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Fueling lobes of radio galaxies: statistical particle acceleration and the extragalactic gamma-ray background

The recent discovery of the gamma-ray emission from the lobes of the closest radio galaxy Centaurus A by Fermi implies the presence of high-energy electrons at least up to gamma ~ 10^5 - 10^6. These high-energy electrons are required to interpret the observed gamma-ray radiation in terms of inverse Compton emission off the cosmic microwave background (IC/CMB); the widely accepted scenario to describe the X-ray emission of radio galaxy lobes. In this Letter, we consider the giant radio lobes of FR II radio galaxies showing that it is possible to maintain electrons at energies gamma ~ 10^5 - 10^6, assuming an acceleration scenario (driven by turbulent magnetic fields) that compensates the radiative losses. In addition, we consider the contribution to the diffuse extragalactic gamma-ray background due to the IC/CMB emission of FR IIs' lobes showing its relevance in the keV to MeV energy range.