Super-Eddington Accretion: Models and Applications

Jian-Min Wang

Institute of High Energy Physics

2005, 4, 26

Implications of SEA

• Theoretical:

one branch of accretion modes

stable

• Applications:

micro-quasars

narrow line Seyfert 1 galaxies

gamma-ray burst

Outline• Polish Doughnut (Abramowicz astro-ph/0411185)

1. Super-Eddington radiation?

2. Wind? 3. Photon trapping?

• Slim disk: 1) numerical results; 2) self-similar solution

• Begelman’s model• Numerical simulation• Applications• Conclusions

EddLL

1. Polish Doughnut:Possibility of Super-Eddington

• Planck Limit

Eddington LimitRadiation cross section

Gravitation cross section

Radiative Equilibrium

Equilibrium Condition:

Vertical Hydrodynamics: thin disk

1max

EddM

M

R

H

For a constant angular momentum, a0, we have

Polish Doughnuts: Bernolli Equation

Polish D

oughnut

PP instability of Polish Doughnut

• Roche lobe:

runaway instability

removes PPI

or

Advection PPI

Slim disk• Abramowicz et al. (1988)

Radial motion

-angular momentum

Energy conservation

Radiation transfer

Vertical equilibrium

Mass conservation

Boundary Condition

• Inner boundary:

free-viscosity stress

• Outer boundary:

standard disk solution

Solutions (1)

Angular momentum distribution

S-shaped curve

Solutions (2)

Transition region?

Solutions (3)

Flux from disk

Spectrum from slim diskWang, Szuszkiewicz et al. (1999, ApJ, 522, 839)

Characteristics:

1. A universe spectrum

F -1

2. Saturate luminosity

L Const.

Self-similar solution• Wang & Zhou (1999, ApJ, 614, 101)

Photon trapping:

saturate luminosity

Bernoulli constant: Be < 0

Comments on Slim Disk

• Inner boundary condition

• Radiation transfer:

1) radiation transfer

2) photon trapping: Qvis=Qrad+Qadv

but tdiff<<tacc

3) decoupling the fluid and radiation

Chen & Wang (2004)

2. Begelman’s model

• Photon bubble instability

(Gammie 1998)

• Begelman (2002):

“leaky” disk

3. Numerical simulations

• 2-D simulations (Ohsuga et al. 2005)

Basic Equations

Boundary/Initial Conditions

3 R/ Rg 500

0 /2

Radiation F.

Viscous F.

mBH=10

Accretion rate=103

t=10s

Velocity

And density profile

Accretion rate at

Different radius

(due to outflow)

Radiation luminosity from SEA,

And compare with slim

cos i =1/8, 3/8, 5/8, 7/8

Future simulations

• Including inhomogeneities due to

photon bubble instability

• FLD (flux limited diffusion)

• SED (Comptonization etc.)

• Viscosity

Slim with corona: applications

Wang & Netzer (2004); Chen & Wang (2004)

Emergent spectrum

Micro-quasars and NLS1s

NLS1 definitions

1) H<2000km/s

2) Fe II or [Fe VII] 6087

[Fe X] 6375

3) [OIII]/ H < 3

* radio-quiet, but loud

Eddington ratio distribution

How do SMBH grow in super-Eddington accretion?

Growth of BH (Kawaguchi et al. (2004)Fraction of NLS1/NLQ:

Marziani et al. (2003):

~11% in 215 low redshift (<0.8)

Williams et al. (2002):

~15% in SDSS DR2

Grupe et al. (1999; 2004)

Salvato et al. (2004):

31-46% in soft X-ray selected AGNs

T~1-3*107years

BLQs: 0.1-5Gyr

Summary

• Theoretical models 1) slim disk? 2) leaky disk driven by photon bubble 3) corona 4) outflow/jet?• Emergent spectrum 1) occulation; 2) GR effects; 3) radiation transfer• Slim with hot corona, jet?• Applications