Constraints on Ω0 and cluster evolution using the ROSAT logN-logS relation

We examine the Likelihoods of different cosmological models and cluster evolutionary histories by comparing semi-analytical predictions of X-ray cluster number counts with observational data from the ROSAT satellite. We model cluster abundance as a function of mass and redshift using a Press-Schechter distribution, and assume that the temperature T(M, z) and bolometric luminosity L-X(M, z) scale as power laws in mass and epoch, in order to construct expected counts as a function of X-ray Aux. The L-X - M scaling is fixed using the local luminosity function, while the degree of evolution in the X-ray luminosity with redshift L-X (proportional to) (1 + z)(s) is left open, with s an interesting free parameter which we investigate. We examine open and flat cosmologies with initial, scale-free fluctuation spectra having indices It = 0, -1 and -2. An independent constraint arising from the slope of the luminosity-temperature relation strongly favours the n = -2 spectrum. The expected counts demonstrate a strong dependence on Omega(0) and s, with lesser dependence on lambda(0) and n. Comparison with the observed counts reveals a 'ridge' of acceptable models in the Omega(0) - s plane, roughly following the relation s similar to 6 Omega (0) and spanning low-density models with a small degree of evolution to Omega = 1 models with strong evolution. Models with moderate evolution are revealed to have a strong lower limit of Omega(0) greater than or equal to 0.3, and low-evolution models imply that Omega(0) < 1 at a very high confidence level. We suggest observational tests for breaking the degeneracy along this ridge, and discuss implications for evolutionary histories of the intracluster medium.