  Self-gravitating systems are generally thought to behavior non-extensively
due to the long-range nature of gravitational forces. We obtain a relation
between the nonextensive parameter q of Tsallis statistics, the temperature
gradient and the gravitational potential based on the equation of hydrostatic
equilibrium of self-gravitating systems. It is suggested that the nonextensive
parameter in Tsallis statistics has a clear physical meaning with regard to the
non-isothermal nature of the systems with long-range interactions and Tsallis
equilibrium distribution for the self-gravitating systems describes the
property of hydrostatic equilibrium of the systems.
