2003ApJ...583..695G

Nonthermal radiation is observed from clusters of galaxies in the radio, hard X-rays, and possibly in the soft X-ray/UV bands. While it is known that radiative processes related to nonthermal electrons are responsible for this radiation, the sites and nature of particle acceleration are not known. We investigate here the acceleration of protons and electrons in the shocks that originated during mergers of clusters of galaxies, where the Fermi acceleration may work. We propose a semianalytical model to evaluate the Mach number of the shocks generated during cluster mergers, and we use this procedure to determine the spectrum of the accelerated particles for each one of the shocks produced during the merger history of a cluster. We follow the proton component, accumulated over cosmological timescales, and the short-lived electron component. We conclude that efficient particle acceleration, resulting in nonthermal spectra that compare with observations, occurs mainly in minor mergers, namely, mergers between clusters with very different masses. Major mergers, often invoked to be sites for the production of extended radio halos, are found to have on average too weak of shocks and are unlikely to result in appreciable nonthermal activity.