Galaxies in X-ray Groups I: Robust Membership Assignment and the Impact of Group Environments on Quenching

Understanding the mechanisms that lead dense environments to host galaxies with redder colors, more spheroidal morphologies, and lower star formation rates than field populations remains an important problem. As most candidate processes ultimately depend on host halo mass, accurate characterizations of the local environment, ideally tied to halo mass estimates and spanning a range in halo mass and redshift are needed. In this work, we present and test a rigorous, probabalistic method for assigning galaxies to groups based on precise photometric redshifts and X-ray selected groups drawn from the COSMOS field. The groups have masses in the range 10^13 < M_200c/M_sun < 10^14 and span redshifts 0