The Phase‐Space Density Profiles of Cold Dark Matter Halos

We examine the coarse-grained phase-space density profiles of a set of recent, highresolution 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, ρ/σ 3 ∝ r −α, with α ≈ 1.875. This behaviour 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 profile corresponding to Bertschinger’s solution (a power-law of slope r 2α−6) differs significantly from the density profiles of CDM halos. CDM halo density profiles are clearly not power laws, and have logarithmic slopes that gradually steepen with radius, roughly as described by Navarro, Frenk White (NFW). We show that isotropic, spherically-symmetric equilibrium mass distributions with power-law phase-space density profiles form a one-parameter family of structures controlled by the ratio of the local velocity dispersion to the “natural ” velocity dispersion at some fiducial radius, r0; κ = 4πGρ(r0)r 2 0 /σ(r0) 2. For κ = α = 1.875 one recovers the power-law solution ρ ∝ r 2α−6. As κ increases, the density profiles