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.
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Original Russian Text © A.V. Kolesnichenko, M.Ya. Marov, 2016, published in Astronomicheskii Vestnik, 2016, Vol. 50, No. 4, pp. 268–279.
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Kolesnichenko, A.V., Marov, M.Y. Modification of the Jeans and Toomre instability criteria for astrophysical fractal objects within nonextensive statistics. Sol Syst Res 50, 251–261 (2016). https://doi.org/10.1134/S0038094616040043
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DOI: https://doi.org/10.1134/S0038094616040043