Velocity Dispersion Profiles in Dark Matter Halos

Numerous numerical studies indicate that dark matter halos show an almost universal radial density profile. The origin of the profile is still under debate. We investigate this topic and pay particular attention to the velocity dispersion profile. To this end, we have performed high-resolution simulations with two independent codes, ART and GADGET. The radial velocity dispersion can be approximated as a function of the potential by σ = a(Φ/Φout)κ(Φout - Φ), where Φout is the outer potential of the halo. For the parameters a and κ, we find that a = 0.29 ± 0.04 and κ = 0.41 ± 0.03. We find that the power-law asymptote, σ2 ∝ Φκ, is valid out to much larger distances from the halo center than any power-law asymptote for the density profile ρ ∝ r-n. The asymptotic slope n(r → 0) of the density profile is related to the exponent κ via n = 2κ/(1 + κ). Thus, the value obtained for κ from the available simulation data can be used to obtain an estimate of the density profile below currently resolved scales. We predict a continuously decreasing n toward the halo center with the asymptotic value n ≲ 0.58 at r = 0.