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Can N-body simulations reliably determine the structural properties of darkmatter halos? Focussing on a Virgo-sized galaxy cluster, we increase theresolution of current ``high resolution simulations'' by almost an order ofmagnitude to examine the convergence of the important physical quantities. Wehave 4 million particles within the cluster and force resolution 0.5 kpc/h(0.05% of the virial radius). The central density profile has a logarithmicslope of -1.5, as found in lower resolution studies of the same halo,indicating that the profile has converged to the ``physical'' limit down toscales of a few kpc. Also the abundance of substructure is consistent with thatderived from lower resolution runs; on the scales explored, the mass andcircular velocity functions are close to power laws of exponents ~ -1.9 and -4.Overmerging appears to be globally unimportant for suhalos with circularvelocities > 100 km/s. We can trace most of the cluster progenitors from z=3 tothe present; the central object (the dark matter analog of a cD galaxy)isassembled between z=3 and 1 from the merging of a dozen halos with v_circ \sim300 km/s. The mean circular velocity of the subhalos decreases by ~ 20% over 5billion years, due to tidal mass loss. The velocity dispersions of halos anddark matter globally agree within 10%, but the halos are spatially anti-biased,and, in the very central region of the cluster, they show positive velocitybias; however, this effect appears to depend on numerical resolution.Comment: 19 pages, 13 figures, ApJ, in press. Text significantly clarifie

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