Galaxy Groups, CDM/CHDM Cosmologies, and the Value of Ω0

We present techniques for identifying and analyzing galaxy groups and apply them to large-scale particle-mesh (PM) N-body simulations of structure formation in three Ω₀ = 1 cosmological models: cold plus hot dark matter (CHDM), with Ω_cold = 0.6, Ω_ν = 0.3, and Ω_baryon = 0.1 at bias b≡σ^-1₈=1.5 and two cold dark matter (CDM) models, at bias b = 1.5 and b = 1.0. Groups are identified with the adaptive friends-of-friends algorithm of Nolthenius. Our most important conclusions follow. The standard group M/L method gives Ω₀ ~= 0.08 for the CfA1 survey (for redshift link parameter V₅ = 350), and, applied to our Ω₀ = 1 simulations, it gives Ω₀ ~= 0.12 for CHDM (V₅ = 350) and Ω₀ ~= 0.35 for CDM (V₅ = 600). This Ω bias appears to be even stronger at higher resolution. We show quantitatively how three different effects conspire to produce this large discrepancy, and we conclude that low observed Ω values need not argue for a low-Ω universe. Our preferred statistics of groups show promise in becoming powerful discriminators between Gaussian cosmological models, whose Ω_ν differ and are robust against several methods for assigning luminosity to dark matter halos, and for merging CfA1 data. However, our latest results at higher resolution show such strong sensitivity to how massive overmergers are broken up that more reliable ways of identifying luminous galaxies within large-scale simulations will be necessary before these statistics can provide reliable discrimination. When overmergers are broken up, the median virial-to-DM mass M_vir/M_DM of three-dimensional-selected groups is ~1 for all simulations. Groups with M_DM > 10¹⁴ M_⊙ appear virialized in all simulations. We measure global (not pairwise) velocity biases b_v, similar to previous studies. Within three-dimensional-selected groups, CHDM and CDM with b = 1.5 show a stronger bias of b_v = 0.7-0.8, while CDM with b = 1.0 shows groups of b_v ~= 1.