Missing dwarf problem in galaxy clusters

We investigated the formation and evolution of CDM subhalos in galaxy-sized and cluster-sized halos by means of N-body simulations. Our aim was to make clear what the dwarf galaxy problem is. It has been argued that the number of subhalos in simulated galaxy-sized halos is too large compared with the observed number of dwarfs in the local group, while that in cluster-sized halos is consistent with the observed number of galaxies in clusters, such as the Virgo cluster. We simulated nine halos with several different mass resolutions and physical scales. We found that the dependence of the cumulative number of subhalos, N-c, on their maximum circular velocity, V-c, is given by Nc proportional to V-c(-3), down to the reliability limit, independent of the mass of the main halo. This implies that simulations for cluster-sized halos give too many halos with V-c similar to 140 km s(-1) or less. Previous comparisons of cluster-sized halos gave a much smaller number of subhalos in this regime, simply because of their limited resolution. Our result implies that any theory that attempts to resolve the missing dwarf problem should also explain the discrepancy of the simulation and observation in cluster-sized halos.