The Origin of Radio Haloes and Non-thermal Emission in Clusters of   Galaxies
  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 supra-thermal 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 uG. Alternatively, if the relativistic electrons are injected from numerous localised `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 uG. 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. 
H. Liang, V. Dogiel, M. Birkinshaw