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.