The role of black radiation in the modification of the Jeans instability criteria for exoplanetary dusty plasma disk with allowance for magnetic viscosity and radiative heat transfer

Within the framework of the problem of modeling the evolution of an exoplanetary disk, the influence of blackbody radiation on the Jeans magneto-gravitational instability for a self-gravitating plasma disk is discussed, taking into account the influence on the critical length of the disturbing wave of rotation, magnetic field, dissipative processes of viscosity and thermal conductivity, as well as radiation pressure and radiation heat loss. Using the analysis of the normal mode, the general dispersion relation is derived. On its basis, modified criteria for the Jeans instability were obtained for a number of special cases associated with different relative orientations of the magnetic field, the axis of rotation, and the propagation vector of the disturbance wave. The stability of the environment is discussed using the Hurwitz criterion. Both in the case of longitudinal and transverse directions of propagation of the disturbance wave, the Jeans instability criterion is modified due to the presence of radiation heat losses and Stokes correction. The results obtained are aimed at solving the problem associated with the instability of exoplanetary accretion disks and with the formation of exoplanets.