Empirical Models for Dark Matter Halos. I. Nonparametric Construction of Density Profiles and Comparison with Parametric Models

We use techniques from nonparametric function estimation theory to extract the density profiles, and their derivatives, from a set of N-body dark matter halos. We consider halos generated from ΛCDM simulations of gravitational clustering, as well as isolated spherical collapses. The logarithmic density slopes γ≡dlogρ/dlogr of the ΛCDM halos are found to vary as power laws in radius, reaching values of γ~-1 at the innermost resolved radii, ~10^-2r_vir. This behavior is significantly different from that of broken-power-law models like the Navarro-Frenk-White (NFW) profile but similar to that of models like de Vaucouleurs's. Accordingly, we compare the N-body density profiles with various parametric models to find which provide the best fit. We consider an NFW-like model with arbitrary inner slope; Dehnen & McLaughlin's anisotropic model; Einasto's model (identical in functional form to Sérsic's model but fitted to the space density); and the density model of Prugniel & Simien that was designed to match the deprojected form of Sérsic's R^1/n law. Overall, the best-fitting model to the ΛCDM halos is Einasto's, although the Prugniel-Simien and Dehnen-McLaughlin models also perform well. With regard to the spherical-collapse halos, both the Prugniel-Simien and Einasto models describe the density profiles well, with an rms scatter some 4 times smaller than that obtained with either the NFW-like model or the three-parameter Dehnen-McLaughlin model. Finally, we confirm recent claims of a systematic variation in profile shape with halo mass.