The Velocity Dispersion Function of Very Massive Galaxy Clusters: Abell
  2029 and Coma
  Based on an extensive redshift survey for galaxy cluster Abell 2029 and Coma,
we measure the luminosity functions (LFs), 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 $\lesssim 100$ km s$^{-1}$. The cluster VDFs also exceed the field
at velocity dispersion $\gtrsim 250$ km s$^{-1}$. The differences between
cluster and field VDFs are potentially important tests of simulations and of
the formation of structure in the universe.
