Galaxy groups: abundance by luminosity and by velocity dispersion

We present a reanalysis of groups in the Center for Astrophysics redshift survey, focusing on properties that can be readily compared with predictions of gravitational clustering theories. The grouping algorithm we employ is optimized using artificial catalogues constructed from N-body simulations that have similar low-order correlations to those of the original survey. We develop a method for estimation of the total luminosity of groups identified in magnitude-limited galaxy surveys, and use it to derive a luminosity function of galactic systems. This statistic measures the abundance of gravitationally bound structures as a function of their luminosity, independently of the detailed arrangement of the luminous material within them