Waves in Radiating Fluids

Abstract

We derive from first principles the equations which govern the behavior of small-amplitude fluctuations in a homogeneous and isotropic radiating fluid. Products of the fluctuating quantities are shown to obey a wave-energy conservation law from which it follows that all perturbations must ultimately decay in time. Under fairly general circumstances the governing equations may be solved through the use of integral transforms which affords an accounting of the various wave modes supported by the radiating fluid. In addition to the familiar radiatively modified acoustic mode, the radiation-diffusion mode, the radiative-relaxation mode, and the isotropization and exchange modes which constitute the discrete spectrum of the differential equation, we find a continuous spectrum of wave modes associated with the "collisionless" nature of the photons on timescales short compared to the photon lifetime. This continuous spectrum is eliminated if an Eddington approximation is used to close the hierarchy of equations that relate the fluctuating angular moments of the radiation field. Quantitative results are obtained 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.