Correlations of Richness and Global Properties in Galaxy Clusters

We measure the optical richness of galaxy clusters from the CNOC1 clusterredshift survey using the galaxy-cluster center correlation amplitude B_gc. Weshow that the B_gc values measured using photometric catalogs are consistentwith those derived from redshift catalogs, indicating that richness can bemeasured reliably from photometric data alone, even at moderate redshifts of\~0.6. We establish the correlations between optical richness and otherimportant attributes of a galaxy cluster, such as velocity dispersion, mass,radius, and X-ray temperature and luminosity. We find that the scalingrelations of these quantities with richness are entirely consistent with thosederived by assuming a simple mass density profile at 0.5 Mpc of rho~r^{-1.8}.The excellent correlations between B_gc and velocity dispersion and X-raytemperature allow one to use richness, an easily measurable quantity usingrelatively shallow optical imaging data alone, as a predictor of thesequantities at moderate redshifts. The B_gc parameter can be used to estimatethe velocity dispersion of a cluster to a precision of approximately 15%(~+/-100 km/s), and X-ray temperature to about 20%. Similar correlations, butwith larger scatter, are also obtained between richness and the characteristicradius 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 ofcorrelations between richness and velocity dispersion, T_x and L_x with asample of low-redshift Abell clusters and find consistent results, but withlarger scatter, which may be the result of a less homogeneous database, orsample-dependent effects.Comment: 18 pages. Accepted; to appear in ApJ, March 200