Empirical Models for Dark Matter Halos. II. Inner profile slopes, dynamical profiles, and rho/sigma³

We have recently shown that both the Prugniel-Simien model and Sersic's function (hereafter referred to as the Einasto model when applied to internal density profiles) describe simulated dark matter halos better than an NFW-like model with equal number of parameters. Here we provide analytical expressions for the logarithmic slopes of these models, and compare them with data from real galaxies. Depending on the Einasto 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. Application of this (better fitting) model therefore alleviates some of the past disagreement with observations on this issue. We additionally provide useful expressions for the concentration and assorted scale radii: r_s, r_{-2}, r_e, R_e, r_virial, and r_max -- the radius where the circular velocity profile has its maximum value. We also present the circular velocity profiles and the radial behavior of rho(r)/sigma(r)^3 for both the Einasto and Prugniel-Simien models. We find this representation of the phase-space density profile to be well approximated by a power-law with slope slightly shallower than -2 near r=r_{-2}.