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.