Particle reacceleration in the Coma cluster and the radio, EUV and hard X-ray emissions

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 scenario in which the relativistic particles injected in the Coma cluster by some processes (merger, accretion shocks, turbulence) are systematically reaccelerated for a relatively long time ($\sim$ 1Gyr). We show that such a scenario can account for the synchrotron radio spectral index distribution, for the radio halo size at different frequencies, and for the total (integrated) radio spectrum of the Coma halo. We also show that for a suitable choice of the parameters the model can also account for the hard X-ray flux observed by BeppoSAX via the inverse Compton scattering of the cosmic microwave background radiation by the synchrotron electrons. The possibility to account for the EUV flux detected with the EUVE satellite by the inverse Compton emission is also discussed.