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 \sim 2 \times 10 ^ { -16 } Gauss if no limit is placed on the livetime of the source or \sim 3 \times 10 ^ { -18 } Gauss if the source livetime is limited to the past \sim 3 years during which Fermi observations have taken place .