MEASURING OMEGA(0) USING CLUSTER EVOLUTION

The evolution of the abundance of galaxy clusters depends sensitively on the value of the cosmological density parameter, Omega(0). Recent A SCA data are used to quantify this evolution as measured by the cluste r X-ray temperature function. A chi(2) minimization fit to the cumulat ive temperature function, as well as a maximum-likelihood estimate (wh ich requires additional assumptions about cluster luminosities), leads to the estimate Omega(0) = 0.45 +/- 0.25 (lo statistical error). Vari ous systematic uncertainties are considered, none of which significant ly enhances the probability that Omega(0) = 1. These conclusions hold for models with or without a cosmological constant, i.e., with Lambda( 0)= 0 or Lambda(0) = 1 - Omega(0). The statistical uncertainties are a t least as large as any of the individual systematic errors that have been considered here, suggesting that additional temperature measureme nts of distant clusters will allow an improvement in this estimate. An alternative method that uses the highest redshift clusters to place a n 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 s tatistical sample of distant clusters, there are still modelling uncer tainties that preclude a firmer conclusion at this time.