Radio Halos of Galaxy Clusters from Hadronic Secondary Electron Injection in Realistic Magnetic Field Configurations

Abstract

We investigate the possibility that radio halos of clusters of galaxies are caused by synchrotron emission of cosmic ray electrons (CRe), which were produced by cosmic ray protons (CRp) interacting hadronically with the intra-cluster medium (ICM) protons. We perform cosmological magneto-hydrodynamics (MHD) simulations to obtain a sample of ten magnetized galaxy clusters. They provide realistic models of the gas and magnetic field distribution, needed to predict the CRe production rates, their cooling, and their synchrotron emissivity. We assume a CRp population within the ICM with an energy density which has a constant ratio to thermal energy density. This ratio is adjusted in such a way that one of the simulated clusters reproduces the radio luminosity of the radio halo of the Coma cluster of galaxies. Our model exhibits the observed low degree of radio polarization and has a similar radial emission profile as the Coma cluster. We provide estimates for the expected gamma ray and neutrino flux. The necessary CRp/thermal energy ratio is 4 ... 14% ${(E_{p,min}/GeV)}^{-0.375}$ (for the range of magnetic field strengths suggested by Faraday measurements), where $E_{p,min}$ is the lower kinetic energy cutoff of the CRp with spectral index $\alpha_p \approx 2.375$. 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 well.