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