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 cluster s. We investigate the ''overmerging'' problem using analytic results a nd new simulations designed to calculate destruction times of halos ow ing to numerical and physical dynamical effects. Current numerical res olution is sufficient to suppress mass loss from two-body relaxation a nd 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 th eir inner density profiles. Singular isothermal halos should always su rvive at some level, although the computational cost of resolving halo cores becomes very large. However, if halos form with large core radi i, then the overmerging problem will always exist within dissipationle ss N-body simulations. In this case a dissipational component can incr ease the halos central density, enabling galaxy halos to survive.