The Vertical Structure of Radiation Dominated Accretion Disks

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## The Vertical Structure of Radiation Dominated Accretion Disks

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**The Vertical Structure**of Radiation Dominated Accretion Disks Omer Blaes with Shigenobu Hirose and Julian Krolik**Huge Theoretical Uncertainties Have Plagued Us for Years -**Even In the Standard Geometrically Thin, Optically Thick Disk Model • How is (turbulent!) dissipation distributed vertically? • What role (if any) do convection and Poynting flux play • in the vertical transport of energy? • Are thermal (and “viscous”) instabilities in the radiation • dominated regime real, or are they merely artifacts of • a bad choice of stress prescription? • How big are fluctuations about equilibrium? • Do magnetic forces play any role in hydrostatic support?**Expectations in Radiation-Dominated Regime**Hydrostatic equilibrium: A radially constant disk half-thickness:**Expectations in Radiation-Dominated Regime**Radiative equilibrium: A vertically constant dissipation rate per unit volume: After vertical and time-averaging, this must be given by turbulent stress times rate of strain: (Shakura & Sunyaev 1976)**IF we choose the dissipation per unit MASS**to be spatially constant as well, then the density must be constant. Ad Hoc Prescription I: The Density Profile The vertical density profile is completely unconstrained! Convective instability! (Bisnovatyi-Kogan & Blinnikov 1977) But perhaps the dissipation per unit mass is not constant???**Ad Hoc Prescription II: The Stress/Pressure Relation**The radial midplane temperature and surface density profiles are completely unconstrained unless we adopt, e.g., an alpha prescription for the vertically averaged stress. If we choose , then the disk is thermally and “viscously” unstable if . or But other choices are possible, e.g. (Sakimoto & Coroniti 1981, …, Merloni & Fabian 2002, …) Or perhaps much of the accretion power is dissipated in a corona above the disk? (Svensson & Zdziarski 1994)**No Observational Evidence for**Radiation Pressure Thermal/“Viscous” Instabilities - Except Perhaps in GRS 1915+105 -Belloni et al. (1997)**MRI Turbulence Can be Highly Compressible**in Radiation Dominated Regime -Turner et al. (2003) Silk damping of turbulence may be important. (Agol & Krolik 1998)**“Photon Bubble Instability”**F g -Turner et al. (2005)**z (vertical)**y (azimuthal) x (radial) Stratified Shearing Box Simulations of MRI Turbulence Cartesian box corotating with fluid at center of box. Boundary conditions are shearing periodic in x, periodic in y, outflow in z.**Altitude**Time Miller & Stone (2000) 25% of magnetic energy generated in turbulence buoyantly rises and dissipates in outer layers. Does this produce a hot corona? Uncertain, as simulation was isothermal.**Thermodynamically consistent, radiation MHD**simulations in vertically stratified shearing boxes:**z (vertical)**y (azimuthal) x (radial) The Simulation Domain Lx=0.45H, 48 zones Ly=1.8H, 96 zones Lz=8.4H, 896 zones (Apologies to Arthur C. Clarke and Stanley Kubrick)**Energy Balance - NO Thermal Instability!**Heating vs. Cooling Radiation, Gas Internal, Magnetic, and Turbulent Kinetic Energies**Heating**vs. Cooling Radiation, Gas Internal, Magnetic, and Turbulent Kinetic Energies**Time-Averaged Vertical Dissipation Profile**Most of the dissipation is concentrated near midplane.**Turbulence near Midplane is Incompressible**-----Silk Damping is Negligible**Density is far from constant with height.**Density profile at 200 orbits. Time-averaged density profile.**r/Pgas**r/(PtotPgas)1/2 r/Ptot**Time-averaged Radiation, Gas, and Magnetic Pressure Profiles****Vertical Hydrostatic Balance**t = 200 orbits**Parker is Clearly Present**t = 200 orbits**Large Density Fluctuations at Effective**and Scattering Photospheres -upper effective photosphere at t=200 orbits**Photospheric Density Fluctuations**Strong density fluctuations, at both scattering and effective photospheres. Strong fluctuations also seen at effective Photosphere in previous simulations with Prad>>Pgas and Prad~Pgas.**Overall Vertical Structure for all Prad/Pgas Regimes**Photospheres Pmag>Prad, Pgas Parker Unstable Regions Prad, Pgas>Pmag MRI - the source of accretion power Parker Unstable Regions Pmag>Prad, Pgas Photospheres**Conclusions**• No evidence for radiation pressure driven thermal instability, • despite fact that turbulent stresses may be tracking total • pressure (causal direction is OTHER way around, though!). • Dissipation is concentrated near disk midplane, with no • energetically significant corona. • Upper layers are always supported by magnetic fields, even • well beneath the photospheres. (Reflection modelers beware!) • Parker instability dominates, and drives strong density • fluctuations in all radiation/gas pressure regimes. Photon • bubble instability is unresolved in this simulation. • Spectra and color correction factors: magnetic field support • should harden spectra, density fluctuations should soften • spectra. Which dominates?**Caveats and Uncertainties**• Simulations are expensive, and much more work needs to be • done to address the following issues: • Numerical convergence with increased resolution and box • size in all three directions (particularly radial and azimuthal). • How does initial magnetic field topology affect things? (We • start with a twisted azimuthal flux tube with net azimuthal • flux, but no net poloidal flux.) • Most of our dissipation is numerical and is captured at the • grid scale. Viscous and resistive scales are therefore • identical (i.e. Prandtl number is unity). Simulations in • non-stratified shearing boxes show that this might matter.**More Details on the (Time-Averaged) Energy Balance**Stress Dissipation Rate Divergences of Poynting flux, Gas energy advection, Radiation energy advection, and Radiative diffusion, Total of last three matches dissipation rate.**Flux from top**Flux from bottom