On two mass estimators for clusters of galaxies

The two most common mass estimators that use velocity dispersions and positions of objects in a stellar system, the virial mass estimator (VME) and the projected mass estimator (PME), are revisited and tested using N-body experiments. We consider here only spherical, isolated, and isotropic velocity dispersion systems. We have found that the PME can overestimate masses by approximate to 20%, for realistic cluster mass profiles, if applied only to regions around the total system's effective radius. The VME can yield a correct mass at different radii provided that the potential energy term is correctly taken into account and the system is completely sampled; otherwise, it may lead to similar errors as the PME. A surface pressure (3PV) term recently alluded to be usually neglected when using the VME and therefore required as a correction term is here found not necessarily required, although it can be used to yield a reasonable correction term. The preferred method here, however, is the virial theorem due to its simplicity and better agreement with N-body experiments. The possible reasons for the mass discrepancies found when using the PME and the VME in some N-body simulations are also briefly discussed.