Nonthermal emission from clusters of galaxies

We show that the spectral and radial distribution of the nonthermal emission of massive, M>10^{14.5}M_sun, galaxy clusters (GCs) may be approximately described by simple analytic expressions, which depend on the GC thermal X-ray properties and on two model parameter, beta_{core} and eta_e. beta_{core} is the ratio of CR energy density (within a logarithmic CR energy interval) and the thermal energy density at the GC core, and eta_{e(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 ICM CRs, which are produced by accretion shocks (primary CRs), we find that beta_{core} ~ eta_{p}/200, nearly independent of GC mass and with a scatter Delta ln(beta_{core}) ~ 1 between GCs of given mass. We show that the HXR and gamma-ray luminosities produced by IC scattering of CMB photons by primary electrons exceed the luminosities produced by secondary particles (generated in hadronic interactions within the GC) by factors ~500(eta_e/eta_p)(T/10 keV)^{-1/2} and ~150(eta_e/eta_p)(T/10 keV)^{-1/2} respectively, where T is the GC temperature. Secondary particle emission may dominate at the radio and VHE (> 1 TeV) gamma-ray bands. Our model predicts, in contrast with some earlier work, that the HXR and gamma-ray emission from GCs are extended, since the emission is dominated at these energies by primary electrons. Our predictions are consistent with the observed nonthermal emission of the Coma cluster for eta_peta_e ~ 0.1. The implications of our predictions to future HXR observations (e.g. by NuStar, Simbol-X) and to (space/ground based) gamma-ray observations (e.g. by Fermi, HESS, MAGIC, VERITAS) are discussed. Finally, we show that our model's results agree with results of detailed numerical calculations.