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Contribution to the Extragalactic Gamma-ray Background from the Cascades of Very-high Energy Gamma Rays from Blazars

As very high energy (VHE) photons propagate through the extragalactic background light (EBL), they interact with the soft photons and initiate electromagnetic cascades of lower energy photons and electrons. The collective intensity of a cosmological population emitting at VHEs will be attenuated at the highest energies through interactions with the EBL and enhanced at lower energies by the resulting cascade. We calculate the cascade radiation created by VHE photons produced by blazars and investigate the effects of cascades on the collective intensity of blazars and the resulting effects on the extragalactic gamma-ray background. We find that cascade radiation greatly enhances the collective intensity from blazars at high energies before turning over due to attenuation. The prominence of the resulting features depends on the blazar gamma-ray luminosity function, spectral index distribution, and the model of the EBL. We additionally calculate the cascade radiation from the distinct spectral sub-populations of blazars, BL Lacertae (BL Lacs) objects and flat-spectrum radio quasars (FSRQs), finding that the collective intensity of BL Lacs is considerably more enhanced by cascade radiation than that of the FSRQs. Finally, we discuss the implications that this analysis and upcoming Fermi observations could have for the nature of the EBL, the evolution of blazars, blazar spectra, and other sources of gamma-ray radiation.