GROWING BLACK HOLES
Mitch Begelman
JILA, University of Colorado
COLLABORATORS
•
•
•
•
•
•
•
Marta Volonteri (Michigan)
Martin Rees (Cambridge)
Elena Rossi (JILA/Leiden)
Phil Armitage (JILA)
Isaac Shlosman (JILA/Kentucky)
Kris Beckwith (JILA)
Jake Simon (JILA)
BLACK HOLES FORMED…
EARLY
QSOs with M>109M at z>6
OFTEN
One per present-day galaxy
HOW DID THESE
BLACK HOLES GET
THEIR START?
2 SCHOOLS OF THOUGHT:
• Pop III remnants
– Stars form, evolve and collapse
– M*~103 M
– MBH~102 M
• Direct collapse
– Massive gas cloud accumulates in nucleus
– Supermassive star forms but never fully relaxes;
keeps growing until collapse
– M*>106 M
– MBH >104 M
Rees’s flow chart
Rees, Physica Scripta, 1978
32 years later …
Begelman & Rees,
“Gravity’s Fatal Attraction”
2nd Edition, 2010
Keeping up with
the times…
Begelman & Rees,
“Gravity’s Fatal Attraction”
3nd Edition E-book?
• Pop III remnants
– ~100 (?) M BHs form at z >
~ 20
– 105-6 M halos, Tvir ~ 102-3 K
– Grow by mergers & accretion
– Problems:
TRADEOFFS:
Smaller seeds,
more growth
time
• Slingshot ejection from merged minihalos?
• Feedback/environment inhibits accretion?
• Direct collapse
– Initial BH mass = ? at z < 12
– 108-9 M halos, Tvir >104 K
– Grow mainly by accretion
– Problem:
• Fragmentation of infalling gas?
Larger seeds,
less growth
time
STAGE I:
COLLECTING THE GAS
The problem: angular momentum
The solution: self-gravitating collapse
SELF-GRAVITATING COLLAPSE: A
GENERIC MECHANISM:
• “Normal” star formation
3 5
3/42
-1

T ~ 10  100 K, M v
~ 10 T
10 MSun yr
 ~
M

• Pop III remnants
G
G
4
 ~ 10
T ~ 100  1000 K, M
• Direct collapse
4
  0.2 M yr -1
T  10 K, M
Sun
 10
2
MSun yr
-1
Halo with slight rotation
DM
Gas collapses if Tgas  Tvirial
DM
gas
rot. en.
 0.25 (approx.)
pot. en.
Dynamical loss of angular
gas nested
momentum through
global gravitational
instabilities
“BARS
WITHIN
BARS”
Shlosman, Frank & Begelman 1989
Collapsing gas in a pre-galactic halo:
R-2 density profile
Wise, Turk, & Abel 2008
Global instability, “Bars within Bars”:
Instability at distinct
scales → nested bars
Wise, Turk, & Abel 2008
WHY DOESN’T THE
COLLAPSING GAS FRAGMENT
INTO STARS?
IT’S COLD ENOUGH …
… BUT IT’S ALSO HIGHLY TURBULENT
Collapse generates supersonic
turbulence, which inhibits fragmentation:
Wise, Turk, & Abel 2008
HOW TURBULENCE COULD SUPPRESS
FRAGMENTATION
BAR
FRAGMENTATION SETS IN
BEFORE BAR INSTABILITY
FRAGMENTS
Razor-thin disk (Toomre
approximation):
⇦ FRAGMENT SIZE
THE KEY IS DISK THICKENING
ROTATIONAL SUPPORT ⇨
    v k  2G k
2
2
2
t
2
Begelman & Shlosman 2009
HOW TURBULENCE COULD SUPPRESS
FRAGMENTATION
BAR
BAR INSTABILITY SETS IN
BEFORE FRAGMENTATION
⇦ FRAGMENT SIZE
Disk thickened by
turbulent pressure:
FRAGMENTS
THE KEY IS DISK THICKENING
WHY?
THICKER DISK HAS
“SOFTER” SELF-GRAVITY
2G k
2
2
2
2
⇨ LESS
  TENDENCY
 v k TO FRAGMENT
t
1FORMATION)
 kh
(DOESN’T AFFECT BAR
ROTATIONAL SUPPORT ⇨
Begelman & Shlosman 2009
HOW TURBULENCE COULD SUPPRESS
FRAGMENTATION
BAR
ENOUGH TO KILL OFF
FRAGMENTATION
MORE SIMULATIONS (WITH
HIGHER RESOLUTION)
NEEDED!
FRAGMENTS
5% of turbulent pressure
used for thickening :
⇦ FRAGMENT SIZE
THE EFFECT IS DRAMATIC
ROTATIONAL SUPPORT ⇨
Begelman & Shlosman 2009
Rapid infall can’t create a black hole
directly…
At
R~4

M
1 M Sol yr
-1
AU
radiation trapped in infalling gas
halts the collapse
STAGE II:
SUPERMASSIVE STAR
SUPERMASSIVE
STARS
Hoyle & Fowler 1963
•
•
•
•
•
Proposed as energy source for RGs, QSOs
Burn H for ~106 yr
Supported by radiation pressure
fragile
Small Pg stabilizes against GR to 106 M
Small rotation stabilizes to 108-109 M
THINGS HOYLE & FOWLER DIDN’T KNOW
ABOUT SUPERMASSIVE STARS
… because they didn’t worry about how they formed
• They are not thermally relaxed
INCOMPLETE THERMAL RELAXATION
SWELLS THE STAR:
R
 AU
R ~ 4m

M
THINGS HOYLE & FOWLER DIDN’T KNOW
ABOUT SUPERMASSIVE STARS
… because they didn’t worry about how they formed
• They are not thermally relaxed
• They are not fully convective
STRUCTURE OF A SUPERMASSIVE STAR
1.0
0.8
CONVECTIVE CORE
P 
4/3
 const.
0.6
T
Tc
POLYTROPE
M*
0.4

M core
0.2
0.0
0
1
2
3
4
5
6
7
Scaled radius
matched to
P 
RADIATIVE ENVELOPE
“HYLOTROPE”
(hyle, “matter” + tropos, “turn”)
Thanks, G. Lodato & A. Accardi!
4/3
M
2/3
(r )
HYLOTROPE,
NOT
HELIOTROPE!!
INCOMPLETE CONVECTION DECREASES
ITS LIFE & MAX. MASS
FULLY CONVECTIVE
PARTLY
CONVECTIVE
THINGS HOYLE & FOWLER DIDN’T KNOW
ABOUT SUPERMASSIVE STARS
… because they didn’t worry about how they formed
• They are not thermally relaxed
• They are not fully convective
• If made out of pure Pop III material they
quickly create enough C to trigger CNO
METAL-POOR STARS BURN HOTTER
A BLACK HOLE FORMS
SMALL (< 103 M) AT FIRST …
… BUT SOON TO GROW RAPIDLY
STAGE III:
QUASISTAR
“QUASISTAR”
• Black hole accretes from envelope, releasing energy
• Envelope absorbs energy and expands
• Accretion rate decreases until energy output =
Eddington limit – supports the “star”
Begelman, Rossi & Armitage 2008
SO THE BLACK HOLE
GROWS AT THE
EDDINGTON LIMIT,
RIGHT?
BUT WHOSE
LIMIT?
EDDINGTON
GROWTH AT EDDINGTON LIMIT FOR
ENVELOPE MASS > 103-4 X BH MASS
EXTREMELY RAPID
GROWTH
“QUASISTAR”
• Resembles a red giant
• Radiation-supported convective envelope
• Photospheric temperature drops as black hole
grows
Radius ~ 100 AU
Central temp. ~106 K
Tphot drops as
BH grows
DEMISE OF A QUASISTAR
• Critical ratio: RM=(Envelope mass)/(BH mass)
• RM < 10: “opacity crisis” (Hayashi track)
• RM < 100: powerful winds, difficulty matching accretion
to envelope (details very uncertain)
Final black hole mass:
M BH



M
 M Sol
~ 10 R 
-1 
 1 M Sol yr 
7
2
M
~ 10  10 M Sol
4
6
STAGE IV:
“BARE” BLACK HOLE
“Normal” growth via accretion & mergers
THE COSMIC CONTEXT
• Collapse occurs only in gas-rich & low ang. mom. halos
• Need ang. mom. parameterλ~0.01-0.02 vs. meanλ~0.03-0.04
• Competition with Pop III seeds
• Pre-existing Pop III remnants may inhibit quasistar formation
• ... but pre-existing quasistars can swallow Pop III remnants
• Merger-tree models vs. observational constraints:
•
•
•
•
•
Number density of BHs vs. z (active vs. inactive)
Mass density of BHs vs. z (active vs. inactive)
BH mass function vs. z
Total AGN light (Soltan constraint)
Reionization
Volonteri & Begelman 2010
BLACK
HOLE
mass
density
All BHs:
(thin lines)
Active BHs:
(thick lines)
Volonteri &
Begelman 2010
TOTAL AGN
LIGHT
POP III
ONLY
CAN SUPERMASSIVE STARS OR
QUASISTARS BE DETECTED?
Supermassive stars:
L ~ 4 10 erg/s
45

Teff ~ 2 10 m
5
1 / 4
...similar to a modest AGN
K
…strong UV source (hard to
distinguish from clusters of hot stars)
Quasistars peak in optical/IR: some hope?
JWST
quasistar
counts
1/JWST field
Tphot=4000 K
Band: 2-10 m
Sens. 10 nJy
Lifetime ~106 yr
λspin<0.02
1/JWST field
λspin<0.01
WHAT ABOUT M-σ?
• Do AGN outflows really clear out entire
galaxies? – or is global feedback a “red
herring”?
• Do BH grow mainly as Eddington-limited
AGN or in smothered, “force-fed” states
(e.g., following mergers)
• if the latter, then BH growth could be coupled
to σthrough infall rate σ3/G
• ... but what is the regulation mechanism?
To conclude …
THE
BOTH
MASSIVE
QUASISTARS
PROCESS
ROUTES
BLACK
ATTO
SUPERMASSIVE
HOLE
INVOLVES
Z~6-10FORMATION
MIGHT
2 NEW
BE
BLACK
BY
CLASSES
DETECTABLE
DIRECT
HOLE
OF WITH
FORMATION
COLLAPSE
OBJECTS
JWST
LOOKS
ARE
STILL IN PLAY
PROMISING
Many unsolved
problems:
Effects stars
of
Supermassive
Requires
self-gravitating
mass loss?
Late
⇨ initial
seeds
infall
without
excessive
formation
after
Quasistars
⇨ rapid
fragmentation
mergers?
growthFormation
in massive
around existing black
cocoon
holes? ....
DIRECT COLLAPSE
LOOKS PROMISING
CORE COLLAPSE
OF SUPERMASSIVE
STARS
RAPID GROWTH
INSIDE MASSIVE
COCOONS
QUASISTARS
DETECTABLE?