  It is natural important question for us to ask what the nonextensive
parameter stands for when Tsallis statistics is applied to the self-gravitating
systems. In this paper, some properties of the nonextensive parameter and
Tsallis equilibrium distribution for the self-gravitating system are discussed
in the framework of nonextensive kinetic theory. On the basis of the solid
mathematical foundation, the nonextensive parameter can be expressed by a
formula with temperature gradient and the gravitational potential and can be
presented the physical meaning with regard to the non-isothermal
(nonequilibrium stationary state) nature of the systems with long-range
interactions. We come to the conclusion that Tsallis equilibrium distribution
is corresponding to the physical state of self-gravitating system at the
hydrostatic equilibrium.
