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 consist of order 2.5e+05 particles of mass $m_p \simeq 10^{10} \Msun$, have triaxial mass distributions, and significant substructure exists within their virial radii. Not surprisingly, the level of agreement between the mass profiles obtained from the various estimators and the actual mass profiles is found to be scale-dependent. The virial estimator yields a good measurement of the total cluster mass, though it is systematically underestimated by of order 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. 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 mass. The weak lensing estimate yields a very good measurement of the total 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 the virial radius). [abridged