Resolving the discrepancy between X-ray and gravitational lensing mass measurements for clusters of galaxies

We present a detailed comparison of mass measurements for clusters of galaxies using ASCA and ROSAT X-ray data and constraints from strong and weak gravitational lensing. Our results, for a sample of thirteen clusters (including six with massive cooling flows, five without cooling flows, and two intermediate systems) provide a consistent description of the distribution of gravitating matter in these systems. For the six cooling-flow clusters, which are the more dynamically-relaxed systems, the X-ray and strong gravitational lensing mass measurements show excellent agreement. The core radii for the mass distributions are small, with a mean value (using a simple isothermal parameterization) of ∼ 50h 50 kpc. These results imply that thermal pressure dominates over non-thermal processes in the support of the X-ray gas against gravity in the central regions of the cooling-flow clusters, and that the hydrostatic assumption used in the X-ray mass determinations is valid. For the non-cooling flow clusters, the masses determined from the strong lensing data exceed the X-ray values by factors of 2− 4. However, significant offsets between the X-ray and lensing centres are observed, indicating that the X-ray and stronglensing data are probing different lines of sight through the clusters. These offsets, and the generally complex dynamical states of the clusters inferred from their X-ray morphologies, lensing data and galaxy distributions, suggest that the gravitational potentials in the central regions of the non-cooling flow systems are evolving rapidly, and that the assumption of hydrostatic equilibrium involved in the X-ray mass measurements is likely to have broken down. The discrepancies between the X-ray and strong lensing mass measurements may be reconciled if the dynamical activity has caused the X-ray analyses to overestimate the core radii of the dominant mass clumps in the clusters. Substructure and line-of-sight alignments of material towards the cluster cores may also contribute to the discrepancies since they will increase the probability of detecting gravitational arcs in the clusters and can enhance the lensing masses, without significantly affecting the X-ray data. On larger spatial scales, comparisons of the X-ray mass results with measurements from weak gravitational lensing show excellent agreement for both cooling-flow and non-cooling flow clusters. Our method of analysis accounts for the effects of cooling flows on the X-ray data. We highlight the importance of this and show how the inappropriate use of simple isothermal models in the analysis of X-ray data for clusters with massive cooling flows will result in significant underestimates of their X-ray temperatures and masses.