Radiation Hydrodynamic
simulations of
super-Eddington Accretion
Flows
①Super-Eddington accretion flows with photon-trapping
(Ohsuga et al. 2005, ApJ, 628, 368)
②Limit-cycle oscillations driven by disk instability
(Ohsuga 2006, ApJ, 640, 923)
Ken OHSUGA
Rikkyo University, Japan
1. Super-Eddington Accretion Flows
Super-Eddington disk accretion flows
•The super-Eddington disk accretion (Mdot > LE/c2 ; LE:Eddington luminosity)
is one of the important physics for formation of the SMBHs.
•The super-Eddington accretion might be an engine of the
high L/LE objects, ULXs, GRBs, NLS1s, …. .
•Mass outflow and radiation of the super-Eddington
accretion flow are thought to affect the evolution of the
host galaxies.
To understand the super-Eddington accretion is very important !
•In the super-Eddington accretion, the radiation
pressure affects the dynamics of the flow. Multidimensional effects are important.
We investigate the super-Eddington disk accretion flows by
performing the 2D Radiation Hydrodynamic simulations.
*Slim disk model (1D) cannot correctly treat the multi-dimensional effects
Radiation
Energy
Outflow
Gas
BH
Accretion
Disk
Photon-Trapping
Photons fall onto BH with
accreting gas
Viscous
Heating
Basic Equations of Radiation Hydrodynamics
Continuity Equation・・・・・・・
D
  v  0
Dt
Radiation Force
Dv
GM
 
 p  

F0   N
Equation of Motion・・・・・・・ 
2
Dt
 r  rs 
c
Viscosity
e
   ev    p v  4 B  c E0  
t
E0
Radiation Energy Equation・・
   E0 v    F0  4 B  c E0  v : P0
t
Gas Energy Equation・・・・・・
Radiative Flux
Absorption/Emission
•Equation of State: p=(1)e, =5/3
•Radiation fields (F0, P0)： FLD approximation
•-viscosity： P (=0.1, P:total pressure)
•Absorption coefficient(=ff+bf), ff: free-free absorption,
bf:bound-free absorption (Hayashi, Hoshi, Sugimoto 1962)
Numerical Method
•Explicit-implicit finite difference scheme on Eulerian grid
(Spherical coordinates : 96 x 96 mesh)
•Axisymmetry with respect to the rotation axis
•Size of computational domain: 500rs
•Initial condition: atmosphere (no disk)
z/ r s
500
•Free outer boundary & absorbing inner boundary
•Matter (0.45 x Keplerian angular
momentum) is continuously injected into the
computational domain from the outer disk
boundary.
Injection
•Parallel computing with PC cluster
BH
r /r s
500
Gas Density
Radiation Energy Density
Black hole mass: M BH  10M
Input mass accretion rate: M input /( LE / c 2 )  103
The quasi-steady structure of the super-Eddington
accretion flows is obtained by our simulations.
Quasi-steady Structure
Density & Velocity fields
Ohsuga et al. 2005,
ApJ, 628, 368
KH instability
Bubbles &
Circular Motion
z/rs
Outflow
Mass-Accretion Rate
Mass-accretion
rate decreases
near the BH.
BH
r/rs
Quasi-steady
Structure
Radiation Energy
Density
Radiation Pressure
Gas Pressure
Radiation
Pressuredominated Disk
High Temperature
Outflow/Corona
Gas Temperature
Radiation Pressuredriven wind
Low Temperature
Disk
Radial Velocity
Escape Velocity
Transport of Radiation
Energy in r-direction
z/rs
Photon-Trapping
F r ~ F0r  vr E0
Luminosity
[L/LE]
Radiation
Kinetic
(Outflow)
2D RHD
simulations
BH
Mass-accretion rate m  M  LE c 2 
We verify that the mass-accretion rate
considerably exceeds the Eddington
rate and the luminosity exceeds LE.
r/rs
Radiation energy is transported
towards the black hole with
accreting gas (photon-trapping).
Viewing-angle dependent Luminosity & Image
Apparent Luminosity

(Intrinsic Luminosity ~3.5LE )
Density
Intensity Map
4D2F()/LE
BH
Our simulations
cos
[]
The observed luminosity is sensitive to the
viewing-angle. It is much larger than LE in
the face-on view.
2. Limit-Cycle Oscillations
GRS1915+105 (micro quasar)
L~2LE
40s
L~0.3LE
Janiuk & Czerny 2005
•Timescale of the luminosity variation is around 40s.
•The disk luminosity oscillates between 2.0LE and
0.3LE (Yamaoka et al. 2001).
•The intermittent JET is observed.
Disk instability in the radiation-pressure dominant region.
If the mass-accretion rate from the disk boundary is around the
Eddington rate, Mdot  LE/c2, the disk exhibits the periodic
oscillations via the disk instability.
Mass-accretion rate
Previous Topic
(Mdot=103LE/c2 )
This Topic
(Mdot=102LE/c2 )
Surface density
We investigate the time
evolution of unstable disks
by performing the 2D RHD
simulations.
Black hole mass: M BH  10M
Super-Eddington state
Input mass accretion rate: M input /( LE / c 2 )  102
outflow
Sub-Eddington state
It is found that the disk
structure changes periodically.
Mass accretion rate
Outflow rate
Trapped luminosity
Luminosity
Ohsuga 2006, ApJ, 640, 923
•The disk luminosity oscillates between 0.3LE and 2.0LE, and
duration time is 30-50s.
•Jet appears only in the high luminosity state.
•These results are nicely fit to the observations of GRS 1915+105.
Conclusions(1) : super-Eddington accretion flow; Mdot >> LE/c2
 The mass accretion rate considerably exceeds the Eddington rate. The black
hole can rapidly grow up due to disk accretion (Mdot/M~106yr).
The luminosity exceeds the Eddington luminosity. The apparent luminosity is
more than 10 times larger than LE in the face-on view.  The luminosity of the
ULXs can be understood by the super-Eddington accretion flow.
The thick disk forms and the complicated structure appears inside the disk. The
radiation-pressure driven outflow is generated above the disk.
We found that the photon-trapping plays an important role.
Conclusions(2) : limit cycle oscillations; Mdot  LE/c2
 The resulting variation amplitude (0.3LE⇔2.0LE) and duration (30-50s) nicely
fit to the observations of microquasar, GRS 1915+105.
The intermittent jet is generated.
The physical mechanism, which causes the limit-cycle oscillations, is the disk
instability in the radiation-pressure dominant region.