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, Dn 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 Dn 4000 > 1.5 and within R200. The cluster velocity dispersion functions all show excesses at σ ≳ 250 km s-1 compared to the field velocity dispersion function. The velocity dispersion function slope at large velocity dispersion (σ > 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 R200 further underscores the probable major role of dry mergers in the growth of massive cluster galaxies during cluster assembly.