Stacking Caustic Masses from Galaxy Clusters
  Ongoing and future spectroscopic surveys will measure numerous galaxy
redshifts within tens of thousands of galaxy clusters. However, the sampling
within these clusters will be low, 15 < N < 50 per cluster. With such data, it
will be difficult to achieve accurate and precise mass estimates for individual
clusters using phase-space mass estimation techniques. We develop and test a
new stacking algorithm based on the caustic technique, which reduces the mass
scatter in <log M_caustic | M_200 > for ensemble clusters from 70% for
individual clusters to less than 10% for ensemble clusters with only 15
galaxies per cluster and 100 clusters per ensemble. With > 1000 galaxies per
ensemble phase-space, the escape-velocity edge becomes readily identifiable and
the presence of interloping galaxies is minimized. We develop and test an
algorithm to trace the projected phase-space surface directly, which results in
minimally biased dynamical mass estimates. We then quantify how binning and
sampling affect the phase-space-based mass estimates when using an
observational proxy that incorporates realistic mass scatter, like richness,
and find the added uncertainty in the binning procedure has minimal influence
on the resulting bias and scatter of the stacked mass estimates.
