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

Introduction: Introduction: Astrophysical BH formation 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)

1.1. Astrophysical black Astrophysical black holes: holes: Observational factsObservational 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

BHs can be found in many places and seem to have had great influence on the evolution of the universe.

mass (solar m

ass)

Our Galaxy nearby galaxies distant galaxies early universe100

102

104

106

108

stellar-mass BHs

intermediate-mass BHs (ULXs)

galactic nuclei

gamma-ray bursts (?)

before 〜 1995 after〜 1995

(NLS1s)

(unknown populations??)

(c) K. Makishima

(quasars)

Sgr A*

Black-Hole Objects (1)Black-Hole Objects (1) Stellar-mass BHs (in binaries)Stellar-mass BHs (in binaries)

Constitute X-ray binaries with

normal companions.

～ 10 stellar-mass BHs in ou

r Galaxy. (Brown & Bethe 1994)

Binary separation

3231

2111103

day(cm)

sunsun

P

M

M

M

Ma

7-9

sun 4 R

Two spectral statesTwo spectral states (Galactic BH candidates) (Galactic BH candidates)

soft

hard

log fν

log hν

soft (high) state

blackbody spec. with kT ～ 1 ke

V

hard (low) state

power-law, fν ν∝ -α

with α ～ 0.7

cutoff at ～ 102 keV

X-ray variability (Cyg X-1) in low/harX-ray variability (Cyg X-1) in low/har

d stated state Negoro (1995)

X-ray light curve (left) and PSD (below)

1/f 1.1

1/f 1.5

log PSD

log f

BH mass estimation: BH mass estimation: Stellar-mass BHs in binaries Stellar-mass BHs in binaries

Observe orbital motion of optical companion M1 = compact star mass, M2 = companion mass, i = inclination, P = period

121221

331

2

3

321

21

122

2

MMMfMM

iM

GP

K

r

MMG

Pr

MM

MrirK

),()(

sin4

)( , ,sin

2

observable M1 lower limitradial velocity

orbital phase

Case of GRS 1915+105 (Greiner et al. 2001)

Black-Hole Objects (2)Black-Hole Objects (2) Massive BHs in galactic nucleiMassive BHs in galactic nuclei

Supermassive BHs seem to lie a

t the center of (active) galaxies.

HST image of gas (dust) disk surroun

ding a central black hole.

Occasionally associated with jet

(s).

Spectra of Sy 1 typeSpectra of Sy 1 type AGNsAGNs

logνfν BBBpower law + exp. cutoff

log hν

Big Blue Bump (UV)

blackbody with Te

ff ～ 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: BH mass estimation: Massive BHs in galactic nuclei 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 > 107 Msun

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 correlationsBH-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)

610

710

810

1010

410

510

910

1110

810 910 11101010 1210 1310

bulgeM M¤

MB

H[M ]¤

Magorrian (1998)

Merritt & Ferrarese (2001)

Seyfert

BH to bulge mass ratio

うめ

Other BH-host galaxy Other BH-host galaxy correlationscorrelations

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

absolute magnitude

Brighter galaxies have flatter density slopes

Narrow-Line Seyfert 1 galaxies (NLSNarrow-Line Seyfert 1 galaxies (NLS1s)1s)

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

microlens timescale, ～ 130 (M/Msun)1/2 d, exceeds 130d.

IMBH in globular clusters(?) Still controversial. Needs confirmation.

X-ray spectra of ULXsX-ray spectra of ULXs

IC342 galaxy

■ MCD (multi-color disk) type ■ PL (power-law) type ■ Transition between MCD⇔PL

Alike Galactic BHCs

(c) A. Kubota

Black hole accretion in GRBs(?)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

viscous t.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

2E

28sun

3sunsun

2 / g/s10/10 cLGMRMM

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?

How can we model QSO formation scenarios?

Quasar (BH) evolution Quasar (BH) evolution (Rees 1990)

Quasars co-moving density reached its maximum at z ～ 2.

High z QSO LFs from SDSS (z ~ 4.3; Fan et al. 2001)

QSO LFs from 2dF QSO redshift survey (0 < z < 2.3; Boyle et al. 2000)

Evolution of Quasar Luminosity FunctiEvolution of Quasar Luminosity Functions (LFs)ons (LFs)

Cosmological evolution of Cosmological evolution of AGN spatial densityAGN spatial density

Number density of higher luminosity AGNs peaked at higher redshifts.

Ueda et al. (ApJ, 2003)

Similar evolutions are found for star-formation rates.

BH mass density (1).BH mass density (1).From quasar luminosity func. From quasar luminosity func.

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)

Yu & Tremaine (MN 335, 965, 2002)

Obscured BH accretionObscured 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).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

PBH

?? stellar-mass IMBH SMBH BH

stars

merger/ accretion

stellar-mass BH

star cluster IMBH

Pop.III

merger/ accretion

IMBH

runaway collapseevaporation

interaction with

galaxies