On the thermal origin of the hard X-ray emission from the Coma cluster

We analyze the origin of the hard X-ray flux from the Coma cluster observed by the Beppo-SAX satellite. This flux is typically assumed to be produced by nonthermal particles accelerated in the Coma medium. We show, however, that in the case of in-situ acceleration of particles from the thermal pool, the hard X-rays in the range of Beppo-SAX observations (30-80 keV) are generated by bremsstrahlung radiation of thermal particles with the Maxwellian spectrum distorted by the acceleration. This mimics the effect of a two-temperature thermal spectrum. The power-law nonthermal spectrum of accelerated particles is formed at energies above 900 keV. The fraction of particles accelerated from the thermal pool is estimated in the range (1-3)* 10^-6. For the acceleration parameters derived from the hard X-ray flux we conclude that the strength of the magnetic field in the Coma halo is about 0.2-7 mu G. In the framework of the model the maximum frequency of the radio emission from Coma is several GHz in agreement with observations. At higher frequencies there is a strong steepening in the radio spectrum. For some values of acceleration parameters and magnetic fields, clusters of galaxies emit only hard X-rays but no radio flux comes from them.