Ω₀ from the Apparent Evolution of Gas Fractions in Rich Clusters of Galaxies

We apply a unique gas fraction estimator to published X-ray cluster properties and we compare the derived gas fractions of observed clusters to simulated ones. The observations are consistent with a universal gas fraction of 0.15+/-0.01h_{50}^{-3/2} for the low redshift clusters that meet our selection criteria. The fair sampling hypothesis states that all clusters should have a universal constant gas fraction for all times. Consequently, any apparent evolution would most likely be explained by an incorrect assumption for the angular-diameter distance relation. We show that the high redshift cluster data is consistent with this hypothesis for \Omega_0<0.63 (95% formal confidence, flat $\Lambda$ model) or \Omega_0<0.60 (95% formal confidence, hyperbolic open model). The maximum likelihood occurs at \Omega_0=0.2 for a spatially flat cosmological constant model.