Jeans criterion and nonextensive velocity distribution function in kinetic theory

The effect of nonextensivity of self-gravitating systems on the Jeans criterion for gravitational instability is studied in the framework of Tsallis statistics. The nonextensivity is introduced in the Jeans problem by a generalized q-nonextensive velocity distribution function through the equation of state of ideal gas in nonextensive kinetic theory. A new Jeans criterion is deduced with a factor that, however, differs from that one in Ref.[21] and new results of gravitational instability are analyzed for the nonextensive parameter q. An understanding of physical meaning of q and a possible seismic observation to find astronomical evidence for a value of q different from unity are also discussed.