Thermodynamics of an Accretion Disk Annulus with Comparable Radiation and Gas Pressure

Abstract

We explore the thermodynamic and global structural properties of a local patch of an accretion disk whose parameters were chosen so that radiation pressure and gas pressure would be comparable in magnitude. Heating, radiative transport, and cooling are computed self-consistently with the structure by solving the equations of radiation magnetohydrodynamics (MHD) in the shearing-box approximation. Using a fully three-dimensional and energy-conserving code, we compute the structure and energy balance of this disk segment over a span of more than 40 cooling times. As is also true when gas pressure dominates, the disk's upper atmosphere is magnetically supported. However, unlike the gas-dominated case, no steady state is reached; instead, the total (i.e., radiation plus gas) energy content fluctuates by factors of 3-4 over timescales of several tens of orbits, with no secular trend. Because the radiation pressure varies much more than the gas pressure, the ratio of radiation pressure to gas pressure varies over the range ~=0.5-2. The volume-integrated dissipation rate generally increases with increasing total energy, but the mean trend is somewhat slower than linear, and the instantaneous dissipation rate is often a factor of 2 larger or smaller than the mean for that total energy level. Locally, the dissipation rate per unit volume scales approximately in proportion to the current density; the time-averaged dissipation rate per unit mass is proportional to m-1/2, where m is the horizontally averaged mass column density to the nearer of the top or bottom surface. As in our earlier study of a gas-dominated shearing box, we find that energy transport is completely dominated by radiative diffusion, with Poynting flux carrying less than 1% of the energy lost from the box.