Measuring Ω0 using cluster evolution

The evolution of the abundance of galaxy clusters depends sensitively on the value of the cosmological density parameter, Ω0. Recent ASCA data are used to quantify this evolution as measured by the cluster X-ray temperature function. A χ minimisation fit to the cumulative temperature function, as well as a maximum likelihood estimate (which requires additional assumptions about cluster luminosities), lead to the estimate Ω0 ≈ 0.45 ± 0.2 (1-σ statistical error). Various systematic uncertainties are considered, none of which enhance significantly the probability that Ω0 = 1. These conclusions hold for models with or without a cosmological constant, i.e. with Λ0 = 0 or 1 − Ω0. The statistical uncertainties are at least as large as any of the individual systematic errors that have been considered here, suggesting that additional temperature measurements of distant clusters will allow an improvement in this estimate. An alternative method that uses the highest redshift clusters to place an upper limit on Ω0 is also presented and tentatively applied, with the result that Ω0 = 1 can be ruled out at the 98 per cent confidence level. Whilst this method does not require a welldefined statistical sample of distant clusters, there are still modelling uncertainties that preclude a firmer conclusion at this time.