The Density and Pseudo-Phase-Space Density Profiles of CDM halos

Cosmological N-body simulations indicate that the spherically-averaged density profiles of cold dark matter halos are accurately described by Einasto profiles, where the logarithmic slope is a power-law of adjustable exponent, \gamma =dln\rho /dlnr ~ r^\alpha $. The pseudo-phase-space density (PPSD) profiles of CDM halos also show remarkable regularity, and are well approximated by simple power laws, Q(r)=\rho /\sigma ^3 ~ r^-\chi . We show that this is expected from dynamical equilibrium considerations, since Jeans' equations predict that the pseudo-phase-space density profiles of Einasto halos should resemble power laws over a wide range of radii. For the values of \alpha typical of CDM halos, the inner Q profiles of equilibrium halos deviate significantly from a power law only very close to the center, and simulations of extremely high-resolution would be needed to detect such deviations unambiguously. We use an ensemble of halos drawn from the Millennium-II simulation to study which of these two alternatives describe best the mass profile of CDM halos. Our analysis indicates that at the resolution of the best available simulations, both Einasto and power-law PPSD profiles (with adjustable exponents \alpha and \chi, respectively) provide equally acceptable fits to the simulations. A full account of the structure of CDM halos requires understanding how the shape parameters that characterize departures from self-similarity, like \alpha or \chi, are determined by evolutionary history, environment or initial conditions.