Semi-Analytical Predictions of ROSAT X-Ray Cluster Abundances for a Wide Range of Cosmological Models

Mathematics – Logic

Scientific paper

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Scientific paper

We examine the likelihoods of different cosmological models by comparing semi-analytical predictions of X-ray cluster number counts to observational data compiled from the ROSAT all-sky survey (RASS). We model the cluster abundance as a function of mass and redshift using a Press-Schechter distribution of dark matter halos (1974). By assuming that the luminosity-mass relationship for clusters follows a power law form we convert the underlying Press-Schechter abundance into a distribution in luminosity and redshift. We then numerically integrate the abundance function to obtain statistical descriptors of the cluster population such as the logN--logS. We examine a large number of models using this method, spanning the following ranges of cosmological parameters: 0.05 <= Omega_0 <= 1.0 and spectral index n = 0, -1, -2 for both open (lambda_0 = 0) and flat (lambda_0 + Omega_0 = 1) models. In addition we look at all of the above models under a wide range in the free parameter s, which measures the degree of positive evolution with redshift in the X-ray luminosity. The results demonstrate a strong dependence on Omega_0 and s, with lesser importance given to lambda_0 and n, in determining the logN--logS. A low-density universe clearly prefers a small degree of evolution in the cluster population, overproducing clusters relative to the observed numbers for s gtrsim 3. Likewise, a universe with Omega_0 = 1 contains fewer clusters than is observed if s is small, but does quite well if there is strong evolution.

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