A Comparison of Simple Mass Estimators for Galaxy Clusters

High-resolution N-body simulations are used to investigate systematic trends in the mass profiles and total masses of clusters as derived from 3 simple estimators: (1) the weak gravitational lensing shear field under the assumption of an isothermal cluster potential, (2) the dynamical mass obtained from the measured velocity dispersion under the assumption of an isothermal cluster potential, and (3) the classical virial estimator. The clusters used for the analysis were obtained from simulations of a standard cold dark matter universe at z = 0.5 and consist of order 2×10 to 3×10 particles of massmp ≃ 10 M⊙. The clusters are not smooth and spherically symmetric but, rather, the mass distribution is triaxial and significant substructure exists within the clusters. Not surprisingly, the level of agreement between the cluster mass profiles obtained from the various estimators and the actual mass profiles is found to be scale-dependent. We define the total cluster mass to be the mass contained within a 3-dimensional radius r200 of the cluster centers, where r200 is the radius inside which the mean interior overdensity is equal to 200. Under this definition the classical virial estimator yields a good measurement of the total cluster mass, though it is systematically underestimated by ∼ 10%. This result suggests that, at least in the limit of ideal data, the virial estimator is quite robust to deviations from pure spherical symmetry and the presence of substructure within a cluster. The dynamical mass estimate based upon a measurement of the cluster velocity dispersion and an assumption of an isothermal potential yields a poor measurement of the total cluster mass, underestimating it by ∼ 40% for the case that σv is computed from an average over the entire cluster. The weak lensing estimate yields a very good measurement of the total cluster mass, provided the mean shear used to determine the equivalent cluster velocity dispersion is computed from an average of the lensing signal over the entire cluster (i.e. the mean shear is computed interior to a projected cluster radius of R200). Subject headings: cosmology: theory — dark matter – gravitational lensing — large-scale structure of the Universe — galaxies: clusters: general — methods: numerical