WAVES IN RADIATING FLUIDS

We derive from first principles the equations which govern the behavio r of small-amplitude fluctuations in a homogeneous and isotropic radia ting fluid. Products of the fluctuating quantities are shown to obey a wave-energy conservation law from which it follows that all perturbat ions must ultimately decay in time. Under fairly general circumstances the governing equations may be solved through the use of integral tra nsforms which affords an accounting of the various wave modes supporte d by the radiating fluid. In addition to the familiar radiatively modi fied acoustic mode, the radiation-diffusion mode, the radiative-relaxa tion mode, and the isotropization and exchange modes which constitute the discrete spectrum of the differential equation, we find a continuo us spectrum of wave modes associated with the ''collisionless'' nature of the photons on timescales short compared to the photon lifetime. T his continuous spectrum is eliminated if an Eddington approximation is used to close the heirarchy of equations that relate the fluctuating angular moments of the radiation field. Quantitative results are obtai ned for the simple case in which the opacity may be regarded as being independent of the frequency of the photon and the source function may be approximated by the (local) Planck function.