Super-Critical Accretion?
Shin Mineshige (Kyoto Univ.)
with K. Ohsuga, K. Vierdayanti, K. Ebisawa, T. Kawaguchi
TIARA Workshop (29/11/2006)
1. General introduction
2. Slim disk model (simplified model)
3. Observational tests - Case of ULXs
4. Multi-dimensional effects
1. Introduction (background)
There are some objects which seem to undergo
super-critical (or super-Eddington) accretion.
・What are ULXs? What are NLS1s?
・What do we know from observations?
・What is key physics in super-critical accretion?
Ultra Luminous X-ray sources (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
IC342 galaxy
„
Two possibilities
„
Sub-critical accretion onto intermediate-mass BHs (M>100Msun).
„
Super-critical accretion onto stellar-mass BHs (M~3-30Msun).
Do ULXs contain IMBHs?
Miller et al. (2003, 2004)
Arguments in favor of intermediate-mass BH (IMBH)
Some ULXs show kT ~ 0.1 keV, indicating large MBH (> 100 Msun)
log Lx
1040
high L & lowT
=IMBHs (?)
erg/s
low L & highT
=stellar-mass BHs
su
n
su
n
1037 erg/s
10
M
„
Luminosities sometimes exceed ~ 1040erg s-1 (=LE of 100 Msun)
10
0M
„
0.1 keV
1.0 keV
log kT (keV)
What determines disk temperature?
Energetics
(Newtonian version)
grav.energy: half → radiation energy
GM BH
−
r
half → rotation energy
That is, (1/2)Egrav = Erad
&
1 GM BH M
≈ 2 ⋅ πr 2 ⋅ σTeff4 .
2
r
BH
For r ~ 3 rS, we have
⎛ M BH
⎝ 10 M sun
⇒ Teff ~ 10 7 K ⎜⎜
⎞
⎟⎟
⎠
−1 / 4
⎛
⎜⎜
⎝
1/4
&
M ⎞
−1 / 4
⎟
∝
M
BH
LE / c 2 ⎟⎠
1 keV for 10 Msun BH, 0.1 keV for 105 Msun BH
Narrow-line Seyfert 1 galaxies (NLS1s)
Boller et al. (NewA 44,
2000)
„
What are NLS1s?
„
„
„
„
Seem to contain less massive BHs
„
„
„
z
Narrow “broad lines” (< 2000 km s-1)
Seyfert 1 type X-ray features
Extreme soft excess & variability
Good analogy with stellar-mass BHs in
their very 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
What is the Eddington luminosity?
Spherical accretion system cannot shine at L > LE.
accreting
gas
accreting
gas
radiation
pressure
Gravity > rad. pressure
⇒ GM/r 2 >κF/c ⇒ L < LE=4πCGM/κ (∵ F=L/4πr 2)
Disk accretion may achieve L>LE
Super-Eddington flux (F > LE/4πr2) is possible in
the z-direction because of radiation anisotropy (!?) .
accreting
gas
radiation
pressure
accreting
gas
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.
Lowenergy
photons
rtrap
Highenergy
photons
.
~ (Mc /L ) r
2
BH
E
Lowenergy
photons
s
radiative
diffusion
& accretion
trapped photons
(c) K. Ohsuga
2. Slim disk model
Slim disk model was proposed for describing
high luminosity flows as an extension of the
standard disk.
・What is distinct from the standard disk
model?
・What are its observational signatures?
Slim disk model
Abramowicz et al. (1988); Watarai et al. (2000)
Basics
1
accretion energy
trapped photons
.
~ (Mc /L ) r
This occurs within trapping radius
„
Model
rtrap
2
E
s
log L/LE
„
L=LE
0
-1
-2
-1
2
3
4
.
.
log m≡log M/(L /c )
0
1
E
Radially 1-D model with radiation entropy advection
vr ΣT
„
Spectrum
d ( srad + sgas )
dr
9
8σT 4
2
= νΣΩ −
4
3τ
τ≫ 1 → multicolor blackbody but with higher T
2
Slim-disk structure
Mineshige, Manmoto et al.
(2002)
Wang & Zhou (1999), Watarai & Fukue (1999)
.
M/(L /c )=1,10,10 ,10
E
2
MBH=105Msun
2
3
.
Low M
rin～ 3rS ;Teff∝r -3/4
.
High M
rin～ rS ; Teff∝r -1/2
3 rS
Slim-disk signatures
1.small innermost radius
2.flatter temp. profile
What determines the inner edge
of a disk?
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)
potential
minimum
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.
slim-disk
solutions
What determines temp. profile?
Standard disk:
Constant fraction of grav.
energy is radiated away.
&
GM BH M
2 ⋅ πr ⋅ σT ∝
∝ r −1
r
−3 / 4
⇒ Teff ∝ r
2
4
eff
Slim disk:
Fraction of energy which is radiated away decreases
inward: tdiff=tacc → Mc2/LE ~r/rtrap∝r
.
& 0
GM BH M
2 ⋅ πr ⋅ σT ∝
∝r
r
⇒ Teff ∝ r −1 / 2
2
4
eff
Spectral properties
(e.g. Kato et al. 1998)
Disk spectra = multi-color blackbody radiation
Temperature profiles affect spectra
T ∝r -p ⇒ F ∝ν3-(2/p)
Fν
ν1/3
・standard disk (p =3/4)
⇒ F ∝ν1/3
・slim disk (p =1/2)
⇒ F ∝ν-1
(small r)
Fν
ν-1
hν
(small r)
hν
3. Observational tests:
Case of ULXs
We examined the XMM/Newton data of
several ULXs which were suggested to
contain intermediate-mass black holes.
・How to test the theory?
・What did we find?
Extended disk-blackbody model
(Mitsuda et al. 1984; Mineshige et al. 1994)
Fitting with superposition of blackbody (Bν) spectra:
rout
Fν = cos i ∫ Bν [T ( r )] 2 π rdr ; T ( r ) = Tin ( r / rin ) − p
rin
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
Spectral fitting 1. Conventional model
(Roberts et al. 2005)
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
log conts
NGC 5204 X-1
log hν
If we set rin~ 3 rS, BH mass is MBH~ 300 Msun.
Problem with DBB+PL fitting
Spectral decomposition of DBB & PL components
DBB comp. is entirely dominated by PL comp.
log conts
NGC 5204 X-1
log hν
Can we trust values derived from the minor component?
Spectral fitting 2. Extended DBB model
(Vierdayanti, SM, Ebisawa, Kawaguchi 2006)
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.)
log conts
NGC 5204 X-1
log hν
MBH~ 12 Msun & L/LE~ 1, supporting slim disk model.
Why can both models give good fits?
Because the spectral shapes are similar below ~10 keV.
power-law
(Γ=2)
extended DBB
with p=0.5
Both show fν ∝ν-1
in 0.1~10keV range.
Temperature-Luminosity diagram
(Vierdayanti et al. 2006, PASJ 58, 915)
log Lx
DBB + PL
ext. DBB
New model fitting
gives MBH <30Msun.
Low-temperature
results should be
re-examined!!
No evidence of
IMBHs so far
The same test is
needed for NLS1s
log kT (keV)
Fate of Prad-driven instability
Radiation pressure-dominated SS disk is unstable.
(1) relaxation oscillation?
Honma et al. (1991),
Szuszkiewicz & Miller (1998)
(2) soft-to-hard transition?
・
M
(2)
(1)
Takeuchi & Mineshige (1998),
Gu & Lu (2000)
(3) strongly clumped disk?
Krolik (1998)
(4) disk-corona structure?
Nakamura & Osaki (1993), Svensson & Zdziarski (1994)
Σ
Bursting behavior of micro-quasar
peak
(slim disk)
and
log Tin
GRS 1915+105
exhibits state
transitions
between
counts
(Yamaoka, Ueda & Inoue 2002)
time
(T ∝ r -1/2 )
(T ∝ r -3/4 )
valley
(thin disk)
log rin
4. Multi-dimensional effects
The slim-disk model applies only to the flow
with L ~ LE. For even higher L, we need to
perform radiation-hydrodynamical (RHD)
simulations.
・What are the multi-dimensional effects?
・What can we understand them?
A simple model
429)
(Ohsuga et al. 2002, ApJ 574, 315; 2003, ApJ 596,
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.
BH
accretion
radiative
diffusion
Can approximately evaluate 2D photon trapping effects.
Photon trapping: observable effects
Luminosity [L/LE]
Luminosity
Sli
sk
i
d
m
lts ing)
u
s
r retrapp
u
O o not
h
P
(
SED Variations
MCD
・
m=10
Photontrapping Slim disk
・
m=100
30
・
m=10
Ohsuga et al. 2002
Mass-accretion rate ⎡⎣ m&≡ M& ( LE c 2 ) ⎤⎦
Ohsuga et al. 2003
Black hole mass: M BH = 10 M e
•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. Ohsuga
Our 2D RHD simulations
Ohsuga, Mori, Nakamoto, SM (2005, ApJ 628, 368)
→ disk-outflow structure
• Flux-limited diffusion adopted.
z/rs
• Matter with 0.45 Keplerian A.M.
is continuously added through
the outer boundary
500
• First simulations of super-critical accretion
flows in quasi-steady regimes.
Injection
• α viscosity with α=0.1.
• Mass input rate: 1000 (LE/c2)
→ luminosity of ~3 LE
BH
r/rs
500
Initially empty disk
Overview of 2D super-critical flow
Ohsuga et al. (2005, ApJ 628,368)
Case of M =10 Msun
・
& M =1000 LE/c 2
z/rs
outflow
disk flow
BH
r/rs
density contours &
velocity fields
gas energy
density
radiation energy
density
(c) K. Ohsuga
Why is accretion possible?
Ohsuga & S.M. (2006, submitted)
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.
Low ρ and steep Erad profile yields super-Eddington flux.
z/rs
Photon trapping
F r=radiation flux in
the rest frame
F0r=radiation flux in
the comoving frame
F r~F0r+vrE0
Photon trapping also
helps reduced radiation
pressure force.
BH
r/rs
Radiation flux (F r ) is inward!
(c) K. Ohsuga
Significant radiation anisotropy
Ohsuga et al. (2005, ApJ 628,368)
luminosity
BH
Density
contours
4πD2F(θ)/LE
θ
12
our simulations
8
cos θ
4
0
The observed luminosity is
sensitive to the viewingangle; Maximum L ~ 12 LE !!
viewing angle
⇒ mild beaming
(c) K. Ohsuga
Why beaming?
Heinzeller, S.M. & Ohsuga (2006, MNRAS 372, 1208,)
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.
gas
gas
radiation
Future issue
Interaction with magnetic fields
Magnetic fields are essential ingredients in disks
• Photon-bubble instability (Begelman 2002)
• Magnetic tower jet → global RHD+MHD simulations necessary
(Kato, SM, & Shibata 2004)
Conclusions
• 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 superEddington luminosity, significant radiation anisotropy
(beaming), high-speed outflow, large absorption, etc.
L can be ~10 LE !!
• Issues: magnetic fields, line spectra, instability,…