Galaxies in X-ray Selected Clusters and Groups in Dark Energy Survey Data II: Hierarchical Bayesian Modeling of Red-Sequence Galaxy Luminosity Function

Using $\sim 100$ X-ray selected clusters in the Dark Energy Survey Science Verification data, we constrain the luminosity function of cluster red sequence galaxies in the redshift range of $0.1redshift evolution and cluster mass dependence. The results from this method are tested by red sequence luminosity function parameters derived in cluster redshift or mass bins. We find a hint that the faint end slope of a Schechter function fit may evolve with redshift at a significance level of $\sim 1.9 \sigma$. Faint cluster red sequence galaxies possibly become more abundant at lower redshift, indicating a different formation time from the bright red sequence galaxies. Optical cluster cosmology analyses may wish to consider this effect when deriving mass proxies. We also constrain the amplitude of the luminosity function with the hierarchical Bayesian method, which strongly correlates with cluster mass and provides an improved estimate of cluster masses. This technique can be applied to a larger sample of X-ray or optically selected clusters from the Dark Energy Survey, significantly improving the sensitivity of the analysis.