Calibration of the Mass‐Temperature Relation for Clusters of Galaxies Using Weak Gravitational Lensing

The main uncertainty in current determinations of the power spectrum normalization, sigma₈, from abundances of X-ray luminous galaxy clusters arises from the calibration of the mass-temperature relation. We use our weak lensing mass determinations of 30 clusters from the hitherto largest sample of clusters with lensing masses, combined with X-ray temperature data from the literature, to calibrate the normalization of this relation at a temperature of 8 keV, M (8 keV) = (0. 78 +/- 0. 14) h^-1 10^15 Mₛun, at z=0. 23. This normalization is consistent with previous lensing-based results based on smaller cluster samples, and with some predictions from numerical simulations, but higher than most normalizations based on X-ray derived cluster masses. Assuming the theoretically expected slope alpha=3/2 of the mass-temperature relation, we derive sigma₈ = 0. 88 +/-0. 09 for a patially-flat Lambda-CDM universe with Omegaₘ = 0. 3. There is significant intrinsic scatter in the mass-temperature relation indicating that this relation may not be very tight, at least at the high mass end. Furthermore, we find that dynamically non-relaxed clusters are 75 +/- 40% hotter than relaxed clusters.