Aspects of the Zel'dovich-Sunyaev mechanism

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Abstract
In this paper we treat aspects of the Compton distortion of the cosmic background radiation (CBR)—what is known as the Zel'dovich-Sunyaev mechanism—which do not appear to have been fully explored in the literature. These include a novel solution to the so-called Kompaneets equation, a treatment of the simultaneous heating and cooling of free electrons, a discussion of electron-proton "recombination," and a demonstration of the ingredients necessary for efficient energy transfer. These matters are illustrated in a scenario in which the excess CBR energy observed by Matsumoto et al. is supplied by a radiatively decaying heavy lepton, so we also provide a careful analytic treatment of the photon spectrum produced by a heavy particle decaying in the early Universe.