Black hole growth and the Eddington limit - Marta Volonteri F. Pacucci, A. Ferrara G. Dubus, J. Silk
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Black hole growth and the
Eddington limit
Marta Volonteri
Institut d’Astrophysique de Paris
F. Pacucci, A. Ferrara
G. Dubus, J. Silk
1. High-z quasars and MBHs 2. Eddington limit? 3. How do the first MBHs grow?
High-redshift quasars
Quasars have been detected at very large
distances, corresponding to a very young age
of the Universe.
Fan 2012
High-redshift quasars
blue/red/green/purple (optical): z>6
orange (X-ray)
High luminosity and large
estimated MBH masses
Some fainter sources found
in X-ray (Fiore+12, Giallongo+15)
Wu et al. 2015
As massive as the largest
MBHs today, but when the
Universe was ~ Gyr old!
Gultekin et al. 2009
The Eddington limit:
the outward radiation pressure equals to the inward
gravitational force
If arad>|g| radiation pushes away the gas, and further
accretion is halted
Note: spherical symmetry
The Eddington limit:
the outward radiation pressure equals to the inward
gravitational force
ε: radiative efficiency, ~0.05-0.3
If H only: Ledd=1.3e38 erg/s (M/Msun)
For a BH accreting at a fraction fEdd of the Eddington
limit, mass grows in time as:
1−ε t
( fEdd )
M (t) = M in e 0.45Gyr SDSS z=6 quasars
ULASJ112010641
ULAS J1120 @ z=7.1
M=2x109 Msun
t~0.75 Gyr
ε~0.1
M in>300-ish Msun and fEdd~0.5-1
Is this an issue only at z=6-7?
Shen et al. 2008
Minimum Eddington
ratio that a MBH must
sustain continuously
throughout the whole
cosmic history to reach
a given mass by a given
redshift
tEdd ε " M (z) %
fEdd,min = ln $ '
t H (z) 1− ε # M 0 &
E.g., to reach 1e9 msun by z=4 a BH with initial mass 1e4 msun has
to accrete at fEdd=0.4 for the whole time or at fEdd=1 for 40% of
the time
E.g., to reach 1e10 msun by
z=4 a BH with initial mass
1e4 msun has to accrete
at fEdd=0.55 for the whole
time or at fEdd=1 for 55%
of the timeEddington ratio distribution peaks near fEdd ∼ 0.05 1
Kelly & ShenThe feeding of high-z MBHs
- Estimate Eddington rate for
BHs in Horizon-AGN -- 3x106
Mpc3 (Dubois+14)
- Supercritical inflows possible,
~10% at z>6
- What happens when they
reach the MBH?
Volonteri, Silk & Dubus 2015Super-Eddington accretion? Super-Eddington accretion vs super-Eddington luminosity Highly super-Eddington accretion does not imply highly super-Eddington luminosities Low “effective” radiative efficiency: ε
• Mass supply rate exceeds Eddington limit:
M! >> M! Edd
• Energy released GMM! c
~ LE where
τ = v
r
c
• Energy accumulates at rAccretion discs
If gas has low angular momentum => gas does not fall
radially on the BH, and forms an accretion disc
capture radius: where gas
becomes bound to the BH
accretion disc radius: set by
gas angular momentumAccretion disks
• Thin disk
– ~ all dissipated energy radiated away
– ~ circular Keplerian orbits, vertical structure decouples
– energy transport: internal torque
• Slim disk
– gas retains enough pressure to affect radial balance
– energy transport: torque + advection
• Radiatively inefficient disk
– Due to low density or high optical depth (Eddington limit)
– must dispose of extra energy, mass, or angular momentum to
avoid becoming unbound
Courtesy of M. BegelmanStarlike accretion
• Dynamical conditions don’t allow a bound disk-
like flow if if specific angular momentum is too
small compared to Keplerian
ZEro BeRnoulli Accretion Flow
(Coughlin & Begelman 2013)
Courtesy of M. BegelmanGRMHD simulations https://www.youtube.com/watch? v=q2DeKxUHae4 McKinney et al. 2014
GRMHD simulations
Sadowski et al. 2014GRMHD simulations
Sadowski et al. 2014Trapping all of it
Trapping of radiation: the time for photons to
escape the disk exceeds the timescale for accretion
Trapped photons are advected inward with the gas,
rather than diffuse out
! M! $
rtrap = 10 # & rg
" M! Edd %
L ! M! $
Luminosity highly suppressed
~ ln # &
LEdd " M! Edd %Trapping all of it
If gas has low angular momentum => the whole accretion
disc may be within the trapping radius and luminosity
highly suppressed
capture radius: where gas
becomes bound to the BH
accretion disc radius: set by
gas angular momentum
trapping radius: set by inflow
rateTrapping all of it
• Rg is the capture radius, aka Bondi radius:
• RD is the disc radius defined by the angular
momentum barrier, with λ parameterizing angular
momentum loss:
! M! $ GM ! M! $ G
• impose RD<
rtrap = 10 # ! & 2 = 10 # & 2
" M Edd % c " tEdd % c
Volonteri, Silk & Dubus 2015Trapping all of it
! M! $ GM
rtrap = 10 # & 2
!
" M Edd % cTrapping all of it
105 Msun MBH could grow to
∼108 Msun, in ∼106 years =>
boost of ~3×102 vs Eddington
- gas inflow rate: 1-10 Msun/yr (∼1% of
the free fall rate)
- only gas with low angular momentum
(λ~1% of the mean) is accreted
Only short periods needed to ease constraints
(e.g.Volonteri & Rees 2005,Volonteri, Silk & Dubus 2015)Trapping all of it
Trapping condition:
The lower the gas angular momentum, via λ, the longer
accretion can continue, the higher the final MBH mass.
In galaxies with much low-angular momentum gas near the
center the MBH can get to a higher mass at fixed gas
velocity dispersion.
Volonteri, Silk, Dubus 2015Inflow rates and column density X-ray absorption: photoelectric absorption τ=σNH Compton-Thin: 21
Inflow rates and column density
• Free fall rate
• Given the inverse dependence on the MBH mass, there is
a mass above which the opacity through the sphere < 1
and the MBH is unveiled
Volonteri, Silk, Dubus 2015Inflow rates and column density The gas density is very high and so accretion is obscured, regardless of any assumption on the accretion disc structure and properties - ULASJ1120: L∼ 2×1047 erg/s, MBH∼ 2×109M⊙, σ∼ 100 km/s - J1148: L∼ 7 × 1047 erg/s, MBH ∼ 6 × 109 M⊙, σ∼ 160 km/s => fff∼ 0.15 − 0.35 => NH ∼ few×1022cm−2 (NH < 1023 cm−2 , Moretti et al. 2014).
How do the first black holes grow?
Mgas=107 Msun
• Spherical symmetry
• Radiation-hydrodynamic simulation
• Accretion disc is unresolved
• No magnetic fields
• Cooling: bremsstrahlung and atomic
105 Msun
• Opacity: Free-Free and Bound-Free
• Gas density profile extracted from
cosmological simulations of direct
collapse BH formation (Latif+2014)
• Standard thin accretion disc
• Slim disc (supercritical accretion)
domain: 10−3 pc to 20 pc
Pacucci & Ferrara 2015, Pacucci,Volonteri & Ferrara 2015How do the first black holes grow?
• Standard thin accretion disc
•
M!
m=
M Edd
• Slim disc (supercritical accretion)
Pacucci,Volonteri & Ferrara 2015How do the first black holes grow?
duty cycle
• •
M / M Edd
duty cycle
Standard accretion:
L \propto Mdot
Luminosity mildly super-Eddington
Pacucci,Volonteri & Ferrara 2015How do the first black holes grow?
How do the first black holes grow?
duty cycle
• •
M / M Edd
duty cycle
Slim disc accretion:
L \propto ln(Mdot)
Luminosity sub-Eddington, while accretion super-critical
Pacucci et al. 2015How do the first black holes grow?
Pacucci,Volonteri & Ferrara 2015How do the first black holes grow?
The timescale for outflows to develop is ~1/ε ~ 60 times longer in
radiatively inefficienf flows than in the standard accretion scenario
The BH can consume most of the available gas before feedback
becomes important
Pacucci,Volonteri & Ferrara 2015Summary – growing MBHs • Highly super-Eddington accretion does not imply highly super-Eddington luminosities • Radiatively inefficient accretion flows may ensure a continuous growth with accretion rates largely exceeding the Eddington value, but with sub-Eddington luminosities
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