The Phase‐Space Density Profiles of Cold Dark Matter Halos

Abstract

We examine the coarse-grained phase-space density pro—les of a set of recent, high-resolution simula- tions 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, o/p3 P r~a, with aB 1.875. This behavior closely matches the self-similar solution obtained by Bertschinger for secondary infall of gas onto a point-mass perturber in a uniformly expanding universe. On the other hand, the density pro—le corresponding to Bertschingers solution (a power law of slope r2a~6) diUers signi—cantly from the density pro—les of CDM halos. CDM halo density pro—les are clearly not power laws, and they have logarithmic slopes that steepen gradually with radius, roughly as described by Navarro, Frenk, & White (NFW). We show that isotropic, spher- ically symmetric equilibrium mass distributions with power-law phase-space density pro—les form a one- parameter family of structures controlled by the ratio of the local velocity dispersion to the ii natural ˇˇ velocity dispersion at some —ducial radius For i a 1.875, one recovers the r 0 ; i 4nGo(r 0 )r2 0 /p2(r 0 ). power-law solution o P r2a~6 .A si increases, the density pro—les become quite complex but still diverge as r2a~6 near the center. For i larger than some critical value solutions become nonphysical, i crit (a), leading to negative densities near the center. The critical solution, corresponds to the case i i crit , where the phase-space density distribution is the narrowest compatible with the power-law phase-space density strati—cation constraint. Over three decades in radius, the critical solution follows closely an NFW pro—le, although its logarithmic slope asymptotically approaches (2a/5 \( 0.75 (rather than (1) at very small radii. Our results thus suggest that the NFW pro—le is the result of a hierarchical assembly process that preserves the phase-space strati—cation of Bertschingers spherical infall model but ii mixes ˇˇ the system maximally, perhaps as a result of repeated merging, leading to a relatively uniform phase- space density distribution across the system. This —nding oUers intriguing clues as to the origin of the similarity in the structure of dark matter halos formed in hierarchically clustering universes. Subject headings: cosmology: theorydark mattergalaxies: formationgalaxies: structure ¨ methods: analyticalmethods: numerical On-line material: color —gures