On the influence of X-ray galaxy clusters in the fluctuations of the cosmic microwave background

The negative evolution found in X--ray clusters of galaxies limits the amountof available hot gas for the inverse Compton scattering of the Cosmic MicrowaveBackground (the Sunyaev--Zel'dovich effect). Using a parametrisation of theX-ray luminosity function and its evolution in terms of a coalescence model (aspresented in the analysis of a flux limited X-ray cluster sample by Edge et al.1990), as well as a simple virialised structure for the clusters (whichrequires a gas to total mass fraction $\approxgt 0.1$ in order to reproduceobserved properties of nearby clusters) we show that the Compton distortion $y$parameter is about two orders of magnitude below the current FIRAS upperlimits. Concerning the anisotropies imprinted on arcmin scales they aredominated by the hottest undetected objects. We show that they are negligible(${\Delta T\over T}\approxlt 10^{-7}$) at wavelengths $\lambda\approxgt 1$~mm.At shorter wavelengths they become more important (${\Delta T\over T}\sim10^{-6}$ at $\lambda\sim 0.3$~mm), but in fact most clusters will produce anisolated and detectable feature in sky maps. After removal of these signals,the fluctuations imprinted by the remaining clusters on the residual radiationare still much smaller. The conclusion is that X-ray clusters can be ignored assources of Cosmic Microwave Background fluctuations.Comment: 20 pages Plain Tex, 7 figures available upon request,UCAST-94-0