Correlations of richness and global properties in galaxy clusters

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-gc values 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 similar to0.6. 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(50)(-1) Mpc of rhosimilar tor(-1.8). The excellent correlations between B-gc and 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-gc parameter can be used to estimate the velocity dispersion of a cluster to a precision of approximately 15% (similar to+/-100 km s(-1)) 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-X as 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.