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

We investigate the mass profile of cold dark matter (ΛCDM) 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 (r200), allowing robust mass profile estimates down to radii <1 per cent of r200. Our analysis confirms the proposal of Navarro, Frenk & White (NFW) that the shape of the 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 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