Jeans Instability of an Astrophysical Self-Gravitating Medium in the Presence of High Radiation Pressure and Diffuse Radiative Transfer

Abstract

Within the problem of modeling the evolution of a protostellar disk, a discussion is presented on the effect of radiation on the Jeans gravitational instability for a self-gravitating optically thick (for intrinsic infrared radiation) gas-and-dust medium, taking into account the influence of radiation pressure perturbations and radiative diffusion transfer on the critical wavelength. Two radiative diffusion approximations are considered: the case of perfect thermal equilibrium with the same temperature of matter and radiation and the case of the time dependence of the radiation field with an energy separation between radiation and matter. An analysis of the normal regime of modes is used to derive dispersion relations, which enable the derivation of modifications of the classical Jeans instability criterion under the influence of radiation pressure and radiation diffusion. In particular, it is shown that, in contrast to the system’s local thermodynamic equilibrium, where the acoustic velocity of perturbed gas propagates with the isothermal speed of sound, in the case of different temperatures of radiation and gas, the perturbing wave propagates with the adiabatic speed of sound in gas. The results obtained are aimed at solving the problem of gravitational instability of individual massive protostellar disks or self-gravitating radiative media characterized by large optical depths for their dust-transformed intrinsic infrared radiation.