Measuring Omega₀ using cluster evolution

The evolution of the galaxy cluster abundance depends sensitively on the value of the cosmological density parameter, Omega_0. Recent ASCA data are used to quantify this evolution as measured by the X-ray temperature function. A chi^2 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 Omega_0 \approx 0.45+/-0.2 (1-sigma statistical error). Various systematic uncertainties are considered, none of which enhance significantly the probability that Omega_0=1. These conclusions hold for models with or without a cosmological constant. The statistical uncertainties are at least as large as 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 Omega_0 is also presented and tentatively applied, with the result that Omega_0=1 can be ruled out at the 98 per cent confidence level. Whilst this method does not require a well-defined statistical sample of distant clusters, there are still modelling uncertainties that preclude a firmer conclusion at this time.