Intracluster Comptonization of the Cosmic Microwave Background: Mean Spectral Distortion and Cluster Number Counts

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Abstract
The mean sky-averaged Comptonization parameter, , describing the scattering of the cosmic microwave background (CMB) by hot gas in clusters of galaxies, is calculated in an array of flat and open cosmological and dark matter models. The models are globally normalized to fit cluster X-ray data, and intracluster gas is assumed to have evolved in a manner consistent with current observations. We predict values of lower than the COBE/FIRAS upper limit. The corresponding values of the overall optical thickness to Compton scattering are 10-4 for relevant parameter values. Of more practical importance are number counts of clusters across which a net flux (with respect to the CMB) higher than some limiting value can be detected. Such number counts are specifically predicted for the COBRAS/SAMBA and BOOMERANG missions.
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