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Limits on Magnetic Fields and Relativistic Electrons in the Coma Cluster from Multifrequency Observations

Relativistic electrons, seen in the large diffuse radio halo of the Coma cluster of galaxies, should scatter background photons to higher energies. We calculate the inverse Compton contributions from the microwave background, from the local radiation field of elliptical galaxies and from the thermal X-ray emission of the intra cluster medium to the different observed energy bands, and draw restrictions to the shape of the spectrum of the relativistic electron population. The expected electron spectra in different halo formation models are discussed, and signatures for a future distinction of these models are presented, tracing the injection processes and the influence of optical thickness of the radio halo for very low frequency emission due to synchrotron self absorption. Some of the upper limits on the electron spectrum translate into lower limits of the halo magnetic fields, since the observed synchrotron radiation is known. Despite uncertainties in the extrapolation of the radio spectrum to lower frequencies a lower limit to the central field strength of B_o > 0.3 muG seems to be sure. This is comparable to the value resulting from minimal energy arguments. If B_o < 1.2 muG, the recently reported extreme ultraviolet excess of Coma (Lieu et al. 1996) could result from inverse Compton scattered microwave photons. Formulae for transrelativistic Thomson scattering are given in the Appendix.