A Measurement of the Density Parameter Derived from the Evolution of Cluster X-Ray Temperatures

We have, for the first time, determined the cluster X-ray temperature function at a redshift other than zero. The observed evolution of the temperatures is mild to a redshift of one-third. The normalization of the luminosity-temperature relation is 0.92 ± 0.07 of the low-redshift relation (1 σ error), assuming that its shape is the same. Such behavior occurs when clusters form with constant central entropy. The evolution of the temperature function implies that Ω0 is 0.50 ± 0.14 assuming an open universe, or 0.55 ± 0.17 assuming that a cosmological constant produces a flat universe (1 σ symmetrized errors). A closed universe, Ω0≥1, is excluded at greater than 99% confidence. The amplitude of the mass density fluctuations averaged over 8 h-1 Mpc spheres, σ8, is 0.66−0.08+0.22 and 0.66−0.17+0.34 (1 σ errors) for the open and flat models, respectively.