The Observational Mass Function of Loose Galaxy Groups
  We analyze the three catalogs of nearby loose groups identified by Garcia (1993). She used a percolation and a hierarchical method, and proposed a third group catalog 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 much larger than their expected virialized region. We compute the virial masses and correct them by taking into account the young dynamical status. We estimate group masses, M, for two cosmological models, a flat one with Omega_0=1 and an open one with Omega_0=0.2. For each of the three catalogs we calculate the mass function, MF. The number density of groups with M>9x10^{12}\msun, which is the adopted limit of sample completeness, ranges within 1.3-1.9x10^{-3}h^3/Mpc^3 for Omega_0=1, and it is about a factor of 15% lower for Omega_0=0.2. The MFs of the hierarchical and combined catalogs have essentially the same shape, while the MF of the percolation catalog shows a flattening towards 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 do a comparison with the results coming from the virial analysis of nearby rich clusters (Girardi et al. 1998). All three group MFs turn out to be a smooth extrapolation of the cluster MF at M<4x10^{14}\msun, which is the completeness limit of the cluster sample. The resulting optical virial MF of galaxy systems, which extends over two orders of magnitude, is fitted to a Schechter expression with a slope of about -1.5 and a characteristic mass of about 3x10^{14}\msun. 
M. Girardi (1) and G. Giuricin (1,2); ((1) Dipartimento di Astronomia,   Univ. di Trieste, Trieste, Italy (2) SISSA, Trieste...