Title:A Probabilistic Quantification of Galaxy Cluster Membership

Abstract: Clusters of galaxies are important laboratories for understanding both galaxy evolution and constraining cosmological quantities. Any analysis of clusters, however, is best done when one can reliably determine which galaxies are members of the cluster. While this would ideally be done spectroscopically, the difficulty in acquiring a complete sample of spectroscopic redshifts becomes rather daunting, especially at high redshift where the background contamination becomes increasingly larger. Traditionally, an alternative approach of applying a statistical background correction has been utilized, which, while useful in a global sense, does not provide information for specific galaxies. In this paper, we develop a more robust technique which uses photometrically estimated redshifts to determine cluster membership. This technique can either be used as an improvement over the commonly used statistical correction method or it can be used to determine cluster candidates on an individual galaxy basis. By tuning the parameters of our algorithm, we can selectively maximize our completeness or, alternatively, minimize our contamination. Furthermore, our technique provides a statistical quantification of both our resulting completeness and contamination from foreground and background galaxies.