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 damped. The shape of the radiation power spectrum is almost independent of the average intracluster gas density profile, gas evolution history, or cluster 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 microwave background blackbody spectra varies in a similar manner. The ratio of the 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 independent determination of the contribution of clusters to the distortion of the blackbody spectrum and the temperature fluctuations of the cosmic microwave background would determine the number density of clusters that contribute to the Sunyaev-Zeldovich effect.