Relativistic radiative hydrodynamics

Abstract

In conventional rediative hydrodynamics, the dissipative fluxes are proportional to the gradients of the temperature, velocity, etc., with proportionality constants inferred from the linearized radiative transfer equation. The dynamical evolution is determined by the conservation of matter, energy, and momentum. Conventional theory breaks down if the geometry under consideration is photospheric, i.e., if emission/absorption processes are weak compared to scattering and photons can “random walk” over large distances without being absorbed. The fundamental dynamical equations of motion include the relativistic transfer equation and form the starting point for establishing extended versions of radiative hydrodynamics. The transfer equation is replaced by a hierarchy of relativistic moment equations and the dissipative fluxes are treated as dynamical variables in their own right. The general moment equations involve source terms which are a priori undetermined. If the radiation is almost thermal the source terms can be expressed with Rosseland means. In this case, the moment equations reproduce the structure equations postulated by Israel for general dissipative continuous media. Quantitative aspects are discussed. In the limit of slow motion, the moment equations are studied separately and interpreted as hyperbolic diffusion equations. These are solved with a relativistic random walk model and the results are applied to time-dependent radiative transfer. Time profiles in every scattering order are given and compared with Monte Carlo simulations. The viscous damping of acoustic modes is reconsidered. Equations of motion for spherical accretion in a Schwarzschild geometry are established and compared with conventional equations used in the literature. Ill-known limitations of conventional radiative hydrodynamics are highlighted.