Resolving the Structure of Cold Dark Matter Halos

We examine the effects of mass resolution and force softening on the densityprofiles of cold dark matter halos that form within cosmological N-bodysimulations. As we increase the mass and force resolution, we resolveprogenitor halos that collapse at higher redshifts and have very highdensities. At our highest resolution we have nearly 3 million particles withinthe virial radius, several orders of magnitude more than previously used and wecan resolve more than one thousand surviving dark matter halos within thissingle virialised system. The halo profiles become steeper in the centralregions and we may not have achieved convergence to a unique slope within theinner 10% of the virialised region. Results from two very high resolution halosimulations yield steep inner density profiles, $\rho(r)\sim r^{-1.4}$. Theabundance and properties of arcs formed within this potential will be differentfrom calculations based on lower resolution simulations. The kinematics ofdisks within such a steep potential may prove problematic for the CDM modelwhen compared with the observed properties of halos on galactic scales.Comment: Final version, to be published in the ApJLetter