Arc Statistics with Realistic Cluster Potentials. III. a Systematic Effect on Cluster Mass Estimates

It is shown in this paper that deviations of galaxy cluster lenses from spherical symmetry can render mass estimates for galaxy clusters based on the formation of large arcs systematically to high. Numerical models show that the mass needed for producing large arcs in clusters can be notably smaller than expected from simple spherically symmetric lens models. The reason is that the enhanced tidal effect in asymmetric and substructured lenses can compensate for part of the convergence necessary for strong lensing effects. An analytic argument is given to explain why deviations from radial symmetry will in general decrease the required lens mass. Mass estimates assuming radially symmetric lenses are on average too high by a factor of $\simeq1.6$, and with a probability of $\simeq20\%$ by a factor of $\simeq2$.