Diagnostic Signatures of Radio and Hard X‐Ray Emission on Particle Acceleration Processes in the Coma Cluster

We investigate theoretical models for the radio halo and hard X-ray (HXR)excess in the Coma galaxy cluster. Time-independent and time-dependentre-acceleration models for relativistic electrons have been carried out tostudy the formation of the radio halo and HXR excess. In these models, therelativistic electrons are injected by merger shocks and re-accelerated byensuing violent turbulence. The effects of different Mach numbers of the mergershocks on the radio and HXR excess emission are also investigated. We adopt 6$\mu$G as the central magnetic field and reproduce the observed radio spectravia the synchrotron emission. We also obtain a central "plateau" in the radiospectral-index distribution, which have been observed in radio emissiondistribution. Our models can also produce the observed HXR excess emission viathe inverse Compton scattering of the cosmic microwave background photons. Wefind that only the merger shocks with the Mach numbers around 1.6--2 canproduce results in agreement with both the radio and HXR emission in the Comacluster.Comment: 29 pages, 10 figures, ApJ in pres