A derivation of masses and total luminosities of galaxy groups and clusters in the maxBCG catalogue

We report the results of a multi-waveband analysis of the masses and luminosities of $\sim$600 galaxy groups and clusters identified in the maxBCG catalogue. These data are intended to form the basis of future work on the formation of the "$m_{12}$ gap" in galaxy groups and clusters. We use SDSS spectroscopy and $g$, $r$ and $i$ band photometry to estimate galaxy group/cluster virial radii, masses and total luminosities. In order to establish the robustness of our results, we compare them with literature studies that utilize a variety of mass determinations techniques (dynamical, X-ray, weak lensing) and total luminosities estimated in the $B$, $r$, $i$, and $K$ wavebands. We also compare our results to predictions derived from the Millennium Simulation. We find that, once selection effects are properly accounted for, excellent agreement exists between our results and the literature with the exception of a single observational study. We also find that the Millennium Simulation does an excellent job of predicting the effects of our selection criteria. Our results show that, over the mass range $\sim10^{13}-10^{15}$ M$_{\odot}$, variations in the slope of the mass-luminosity scaling relation with mass detected in this and many other literature studies is in part the result of selection effects. We show that this can have serious ramifications on attempts to determine how the mass-to-light ratio of galaxy groups and cluster varies with mass.