Galaxy Clusters and Microwave Background Anisotropy

Previous estimates of the microwave background anisotropies produced by freely falling spherical clusters are discussed. These estimates are based on the Swiss-Cheese and Tolman-Bondi models. It is proved that these models give only upper limits to the anisotropies produced by the observed galaxy clusters. By using spherically symmetric codes including pressureless matter and a hot baryonic gas, new upper limits are obtained. The contributions of the hot gas and the pressureless component to the total anisotropy are compared. The e ects produced by the pressure are proved to be negligible; hence, estimations of the cluster anisotropies based on N-body simulations are hereafter justi ed. After the phenomenon of violent relaxation, any realistic rich cluster can only produce small anisotropies with amplitudes of order 10 . During the rapid process of violent relaxation, the anisotropies produced by nonlinear clusters are expected to range in the interval (10 ; 10 ). The angular scales of these anisotropies are discussed.