Galaxy groups: abundance by luminosity and by velocity dispersion

Abstract

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. We also estimate the abundance of groups as a function of velocity dispersion. There is a smooth transition in the luminosity function from single galaxies to luminous rich clusters. The distribution of velocity dispersion, on the other hand, shows a discontinuity in slope at the transition between poor groups and rich clusters. We suggest that this is a result of contamination and projection effects artificially inflating the velocity dispersions of many rich clusters. Finally, we compare our results in detail with predictions of the cold dark matter cosmogony using analyses of ‘galaxy’ catalogues constructed from N-body simulations. We find good agreement between the model predictions and the data.