Measuring the Ultimate Mass of Galaxy Clusters: Redshifts and Mass
  Profiles from the Hectospec Cluster Survey (HeCS)
  The infall regions of galaxy clusters represent the largest gravitationally
bound structures in a $\Lambda$CDM universe. Measuring cluster mass profiles
into the infall regions provides an estimate of the ultimate mass of these
haloes. We use the caustic technique to measure cluster mass profiles from
galaxy redshifts obtained with the Hectospec Cluster Survey (HeCS), an
extensive spectroscopic survey of galaxy clusters with MMT/Hectospec. We survey
58 clusters selected by X-ray flux at 0.1$<$$z$$<$0.3. The survey includes
21,314 unique MMT/Hectospec redshifts for individual galaxies; 10,275 of these
galaxies are cluster members. For each cluster we acquired high signal-to-noise
spectra for $\sim 200$ cluster members and a comparable number of
foreground/background galaxies. The cluster members trace out infall patterns
around the clusters. The members define a very narrow red sequence. The
velocity dispersions decline with radius; we demonstrate that the determination
of the velocity dispersion is insensitive to the inclusion of bluer members (a
small fraction of the cluster population). We apply the caustic technique to
define membership and estimate the mass profiles to large radii. The ultimate
halo mass of clusters (the mass that remains bound in the far future of a
$\Lambda$CDM universe) is on average (1.99$\pm$0.11)$M_{200}$, a new
observational cosmological test in essential agreement with simulations. Summed
profiles binned in $M_{200}$ and in $L_X$ demonstrate that the predicted NFW
form of the density profile is a remarkably good representation of the data in
agreement with weak lensing results extending to large radius. The
concentration of these summed profiles is also consistent with theoretical
predictions.
