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 eld 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 spec- trum of the relativistic electron population. The expected elec- tron spectra in different halo formation models are discussed, and signatures for a future distinction of these models are pre- sented, tracing the injection processes and the influence of opti- cal thickness of the radio halo for very low frequency emission due to synchrotron self absorption. Some of the upper limits on theelectronspectrumtranslateintolowerlimitsofthehalomag- netic elds, 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 eld strength of Bo > 0:3G seems to be sure. This is comparable to the value resulting from minimal energy arguments. If Bo 1:2G, the recentlyreportedextremeultravioletexcessofComa(Lieuetal. 1996) could result from inverse Compton scattered microwave photons. Formulae for transrelativistic Thomson scattering are given in the Appendix.