Distribution Function in Center of Dark Matter Halo

Abstract

N-body simulations of dark matter halos show that the density profiles of halos behave as $\ddot{I}(r)\propto r^{-\hat{I}\pm (r)}$, where the density logarithmic slope $\hat{I}\pm \simeq 1\sim 1.5$ in the center and $\hat{I}\pm \simeq 3\sim 4$ 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 ${\hat{I}}^2\approx 0$ in the inner part of the halo and the so called "pseudo phase-space density" $\ddot{I}/\ddot{I}{ƒ}^3$ behaves as a power-law in radius $r$. With these results in mind, we study the distribution function and the pseudo phase-space density $\ddot{I}/\ddot{I}{ƒ}^3$ of the center of dark matter halos and find that they are closely-related.

8 pages, accepted by Int. J. Mod. Phys. D, add a quotation and remove the appendix