Evolution of Massive Red Galaxies in Clusters from z=1.0 to z=0.3

A critical issue in studying the evolution of galaxy clusters is to find ways that enable meaningful comparisons of clusters observed at different redshifts, as well as in various stages of their growth. Studies in the past have typically suffered from uncertainties in cluster mass estimates due to the scatter between cluster observables and mass. Here we propose a novel and general approach that uses the probability distribution function of an observable-cluster mass relation, together with dark matter halo merger trees extracted from numerical simulations, such that one can trace the evolution in a self-contained fashion, for clusters chosen to lie in a specified range in mass and redshift. This method, when applied to clusters of different mass ranges, further allows one to examine the evolution of various observable-cluster mass scaling relations. We illustrate the potential of this method by studying the stellar mass content of red cluster member galaxies, as well as the growth of brightest cluster galaxies, from z=1.0 to z=0.3, using a large optically-detected cluster sample from the Subaru Hyper Suprime-Cam Survey, finding good agreement with previous studies.