The Inner Structure of ΛCDM Halos III: Universality and Asymptotic Slopes

We investigate the mass profile of ΛCDM halos using a suite of numerical simulations spanning five decades in halo mass, from dwarf galaxies to rich galaxy clusters. These halos typically have a few million particles within the virial radius (r200), allowing robust mass profile estimates down to radii below 1% of r200. Our analysis confirms the proposal of Navarro, Frenk & White (NFW) that the shape of ΛCDM halo mass profiles differs strongly from a power law and depends little on mass. The logarithmic slope of the spherically-averaged density profile, as measured by β = −d ln ρ/d ln r, decreases monotonically towards the center and becomes shallower than isothermal (β < 2) inside a characteristic radius, r −2. The fitting formula proposed by NFW provides a reasonably good approximation to the density and circular velocity profiles of individual halos; circular velocities typically deviate from best NFW fits by less than 10% over the radial range which is well resolved numerically. On the other hand, systematic deviations from the best NFW fits are also noticeable. Inside r −2, the profile of simulated halos gets shallower with radius more gradually than predicted and, as a result, NFW fits tend to underestimate the dark matter density in these regions. This discrepancy has been interpreted as indicating a steeply divergent cusp with asymptotic inner slope, β0 ≡ β(r = 0) ∼ 1.5. Our results suggest a different interpretation. We use the density and enclosed mass at our innermost resolved radii to place strong constraints on β0: density cusps as steep as r −1.5 are inconsistent with most of our simulations, although β0 = 1 is still consistent with our data. Our density profiles show no sign of converging to a well-defined asymptotic inner power law. We propose a simple formula that reproduces the radial dependence of the slope better than the NFW profile, and so may minimize errors when extrapolating our results inward to radii not yet reliably probed by numerical simulations.