Constraints on Ω_0 and Cluster Evolution Using the ROSAT LogN-LogS

Abstract

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 L_X(M,z) scale as power laws in mass and epoch, in order to construct expected counts as a function of X-ray flux. 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 \propto (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 Ω_0 and s, with lesser dependence on λ_0 and n. Comparison with the observed counts reveals a "ridge" of acceptable models in the Ω_0 - s plane, roughly following the relation s = 6 Ω_0 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 Ω_0 \gtrsim 0.3, and low-evolution models imply that Ω_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.

MNRAS LaTeX style format, submitted to MNRAS 3/26/97. Thirteen pages, eleven postscript figures. Uses epsf macros to include figures