Thermodynamics and Spectra of
Optically Thick Accretion Disks
Omer Blaes, UCSB
With Shane Davis, Shigenobu Hirose and Julian Krolik
Standard Disks are Observed to be
Simple And Stable
E.g. Cyg X-1 (Churazov et al. 2001):
Plenty of X-ray Binaries Get to High Eddington Ratios,
And Do NOT Show Signs of Putative Thermal Instability
Except Perhaps GRS 1915+105?
L
2
10
LEdd
-Belloni et al. (1997)
Black HoleDisk Models
AGNSPEC & BHSPEC
i

-Hubeny & Hubeny 1997, 1998; Hubeny et al. (2000, 2001),
Davis & Hubeny (2006), Hui & Krolik (2008)
The Good:
• Models account for relativistic disk structure and relativistic
Doppler shifts, gravitational redshifts, and light bending in
a Kerr spacetime.
• Models include a detailed non-LTE treatment of abundant
elements.
• Models include continuum opacities due to bound-free and
free-free transitions, as well as Comptonization. (No lines
at this stage, though.)
The Bad --- Ad Hoc Assumptions:
• Stationary, with no torque inner boundary condition.
• RPtot with  constant with radius - determines surface
density.
• Vertical structure at each radius depends only on height
and is symmetric about midplane.
• Vertical distribution of dissipation per unit mass assumed
constant.
• Heat is transported radiatively (and not, say, by bulk
motions, e.g. convection).
• Disk is supported vertically against tidal field of black
hole by gas and radiation pressure only.
BHSPEC Does a Pretty Good Job
With Black Hole X-ray Binaries
-McClintock, Narayan & Shafee (2007)
LMC X-3 in the thermal dominant state
- there is NO significant corona!
BeppoSAX
RXTE
-Davis, Done, & Blaes (2005)
Thermodynamically consistent, radiation MHD
simulations in vertically stratified shearing boxes:
Paper
Black Hole
Mass
R/(GM/c2)
Thermal
Pressure
Resolution/
Dimension
s
Turner (2004)
108 M
200
Prad>>Pgas
32X64X256/
1.5X6X12
Hirose et al.
(2006)
6.62 M
300
Prad<<Pgas
32X64X256/
2X8X16
Krolik/Blaes
et al. (2006)
6.62 M
150
Prad~Pgas
32X64X512/
0.75X3X12
Hirose et al.
(2008, in
prep.)
6.62 M
30
Prad>>Pgas
48X96X896/
0.45X1.8X8.4
Convergence???
Simulation
Resolution/
Dimensions
z/H

Prad<<Pgas
32X64X256/
2X8X16
0.0625
0.016
Prad~Pgas
32X64X512/
0.75X3X12
0.0234
0.03
Prad>>Pgas
48X96X896/
0.45X1.8X8.4
0.0094
0.02
(But magnetic Prandtl number ~ 1)
Does the stress prescription matter?
Disk-integrated spectrum for Schwarzschild, M=10 M,
L/Ledd=0.1, i=70and =0.1 and 0.01.
-Davis et al. 2005
Azimuthal Flux Reversals
Prad<<Pgas
3D visualization of
tension/density
fluctuation
correlation due
to Parker instability.
Time Averaged Vertical Energy Transport
Radiation
Diffusion
Advection of
radiation
Poynting
Flux
Advection of
gas internal energy
Prad>>Pgas
The (Numerical!)
Dissipation Profile is
Very Robust Across
All Simulations
Prad>>Pgas
Prad~Pgas,
Prad<<Pgas,
Turner (2004)
CVI K-edge
i=55
-Blaes et al. (2006)
Time and Horizontally Averaged Acceleration Profiles
g/Total
Magnetic
Radiation Pressure
Gas Pressure
Prad>>Pgas
CVI K-edge
With magnetic
fields
No magnetic
fields
~18% increase in color temperature
-Blaes et al. (2006)
Large Density Fluctuations at Effective
and Scattering Photospheres
-upper effective photosphere
at t=200 orbits in Prad>>Pgas
simulation.
Photospheric Density Fluctuations
Strong density fluctuations,
at both scattering and
effective photospheres.
Strong fluctuations also
seen at effective
photosphere in previous
simulations with Pgas>>Prad
and Prad~Pgas.
Effects of Inhomogeneities:
3D vs. Horizontally Averaged Atmospheres
Prad<<Pgas
(60 orbits)
Prad~Pgas
(90 orbits)
Prad>>Pgas
(200 orbits)
Flux enhancements in 3D imply decreases in color temperatures
compared to 1D atmosphere models:
9%
6%
11%
Faraday Depolarization
Magnetic fields in disk atmospheres might be strong
enough to cause significant Faraday rotation of polarized
photons (Gnedin & Silant’ev 1978):
Pmag 
  0.8 T   radians
Prad 
1/ 2

Effects of Faraday Depolarization
Prad<<Pgas
(60 orbits)
Prad~Pgas
(90 orbits)
(i  79 )
Prad>>Pgas
(200 orbits)
Summary: The Vertical Structure of Disks
• Hydrostatic balance: Disks are supported by thermal
pressure near the midplane, but by magnetic forces in
the outer (but still subphotospheric layers).
• Thermal balance: Dissipation (numerical) occurs at great
depth, and accretion power is transported outward largel
by radiative diffusion. There is no locally generated corona,
in agreement with observations!
• Stability: There is no radiation pressure driven thermal
instability, in agreement with observations!
Implications of Simulation Data on Spectra
• Actual stress (“alpha”) and vertical dissipation profiles
are irrelevant, provided disk remains effectively thick.
• Magnetically supported upper layers decrease density at
effective photosphere, producing a (~20%) hardening of
the spectrum.
• Strong density inhomogeneities at photosphere produce
a (~10%) softening of the spectrum.
• Polarization is reduced only slightly by photospheric
inhomogeneities, and is Faraday depolarized only below
the peak - a possible diagnostic for accretion disk B-fields
with X-ray polarimeters???
Vertical Hydrostatic Balance
t = 200 orbits
Time-Averaged Vertical Dissipation Profile
c 2


Most of the dissipation is concentrated near midplane.
Turbulence near Midplane is Incompressible
-----Silk Damping is Negligible