Constraints on Ω0 and Cluster Evolution using the ROSAT LogN–LogS

We examine the likelihoods of different cosmological models and cluster evolutionary histories by comparing semi-analytical predictions of X-ray cluster number counts to observational data from the ROSAT satellite. We model cluster abundance as a function of mass and redshift using a Press-Schechter distribution, and assume the temperature T (M, z) and bolometric luminosity LX(M, z) scale as power laws in mass and epoch, in order to construct expected counts as a function of X–ray flux. The Lx−M scaling is fixed using the local luminosity function while the degree of evolution in the X-ray luminosity with redshift LX ∝(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 n = 0, −1 and −2. An independent constraint arising from the slope of the luminosity–temperature relation strongly favors the n=−2 spectrum. The expected counts demonstrate a strong dependence on Ω0 and s, with lesser dependence on λ0 and n. Comparison with the observed counts reveals a “ridge” of acceptable models in Ω0−s plane, roughly following the relation s ∼ 6Ω0 and spanning low-density models with a small degree of evolution to Ω = 1 models with strong evolution. Models with moderate evolution are revealed to have a strong lower limit of Ω0 ∼ > 0.3, and low-evolution models imply that Ω0 < 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.