A Phase Transition of Luminous Atmospheres

We show that atmospheres having a nonnegligible radiative support undergo a second order phase transition above a critical radiative ux. This ux is less than but of order of the ux that corresponds to the Eddington luminosity limit. The trivial exponentially decaying solution, namely, the horizontally uniform solution, is energetically preferred for uxes below the critical one. However, the preferred connguration for larger uxes is a stratiied atmosphere with a horizontally propagating acoustic or gravity wave. The eeective opacity is reduced and the Eddington limit is increased when the atmosphere is in the super critical phase. This phase, which is in a dynamic equilibrium, is intrinsically variable.