Distribution Function of Dark Matter with Constant Anisotropy

N-body simulations of dark matter halos show that the density is cusped near the center of the halo. The density profile behaves as $r^{-\gamma }$ in the inner parts, where $\gamma \simeq 1$ for the NFW model and $\gamma \simeq 1.5$ for the Moore’s model, but in the outer parts, both models agree with each other in the asymptotic behavior of the density profile. The simulations also show the information about anisotropy parameter $\beta (r)$ of velocity distribution. $\beta \approx 0$ in the inner part and $\beta \approx 0.5$ (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 $ϵ$ for those two generalized models to determine the asymptotic behavior of the density profile. In this paper, we concentrate on the situation of $\beta (r)=1\mathrm{/}2$ from the viewpoint of the simulation.