The Velocity Dispersion Function of Very Massive Galaxy Clusters: Abell 2029 and Coma

Based on an extensive redshift survey for galaxy clusters Abell 2029 and Coma, we measure the luminosity functions (LFs) and stellar mass functions (SMFs) for the entire cluster member galaxies. Most importantly, we measure the velocity dispersion functions (VDFs) for quiescent members. The MMT/Hectospec redshift survey for galaxies in A2029 identifies 982 spectroscopic members; for 838 members, we derive the central velocity dispersion from the spectroscopy. Coma is the only other cluster surveyed as densely. The LFs, SMFs, and VDFs for A2029 and Coma are essentially identical. The SMFs of the clusters are consistent with simulations. The A2029 and Coma VDFs for quiescent galaxies have a significantly steeper slope than those of field galaxies for velocity dispersion $\lesssim 100km{s}^{-1}$. The cluster VDFs also exceed the field at velocity dispersion $\gtrsim 250km{s}^{-1}$. The differences between cluster and field VDFs are potentially important tests of simulations and of the formation of structure in the universe.