Resolving the structure of cold dark matter halos

We examine the effects of mass resolution and force softening on the density profiles of cold dark matter halos that form within cosmological N-body simulations. As we increase the mass and force resolution, we resolve progenitor halos that collapse at higher redshifts and have very high densities. At our highest resolution we have nearly 3 x 10(6) particles within the virial radius, which is several orders of magnitude more than previously used, and we can resolve more than 1000 surviving dark matter halos within this single virialized system. The halo profiles become steeper in the central regions, and we may not have achieved convergence to a unique slope within the inner 10% of the virialized region. Results from two very high resolution halo simulations yield steep inner density profiles, p(r) similar to r(-1.4). The abundance and properties of arcs formed within this potential will be different from calculations based on lower resolution simulations. The kinematics of disks within such a steep potential may prove problematic for the cold dark matter model when compared with the observed properties of halos on galactic scales.