Abstract—
In the framework of Tsallis statistics, we study the effect of medium nonextensivity on the Jeans gravitational instability criterion for a self-gravitating protoplanetary cloud, the substance of which consists of a mixture of perfect gas and blackbody radiation. Generalized Jeans instability criteria have been found from the corresponding dispersion relations obtained both for a uniform cloud with radiation and for a rotating protoplanetary cloud. An integral generalized Chandrasekhar stability criterion for a gravitating spherical cloud has also been obtained. The presented results are analyzed for various values of deformation parameters \(q,\) dimensionality \(D\) of the velocity space and coefficient \(\beta \), characterizing the fraction of radiation in the total pressure of the system. It is shown that radiation stabilizes the substance of nonextensive protoplanetary clouds, and for rotating clouds, the Jeans instability criterion is modified by the Coriolis force only in the transverse modes of perturbation wave propagation.
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Numerous journal articles, collections and monographs are devoted to surveys of studies within the framework of nonextensive Tsallis statistics. In addition, there is a constantly updated full bibliography (Nonextensive statistical mechanics and thermodynamics: Bibliography/ http://tsallis.cat.cbpf.br/biblio.htm), which today includes more than 5600 references.
In the cited paper, the kinetic theory was based on the Bhatnagar-Gross-Krook collision integral (BGK), which was generalized for an arbitrary value of parameter \(q\).
In what follows, index “q” for some hydrodynamic and thermodynamic variables will be omitted.
Eddington first pointed out the special importance of quantity \((1 - \beta )\) for the theory of stellar structure. In a famous passage from his book “The Internal Structure of the Stars”, Eddington associated this quantity with the “happening of the stars.”
When studying perturbed states of self-gravitating cosmic matter, one often has to deal with some form of sound waves.
It should be noted that the linearized equation of momentum requires that the velocity u be parallel to the wave vector \( \pm {\mathbf{k}}\) (see Landau, Lifshitz, 1976). Consequently, the velocities of the fluid particles associated with adiabatic sound waves are parallel to the direction of wave propagation.
In particular, it follows from (60) that for a star with a mass equal to the solar mass and with an average molecular weight equal to unity, the radiation pressure in the center of the star cannot exceed three percent of the total pressure, i.e., \(1 - \beta_* \cong 0.03\) (Chandrasekhar, 1985).
It is known that the problem of stability of a self-gravitating two-dimensional gas cloud cannot be described, in principle, in the framework of the two-dimensional approximation, since it is a priori very unstable (see, for example, Fridman and Khoperskov, 2011). However, when the angular velocity of rotation is sufficiently high, in the presence of a strong external gravitational field with cylindrical geometry and with a generatrix along the axis of rotation of the cloud, it is possible to ensure its stability. In this case, the structure of the protoplanetary cloud along the axis of rotation will be determined solely by its self-gravity. It is clear that this case is artificial, since such cylindrical fields, if they occur in real astrophysical systems, are without embedded disks. At the same time, the analysis of such a self-gravitating thick gas disk embedded in the cylinder is of certain theoretical interest, since only in this case one can allocate the effects arising under the action of pure gravity. It is precisely such models were studied in most classical works on astrophysical disks (see, for example, Goldreich and Lynden-Bell, 1965; Hunter, 1972; Toomre, 1964).
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Kolesnichenko, A.V. Jeans Instability of a Protoplanetary Gas Cloud with Radiation in Nonextensive Tsallis Kinetics. Sol Syst Res 54, 137–149 (2020). https://doi.org/10.1134/S0038094620020045
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DOI: https://doi.org/10.1134/S0038094620020045