Cosmic Rays, Radio Halos and Non-Thermal X-ray Emission in Clusters of Galaxies

We calculate the flux of radio, hard X-ray and UV radiation from clusters of galaxies as produced by synchrotron emission and Inverse Compton Scattering of electrons generated as secondaries in cosmic ray interactions in the intracluster medium. Both the spatial distribution of cosmic rays due to their diffusion and the spatial distribution of the intracluster gas are taken into account. Our calculations are specifically applied to the case of the Coma cluster. The fluxes and spectra of the radio halo emission and of the hard X-ray excess from Coma can be explained in this model if an average magnetic field $B \sim 0.1\mu G$ is assumed. However, such a low value for the intracluster magnetic field implies a large cosmic ray energy density which in turn is responsible, through neutral pion decay, for a gamma ray flux above 100 MeV which exceeds the EGRET upper limit. This gamma ray bound can be relaxed if the hard X-ray excess and the radio halo emission from Coma are not due to the same population of electrons. We finally stress the unique role that the new generation gamma ray satellites will play to discriminate among different models for the non thermal emission in clusters of galaxies.