Eddington limit and radiative transfer in highly inhomogeneous   atmospheres
  Radiation dominated accretion disks are likely to be subject to the ``photon bubble'' instability, which may lead to strong density inhomogeneities on scales much shorter than the disk scale height. Such disks -- and magnetized, radiation-dominated atmospheres in general -- could radiate well above the Eddington limit without being disrupted. When density contrasts become large over distances of order the photon mean free path, radiative transfer cannot be described adequately using either the standard diffusion approximation or existing prescriptions for flux-limited diffusion. Using analytical and Monte Carlo techniques, we consider the effects of strong density gradients deep within radiation- and scattering-dominated atmospheres. We find that radiation viscosity -- i.e., the off-diagonal elements of the radiation stress tensor -- has an important effect on radiative transfer under such conditions. We compare analytical and numerical results in the specific case of a plane-parallel density wave structure and calculate Eddington enhancement factors due to the porosity of the atmosphere. Our results can be applied to the study of dynamical coupling between radiation forces and density inhomogeneities in radiation dominated accretion disks in two or three dimensions. 
Mateusz Ruszkowski and Mitchell C. Begelman