Convective-Dynamical Instability in Radiation-Supported Accretion Disks

We study radiation-hydrodynamical normal modes of radiation-supported accretion disks in the WKB limit. It has long been known that in the large optical depth limit the standard equilibrium is unstable to convection. We study how the growth rate depends on location within the disk, optical depth, disk rotation, and the way in which the local dissipation rate depends on density and pressure. The greatest growth rates are found near the disk surface. Rotation stabilizes vertical wavevectors, so that growing modes tend to have nearly-horizontal wavevectors. Over the likely range of optical depths, the linear growth rate for convective instability has only a weak dependence on disk opacity. Perturbations to the dissipation have little effect on convective mode growth rates, but can cause growth of radiation sound waves.Comment: 20 pages, AAS LaTe

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

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 MHD in the shearing-box approximation. Using a fully 3-d and energy-conserving code, we compute the structure and energy balance of this disk segment over a span of more than forty 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 approximate 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 two 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-average 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.Comment: ApJ, in pres

The Inverse Compton Thermostat in Hot Plasmas Near Accreting Black Holes

The hard X-ray spectra of accreting black holes systems are generally well-fit by thermal Comptonization models with temperatures $\sim 100$ keV. We demonstrate why, over many orders of magnitude in heating rate and seed photon supply, hot plasmas radiate primarily by inverse Compton scattering, and find equilibrium temperatures within a factor of a few of 100 keV. We also determine quantitatively the (wide) bounds on heating rate and seed photon supply for which this statement is true. Plasmas in thermal balance in this regime obey two simple scaling laws, one relating the product of temperature and optical depth to the ratio of seed photon luminosity to plasma heating rate $l_s/l_h$, the other relating the spectral index of the output power-law to $l_s/l_h$. Because $\alpha$ is almost independent of everything but $l_s/l_h$, the observed power law index may be used to estimate $l_s/l_h$. In both AGN and stellar black holes, the mean value estimated this way is $l_s/l_h \sim 0.1$. As a corollary, $\Theta \tau_T$ must be $\simeq 0.1$ -- 0.2, depending on plasma geometry.Comment: 26 pages, AASLaTeX, to appear in July 10 Ap.J. Figures available in uuencoded form at ftp://jhufos.pha.jhu.edu/pub/put/jhk/comptfigs.u