Modeling Supercritical Accretion Flow

Shin Mineshige (Kyoto) & Ken Ohsuga (RIKEN)

Outline Introduction

Basics of supercritical (super-Eddington) accretion

Slim disk model for ULXs Properties of “slim” disks Spectral fits to ULXs

Global radiation-hydrodynamic simulations Multi-dimensional effects Why is supercritical accretion feasible?

Global radiation-magnetohydrodynamic simulations Three different regimes of accretion flow

1. Introduction1. IntroductionBinary black holes show distinct spectral Binary black holes show distinct spectral

states, (probably) depending on the states, (probably) depending on the mass accretion rate. mass accretion rate.

・・ What happens at high accretion rates?What happens at high accretion rates?・・ What physical processes are important What physical processes are important

there?there?

State transition in BH binaryState transition in BH binary Esin et al. (1997)

Standard disk+corona

Standard disk

Radiatively inefficient flow (ADAF/CDAF/MHD Flow)

Very high state

High/soft state

Intermediate

state

Low/hard state

Quiescence

m ..Supercritical state 　　　　　　　　　　　　　　　　 Slim disk (with outflow)

~10% LE

~ LE

Super-Eddington flux (F > LE/4πr 2) is possible in the z-direction

because of radiation anisotropy (!?) .

DiskDisk accretion may achieve accretion may achieve L>LL>LEE

radiation

pressureaccreti

nggas

accretinggas

Shakura & Sunyaev (1973)

BH

Low-energy photons

trapped photons

Low-energy photons

High-energy photons

radiative diffusion & accretion

　 (c) K. Ohsuga

What is Photon trapping?What is Photon trapping? Begelman (1978), Ohsuga et al. (2002)

When photon diffusion time,tdiff~Hτ/c, exceeds accretion time tacc~r/|vr |, photons are trapped.

rtrap~ (Mc2/LE) rs .

2. Slim disk model for ULXs2. Slim disk model for ULXsSlim disk model was proposed for Slim disk model was proposed for

describing high luminosity, supercritical describing high luminosity, supercritical accretion flows. We examined the accretion flows. We examined the XMM/Newton data of several ULXs based XMM/Newton data of several ULXs based on the slim disk model.on the slim disk model.

・・ What is the slim disk model?What is the slim disk model?・・ What features are unique to the slim What features are unique to the slim

disk?disk?・・ What did we find in ULX data?What did we find in ULX data?

Basics

This occurs within trapping radius

rtrap~ (Mc2/LE) rs

Model One-dim. model (in r direction) with radiation entropy advection

Slim disk modelSlim disk model Abramowicz et al. (1988); Watarai et al. (2000)

-2

-1

0

1

-1 0 1 2 3 4

log

L/L E

L=LE

log m≡log M/(LE/c2). .

accretion energy

trapped photons.

3

8 49

)( 42gasrad T

drssd

Tvr

viscous radiative heating cooling

Slim disk structureSlim disk structure Beloborodov (1998), Mineshige, Manmoto et al. (2002)

Low M rin～ 3rS ;Teff∝r

-3/4

High M rin～ rS

; Teff∝r -1/2

3 rS

.

M/(LE/c2)=1,10,102,103 　　　　　　 MBH=105Msun

. .

Slim-disk signatures 1.small innermost radius2.flatter temp. profile

Wang & Zhou (1999), Watarai & Fukue (1999)

Case of non-spinning BHs:

(=rms )

1.1. Small innermost radiusSmall innermost radius (Abramowicz, Kato, … Watarai & Mineshige 2003)

Classical argument:Circular orbits of a test particle become unstable at r < rms

(=3 rS for no spin BH).

Case of slim disk:The classical argument can- not apply because the disk is not in force balance. The inner edge can be at r < rms.

Same is true for ADAF.

The disk inner disk is not always at rin = rms.

potential minimum

slim-disksolutions

Standard disk: Constant fraction of grav. energy

is radiated away.

Slim disk: Fraction of energy which is radiated away decreases inward: Qrad/Qvis ~ tacc/tdiff ∝r/rtrap∝r

2.2. Flatter temperature Flatter temperature profileprofile

4/3eff

1BH4eff

2

2

rT

rr

MGMTr

2/1eff

0

diff

accBH4eff

2

2

rT

rtt

rMGMTr

Disk spectra = multi-color blackbody radiation

Temp. profiles affect spectra: Fν∝∫Bν(T(r )) 2πrdr

T ∝r -p ⇒ Fν∝ν3-(2/p)

・standard disk (p =3/4)

⇒ Fν∝ν1/3

・slim disk (p =1/2)

　　　　　　　 ⇒ Fν∝ν-1

Spectral propertiesSpectral properties (e.g. Kato et al. 1998,2008)

ν1/3

ν-1hν

Fν

hν

Fν

(small r)

(small r)

UltraUltra LuminousLuminous X-rayX-ray sourcessources (ULXs)(ULXs) Colbert & Mushotzky (1999), Makishima et al. (2000), van der Karel (2003)

Bright (>~1040 erg s-1) compact X-ray sources Successively found in off-center regions of nearby galaxies. If L < LE, black hole mass should be > 100 Msun.

LE ~ 1038 (M/Msun) erg s-1

Two possibilities Sub-critical accretion onto intermediate-mass BHs (M>100Msun). Super-critical accretion onto stellar-mass BHs (M~3-30Msun).

IC342 galaxy

Extended disk-blackbody modelExtended disk-blackbody model (Mitsuda et al. 1984; Mineshige et al. 1994)

Fitting with superposition of blackbody (Bν) spectra:

Three fitting parameters: Tin = temp.of innermost region (～ max. temp.)

rin = size of the region emitting with Bν(Tin)

p = temperature gradient (=0.75 in disk-blackbody model)

Corrections: Real inner edge is at ～ ξrin with ξ～0.4

Higher color temp.; Tc =κTin with κ～1.7

⇒ Good fits to the Galactic BHs with p =0.75

pr

r

rrTrTrdrrTBiFout

in

)/()( ;2)]([cos inin

Fitting with disk blackbody (p=0.75) + power-law

We fit XMM-Newton data of several ULXs ⇒ low Tin ～0.2 keV and photon index ofΓ=1.9　

If we set rin~ 3 rS, BH mass is MBH~ 300 Msun.

SpectralSpectral fittingfitting 1.1. ConventionalConventional modelmodel (Miller et al. 2004, Roberts et al. 2005)

NGC 5204 X-1

log hν

log conts

However, PL comp. entirely dominates over DBB comp.

Model fitting, assuming T ∝ r -p

We fit the same ULX data with extended DBB model ⇒ high Tin ~ 2.5 keV and p =0.50±0.03 (no PL comp.)

MBH~ 12 Msun & L/LE~ 1, supporting slim disk model.

SpectralSpectral fittingfitting 2.2. Extended DBB modelExtended DBB model (Vierdayanti, SM, Ebisawa, Kawaguchi 2006)

NGC 5204 X-1

log hν

log conts

log kT (keV)

log Lx

Temperature-Luminosity diagramTemperature-Luminosity diagram

(Vierdayanti et al. 2006, PASJ 58, 915)

New model fitting gives MBH <30Msun.

Low-temperature results should be re-examined!! DBB + PL ext. DBB

Standard disk with outflow Set L (r ) ≡2πr

2F (r ) = LE → M (r ) ∝r (∵F ∝M (r )/r 3)

Comment on outflowComment on outflow (Shakura & Sunyaev 1973; Poutanen et al. 2007)

2/1eff

04eff

2 2 rTrTr

・

Same as that of slim disks !!

BH

outflow

disk wind

accreting gas accretio

n

・

spherization radius, Rsp~ rtrap

Rsp

⇒ Similar effects are expected.

3.Radiation-hydro. simulation3.Radiation-hydro. simulation

The slim-disk model is one-dimensional model, The slim-disk model is one-dimensional model, although multi-dimensional effects, such as although multi-dimensional effects, such as outflow, could be important when L >~ Loutflow, could be important when L >~ LEE. We . We thus perform radiation-hydrodynamic (RHD) thus perform radiation-hydrodynamic (RHD) simulations.simulations.

・・ What are the multi-dimensional effects?What are the multi-dimensional effects?・・ What can we understand them?What can we understand them?

Our global 2D RHD simulationsOur global 2D RHD simulations Ohsuga, Mori, Nakamoto, SM (2005, ApJ 628, 368)

• First simulations of super-critical accretion flows in quasi-steady regimes.

• Matter (with 0.45 Keplerian ang. mom. at 500 rS) is continuously added through the outer boundary

→ disk-outflow structure

• Flux-limited diffusion adopted.

• α viscosity (α=0.1), MBH=10Msun

• Mass input rate: 1000 (LE/c2) 　→ luminosity of ~3 LE

Injection

BH r/rs

z/r s

50050

0

Initially empty disk

gas density

　 (c) K. Ohsuga

Overview of 2D super-critical Overview of 2D super-critical flowflow

Ohsuga et al. (2005)

BH r/rs

z/r s

density contours & velocity fields

disk flow

outflow

Case of M =10 Msun a

nd M =1000 LE/c 2

・

gas density radiation energy density

Why is supercritical accretion Why is supercritical accretion feasible?feasible?

Ohsuga & S.M. (2007, ApJ 670, 1283)

Steep Erad profile yield super-Eddington flux.

Radiation energy density is high; Erad

≫ EE≡LE/4πr 2c, but

Why is then radiation pressure force so weak ?

Note radiation energy flux is 　 　 Frad ∝(κρ)-1∇Erad.

→ Because of relatively flat Erad profile.

ffcentradgrav || ~ vvfff rrr

ffradgrav vvff rr

fast outflo

w

slow accretion

　 (c) K. Ohsuga

Photon Photon trappingtrapping

BH

z/r s

r/rsRadiation flux (F r ) is

inward!

Photon trapping also helps reducing radiation pressure force.

F r=radiation flux in 　　

the rest frame

F0r=radiation flux in

　 the comoving frame

　 is F r~F0r+vrE0

The observed luminosity is sensitive to the viewing-angle; Maximum L ~ 12 LE !!

cos

luminosity

BH

Density contours

12

8

44

D2 F

()/

L E

our simulations

　 (c) K. Ohsuga

SignificantSignificant radiationradiation anisotropyanisotropy

⇒ mild beaming

0

viewing angle

4.Global radiation-magneto-4.Global radiation-magneto- hydrodynamic simulations hydrodynamic simulations

Alpha viscosity adopted in RHD simulations Alpha viscosity adopted in RHD simulations is not so realistic. We have just obtained is not so realistic. We have just obtained preliminary results of 2-dim. global RMHD preliminary results of 2-dim. global RMHD simulations of black hole accretion flows.simulations of black hole accretion flows.

・・ Can we reproduce different spectral Can we reproduce different spectral states?states?

Our global 2D RMHD simulationsOur global 2D RMHD simulations Ohsuga, Mori, SM (2008, in preparation)

• Extension of MHD simulations to incorporate radiation effects (through flux-limited diffusion).• Start with a torus threaded weak poloidal fields:

• Three different regimes (0=density normalization), MBH=10 Msun

Model A (0=100 g/cm3) : supercritical accretion

Model B (0=10-4 g/cm3) : standard-disk type accretion

Model C (0=10-8 g/cm3) : radiatively inefficient accretion

non-radiative MHD simulation for 4.5 rotation periods

turn on radiation terms

z /rs

r /rs

log /0 v/vesc

Model A ： Supercritical accretion 　（ｌ og ρ0=1 g/cm3)

r /rs r /rs

z /rs z /rs

v/vesc

Model B ： Standard-disk type accretion （ｌ og ρ0=10-4 g/cm3)

log /0

r /rs r /rs

z /rs z /rs

v/vesc

Model C ： Radiatively inefficient accretion （ｌ og ρ0=10-8 g/cm3)

log /0

r /rs r /rs

z /rs z /rs

　 (c) K. Ohsuga

luminosity/LE

accretion rate/ （ LE/c2 ）outflow rate/ （ LE/c2 ）Model A

(supercritical)

Model B(standard)

Model C(RIAF)

Not yet ina quasi-steady state.

~ 1 sec

SummarySummary ofof RMHDRMHD simulationssimulations

Model density & temperatur

e

luminosity,

L /L E

energetics kin. luminosity, L

kin/L

Model A(supercritic

al)

ρ~10-2 g/cm3

T ~108 K~100 Erad >> Egas

>~ Emag~0.2

Model B(standard)

ρ~10-5 g/cm3

T ~106 K~10-2 Egas ~ Emag

~ Erad~0.003

Model C(RIAF)

ρ~10-9 g/cm3

T ~1010 K~10-8 Egas > Emag

>> Erad~3

Model A: similar to the results of RHD simulationsModel B: moderate variations and outflow (??)Model C: similar to the results of MHD simulations

ConclusionsConclusions • Near- or supercritical accretion flows seem to occur in some systems

(ULXs…?).

• Slim disk model predicts flatter temperature profile. Spectral fitting with variable p (temp. gradient) proves the presence of supercritical accretion in some ULXs.

• 2D RHD simulations of supercritical flow show super- Eddington luminosity, significant radiation anisotropy (beaming), high-speed outflow etc.

L can be >~ 10 LE !!

• 2D RMHD simulations are in progress. We can basically reproduce three different regimes of accretion flow.