The density and pseudo-phase-space density profiles of cold dark matter haloes

Cosmological N-body simulations indicate that the spherically averaged density profiles of cold dark matter (CDM) haloes are accurately described by Einasto profiles, where the logarithmic slope is a power law of adjustable exponent, gamma d ln rho/d ln r proportional to r(alpha). The pseudo-phase-space density (PPSD) profiles of CDM haloes also show remarkable regularity, and are well approximated by simple power laws, Q(r) = rho/sigma(3) proportional to r(-chi). As reported in earlier work, this is because Jeans' equations imply, for values of a typical of CDM haloes, that the PPSD profiles of Einasto haloes should resemble power laws over a wide radial range. Significant deviations from a power-law Q profile are nevertheless expected near the centre of Einasto haloes. Conversely, density profiles must deviate from a simple Einasto form if a power-law Q(r) profile holds at all radii. We use an ensemble of haloes drawn from the Millennium-II Simulation to study which of these two descriptions describes best the mass profile of CDM haloes. 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. Although we are unable to discriminate between these two models, our results confirm the need for a 'shape' parameter, like alpha or chi, to specify fully the mass profile of a CDM halo. Understanding what determines this shape parameter in the case of individual haloes would help us gain insight into what drives departures from self-similarity in CDM halo structure and how they correlate with evolutionary history, environment or initial conditions.