Dark matter distribution function from non-extensive statistical mechanics

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Abstract
We make an analytical and semi-numerical study of the velocity distribution function of self gravitating collisionless particles, which include dark matter and star clusters. We show that the velocity distribution derived through the Eddington's formula is identical to the analytical one derived directly from the generalized entropy of non-extensive statistical mechanics. This implies that self gravitating collisionless structures are to be described by non-extensive thermo-statistics. We identify a connection between the density slope of dark matter structures, gamma, from rho ~ r^(-gamma), and the entropic index, q, from the generalized entropy, S_q. We use this result to conclude that from a fundamental statistical mechanics point of view the central density slope of self gravitating collisionless dark matter structures is not constrained, and even cored dark matter structures are allowed.

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