Jeans instability of an astrophysical self-gravitating medium in the presence of high radiation pressure and diffusion transfer of radiation

Within the framework of the problem of modeling the evolution of a protostellar disk, the influence of radiation on the Jeans gravitational instability for a self-gravitating optically thick (for intrinsic infrared radiation) gas-dust medium is discussed, taking into account the influence of radiation pressure and diffusion transfer of radiation on the critical wavelength of the perturbing wave. Two approximations of radiative diffusion are considered: 1. the case of ideal radiative equilibrium, when the temperatures of matter and radiation are the same; 2. the case of the time dependence of the radiation field, when there is an energy decoupling between radiation and matter. Using the analysis of the normal regime, dispersion relations are derived that allow one to obtain modifications of the Jeans gravitational instability criterion under the influence of radiation pressure and radiation diffusion. In particular, it is shown that, in contrast to local radiation equilibrium, when the acoustic velocity of the gas coincides with the isothermal speed of sound, in the case of a difference in the temperatures of radiation and gas, the perturbing wave propagates with the adiabatic speed of sound in the gas. The results obtained are aimed at solving the problem of gravitational instability of individual massive protostellar disks or self-gravitating radiation media characterized by large optical depths for their own infrared radiation transformed by dust.