Study On The Relation Of Dark Matter's Density Slope And The Non-extensive Index

This paper introduces the proposition of nonextensive entropy and the application in astrophysics on the base of q-maxwell velocity distrubution function and nonextensive. This is one of the most forland of problem of physics and astronomy. We use the q-maxwell velocity distrubution function to study the structures of the dark matter, and get the velocity distrubution function figure of dark matter by using the numerical simulations. We found it is well fitted with the q-maxwell velocity distrubution function. It is a strong indicator that equilibrium self gravitating structures indeed are to be described by non-extensive statistical mechanics. The relation of nonextensive parameter and density slope is given by using the concept of"polytropes". Then we draw the picture of the relation of dark matter's density slope and the non-extensive index. And discuss the scope of the non-extensive index. A judge to the dispute that exists in the nonextensive theory at present is made by it, as well.