Post on 17-Dec-2015
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. Introduction
Binary 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-directi
on because of radiation anisotropy (!?) .
DiskDisk accretion may achieve accretion may achieve L>LL>LEE
radiation
pressure
accretinggas
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
4
9
)( 42gasrad T
dr
ssdTvr
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
rt
t
r
MGMTr
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
accretion
・
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 Alpha viscosity adopted in RHD simulations is not so realistic. We have simulations is not so realistic. We have just obtained preliminary results of 2-just obtained preliminary results of 2-dim. global RMHD simulations of black dim. global RMHD simulations of black hole accretion flows.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.