A Quantitative Measure of the Richness of Galaxy Clusters

Using photometric catalogs from wide-field CCD images, we derive thecluster-galaxy correlation amplitudes, Bgc, for 47 low-redshift Abell clusters.We apply a number of tests to establish the robustness of the Bgc parameter asa quantitative measure of richness of galaxy clusters. These include usingdifferent galaxy luminosity functions to normalize the excess galaxy counts,counting galaxies to different absolute magnitude limits, and counting galaxiesto different cluster-centric radii. These tests show that with a properlynormalized luminosity function, the Bgc parameter is relatively insensitive (atbetter than 1/2 of an Abell Richness class) to magnitude limit, areal coverage,and photometric errors of up to about 0.25 mag. We compare the Bgc values toboth the Abell Richness Class (ARC) and Abell count numbers (N_A). It is foundthat there is a good correlation between Bgc and N_A for Abell clusters withz<~0.1, with a dispersion of about one ARC; whereas the Abell Richnessclassifications for Abell clusters at z>~0.1 are much less well correlated withthe true cluster richness. We also find evidence that the richness of ARC>=3clusters has the tendency of being over estimated in the Abell catalog.Comment: 28 pages, Latex, 7 postscript figures included. Accepted by the Astronomical Journal, to appear in May 199