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 ? -Belloni et al. (1997)

Black Hole  Disk Models  AGNSPEC & 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.  R   P tot 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! RXTE -Davis, Done, & Blaes (2005) BeppoSAX

Thermodynamically consistent, radiation MHD simulations in vertically stratified shearing boxes: PaperBlack Hole Mass R/(GM/c 2 )Thermal Pressure Resolution/ Dimension s Turner (2004) 10 8 M200 P rad >>P gas 32X64X256/ 1.5X6X12 Hirose et al. (2006) 6.62 M300 P rad <<P gas 32X64X256/ 2X8X16 Krolik/Blaes et al. (2006) 6.62 M150 P rad ~P gas 32X64X512/ 0.75X3X12 Hirose et al. (2008, in prep.) 6.62 M30 P rad >>P gas 48X96X896/ 0.45X1.8X8.4

SimulationResolution/ Dimensions  z/H  P rad <<P gas 32X64X256/ 2X8X P rad ~P gas 32X64X512/ 0.75X3X P rad >>P gas 48X96X896/ 0.45X1.8X Convergence??? (But magnetic Prandtl number ~ 1)

Does the stress prescription matter? -Davis et al Disk-integrated spectrum for Schwarzschild, M=10 M , L/L edd =0.1, i=70   and  =0.1 and 0.01.

Azimuthal Flux Reversals P rad <<P gas

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 P rad >>P gas

The (Numerical!) Dissipation Profile is Very Robust Across All Simulations P rad >>P gas P rad ~P gas, P rad <<P gas, Turner (2004)

-Blaes et al. (2006) i=55  CVI K-edge

Time and Horizontally Averaged Acceleration Profiles g/Total Magnetic Radiation Pressure Gas Pressure P rad >>P gas

C VI K-edge -Blaes et al. (2006) No magnetic fields With magnetic fields ~18% increase in color temperature

Large Density Fluctuations at Effective and Scattering Photospheres -upper effective photosphere at t=200 orbits in P rad >>P gas simulation.

Strong density fluctuations, at both scattering and effective photospheres. Strong fluctuations also seen at effective photosphere in previous simulations with P gas >>P rad and P rad ~P gas. Photospheric Density Fluctuations

P rad <<P gas (60 orbits) P rad ~P gas (90 orbits) P rad >>P gas (200 orbits) Effects of Inhomogeneities: 3D vs. Horizontally Averaged Atmospheres 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):

P rad <<P gas (60 orbits) P rad ~P gas (90 orbits) P rad >>P gas (200 orbits) Effects of Faraday Depolarization

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 Most of the dissipation is concentrated near midplane.

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