Super-Critical Accretion?Super-Critical Accretion?Shin MineshigeShin Mineshige (Kyoto Univ.)(Kyoto Univ.)

with K.with K. Ohsuga, K.Ohsuga, K. Vierdayanti, K.Vierdayanti, K. Ebisawa, T.Ebisawa, T. KawaguchiKawaguchi

TIARA Workshop TIARA Workshop (29/11/2006)(29/11/2006)

1.1. General introductionGeneral introduction

2.2. Slim disk model (simplified model)Slim disk model (simplified model)

3.3. Observational tests - Case of ULXsObservational tests - Case of ULXs

4.4. Multi-dimensional effectsMulti-dimensional effects

1. Introduction 1. Introduction (background)(background)

There are some objects which seem to There are some objects which seem to undergo super-critical (or super-undergo super-critical (or super-Eddington) accretion.Eddington) accretion.

・・What are ULXs? What are NLS1s?What are ULXs? What are NLS1s?

・・What do we know from observations?What do we know from observations?

・・What is key physics in super-critical What is key physics in super-critical accretion?accretion?

UltraUltra LuminousLuminous X-rayX-ray sourcessources (ULXs)(ULXs) 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

Arguments in favor of intermediate-mass BH (IMBH) Luminosities sometimes exceed ~ 1040erg s-1 (=LE of 100 Msun) Some ULXs show kT ~ 0.1 keV, indicating large MBH (> 100 Msun)

Do ULXs contain IMBHs?Do ULXs contain IMBHs? Miller et al. (2003, 2004)

log Lx

0.1 keV 1.0 keV

low L & highT =stellar-mass BHs

log kT (keV)

1040 erg/s

1037 erg/s

10M

sun

100M

sun

high L & lowT =IMBHs (?)

4/1BH

1/4

2E

4/1

sun

BH7eff /10

K 10~

M

cL

M

M

MT

WhatWhat determinesdetermines diskdisk temperature?temperature?

Energetics (Newtonian version)

grav.energy: half → radiation energy

half → rotation energy

That is, (1/2)Egrav = Erad

For r ~ 3 rS, we have

⇒

.22

1 4

eff2BH Tr

r

MGM

r

GMBH

BH

1 keV for 10 Msun BH, 0.1 keV for 105 Msun BH

Narrow-lineNarrow-line SeyfertSeyfert 11 galaxiesgalaxies (NLS1s)(NLS1s)

What are NLS1s? Narrow “broad lines” (< 2000 km s-1) Seyfert 1 type X-ray features Extreme soft excess & variability

Seem to contain less massive BHs Good analogy with stellar-mass BHs in their ve

ry high (large L ) state. High Tbb (∝MBH

-1/4) ⇒ large soft excess Small (GMBH/RBLR)1/2 ⇒ narrow line width

NLS1s = high L/LE system

Boller et al. (NewA 44, 2000)

Spherical accretion system cannot shine at L > LE.

What is the Eddington What is the Eddington luminosity?luminosity?

radiationpressure

accretinggas

accretinggas

Gravity > rad. pressure

⇒ GM/r 2 >κF/c ⇒ L < LE=4πCGM/κ (∵ F=L/4πr

2)

Super-Eddington flux (F > LE/4πr2) is possible in the z-directi

on because of radiation anisotropy (!?) .

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

radiation

pressure

accretinggas

accretinggas

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 model2. Slim disk model

Slim disk model was proposed for Slim disk model was proposed for describing high luminosity flows as an describing high luminosity flows as an extension of the standard disk.extension of the standard disk.

・・What is distinct from the standard disk What is distinct from the standard disk

model?model?

・・What are its observational signatures?What are its observational signatures?

Basics

This occurs within trapping radius

rtrap~ (Mc2/LE) rs

Model Radially 1-D model with radiation entropy advection

Spectrum τ≫ 1 → multicolor blackbody but with higher T

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

4

9

)( 42gasrad T

dr

ssdTvr

Slim-disk structureSlim-disk structure 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)

What determines the inner edge ofWhat determines the inner edge of aa ddisk? isk? Watarai & Mineshige (PASJ 55, 959, 2003)

Classical argument:Circular orbits of a test particle become unstable at r < rms (=3 rS for no spin BH)

Case of slim disk:

Usual stability analysis　　　 cannot apply because of 　no force balance.

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: tdiff=tacc → Mc2/LE ~r/rtrap∝r

What determines temp. What determines temp. profile?profile?

4/3eff

1BH4eff

2

2

rT

rr

MGMTr

2/1eff

0BH4eff

2

2

rT

rr

MGMTr

.

Disk spectra = multi-color blackbody radiation

Temperature profiles affect spectra

T ∝r -p ⇒ F ∝ν3-(2/p)

・standard disk (p =3/4)

⇒ F ∝ν1/3

・slim disk (p =1/2)

　　　　　　　 ⇒ F ∝ν-1

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

ν1/3

ν-1hν

Fν

hν

Fν

(small r)

(small r)

3. Observational tests: 3. Observational tests: Case of ULXsCase of ULXs

We examined the XMM/Newton data We examined the XMM/Newton data of several ULXs which were of several ULXs which were suggested to contain suggested to contain intermediate-mass black holes.intermediate-mass black holes.

・・ How to test the theory?How to test the theory?

・・What did we find?What did we find?

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

Fitting with superposition of blackbody (Bν) spectra:

Fitting parameters:

Tin = temp.of innermost region (～ max. temp.)

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

p = temperature gradient

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 BBHs 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 (Roberts et al. 2005)

NGC 5204 X-1

log hν

log conts

Spectral decomposition of DBB & PL components

DBB comp. is entirely dominated by PL comp.

Can we trust values derived from the minor component?

Problem with DBB+PLProblem with DBB+PL fittingfitting

log hν

log conts

NGC 5204 X-1

Model fitting, assuming T ∝ r -p

We fit the same data but with the 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. ExtendedExtended DBBDBB modelmodel (Vierdayanti, SM, Ebisawa, Kawaguchi 2006)

NGC 5204 X-1

log hν

log conts

Why can both models give good Why can both models give good fits?fits?

Because the spectral shapes are similar below ~10 keV.

Both show fν ∝ν-1

in 0.1~10keV range.

power-law (Γ=2)

extended DBB with p=0.5

log kT (keV)

log Lx

Temperature-Luminosity diagramTemperature-Luminosity diagram

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

No evidence of IMBHs so far

New model fitting gives MBH <30Msun.

Low-temperature results should be re-examined!!

The same test is needed for NLS1s

DBB + PL ext. DBB

FateFate ofof Prad-drivenPrad-driven instabilityinstability

Radiation pressure-dominated SS disk is unstable.

(1) relaxation oscillation?Honma et al. (1991),Szuszkiewicz & Miller (1998)

(2) soft-to-hard transition? Takeuchi & Mineshige (1998),Gu & Lu (2000)

(3) strongly clumped disk?Krolik (1998)

(4) disk-corona structure?Nakamura & Osaki (1993), Svensson & Zdziarski (1994)

Σ

M・

(1)(2)

Bursting behavior of micro-Bursting behavior of micro-

quasarquasar 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 (Yamaoka, Ueda & Inoue 2002)

GRS 1915+105 e

xhibits state transitions between

peak (slim disk)

and

valley (thin disk)

log rin

log

Tin

time

cou

nts

(T ∝ r -1/2 )

(T ∝ r -3/4 )

4. Multi-dimensional effects4. Multi-dimensional effects

The slim-disk model applies only to the flow with L ~ LThe slim-disk model applies only to the flow with L ~ LEE. For even higher L, we need to perform radiation-hyd. For even higher L, we need to perform radiation-hydrodynamical (RHD) simulations.rodynamical (RHD) simulations.

・・ What are the multi-dimensional effects?What are the multi-dimensional effects?

・・ What can we understand them?What can we understand them?

A simple modelA simple model (Ohsuga et al. 2002, ApJ 574, 315; 2003, ApJ 596, 429)

Problem with the slim-disk formulation Radiative cooling rate is evaluated as ~ 4σT 4/3τ (at same r)

Consider a part of the disk which is moving inward Dynamics is given. Solve radiation transfer in z-direction.

Can approximately evaluate 2D photon trapping effects.

BH accretio

nradiativ

e diffusio

n

•The slim-disk model overestimates the luminosity.•The frequency of the SED peak first increases then 　 decreases with increase of mass-accretion rate. 　 (c) K. Ohsug

a

Photon trapping:Photon trapping: observable observable effectseffects

Lu

min

osit

y [L/LE] Slim disk

Our results

(Photon-trapping)

Mass-accretion rate

m=10・

m=100・

30

m=10・MCD

Luminosity SED Variations

Photon-trapping Slim disk

Ohsuga et al. 2003Ohsuga et al. 2002

Black hole mass: 10BHM M 2

Em M L c

Our 2D RHD simulationsOur 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 A.M. is continuously added through the outer boundary

→ disk-outflow structure

• Flux-limited diffusion adopted.

• α viscosity with α=0.1.

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

Injection

BH r/rs

z/r

s

50050

0

Initially empty disk

　 (c) K. Ohsuga

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

Ohsuga et al. (2005, ApJ 628,368)

gas energy radiation energy density density

BH r/rs

z/r

s

density contours & velocity fields

disk flow

outflow

Case of M =10 Msun & M =1000 LE/c

2・

Why is accretion Why is accretion possible?possible?

Ohsuga & S.M. (2006, submitted)

Low ρ and steep Erad profile yields super-Eddington flux.

Radiation energy density is high; Erad ≫ EE≡LE/4πr 2c .

Then why is the radiation 　 pressure force so weak?

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

→ Because of high ρ and 　　　 relatively flat Erad profile.

　 (c) K. Ohsuga

Photon Photon trappingtrapping

BH

z/r

s

r/rsRadiation flux (F r ) is

inward!

Photon trapping also helps reduced radiation pressure force.

F r=radiation flux in 　　

the rest frame

F0r=radiation flux in 　

the comoving frame

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

Ohsuga et al. (2005, ApJ 628,368)

0

viewing angle

Why beaming?Why beaming?

Photon energy increases as θ decreases, why? - Because we see photons from deeper, hot region. - Because of Doppler effect.

Why photon number increases as θ decreases, why? - Because of anisotropic gas distribution. - Because Iν/ν3 is Lorentz invariant & hν increases.

radiation

gasgas

Heinzeller, S.M. & Ohsuga (2006, MNRAS 372, 1208,)

Future issueFuture issueInteraction with magnetic Interaction with magnetic fieldsfields

Magnetic fields are essential ingredients in disks• Photon-bubble instability (Begelman 2002) • Magnetic tower jet → global RHD+MHD simulations necessary

(Kato, SM, & Shibata 2004)

ConclusionsConclusions

• Near- and super-critical accretion flows seem to occur in some systems (ULXs, NLS1s…?).

• Slim disk model predicts flatter temperature profile. Spectral fitting with variable p proves the presence of supercritical accretion in ULXs. How about NLS1s?

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

L can be ~10 LE !!

• Issues: magnetic fields, line spectra, instability,…