Radio halos of galaxy clusters from hadronic secondary electron injection in realistic magnetic field configurations

We investigate the possibility that radio halos of clusters of galaxies are caused by synchrotron emission of cosmic ray electrons (CRe), which were p roduced by cosmic ray protons (CRp) interacting hadronically with the intra -cluster medium (ICM) protons. We perform cosmological magnetohydrodynamics (MHD) simulations to obtain a sample of ten magnetized galaxy clusters. Th ey provide realistic models of the gas and magnetic field distribution, nee ded to predict the CRe production rates, their cooling, and their synchrotr on emissivity. We assume a CRp population within the ICM with an energy den sity which has a constant ratio to thermal energy density. This ratio is ad justed in such a way that one of the simulated clusters reproduces the radi o luminosity of the radio halo of the Coma cluster of galaxies. Our model e xhibits the observed low degree of radio polarization and has a similar rad ial emission profile as the Coma cluster. We provide estimates for the expe cted gamma ray and neutrino flux. The necessary CRp/thermal energy ratio is 4... 14% (E-p,E-min/GeV)(-0.375) (for the range of magnetic field strength s suggested by Faraday measurements), where E-p,E-min is the lower kinetic energy cutoff of the CRp with spectral index alpha (p) approximate to 2.375 . Assuming this ratio to be the same in the whole set of simulated clusters a T-x - L-nu relation is predicted which follows the observed relation wel l.