C

Abstract

We use a sample of galaxies from the Two Micron All Sky Survey Extended Source Catalog to refine a matched filter method of finding galaxy clusters that takes into account each galaxy’s position, magnitude, and redshift if available. The matched filter postulates a radial density profile, luminosity function, and line-of-sight velocity distribution for cluster galaxies. We use this method to search for clusters in the galaxy catalog, which is complete to an extinction-corrected K-band magnitude of 13.25 and has spectroscopic redshifts for roughly 40% of the galaxies, including nearly all brighter than K = 11.25. We then use a stacking analysis to determine the average luminosity function, radial distribution, and velocity distribution of cluster galaxies in several richness classes, and use the results to update the parameters of the matched filter before repeating the cluster search. We also investigate the correlations between a cluster’s richness and its velocity dispersion and core radius using these relations to refine priors that are applied during the cluster search process. After the second cluster search iteration, we repeat the stacking analysis. We find a cluster galaxy luminosity function that fits a Schechter form, with parameters MK∗ − 5 log h = −23.64 ± 0.04 and α = −1.07 ± 0.03. We can achieve a slightly better fit to our luminosity function by adding a Gaussian component on the bright end to represent the brightest cluster galaxy population. The radial number density profile of galaxies closely matches a projected Navarro–Frenk–White profile at intermediate radii, with deviations at small radii due to well-known cluster centering issues and outside the virial radius due to correlated structure. The velocity distributions are Gaussian in shape, with velocity dispersions that correlate strongly with richness.