Radiation Radiation Hydrodynamic Hydrodynamic simulations of simulations of
super-Eddington super-Eddington Accretion Flows Accretion Flows
Radiation Radiation Hydrodynamic Hydrodynamic simulations of simulations of
super-Eddington super-Eddington Accretion Flows Accretion Flows
Ken OHSUGA Rikkyo University, Japan
①①Super-Eddington accretion flows with photon-trapping Super-Eddington accretion flows with photon-trapping (Ohsuga et al. 2005, ApJ, 628, 368)
②②Limit-cycle oscillations driven by disk instability Limit-cycle oscillations driven by disk instability (Ohsuga 2006, ApJ, 640, 923)
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 !To understand the super-Eddington accretion is very important !
1. Super-Eddington Accretion 1. Super-Eddington Accretion FlowsFlows
•In the super-Eddington accretion, the radiation pressure affects the dynamics of the flow. Multi-dimensional effects are important.
BHAccretion
Disk
Viscous Heating
Photon-TrappingPhoton-TrappingPhotons fall onto BH with accreting gas
Outflow
Gas
Radiation Energy
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
Basic Equations of Radiation Hydrodynamics
0D
Dt
v
02
s
D GMp
Dt cr r
v
F N
00 0 0 04 :
EE B c E
t
v F v P
04e
e p B c Et
v v
Continuity Equation ・・・・・・・
Equation of Motion ・・・・・・・Gas Energy Equation ・・・・・・
Radiation Energy Equation ・・
Radiation Force
Viscosity
Absorption/EmissionRadiative Flux
•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)
•Free outer boundary & absorbing inner boundary
Injection
BH r/rs z
/rs
50050
0
•Matter (0.45 x Keplerian angular momentum) is continuously injected into the computational domain from the outer disk boundary.
•Parallel computing with PC cluster
2 3
Black hole mass: 10
Input mass accretion rate: /( / ) 10
BH
input E
M M
M L c
Radiation Energy DensityGas Density
The quasi-steady structure of the super-Eddington accretion flows is obtained by our simulations.
Density & Velocity fields
Outflow
KH instability
Quasi-steady Structure
Mass-Accretion Rate
Mass-accretion rate decreases near the BH.
BH r/rs
z/r
s
Ohsuga et al. 2005, ApJ, 628, 368
Bubbles & Circular Motion
Radiation Pressure-driven wind
Radiation Pressure-dominated Disk
High Temperature Outflow/Corona
Radiation Energy Density
Radiation PressureGas Pressure
Gas Temperature
Radial VelocityEscape Velocity
Low Temperature Disk
Quasi-steady Structure
Photon-Trapping
Mass-accretion rate 2Em M L c
Lum
inos
ity
[L/L
E]
2D RHD simulations
BH
z/r
s
r/rs
Transport of Radiation Energy in r-direction
Radiation energy is transported towards the black hole with accreting gas (photon-trapping).
0 0~r rrF F v E
We verify that the mass-accretion rate considerably exceeds the Eddington rate and the luminosity exceeds LE.
Radiation
Kinetic(Outflow)
Viscou
s Hea
ting
Viewing-angle dependent Luminosity & Image
BH
The observed luminosity is sensitive to the viewing-angle. It is much larger than LE in the face-on view.
cos
Intensity Map
Apparent Luminosity
Density
4D
2 F(
)/L
E
Our simulations
[]
(Intrinsic Luminosity ~3.5LE )
2. Limit-Cycle Oscillations 2. Limit-Cycle Oscillations 2. Limit-Cycle Oscillations 2. Limit-Cycle Oscillations
•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.
Janiuk & Czerny 2005
GRS1915+105 (micro quasar)
LL~2~2LLEE
LL~0.3~0.3LLEE
40s40s
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.
stable
stable
unstable
Surface density
Mas
s-ac
cret
ion
rate High sta
te
Low state
This Topic (Mdot=102LE/c2 )
Previous Topic (Mdot=103LE/c2 )
We investigate the time We investigate the time evolution of unstable disks evolution of unstable disks by performing the 2D RHD by performing the 2D RHD simulations. simulations.
Sub-Eddington state
It is found that the disk structure changes periodically.
2 2
Black hole mass: 10
Input mass accretion rate: /( / ) 10
BH
input E
M M
M L c
Super-Eddington state
outflow
•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.
Mass accretion rate
Outflow rate
Trapped luminosity
Luminosity
Ohsuga 2006, ApJ, 640, 923
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.