2002MNRAS.337..567L

We study the origin of the non-thermal emission from the intracluster medium, including the excess hard X-ray emission and cluster-wide radio haloes, through fitting two representative models to the Coma cluster. If the synchrotron-emitting relativistic electrons are accelerated in situ from the vast pool of thermal electrons, then a quasi-stationary solution of the kinetic equation with particle acceleration through turbulence at high energies (>200 keV) naturally produces a population of suprathermal electrons responsible for the excess hard X-ray emission through bremsstrahlung. Inverse Compton scattering is negligible at hard X-ray energies in this case. The radio halo flux density constrains the magnetic field strength to a value close to that of equipartition, ∼1 µG. Alternatively, if the relativistic electrons are injected from numerous localized `external' sources, then the hard X-rays are best explained by inverse Compton scattering from GeV electrons, and little of the hard X-radiation has a bremsstrahlung origin. In this case, the magnetic field strength is constrained to ∼0.1-0.2 µG. Both models assume that the non-thermal emissions are generated by a single electron spectrum, so that only two free parameters, well constrained by the observed hard X-ray and radio halo spectra, are needed in either case. Measurements of the cluster magnetic field will distinguish between the models.