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 is 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 to the observed number of dwarfs in the local group, while that in cluster-sized halos is consistent with 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 N_c \propto 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 ~ 140km/s or less. Previous comparisons of cluster-sized halos gave much smaller number of subhalos in this regime simply because of their limited resolution. Our result implies that any theory which attempts to resolve the missing dwarf problem should also explain the discrepancy of the simulation and observation in cluster-sized halos. 
Hiroyuki Kase, Junichiro Makino, Yoko Funato