Empirical models for Dark Matter Halos

We use techniques from nonparametric function estimation theory to extract the density profiles, and their derivatives, from a set of N -body halos, and compare these with a variety of parametric models. We consider N -body halos generated from (i) ΛCDM simulations of gravitational clustering, and (ii) isolated, spherical collapses. The parametric models include a double power-law model (an NFW-like model with arbitrary inner power-law slope γ), Sérsic’s r model (traditionally applied to projected light-profiles), and the density model of Prugniel & Simien that was designed to match the deprojected form of the Sérsic model and is applied here for the first time to dark matter halos. Perhaps not surprising, these 3-parameter models provide a better description of the data than the 2-parameter NFW, Burkert, and Dehnen-McLaughlin models. With regard to the spherical collapse systems, both the Prugniel-Simien and Sérsic models describe the density distribution well, with an rms scatter some four times smaller than that obtained with the NFW-like model. For the cluster-sized ΛCDM halos, the Prugniel-Simien model performs the best, having the lowest residual scatter. Curiously, for the galaxy-sized ΛCDM halos, Sérsic’s model performs the best. We also observe a slight variation in Sérsic index n with halo mass, as reported in Merritt et al., suggesting a departure from a universal profile. The location of the 10M⊙, galaxy-sized halos in the 〈μ〉e–logRe and log ρe–logRe diagrams coincides with that of brightest cluster galaxies. More specifically, the halos appear consistent with the new relation log(ρe) = 1.15−2.5 log(Re), log(Re) & 0.5 kpc, defined by elliptical galaxies and galaxy clusters. The galaxy-sized halos also appear to be the high-mass extension of the elliptical galaxy distribution in the mass-size and mass-density plane. We provide analytical expressions for the slopes of the empirical models, and compare these with data from real galaxies. Depending on the Sérsic parameters of the dark matter halo, one can expect an extrapolated, inner (0.01–1 kpc), logarithmic profile slope ranging from ∼ -0.2 to ∼ -1.5, with a typical value at 0.1 kpc around -0.7. For the Sérsic and Prugniel-Simien model, we additionally provide useful expressions for the concentration and assorted scale radii: rs, r−2, re, Re, rvir, and rmax — the radius where the circular velocity profile has its maximum value. We also present the circular velocity profiles and the radial behavior of ρ(r)/σ(r) for these two models, where σ(r) is the velocity dispersion associated with the density profile ρ(r), finding they are well approximated by a power-law with slope slightly shallower than -2 near 1