Distribution Function in Center of Dark Matter Halo

N-body simulations of dark matter halos show that the density profiles of halos behave as ρ(r) ∝ r−α(r), where the density logarithmic slope α ≃ 1 ∼ 1.5 in the center and α ≃ 3 ∼ 4 in the outer parts of halos. However, some observations are not in agreement with simulations in the very central region of halos. The simulations also show that velocity dispersion anisotropy parameter β ≈ 0 in the inner part of the halo and the so called ”pseudo phase-space density” ρ/σ3 behaves as a power-law in radius r. With these results in mind, we study the distribution function and the pseudo phase-space density ρ/σ3 of the center of dark matter halos and find that they are closely-related.