Particle reacceleration in the Coma cluster: radio properties and hard X-ray emission

The radio spectral index map of the Coma halo shows a progressive steepening of the spectral index with increasing radius. Such a steepening cannot be simply justified by models involving continuous injection of fresh particles in the Coma halo or by models involving diffusion of fresh electrons from the central regions. We propose a two-phase model in which the relativistic electrons injected in the Coma cluster by some processes (starbursts, AGNs, shocks, turbulence) during a first phase in the past are systematically reaccelerated during a second phase for a relatively long time (similar to1 Gyr) up to the present time. We show that for reacceleration time-scales of similar to0.1 Gyr this hypothesis can well account for the radio properties of Coma C. For the same range of parameters which explain Coma C we have calculated the expected fluxes from the inverse Compton scattering of the Cosmic Microwave Background (CMB) photons, finding that the hard X-ray tail discovered by BeppoSAX may be accounted for by the stronger reacceleration allowed by the model. The possibility of extending the main model assumptions and findings to the case of the other radio haloes is also discussed, the basic predictions being consistent with the observations.