On the efficiency and reliability of cluster mass estimates based on member galaxies

We study the efficiency and reliability of cluster mass estimators that are based on the projected phase-space distribution of galaxies in a cluster region. To this aim, we analyse a data-set of 62 clusters extracted from a concordance LCDM cosmological hydrodynamical simulation. Galaxies (or Dark Matter particles) are first selected in cylinders of given radius (from 0.5 to 1.5 Mpc/h) and ~200 Mpc/h length. Cluster members are then identified by applying a suitable interloper removal algorithm. Two cluster mass estimators are considered: the virial mass estimator (Mvir), and a mass estimator (Msigma) based entirely on the cluster velocity dispersion estimate. Mvir overestimates the true mass by ~10%, and Msigma underestimates the true mass by ~15%, on average, for sample sizes of > 60 cluster members. For smaller sample sizes, the bias of the virial mass estimator substantially increases, while the Msigma estimator becomes essentially unbiased. The dispersion of both mass estimates increases by a factor ~2 as the number of cluster members decreases from ~400 to ~20. The bias in the Mvir estimates is reduced in clusters without significant evidence for subclustering, and when only early-type galaxies are selected. Radially-dependent incompleteness can drastically affect Mvir estimates, but leaves the Msigma estimates almost unaffected. Other observational effects, like centering and velocity errors, and different observational apertures, have little effect on the mass estimates. (Abridged