Velocity distributions from nonextensive thermodynamics

There is no accepted mechanism that explains the equilibrium structures that form in collisionless cosmological N-body simulations. Recent work has identified nonextensive thermodynamics as an innovative approach to the problem. The distribution function that results from adopting this framework has the same form as for polytropes, but the polytropic index is now related to the degree of nonextensiveness. In particular, the nonextensive approach can mimic the equilibrium structure of dark matter density profiles found in simulations. We extend the investigation of this approach to the velocity structures expected from nonextensive thermodynamics. We find that the nonextensive and simulated N-body upsilon(rms) distributions do not match one another. The nonextensive upsilon(rms) profile is either monotonically decreasing or displays little radial variation, each of which disagrees with the upsilon(rms) distributions seen in simulations. We conclude that the currently discussed nonextensive models require further modifications in order to corroborate dark matter halo simulations.