Empirical Models for Dark Matter Halos. II. Inner Profile Slopes, Dynamical Profiles, and ρ/σ3

We have recently shown that both the Prugniel-Simien model and Sérsic's function (hereafter referred to as the Einasto model when applied to internal density profiles) describe simulated dark matter halos better than a Navarro-Frenk-White-like model with an 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 approximately -0.2 to approximately -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. In addition, we provide useful expressions for the concentration and assorted scale radii: r_s, r_-2, r_e, R_e, r_vir, 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 ρ(r)/σ(r)³ for both the Einasto and Prugniel-Simien models, where σ(r) is the velocity dispersion associated with the density profile ρ(r). We find this representation of the phase-space density profile to be well approximated by a power law with a slope slightly shallower than -2 near r=r_-2.