The Structure of Halos: Implications for Group and Cluster Cosmology

The dark matter halo mass function is a key repository of cosmological information over a wide range of mass scales, from individual galaxies to galaxy clusters. N-body simulations have established that the friends-of-friends (FOF) mass function has a universal form to a surprising level of accuracy (lsim10%). The high-mass tail of the mass function is exponentially sensitive to the amplitude of the initial density perturbations, the mean matter density parameter, Ω _m , and to the dark energy controlled late-time evolution of the density field. Observed group and cluster masses, however, are usually stated in terms of a spherical overdensity (SO) mass which does not map simply to the FOF mass. Additionally, the widely used halo models of structure formation—and halo occupancy distribution descriptions of galaxies within halos—are often constructed exploiting the universal form of the FOF mass function. This again raises the question of whether FOF halos can be simply related to the notion of a spherical overdensity mass. By employing results from Monte Carlo realizations of ideal Navarro-Frenk-White (NFW) halos and N-body simulations, we study the relationship between the two definitions of halo mass. We find that the vast majority of halos (80%-85%) in the mass-range 10^12.5-10^15.5 h ^-1 M _sun indeed allow for an accurate mapping between the two definitions (~5%), but only if the halo concentrations are known. Nonisolated halos fall into two broad classes: those with complex substructure that are poor fits to NFW profiles and those "bridged" by the (isodensity-based) FOF algorithm. A closer investigation of the bridged halos reveals that the fraction of these halos and their satellite mass distribution is cosmology dependent. We provide a preliminary discussion of the theoretical and observational ramifications of these results.