Galaxy Groups in Cold + Hot and CDM Universes: Comparison with CfA

This letter presents results of new high resolution $\Omega=1$ Cold + Hot Dark Matter (CHDM) and Cold Dark Matter (CDM) simulations. Properties of groups in these simulations reflect the lower small-scale velocities and the greater tendency to form distinct filaments on both small and large scales in CHDM as compared to CDM. The fraction of galaxies in groups and the median group rms velocity are found to be powerful discriminators between models. We combine these two features into a very robust statistic, median group rms velocity $v_{\rm gr}(f_{\rm gr})$ as a function of the fraction $f_{\rm gr}$ of galaxies in groups. Using this statistic, we compare ``observed'' simulations to CfA data in redshift space in a careful and consistent way. We find that CHDM remains a promising model, with for example $v_{\rmgr}(0.45) \approx 125 \pm 25 \kms$ in agreement with the CfA data, while CDM with bias b=1.0 (COBE-compatible) or b=1.5, both giving $v_{\rm gr}(0.45) \approx 400 \pm 25 \kms$, can be virtually ruled out. Using median $M/L$, the observed value of $\Omega$ is $0.10$ (CHDM) to $0.38$ (CDM).