Cusps in cold dark matter haloes

We resolve the inner region of a massive cluster forming in a cosmologicalcold dark matter (CDM) simulation with a mass resolution of 2 × 10 6 Mand before z = 4.4 even 3 × 10 5 M� . This is a billion times less than the cluster's final virial mass and a substantial increase over currentCDM simulations. We achieve this resolution using a new multimass refinement procedure and are now able to probe a dark matter halo density profile down to 0.1 per cent of the virial radius. The inner density profile of this cluster halo is well fitted by a power law ρ ∝ r −γ down to the smallest resolved scale. An inner region with roughly constant logarithmic slope is now resolved, which suggests that cuspy profiles describe the inner profile better than recently proposed profiles with a core. The cluster studied here is one out of a sample of six high-resolution cluster simulations, and its inner slope of about γ = 1.2 lies close to the sample average. Ke yw ords: methods: N-body simulations - methods: numerical - galaxies: clusters: general - galaxies: haloes - dark matter.