Modification of the Jeans and Toomre instability criteria for astrophysical fractal objects within nonextensive statistics


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Abstract

Within the formalism of Tsallis nonextensive statistics designed to describe the behavior of anomalous systems, systems with a strong gravitational interaction between their individual parts and the fractal nature of phase space, we have obtained linearized equations for the oscillations of a rigidly rotating disk by taking into account dissipative effects and give a derivation of the dispersion equation in the WKB approximation. Based on the previously derived modified Navier—Stokes hydrodynamic equations (the so-called equations of q-hydrodynamics), we have analyzed the axisymmetric oscillations of an astrophysical, differentially rotating gas—dust cosmic object and obtained modified Jeans and Toomre gravitational instability criteria for disks with a fractal phase-space structure.

About the authors

A. V. Kolesnichenko

Keldysh Institute of Applied Mathematics

Author for correspondence.
Email: al-vl-kolesn@yandex.ru
Russian Federation, Miusskaya pl. 4, Moscow, 125047

M. Ya. Marov

Keldysh Institute of Applied Mathematics

Email: al-vl-kolesn@yandex.ru
Russian Federation, Miusskaya pl. 4, Moscow, 125047

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