Temperature anisotropies and distortions induced by hot intracluster gas on the cosmic microwave background

The power spectrum of temperature anisotropies induced by hot intracluster gas on the cosmic background radiation is calculated. For low multipoles it remains constant, while at multipoles above I > 2000 it is exponentially d amped. The shape of the radiation power spectrum is almost independent of t he average intracluster gas density profile, gas evolution history, or clus ter core radii, but the amplitude depends strongly on those parameters. Its exact value depends on the global properties of the cluster population and the evolution of the intracluster gas. The distortion on the cosmic microw ave background blackbody spectra varies in a similar manner. The ratio of t he temperature anisotropy to the mean Comptonization parameters is shown to be almost independent of the parameters of the cluster model, and at first approximation depends only on the number density of clusters. An independe nt determination of the contribution of clusters to the distortion of the b lackbody spectrum and the temperature fluctuations of the cosmic microwave background would determine the number density of clusters that contribute t o the Sunyaev-Zeldovich effect.