Nonthermal emission from clusters of galaxies

We show that the spectral and radial distribution of the nonthermal emission of massive, M ∼> 1014.5M☉, galaxy clusters may be approximately described by simple analytic expressions, which depend on the cluster thermal X-ray properties and on two model parameter, βcore and ηe. βcore is the ratio of the cosmic-ray (CR) energy density (within a logarithmic CR energy interval) and the thermal energy density at the cluster core, and ηe(p) is the fraction of the thermal energy generated in strong collisionless shocks, which is deposited in CR electrons (protons). Using a simple analytic model for the evolution of intra-cluster medium CRs, which are produced by accretion shocks, we find that βcore ≅ ηp/200, nearly independent of cluster mass and with a scatter Δln βcore ≅ 1 between clusters of given mass. We show that the hard X-ray (HXR) and γ-ray luminosities produced by inverse Compton scattering of CMB photons by electrons accelerated in accretion shocks (primary electrons) exceed the luminosities produced by secondary particles (generated in hadronic interactions within the cluster) by factors ≅ 500(ηe/ηp)(T/10 keV)−1/2 and ≅ 150(ηe/ηp)(T/10 keV)−1/2 respectively, where T is the cluster temperature. Secondary particle emission may dominate at the radio and very high energy (∼> 1 TeV) γ-ray bands. Our model predicts, in contrast with some earlier work, that the HXR and γ-ray emission from clusters of galaxies are extended, since the emission is dominated at these energies by primary (rather than by secondary) electrons. Our predictions are consistent with the observed nonthermal emission of the Coma cluster for ηp ∼ ηe ∼ 0.1. The implications of our predictions to future HXR observations (e.g. by NuStar, Simbol-X) and to (space/ground based) γ-ray observations (e.g. by Fermi, HESS, MAGIC, VERITAS) are discussed. In particular, we identify the clusters which are the best candidates for detection in γ-rays. Finally, we show that our model's results agree with results of detailed numerical calculations, and that discrepancies between the results of various numerical simulations (and between such results and our model) are due to inaccuracies in the numerical calculations