Distribution function of dark matter with constant anisotropy

摘要

N-body simulations of dark matter halos show that the density is cusped near the center of the halo. The density pro. le behaves as r(-gamma). in the inner parts, where gamma similar or equal to 1 for the NFW model and gamma similar or equal to 1.5 for the Moore model, but in the outer parts the two models agree with each other in the asymptotic behavior of the density profile. The simulations also show information about the anisotropy parameter beta(r) of the velocity distribution: beta approximate to 0 in the inner part and beta approximate to 0.5 (radially anisotropic) in the outer part of the halo. We provide some distribution functions F(E, L) with the constant anisotropy parameter beta for the two spherical models of dark matter halos: a new generalized NFW model and a generalized Moore model. There are two parameters alpha and epsilon for those two generalized models to determine the asymptotic behavior of the density pro. le. In this paper, we concentrate on the situation of beta(r) = 1/2 from the viewpoint of the simulation.