The Nature of the Radiative Hydrodynamic Instabilities in Radiatively   Supported Thomson Atmospheres
  Atmospheres having a significant radiative support are shown to be intrinsically unstable at luminosities above a critical fraction Gamma_crit ~ 0.5-0.85 of the Eddington limit, with the exact value depending on the boundary conditions. Two different types of absolute radiation-hydrodynamic instabilities of acoustic waves are found to take place even in the electron scattering dominated limit. Both instabilities grow over dynamical time scales and both operate on non radial modes. One is stationary and arises only after the effects of the boundary conditions are taken into account, while the second is a propagating wave and is insensitive to the boundary conditions. Although a significant wind can be generated by these instabilities even below the classical Eddington luminosity limit, quasi-stable configurations can exist beyond the Eddington limit due to the generally reduced effective opacity.   The study is done using a rigorous numerical linear analysis of a gray plane parallel atmosphere under the Eddington approximation. We also present more simplified analytical explanations. 
Nir J. Shaviv