On the Destruction and Overmerging of Dark Halos in Dissipationless N-Body Simulations

N-body simulations of collisionless dark matter have failed to produce galaxy halos or substructure within the dense environments of clusters. We investigate the "overmerging" problem using analytic results and new simulations designed to calculate destruction times of halos owing to numerical and physical dynamical effects. Current numerical resolution is sufficient to suppress mass loss from two-body relaxation and particle- halo heating. Substructure in these simulations can still be destroyed by the combined action of large-force softening together with tidal heating by the cluster and encounters with other dissolving halos. In the limit of infinite numerical resolution, whether or not individual halos or substructure can survive depends sensitively on their inner density profiles. Singular isothermal halos should always survive at some level, although the computational cost of resolving halo cores becomes very large. However, if halos form with large core radii, then the overmerging problem will always exist within dissipationless N-body simulations. In this case a dissipational component can increase the halos central density, enabling galaxy halos to survive.