Jeans’ Instability of a Protoplanetary Disk with Accounting for the Magnetic Field and Radiation Modified within the Nonextensive Tsallis Kinetics

Abstract

In the framework of nonextensive Tsallis statistics, we derive the Jeans gravitational instability criteria for a self-gravitating protoplanetary disk, the matter of which consists of a mixture of a conducting ideal q-gas and modified radiation of a photon gas. The instability criteria are derived from the corresponding dispersion relations written for both neutral matter of the disk and magnetized plasma with modified blackbody radiation. We construct the thermodynamics of a photon gas based on the nonextensive Tsallis quantum entropy that depends on the deformation parameter. It has been shown that the blackbody q-radiation can stabilize the state of a nonextensive medium of a purely gaseous disk, while for an electrically conducting disk, the Jeans instability criterion is modified by the magnetic field and radiation pressure only in the transverse mode of propagation of a perturbation wave.