2003ApJ...585..215Y

Richness is a key defining characteristic of a galaxy cluster. We measure the optical richness of galaxy clusters from the Canadian Network for Observational Cosmology Cluster Redshift Survey using the galaxy cluster center correlation amplitude B_gc. We show that the B_gcvalues measured using photometric catalogs are consistent with those derived from redshift catalogs, indicating that richness can be measured reliably from photometric data alone, even at moderate redshifts of ∼0.6. We establish the correlations between optical richness and other important attributes of a galaxy cluster, such as velocity dispersion, mass, radius, and X-ray temperature and luminosity. We find that the scaling relations of these quantities with richness are entirely consistent with those derived by assuming a simple mass density profile at 0.5 h^–1₅₀ Mpc of ρ∼r^–1.8. The excellent correlations between B_gcand velocity dispersion and X-ray temperature allow one to use richness, an easily measurable quantity using relatively shallow optical imaging data alone, as a predictor of these quantities at moderate redshifts. The B_gcparameter can be used to estimate the velocity dispersion of a cluster to a precision of approximately 15% (~±100 km/s) and X-ray temperature to about 20%. Similar correlations, but with larger scatter, are also obtained between richness and the characteristic radius and mass of the clusters. We compare the relative merits of B_gc, T_X, and L_Xas predictors of the dynamical mass and find that they are comparable, providing estimates at an accuracy of ∼30%. We also perform similar analyses of correlations between richness and velocity dispersion, T_X, and L_X with a sample of low-redshift Abell clusters and find consistent results, but with larger scatter, which may be the result of a less homogeneous database or sample-dependent effects.