The Observational Mass Function of Loose Galaxy Groups

We analyze the three catalogs of nearby loose groups compiled by A. M. Garcia. She identified groups in a magnitude-limited redshift galaxy catalog, which covers about ~ of sky within cz = 5500 km s^-1, using two methods, a percolation method and a hierarchical method. The free parameters of the group-selection algorithms were tuned to obtain similar catalogs of groups. The author also proposed a third catalog of groups, defined as a combination of the two. Each catalog contains almost 500 groups. In agreement with previous works on earlier catalogs, we find that groups can be described as collapsing systems. Their sampled size is in general considerably larger than their expected virialized region. We compute the virial masses and correct them by taking into account the young dynamical status of these groups. We estimate corrected group masses, M, for two reference cosmological models, a flat one with a matter density parameter Ω₀ = 1 and an open one with Ω₀ = 0.2. We calculate the mass function for each of the three catalogs. We find that the amplitude of the mass function is not very sensitive to the choice of the group-identification algorithm. The number density of groups with M > 9 × 10¹² h^-1 M_☉, which is the adopted limit of sample completeness, ranges in the interval 1.3-1.9 × 10^-3 h³ Mpc^-3 for Ω₀ = 1, and it is about a factor of 15% lower for Ω₀ = 0.2. The mass functions of the hierarchical and combined catalogs have essentially the same shape, while the mass function of the percolation catalog shows a flattening toward large masses. However, the difference decreases if we do not consider the most massive groups, for which reliable results come from galaxy cluster studies. After having estimated the mass contained within the central, presumably virialized, regions of groups by adopting a reduction in mass of ~30%-40%, we make a comparison with the results from the virial analysis of nearby rich clusters. All three group mass functions turn out to be a smooth extrapolation of the cluster mass function at M < 4 × 10¹⁴ h^-1 M_☉, which is the completeness limit of the cluster sample. The resulting optical virial mass function of galaxy systems, which extends over 2 orders of magnitude, is fitted to a Schechter expression with a slope of ~ 1.5 and a characteristic mass of M_* ~ 3 × 10¹⁴ h^-1 M_☉. We also verify that our group mass function agrees reasonably well with the Press-Schechter predictions of models which at large masses describe the virial mass function of clusters.