We use a sample of galaxies from the Two Micron All Sky Survey ( 2MASS ) 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 M _ { K* } -5 \log h = -23.64 \pm 0.04 and \alpha = -1.07 \pm 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 ( BCG ) population .
The radial number density profile of galaxies closely matches a projected Navarro-Frenk-White ( NFW ) 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 .