The inner structure of ΛCDM haloes – III. Universality and asymptotic slopes

We investigate the mass profile of cold dark matter (ACDM) haloes using a suite of numerical simulations spanning five decades in halo mass, from dwarf galaxies to rich galaxy clusters. These haloes typically have a few million particles within the virial radius (r 200 ), allowing robust mass profile estimates down to radii <1 per cent of r 200 . Our analysis confirms the proposal of Navarro, Frenk & White (NFW) that the shape of the ACDM 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 In p/d In r, decreases monotonically towards the centre 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 haloes; circular velocities typically deviate from NFW best fits by <10 per cent over the radial range that is numerically well resolved. Alternatively, systematic deviations from the NFW best fits are also noticeable. Inside r -2 , the profile of simulated haloes becomes 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, β 0 ≡ 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 β 0 : density cusps as steep as r -1.5 are inconsistent with most of our simulations, although β 0 = 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.