A Comparison of Direct and Indirect Mass Estimates for Distant Clusters of Galaxies^*

We present weak lensing results for 12 distant clusters determined from images obtained with the refurbished Hubble Space Telescope. We detect the signature of gravitational lensing in 11 of the 12 clusters; the clusters span nearly 1 order of magnitude in lensing strength. The sample thus provides an excellent database for correlating direct mass estimates based on lensing with indirect ones that rely on baryonic tracers. We examine the correlation between the cluster X-ray luminosities and the mean gravitational shear strengths and develop a model that allows us to predict the relationship expected from the properties of local clusters. After allowing for various observational effects, we find that the predicted correlation is a reasonable match to the available data, indicating that there has been little evolution in the X-ray luminosity-central mass relationship between z ~ 0.4 and now. We discuss the implications of this result in the context of the evolution of the X-ray luminosity function found by earlier investigators. The comparison between shear amplitudes and velocity dispersions, estimated from a modest sample of members (~30), reveals a discrepancy in the sense that these velocity dispersions are typically overestimated by factors of about 50%. This supports earlier suggestions that high dispersions measured for distant clusters may be seriously affected by both unidentified substructure and outliers. Combining our shear-based mass estimates with morphologically based luminosity estimates, we determine mass-to-light ratios of M/L=180₋₁₁₀⁺²¹⁰ h (M/L)_☉ for the entire population and 620₋₂₄₀⁺²⁵⁰ h for spheroidal populations, in which the evolutionary effects can be best treated. We argue that this provides an upper bound to the present-day cluster mass-to-light ratio corresponding to Ω ~ 0.4. Our results demonstrate the important role weak gravitational lensing can play in the study of the evolution of distant clusters, as the most direct and least biased probe of their growth.