Formation of radio halos in clusters of galaxies from cosmic-ray protons

Relativistic protons produced in radio galaxies in a cluster can diffuse over distances about 1 Mpc in the intracluster medium before suffering inelastic collisions with thermal protons. This results in a population of relativistic secondary electrons and positrons formed in situ on this scale. It is shown that these secondary particles can be entirely responsible for the observed radio halo in Coma, if it is assumed that the ratio of the energy-dependent production rate of primary protons to primary electrons is the same as that apparent from cosmic rays in our Galaxy, and that the intracluster magnetic field is in approximate equipartition (approximately 2 microgauss) with relativistic particles. Clearly, this model eliminates the theoretical difficulties involved in the transport of primary electrons at speeds orders of magnitude in excess of the Alfven speed, as required to reach the outer halo in less than a radiative lifetime. In addition, low-energy protons may play a significant role in heating the intracluster gas through Coulomb collisions.