at R  640GM / c 2
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
～ 0.75 (Kerr BH)
Kerr parameter 
うめ
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
if core 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).
Inter-mediate mass BHs to
Supermassive BHs (coutesy of T. Tsuru)
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 starformation 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 on MBH, but spectra do,
since the BBB peak frequency, νpeak∝ MBH-1/4
Calculated quasar LFs at z～3
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.
(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.
log(MBH/Msun)
Silk-Rees picture for quasargalaxy 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 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
Radiation drag model for
quasar BH formation


Umemura (ApJ 520, L29,
2001)
mass accretion rate (τ=1 limit)
L*
L*    M BH 
-1 

  M Edd  8

M  2  0.1M sun yr  12
c
 10 Lsun 
 10 M sun 
accretion time
1
1
 L 
c2 R2
2 Z 
7

 8.6  10 yr  12  Rkpc  
 L
 10 L 
Z 
tdrag

radiation energy from stars
erad  l*t* ～ 0.14  m*c 2
( = 0.007 : H  He nuclear fusion energy conversion efficiency)

massive dark object
t
M MDO   Mdt
0
～

t
0
L / c2dt
M MDO

M bulge
～ 0.14
 0.002
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, 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. 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 (ApJ 552, 459, 2001)
SDSS 1044-0125 at z ～ 5.80 (Fan et al. 2000)  MBH～ 3.4×109 Msun

Salpeter timescale (e-fold time):
Mc2/LEdd～ 4×107 yr
L = LEdd

Growth time for a 10 MsunBH 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??
minimum η≡ L/LEdd vs.
ε≡L/Mc2
.
Open 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:
possible BH formation paths
PBH
stars
evaporation
Pop.III
star
cluster
stellarmass BH
merger/
accretion
??
stellar-mass
BH
IMBH
runaway
collapse
merger/
IMBH accretion
IMBH
interaction
with
galaxies
SMBH