Estimating Masses in Clusters of Galaxies

The projected (PME) and virial mass estimator (VME) are revisited and tested using an N-body equilibrium system. It is found that the PME can overestimate the mass by approx 40% if a cluster is sampled only about its effective radius, Re. The exact value of this error depends on the mass profile of the cluster. The VME can yield errors of approx 20% if we are also able to sample about one Re. Both estimators yield the correct total mass for an equilibrium system. Theoretically, if we know the total extent of the system, the VME provides an accurate mass at different radii provided its gravitational potential term is correctly taken into consideration. The VME can provide acceptable masses for equilibrium systems with anisotropic velocity dispersions.