Galaxy Groups
  Galaxy groups can be characterized by the radius of decoupling from cosmic expansion, the radius of the caustic of second turnaround, and the velocity dispersion of galaxies within this latter radius. These parameters can be a challenge to measure, especially for small groups with few members. In this study, results are gathered pertaining to particularly well studied groups over four decades in group mass. Scaling relations anticipated from theory are demonstrated and coefficients of the relationships are specified. There is an update of the relationship between light and mass for groups, confirming that groups with mass of a few times 10^12 Msun are the most lit up while groups with more and less mass are darker. It is demonstrated that there is an interesting one-to-one correlation between the number of dwarf satellites in a group and the group mass. There is the suggestion that small variations in the slope of the luminosity function in groups are caused by the degree of depletion of intermediate luminosity systems rather than variations in the number per unit mass of dwarfs. Finally, returning to the characteristic radii of groups, the ratio of first to second turnaround depends on the dark matter and dark energy content of the universe and a crude estimate can be made from the current observations of Omega_matter ~ 0.15 in a flat topology, with a 68% probability of being less than 0.44. 
R. Brent Tully
astro-ph.GA