Density Profiles and Substructure of Dark Matter Halos: Converging Results at Ultra‐High Numerical Resolution

Can N-body simulations reliably determine the structural properties of dark matter halos? Focussing on a Virgo-sized galaxy cluster, we increase the resolution of current ``high resolution simulations'' by almost an order of magnitude to examine the convergence of the important physical quantities. We have 5 million particles within the cluster and force resolution 0. 5 kpc/h (0. 05% of the virial radius). The central density profile has a logarithmic slope of -1. 5, as found in lower resolution studies of the same halo, indicating that the profile has converged to the ``physical'' limit down to scales of a few kpc. Also the abundance of substructure is consistent with that derived from lower resolution runs, yielding power law mass and circular velocity functions (exponents ~ -1. 9 and -4). Overmerging appears to be globally unimportant for suhalos with circular velocities > 100 km/s. We can trace most of the cluster progenitors from z=3 to the present; the central object (the dark matter analog of a cD galaxy) is assembled between z=3 and 1 from the merging of a dozen halos with vcirc \ 300 km/s. The mean circular velocity of the subhalos decreases by ~ 20% over 5 billion years, due to tidal mass loss. The velocity dispersions of halos and dark matter globally agree within 10%, but the halos are spatially anti-biased, and, in the very central region of the cluster, they show positive velocity bias; however, this effect appears to depend on numerical resolution.