The Canada-France-Hawaii telescope optical PDCS survey. II. Evolution in the space density of clusters of galaxies

We present the first dynamical study of the optically selected Palomar Dist ant Cluster Survey (PDCS). We have measured redshifts for 17 clusters of ga laxies in the PDCS and velocity dispersions for a subset of ii. Using our n ew cluster redshifts, we redetermine the X-ray luminosities and upper limit s. We show that 11 of 12 PDCS clusters we observed are real overdensities o f galaxies. Most clusters have velocity dispersions appropriate for cluster s of galaxies. However, we find a fraction (about one-third) of objects in the PDCS that have velocity dispersions in the range of groups of galaxies (200 +/- 100 km s(-1)) but have richnesses appropriate for clusters of gala xies. Within our survey volume of 31.7(-0.8)(+0.5) x 10(4) h(-3) Mpc(3) (q(0) = 0 .1) for richness class 2 and greater clusters, we measure the richness func tion, X-ray luminosity function (using both the detections and upper limits ), and the mass function derived from our velocity dispersions. We confirm that the space density, as a function of richness, of clusters of galaxies in the PDCS is similar to 5 times that of the Abell catalog. Excluding the above fraction of one-third of objects with low velocity dispersions, we me asure a space density similar to 3 times that of the Abell catalog for equi valent mass clusters of galaxies, raising the possibility that the Abell ca talog is incomplete. However, our space density estimates are in agreement with other low-redshift, optically selected cluster surveys such as the EDC C, APM, and EDCC2. Our X-ray luminosity function agrees with other measurem ents based on both X-ray and optically selected samples, so we find that th e PDCS does not miss clusters of galaxies that would be found in an X-ray s elected survey. Our resulting mass function, centered on 10(14) M-. h(-1), agrees with the expectations from such surveys as the Canadian Network for Observational Cosmology cluster survey, though errors on our mass measureme nts are too large to constrain cosmological parameters. We do show that fut ure machine-based, optically selected surveys can be used to constrain cosm ological parameters.