Mitch Begelman

JILA, University of Colorado

THE FIRST SUPERMASSIVE BLACK

HOLES?

COLLABORATORS

• Marta Volonteri (Cambridge/Michigan)• Martin Rees (Cambridge)• Elena Rossi (JILA)• Phil Armitage (JILA)

NEED TO EXPLAIN:

• Ubiquity of BHs in present-day galaxies

• QSOs with M>109M at z>6 – Age of Universe < 20 tSalpeter

Eddington-limited accretion would have to:– Start early– Be nearly continuous

– Start with MBH >10 – 100 M

)1.0~for (

Begelman & Rees, MNRAS 1978

The Rees Flow Chart

Rees, Physica Scripta, 1978

One more time, with calligraphy…

18 years later…with 4-color printing!

Begelman & Rees, “Gravity’s Fatal Attraction” 1996

ORIGIN OF SEEDS: 2 APPROACHES • Pop III remnants

– ~100 (?) M BHs form at z~20– Sink to center of merged haloes– Accrete gas/merge with other seeds

• Direct collapse– Initial BH mass = ?– How is fragmentation avoided?– Growth mainly by accretion of gas

• Problems faced by both:– angular momentum transport– Can be exceeded?EddM

• WHAT ANGULAR MOMENTUM PROBLEM?

• WHOSE LIMIT? EDDINGTON• SEEDS FROM DIRECT COLLAPSE?• OBSERVING SEED BH FORMATION

DM

gas

DM

gas

(approx.) 25.0en. pot.

en. rot.

Halo with slight rotation Gas collapses if virialgas TT

“BARS

WITHIN

BARS”

(Shlosman, Frank & Begelman 89)

Dynamical loss of angular momentum

through nested global gravitational instabilities

WHEN IS GAS UNSTABLE?

• Init. collapse with conserved ang. mom.– Mestel, rigid, exponential disk

– Include NFW halo potential

– Vary fraction of gas collapsing, fd

• Choose halo ang. mom. parameter λspin

from lognormal distribution • Stability threshold: f T/W > 0.25

– Christodoulou et al. 1995, f = form factor

Max. halo spin parameter for instability, as function of gas infall fraction

Mestel

exponential

rigidSTABLE

UNSTABLE

Probability of instability, lognormal distibution

5.0,05.0spin

Global ang. mom. transport (“Bars within Bars”) : M yr-1

• Mass distribution isothermal,

• Accumulated mass dominates for

• BWB fails at ?

2/34

3.0~3

TG

vBWB

M vir

pc 10~ 2/14 MyrBWB tTrr

rrM )(

BWBrr

Local ang. mom. transport ( ) : M yr-1

viscosity parameter (~1: Gammie 2001)

• If T const. or incr. inwards, likely to reach center

113

2/34

3.0~ QTQG

clocal

M s

unstable 1

stable 1 Parameter Toomre {

G

cQ s

1

BWBrr

BWBM of fraction

FRAGMENTATION UNLIKELY TO STOP INFALL

TEMP./METALLICITY DEPENDENCE

• – Metal-free, H2-dissociated gas falls in

• (Metal rich and/or H2 fragments?)

– Inflow rate, mass accumulation HIGH

• – Infall requires H2 or pollution by Pop III– Inflow rate, mass accumulation LOW

Solarhalohalo MMT 94 10~ K 10~

Solarhalohalo MMT 62 10~ K 10~

FAVORS DIRECT BH FORMATION

FAVORS POP III STAR FORMATION

WHOSE LIMIT?

SUPPOSE A SEED BH SETTLES IN THE MIDDLE OF THE ACCUMULATED GAS

Max. BH accretion rate is for the mass of the ENVELOPE

)(~ *BHE

BHMax MM

M

MM

EMACCUMULATED GAS

BH

*M

BHM

RAPID GROWTH OF A PREGALACTIC BH

BHM

BHMM *

“QUASISTAR”

Pregalactic halo -1

10 skm10~

2/1

2/11.0

310

3 )(103~

Sol

BH

E

BH

M

M

M

M

GM

3

* ~

Could seed BH grow from ~10 to >105 MSol at ?

(Begelman, Volonteri & Rees 06)

EMM

ACCUMULATED GAS

+ FORMATION OF THE SEED?

WHAT IS A “QUASISTAR”? • Self-gravitating structure laid down by infall• Radiation-dominated, rotation crucial• Pre-BH:

– Entropy small near center, increases with r – Very different from the supermassive stars

postulated by Hoyle and Fowler

YOU’VE GOT TO BE

KIDDING

WHAT IS A “QUASISTAR”? • Self-gravitating structure laid down by infall• Radiation-dominated, rotation crucial• Pre-BH:

– Entropy small near center, increases with r – Very different from the supermassive stars

postulated by Hoyle and Fowler

• Post-BH:– “Nuclear” energy source is BH accretion– Expands and becomes fully convective– Like radiation-dominated, metal-free red giant

THAT’S BETTER

QUASISTAR STRUCTURE : PRE-BH

• Mass m* (M) increases with time M yr-1 • Core with • Envelope

– Entropy increases outward – convectively stable– Rotation increases binding energy

• Outer radius constant• Core radius shrinks

– Nuclear burning inadequate to unbind star

• Core mass ~ 10 M constant• When core temp.

rapid cooling by thermal neutrinos

radgas pp ~

1/ 2/1 rpp gasrad

AU 5.0~ 1* mr

** /~ mrrc

,1800~ 1* mm K 105~ 8

11.0 m

CORE COLLAPSE AND FORMATION OF ~10-20 M SEED

BH

SUBSEQUENT ACCRETION AT EDDINGTON LIMIT FOR

QUASISTAR MASS

+

QUASISTAR STRUCTURE : POST-BH• BH accretes adiabatically from quasistar interior

• Adjusts so energy liberated • Radiation-supported convective envelope (w/rotation)

– Central temp drops to ~ 106 K

– Radius expands to ~ 100 AU

– Convection becomes inefficient well inside photosphere, where , but photosphere temp. drops as BH grows

• Teff < 5000 K opacity crisis

)(~ *MLEdd

es ~

2

~

c

cMM s

BondiBH

OPACITY CRISIS• Pop III opacity plummets below T~5000 K

– Higher temp than for solar abundances

Mayer & Duschl 2005

Metal-free opacities

Mayer & Duschl 2005

Metal-free opacities

Plausible range of photosphere densitiesAnalogous to

Hayashi track, but match to radiation- dominated convective envelope

Mayer & Duschl 2005

Est. min. temp.

If Tphot drops below minimum (~5000 K), flux inside quasistar exceeds Eddington limit, dispersing it.

OPACITY CRISIS• Pop III opacity plummets below T~5000 K

– Higher temp than for solar abundances

• Convection is relatively inefficient– Transition to radiative envelope at T~55,000 K ~

10 Tphot

– κ ~ κes at transition, but much lower at photosphere

• If Tphot < Tmin , flux exceeds Eddington limit at transition quasistar disperses

• Connect BH accretion physics to quasistar structure, predict Tphot(mBH, m*)

CONNECTION TO BH ACCRETION

9/89/7*~ BH

E

mmL

L

Once limiting temperature is reached,

5/220/7*

20/9

5/12.0~K 5000

BH

E

phot mmL

LT

… dispersal is inevitable (and accelerates)

QUASISTAR MODELS WITH “TOY” OPACITY

13)K8000/(1

Tes

Begelman, Rossi & Armitage 2007

QUASISTAR MODELS WITH “TOY” OPACITY

13)K8000/(1

Tes

Begelman, Rossi & Armitage 2007

GROWING THE BLACK HOLE• Eddington-limited growth:

• Ignoring opacity crisis: M yr-1

– Super-Eddington growth to ~107 M in 108 yr

• Onset of opacity crisis: Teff ~ 5000 K when

– Estimates sensitive to:

• Value of Tmin

• Details of BH accretion

• Energy loss details: rotational funnel, photon bubbles….

*mmBH 1* 1.0~ mm

1

2*710~

m

mmBH

2/1

13000~)(

BHBHEdd

BH

m

m

mm

m

11

m

9/71

9/81.0

310~ mmBH 9/8

19/4

1.05

* 10~ mm

CAN QUASISTARS BE DETECTED?

DETECTING A QUASISTAR

• Most time spent as ~5000 K blackbody

• Radiates at Eddington limit for 105m5 M

• Max flux ~ mTz

DzTmF GpcL

5000max

2,

150005

5max,

)1(

Jy )1(103.2~

65*

78 1010~,206~for Jy 10510 mz

nintegratio s10 ,10 5

JWST

z=6

z=20

6* 10m

5* 10m

z=10

PEAK OF BLACKBODY

DETECTING A QUASISTAR

• Most time spent as ~5000 K blackbody

• Radiates at Eddington limit for 105m5 M

• Max flux ~

• Better to observe @ 3.5µm, on Wien tail

• Corona/mass loss hard tail, easier detection

mTz

DzTmF GpcL

5000max

2,

150005

5max,

)1(

Jy )1(103.2~

65*

78 1010~,206~for Jy 10510 mz

nintegratio s10 ,10 5

JWST

z=6

z=20

6* 10m

5* 10m

z=10

WIEN TAIL – MASS LOSS MAY IMPROVE FURTHER

Cumulative comoving no. density of seeds

HOW COMMON ARE QUASISTARS?

0005.0

005.0

05.0

5.0

5

1

Nse

eds (

Mp

c-3) 5.0df

1.0df

100 per L* galaxy

1 per L* galaxy

…but their lifetimes are short

Lifetime = 106

yr

No enrichment

Some enrichment

Heavy enrichment

Metal enrichment model from Scannapieco et al. 2003

L* galaxies

COMOVING DENSITY OF QUASISTARS

COMOVING DENSITY OF QUASISTARSLifetime = 106

yr

Metal enrichment model from Scannapieco et al. 2003

1 per L* galaxy

All 104 K haloes

104 K haloes with λ<0.02

100 per L* galaxy

DENSITY ON SKY

• • 10-3 seeds Mpc-3 (1/L* gal.) 103.5 QS deg.-2

• JWST FOV ~ 4.8 arcmin2 ~ 1 per random field

Could be ~10-100x more common

• How to distinguish from other objects?– Colors: ~pure blackbody (not dust reddened)

• Observe on Wien tail • No lines (distinguish from T dwarfs)

– Unresolved (distinguish from nearby starbursts)– Clustering (like 104 K haloes)

) of indep. more,(or yr 10~ lifetime, 9/41

6 m

1/JWST fieldLifetime = 106 yr

10/JWST field

QUASISTAR DENSITY ON SKY

WHAT HAPPENS NEXT?

• If super-Edd. phase extends beyond opacity crisis, BH seeds could be as massive as 106 M

• Worst case: super-Edd. phase ends at ~103 M

• 10 tSalpeter between z=10 and z=6 growth by (only) 20,000

BUT – Exceeding LEdd by factor 2 squares growth

factor!– Mergers can account for factor 10-100 of growth

CONCLUSIONS II. Angular momentum transport is fast

if global gravitational instabilities set in (“Bars within Bars”)

II. BH can grow at Eddington limit for the surrounding envelope, which can be cvcvcvcfor the BH

III. BH seed can form in situ from the infalling envelope itself (aided by ν cooling) or can be captured Pop III remnant

EddM

CONCLUSIONS IIIV. BH seeds grow inside a “quasistar”

powered by BH accretion, with a radiation pressure-supported convective envelope

V. Min. Teff of quasistar is ~5000 K, lifetime is > 106 yr

VI. Quasistars could be common and may be detectable by JWST