Thermodynamics and Spectra ofOptically Thick Accretion Disks

Omer Blaes, UCSB

With Shane Davis, Shigenobu Hirose and Julian Krolik

Standard Disks are Observed to beSimple 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?

-Belloni et al. (1997)

€

2 <L

LEdd

<10

€

i

Black Hole Disk ModelsAGNSPEC & BHSPEC

-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.• RPtot 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 JobWith Black Hole X-ray Binaries

-McClintock, Narayan & Shafee (2007)

LMC X-3 in the thermal dominant state- there is NO significant corona!

RXTE

-Davis, Done, & Blaes (2005)

BeppoSAX

Thermodynamically consistent, radiation MHDsimulations in vertically stratified shearing boxes:

Paper Black Hole Mass

R/(GM/c2) Thermal Pressure

Resolution/Dimensions

Turner (2004) 108 M 200 Prad>>Pgas32X64X256/

1.5X6X12

Hirose et al. (2006)

6.62 M 300 Prad<<Pgas32X64X256/

2X8X16

Krolik/Blaes et al. (2006)

6.62 M 150 Prad~Pgas32X64X512/

0.75X3X12

Hirose et al. (2008, in prep.)

6.62 M 30 Prad>>Pgas48X96X896/

0.45X1.8X8.4

Simulation Resolution/Dimensions

z/H

Prad<<Pgas32X64X256/

2X8X160.0625 0.016

Prad~Pgas32X64X512/

0.75X3X120.0234 0.03

Prad>>Pgas48X96X896/

0.45X1.8X8.40.0094 0.02

Convergence???

(But magnetic Prandtl number ~ 1)

Does the stress prescription matter?

-Davis et al. 2005

Disk-integrated spectrum for Schwarzschild, M=10 M,L/Ledd=0.1, i=70 and =0.1 and 0.01.

Azimuthal Flux Reversals

Prad<<Pgas

3D visualization oftension/densityfluctuationcorrelation dueto Parker instability.

Time Averaged Vertical Energy Transport

RadiationDiffusion

Advection ofradiation

PoyntingFlux

Advection ofgas internal energy

Prad>>Pgas

The (Numerical!)Dissipation Profile isVery Robust Across

All Simulations

Prad>>Pgas

Prad~Pgas,

Prad<<Pgas,

Turner (2004)

-Blaes et al. (2006)i=55

CV

I K-e

dg

e

Time and Horizontally Averaged Acceleration Profiles

g/TotalMagneticRadiation PressureGas Pressure

Prad>>Pgas

CV

I K-e

dg

e-Blaes et al. (2006)

No magneticfields

With magneticfields

~18% increase in color temperature

Large Density Fluctuations at Effectiveand Scattering Photospheres

-upper effective photosphereat t=200 orbits in Prad>>Pgas

simulation.

Strong density fluctuations,at both scattering andeffective photospheres.

Strong fluctuations alsoseen at effectivephotosphere in previoussimulations with Pgas>>Prad

and Prad~Pgas.

Photospheric Density Fluctuations

Prad<<Pgas

(60 orbits)Prad~Pgas

(90 orbits)Prad>>Pgas

(200 orbits)

Effects of Inhomogeneities:3D vs. Horizontally Averaged Atmospheres

Flux enhancements in 3D imply decreases in color temperaturescompared to 1D atmosphere models:

9% 6% 11%

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θ ≈0.8τ TPmag

Prad

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 2

radians

Faraday Depolarization

Magnetic fields in disk atmospheres might be strongenough to cause significant Faraday rotation of polarizedphotons (Gnedin & Silant’ev 1978):

Prad<<Pgas

(60 orbits)Prad~Pgas

(90 orbits)Prad>>Pgas

(200 orbits)

Effects of Faraday Depolarization

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(i = 79o)

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

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cΩ2

κ

Most of the dissipation is concentrated near midplane.

Turbulence near Midplane is Incompressible-----Silk Damping is Negligible