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Thermodynamics and Spectra of Optically Thick Accretion Disks

Explore models of optically thick accretion disks, focusing on the thermodynamics and stability in black hole X-ray binaries, with implications drawn from simulation data on disk spectra. Discover the nuances of radiation transport, magnetic fields, and gas dynamics in disk atmospheres.

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Thermodynamics and Spectra of Optically Thick Accretion Disks

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  1. Thermodynamics and Spectra of Optically Thick Accretion Disks Omer Blaes, UCSB With Shane Davis, Shigenobu Hirose and Julian Krolik

  2. Standard Disks are Observed to be Simple And Stable E.g. Cyg X-1 (Churazov et al. 2001):

  3. Plenty of X-ray Binaries Get to High Eddington Ratios, And Do NOT Show Signs of Putative Thermal Instability

  4. Except Perhaps GRS 1915+105? -Belloni et al. (1997)

  5. Black HoleDisk Models AGNSPEC & BHSPEC -Hubeny & Hubeny 1997, 1998; Hubeny et al. (2000, 2001), Davis & Hubeny (2006), Hui & Krolik (2008)

  6. 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.)

  7. 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.

  8. BHSPEC Does a Pretty Good Job With Black Hole X-ray Binaries -McClintock, Narayan & Shafee (2007)

  9. LMC X-3 in the thermal dominant state - there is NO significant corona! BeppoSAX RXTE -Davis, Done, & Blaes (2005)

  10. Thermodynamically consistent, radiation MHD simulations in vertically stratified shearing boxes:

  11. Convergence??? (But magnetic Prandtl number ~ 1)

  12. 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

  13. Azimuthal Flux Reversals Prad<<Pgas

  14. 3D visualization of tension/density fluctuation correlation due to Parker instability.

  15. Time Averaged Vertical Energy Transport Radiation Diffusion Advection of radiation Poynting Flux Advection of gas internal energy Prad>>Pgas

  16. The (Numerical!) Dissipation Profile is Very Robust Across All Simulations Prad>>Pgas Prad~Pgas, Prad<<Pgas, Turner (2004)

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

  18. Time and Horizontally Averaged Acceleration Profiles g/Total Magnetic Radiation Pressure Gas Pressure Prad>>Pgas

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

  20. Large Density Fluctuations at Effective and Scattering Photospheres -upper effective photosphere at t=200 orbits in Prad>>Pgas simulation.

  21. 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.

  22. 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 temperatures compared to 1D atmosphere models: 9% 6% 11%

  23. Faraday Depolarization Magnetic fields in disk atmospheres might be strong enough to cause significant Faraday rotation of polarized photons (Gnedin & Silant’ev 1978):

  24. Prad<<Pgas (60 orbits) Prad~Pgas (90 orbits) Prad>>Pgas (200 orbits) Effects ofFaraday Depolarization

  25. 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!

  26. 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???

  27. Vertical Hydrostatic Balance t = 200 orbits

  28. Time-Averaged Vertical Dissipation Profile Most of the dissipation is concentrated near midplane.

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

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