  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.
