A Systematic Analysis of Caustic Methods for Galaxy Cluster Masses

Abstract: We quantify the expected observed statistical and systematic uncertainties of the escape velocity as a measure of the gravitational potential and total mass of galaxy clusters. We focus our attention on low redshift (z < 0.15) clusters, where large and deep spectroscopic datasets currently exist. Utilizing a suite of Millennium Simulation semi-analytic galaxy catalogs, we find that the dynamical mass, as traced by either the virial relation or the escape velocity, is robust to variations in how dynamical friction is applied to "orphan" galaxies in the mock catalogs (i.e., those galaxies whose dark matter halos have fallen below the resolution limit). We find that the caustic technique recovers the known halo masses (M_200) with a third less scatter compared to the virial masses. The bias we measure increases quickly as the number of galaxies used decreases. For N_gal > 25, the scatter in the escape velocity mass is dominated by projections along the line-of-sight. Algorithmic uncertainties from the determination of the projected escape velocity profile are negligible. We quantify how target selection based on magnitude, color, and projected radial separation can induce small additional biases into the escape velocity masses. Using N_gal = 150 (25), the caustic technique has a per cluster scatter in ln(M|M_200) of 0.3 (0.5) and bias 1+/-3% (16+/-5%) for clusters with masses > 10^14M_solar at z<0.15.