Jeans instability of the protoplanetary circumstellar disk taking into account the magnetic field and radiation in the nonextensive Tsallis kinetics

Within the framework of the Tsallis non-extensive statistics, a derivation of the Jeans gravitational instability criteria is given for a self-gravitating protoplanetary disk, the substance 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 disk matter and magnetized plasma with modified blackbody radiation. The thermodynamics of a photon gas is constructed based on the nonextensive quantum entropy Tsallis, which depends on the deformation parameter. It is shown that blackbody radiation can stabilize the state of a nonextensive medium for a purely gaseous disk, and for an electrically conducting disk, the Jeans instability criterion is modified by a magnetic field and radiation pressure only in the transverse regime of propagation of the disturbance wave.