2000AJ....120...23H

We present the first dynamical study of the optically selected Palomar Distant Cluster Survey (PDCS). We have measured redshifts for 17 clusters of galaxies in the PDCS and velocity dispersions for a subset of 11. Using our new cluster redshifts, we redetermine the X-ray luminosities and upper limits. We show that 11 of 12 PDCS clusters we observed are real overdensities of galaxies. Most clusters have velocity dispersions appropriate for clusters 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 galaxies.

Within our survey volume of 31.7^+0.5_–0.8x10⁴ h^–3 Mpc³ (q₀=0.1) for richness class 2 and greater clusters, we measure the richness function, 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 ∼5 times that of the Abell catalog. Excluding the above fraction of one-third of objects with low velocity dispersions, we measure a space density ∼3 times that of the Abell catalog for equivalent mass clusters of galaxies, raising the possibility that the Abell catalog is incomplete. However, our space density estimates are in agreement with other low-redshift, optically selected cluster surveys such as the EDCC, APM, and EDCC2. Our X-ray luminosity function agrees with other measurements based on both X-ray and optically selected samples, so we find that the PDCS does not miss clusters of galaxies that would be found in an X-ray selected survey. Our resulting mass function, centered on 10¹⁴ M_☉ h^–1, agrees with the expectations from such surveys as the Canadian Network for Observational Cosmology cluster survey, though errors on our mass measurements are too large to constrain cosmological parameters. We do show that future machine-based, optically selected surveys can be used to constrain cosmological parameters.