On the definition of the power-law of particle distribution and of the criterion of thermal stability for self-gravitating astrophysical systems within the limits of non-extensive kinetics
We propose a procedure of introduction of the newtonian potential of self-gravitation and the centrifugal potential in quasi-equilibrium of particle distribution in the phase space, received within the non-extensive statistics on the basis of the modified kinetic equation of Boltzmann when averaged on non-normalized distribution. It is shown that if power distribution satisfies to the kinetic stationary equation this the latter imposes clearly defined restrictions on the character of a long-range force field, and on possible dependence of hydrodynamic parameters on coordinates, thereby defining these parameters uniquely. The thermodynamic stability criterion of equilibrium of a non-extensive system is given. The obtained results allow to model more adequately the evolution of gaseous astrophysical systems, and, in particular, the gravitational stability of twirled protoplanetary accretion disks.
nonextensive statistics, Tsallis entropy, self-gravitating system, q-kinetic theory, power-law distribution
Mathematical modelling in actual problems of science and technics