Measuring Cosmological Parameters from the Evolution of Cluster X‐Ray Temperatures

We have determined the cluster X-ray temperature function from two flux- andredshift-limited samples of clusters. The first sample is comprised of 25clusters with average redshift 0. 05. The local temperature function derivedfrom it supersedes the one we previously published. Fourteen clusters withaverage redshift 0. 38 comprise the second sample. We perform maximum likelihoodfits of cluster evolution models to these data in order to constraincosmological parameters. For an open model with zero cosmological constant wefind that the density parameter is Omega₀ = 0. 49+/-0. 12, the rms mass densityfluctuation averaged over 8 h-1 Mpc spheres is sigma₈ = 0. 72+/-0. 10, and theeffective index of the mass density fluctuation spectrum on cluster scales is n= - (1. 72+/-0. 34) where all errors are symmetrized at 68onfidence. Thecorresponding results for the case where a cosmological constant produces aflat universe are: 0. 44+/-0. 12, 0. 77+/-0. 15, and - (1. 68+/-0. 38). These resultsagree with those determined from a variety of different independent methods, including supernovae, galaxy-galaxy correlations, fluctuations in the microwavebackground, gravitational lens statistics, and cluster peculiar velocities.