Modeling Supercritical Accretion Flow Shin Mineshige (Kyoto)

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Modeling Supercritical Accretion FlowShin
Mineshige (Kyoto) Ken Ohsuga (RIKEN)
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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

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1. Introduction

• Binary black holes show distinct spectral states,
  (probably) depending on the mass accretion rate.
• What happens at high accretion rates?
• What physical processes are important there?

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

• Standard diskcorona
• Standard disk
• Radiatively inefficient flow (ADAF/CDAF/MHD Flow)

Very high state High/soft state Intermediate
state Low/hard state Quiescence
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Disk accretion may achieve LgtLE

• Super-Eddington flux (F gt LE/4pr 2) is possible
  in the z-direction because of radiation
  anisotropy (!?) .

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What is Photon trapping?
Begelman (1978), Ohsuga et al. (2002)
When photon diffusion time,tdiffHt/c, exceeds
accretion time taccr/vr , photons are trapped.
Low-energy photons
Low-energy photons
BH
radiative diffusion accretion
High-energy photons
trapped photons
(c) K. Ohsuga
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2. Slim disk model for ULXs

• Slim disk model was proposed for describing high
  luminosity, supercritical accretion flows. We
  examined the XMM/Newton data of several ULXs
  based on the slim disk model.
• What is the slim disk model?
• What features are unique to the slim disk?
• What did we find in ULX data?

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

• Basics
• This occurs within trapping radius
• rtrap (Mc2/LE) rs
  
  
• Model
• One-dim. model (in r direction) with
  radiation entropy advection

accretion energy
trapped photons
.
viscous radiative heating cooling
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Slim disk structure Beloborodov
(1998), Mineshige, Manmoto et al. (2002)
Wang Zhou (1999), Watarai Fukue (1999)
Case of non-spinning BHs
.

• Low M
• rin 3rS Teff?r -3/4
• High M
• rin rS Teff?r -1/2

.
Slim-disk signatures 1.small innermost
radius 2.flatter temp. profile
(rms )
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1. Small innermost radius
(Abramowicz, Kato, Watarai Mineshige 2003)

• Classical argument
• Circular orbits of a test particle become
  unstable at r lt 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 lt rms.
• Same is true for ADAF.

potential minimum
slim-disk solutions
The disk inner disk is not always at rin rms.
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2. Flatter temperature profile

• 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

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

• Disk spectra multi-color blackbody radiation
• Temp. profiles affect spectra F???B?(T(r ))
  2prdr
• T ?r -p ? F???3-(2/p)
• standard disk (p 3/4)
• ? F???1/3
• slim disk (p 1/2)
• ? F???-1

?1/3
F?
(small r)
h?
?-1
F?
(small r)
h?
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Ultra Luminous X-ray sources (ULXs)
Colbert Mushotzky (1999), Makishima et al.
(2000), van der Karel (2003)

• Bright (gt1040 erg s-1) compact X-ray sources
• Successively found in off-center regions of
  nearby galaxies.
• If L lt LE, black hole mass should be gt 100 Msun.
• LE 1038
  (M/Msun) erg s-1
• Two possibilities
• Sub-critical accretion onto intermediate-mass BHs
  (Mgt100Msun).
• Super-critical accretion onto stellar-mass BHs
  (M3-30Msun).

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

• Fitting with superposition of blackbody (B?)
  spectra
• Three fitting parameters
• Tin temp.of innermost region ( max.
  temp.)
• rin size of the region emitting with
  B?(Tin)
• p temperature gradient (0.75 in
  disk-blackbody model)
• Corrections
• Real inner edge is at ?rin with ?0.4
• Higher color temp. Tc ?Tin with ?1.7
• ? Good fits to the Galactic BHs with p 0.75

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Spectral fitting 1. Conventional model
(Miller et al. 2004, Roberts et al. 2005)

• Fitting with disk blackbody (p0.75) power-law
• We fit XMM-Newton data of several ULXs
• ? low Tin 0.2 keV and photon index ofG1.9
• If we set rin 3 rS, BH mass is MBH 300 Msun.

log conts
NGC 5204 X-1
However, PL comp. entirely dominates over DBB
comp.
log h?
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Spectral fitting 2. Extended DBB model
(Vierdayanti, SM, Ebisawa, Kawaguchi 2006)

• Model fitting, assuming T ? r -p
• We fit the same ULX data with extended DBB model
• ? high Tin 2.5 keV and p 0.500.03 (no PL
  comp.)
• MBH 12 Msun L/LE 1, supporting slim disk
  model.

log conts
NGC 5204 X-1
log h?
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Temperature-Luminosity diagram

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

• New model fitting
• gives MBH lt30Msun.
• Low-temperature
• results should be
• re-examined!!

log Lx
DBB PL
ext. DBB
log kT (keV)
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Comment on outflow
(Shakura Sunyaev
1973 Poutanen et al. 2007)

• Standard disk with outflow
• Set L (r ) 2pr 2F (r ) LE ? M (r ) ?r
  (?F ?M (r )/r 3)

Same as that of slim disks !!
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3.Radiation-hydro. simulation

• The slim-disk model is one-dimensional model,
  although multi-dimensional effects, such as
  outflow, could be important when L gt LE. We
  thus perform radiation-hydrodynamic (RHD)
  simulations.
• What are the multi-dimensional effects?
• What can we understand them?

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Our 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.
• a viscosity (a0.1), MBH10Msun
• Mass input rate 1000 (LE/c2)
  ? luminosity of 3 LE

gas density
Initially empty disk
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Overview of 2D super-critical flow
Ohsuga et al. (2005)
Case of M 10 Msun and M 1000 LE/c 2

gas density radiation energy
density
(c) K. Ohsuga
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Why is supercritical accretion feasible?
Ohsuga S.M. (2007, ApJ 670, 1283)
Radiation energy density is high Erad
EELE/4pr 2c, but Why is then radiation pressure
force so weak ? Note radiation energy flux is
Frad ?(??)-1?Erad. ? Because of
relatively flat Erad profile.
fast outflow
slow accretion
Steep Erad profile yield super-Eddington flux.
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Photon trapping
F rradiation flux in the rest
frame F0rradiation flux in the comoving
frame is F rF0rvrE0
z/rs
Photon trapping also helps reducing radiation
pressure force.
BH
r/rs
Radiation flux (F r ) is inward!
(c) K. Ohsuga
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Significant radiation anisotropy
luminosity
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our simulations
4?D2F(?)/LE
8
4
0
viewing angle
The observed luminosity is sensitive to the
viewing-angle Maximum L 12 LE !!
? mild beaming
(c) K. Ohsuga
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4.Global radiation-magneto- hydrodynamic
simulations

• Alpha viscosity adopted in RHD simulations is
  not so realistic. We have just obtained
  preliminary results of 2-dim. global RMHD
  simulations of black hole accretion flows.
• Can we reproduce different spectral states?

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Our 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 (?0density
  normalization), MBH10 Msun
• Model A (?0100 g/cm3) supercritical
  accretion
• Model B (?010-4 g/cm3) standard-disk type
  accretion
• Model C (?010-8 g/cm3) radiatively
  inefficient accretion

z /rs
non-radiative MHD simulation for 4.5 rotation
periods
turn on radiation terms
r /rs
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Model A Supercritical accretion (log ?01 g/cm3)
log ?/?0
v/vesc
z /rs
z /rs
r /rs
r /rs
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Model B Standard-disk type accretion (log
?010-4 g/cm3)
v/vesc
log ?/?0
z /rs
z /rs
r /rs
r /rs
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Model C Radiatively inefficient accretion (log
?010-8 g/cm3)
v/vesc
log ?/?0
z /rs
z /rs
r /rs
r /rs
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accretion rate/(LE/c2)
Model A (supercritical)
outflow rate/(LE/c2)
luminosity/LE
Model B (standard)
Not yet in a quasi- steady state.
Model C (RIAF)
1 sec
(c) K. Ohsuga
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Summary of RMHD simulations
Model density temperature luminosity, L /L E energetics kin. luminosity, L kin/L
Model A (supercritical) ?10-2 g/cm3 T 108 K 100 Erad gtgt Egas gt Emag 0.2
Model B (standard) ?10-5 g/cm3 T 106 K 10-2 Egas Emag Erad 0.003
Model C (RIAF) ?10-9 g/cm3 T 1010 K 10-8 Egas gt Emag gtgt Erad 3
Model A similar to the results of RHD
simulations Model B moderate variations and
outflow (??) Model C similar to the results of
MHD simulations
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Conclusions

• 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 gt 10 LE !!
• 2D RMHD simulations are in progress. We can
  basically reproduce three different regimes of
  accretion flow.