The spatial distribution of radio and X-ray fluxes from rich and regular clusters of galaxies is discussed. A diffusion model is investigated in which high-energy electrons are ejected from a point source at the center of the cluster. While diffusing out, the electrons lose energy by Compton scattering with the universal blackbody photons, thus producing the X-ray emission. Traversing intracluster magnetic fields, the electrons emit synchrotron radio emission. For the Coma cluster of galaxies good agreement is found between the observed and predicted X-ray counting-rate distribution for the Compton model. From the observed radio data a value of about 3 by 10 to the -8th power gauss is deduced for the average magnetic-field strength in the central region of Coma.
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Yoel Rephaeli (1977) studied this question.