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.