The Velocity Dispersion Function for Quiescent Galaxies in Nine Strong-lensing Clusters

We measure the central stellar velocity dispersion function for quiescent galaxies in a set of nine northern clusters in the redshift range 0.18 < z < 0.29 and with strong lensing arcs in Hubble Space Telescope images. The velocity dispersion function links galaxies directly to their dark matter halos. From dense SDSS and MMT/Hectospec spectroscopy, we identify 222-463 spectroscopic members in each cluster. We derive physical properties of cluster members including redshift, D(n)4000, and central stellar velocity dispersion and we include a table of these measurements for 3419 cluster members. We construct the velocity dispersion functions for quiescent galaxies with D(n)4000 > 1.5 and within R-200. The cluster velocity dispersion functions all show excesses at sigma greater than or similar to 250 kms(-1) compared to the field velocity dispersion function. The velocity dispersion function slope at large velocity dispersion (sigma > 160 km s(-1)) is steeper for more massive clusters, consistent with the trend observed for cluster luminosity functions. The spatial distribution of galaxies with large velocity dispersion at radii larger than R-200 further underscores the probable major role of dry mergers in the growth of massive cluster galaxies during cluster assembly.