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

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 rigidl...

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Bibliographic Details
Published in:Solar system research 2016-07, Vol.50 (4), p.251-261
Main Authors: Kolesnichenko, A. V., Marov, M. Ya
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics
Astrophysics and Astroparticles
Astrophysics and Cosmology
Criteria
Dispersion
Fractal analysis
Fractals
Gravitational waves
Hydrodynamics
Mathematical analysis
Navier-Stokes equations
Observations and Techniques
Oscillations
Physics
Physics and Astronomy
Planetology
Solar system
Statistics
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Summary: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.
ISSN:0038-0946
1608-3423
DOI:10.1134/S0038094616040043