Modification of the jeans instability criterion for fractal-structure astrophysical objects in the framework of nonextensive statistics

Abstract

Unlike classical studies in which the gravitational instability criterion for astrophysical disks is derived in the framework of traditional kinetics or hydrodynamics, we propose to consider the totality of fluffy dust clusters of various astrophysical objects, in particular, protoplanetary subdisks, as a special type of continuous medium, i.e., fractal medium for which there are points and areas not filled with its components. Within the deformed Tsallis statistics formalism, which is intended to describe the behavior of anomalous systems with strong gravitational interaction and fractal nature of phase space, we derive, on the basis of the modified kinetic equation (with the collision integral in the Bhatnagar-Gross-Krook form), the generalized hydrodynamic Euler equations for a medium with the fractal mass dimension. Considering the linearization of the q-hydrodynamics equations, we investigate the instability of an infinitely homogeneous medium to obtain a simplified version of the modified gravitational instability criterion for an astrophysical disk with fractal structure.