The Phase-Space Density Profiles of Cold Dark Matter Halos

Abstract

We examine the coarse-grained phase-space density profiles of a set of recent, high-resolution simulations of galaxy-sized Cold Dark Matter (CDM) halos. Over two and a half decades in radius the phase-space density closely follows a power-law, $\rho /{\sigma }^3\propto r^{-\alpha }$, with $\alpha =1.875$. This behaviour matches the self-similar solution obtained by Bertschinger for secondary infall in a uniformly expanding universe. On the other hand, the density profile corresponding to Bertschinger's solution (a power-law of slope $r^{2\alpha -6}$) differs significantly from the density profiles of CDM halos. We show that isotropic mass distributions with power-law phase-space density profiles form a one-parameter family of structures controlled by $\kappa$, the ratio of the velocity dispersion to the peak circular velocity. For $\kappa =\alpha =1.875$ one recovers the power-law solution $\rho \propto r^{2\alpha -6}$. For $\kappa$ larger than some critical value, ${\kappa }_{cr}$, solutions become non-physical, leading to negative densities near the center. The critical solution, $\kappa ={\kappa }_{cr}$, has the narrowest phase-space density distribution compatible with the power-law phase-space density stratification constraint. Over three decades in radius the critical solution is indistinguishable from an NFW profile. Our results thus suggest that the NFW profile is the result of a hierarchical assembly process that preserves the phase-space stratification of Bertschinger's infall model but which ``mixes'' the system maximally, perhaps as a result of repeated merging.

16 pages, 4 figures; submitted to The Astrophysical Journal

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