Cluster temperature evolution: The mass-temperature relation

Evolution of the cluster temperature function is extremely sensitive to the mean matter density of the universe. Current measurements based on cluster temperature surveys indicate that Omega (M) approximate to 0.3 with a 1 sigma statistical error similar to0.1, but the systematic errors in this method are of comparable size. Many more high-z cluster temperatures will be arriving from Chandra and XMM in the near future. In preparation for future duster temperature surveys, this paper analyzes the cluster mass-temperature relation, with the intention of identifying and reducing the systematic errors it introduces into measurements of cosmological parameters. We show that the usual derivation of this relation from spherical top-hat collapse is physically inconsistent and propose a more realistic derivation based on a hierarchical merging model that more faithfully reflects the gradual ceasing of cluster evolution in a low-Omega (M) universe. We also analyze the effects of current systematic uncertainties in the M-vir-T-X relation and show that they introduce a systematic uncertainty of similar to0.1 in the best-fitting Omega (M). Future improvements in the accuracy of the M-vir-T-X relation will most likely come from comparisons of predicted cluster temperature functions with temperature functions derived directly from large-scale structure simulations.