A New Model for Gamma-Ray Cascades in Extragalactic Magnetic Fields

Abstract: Very-high-energy (VHE, E \gtrsim 100 GeV) gamma rays emitted by extragalactic sources, such as blazars, initiate electromagnetic cascades in the intergalactic medium. The cascade photons arrive at the earth with angular and temporal distributions correlated with the extragalactic magnetic field (EGMF). We have developed a new semi-analytical model of the cascade properties which is more accurate than previous analytic approaches and faster than full Monte Carlo simulations. Within its range of applicability, our model can quickly generate cascade spectra for a variety of source emission models, EGMF strengths, and assumptions about the source livetime. In this Letter, we describe the properties of the model and demonstrate its utility by exploring the gamma-ray emission from the blazar RGB J0710+591. In particular, we predict, under various scenarios, the VHE and high-energy (HE, 100 MeV \lesssim E \lesssim 300 GeV) fluxes detectable with the VERITAS and Fermi Large Area Telescope (LAT) observatories. We then develop a systematic framework for comparing the predictions to published results, obtaining constraints on the EGMF strength. At a confidence level of 95%, we find the lower limit on the EGMF strength to be ~ 2 \times 10^{-16} Gauss if no limit is placed on the livetime of the source or ~ 3 \times 10^{-18} Gauss if the source livetime is limited to the past ~ 3 years during which Fermi observations have taken place.