Modelling gamma-ray burst observations by Fermi and MAGIC including attenuation due to diffuse background light

Gamma rays from extragalactic sources are attenuated by pair-production interactions with diffuse photons of the extragalactic background light (EBL). Gamma-ray bursts (GRBs) are a source of high-redshift photons above 10 GeV, and could be therefore useful as a probe of the evolving ultraviolet background radiation. In this paper, we develop a simple phenomenological model for the number and redshift distribution of GRBs that can be seen at GeV energies with the Fermi satellite and Major Atmospheric Gamma-ray Imaging Cherenkov Telescope (MAGIC) atmospheric Cherenkov telescope. We estimate the observed number of gamma rays per year, and show how this result is modified by considering interactions with different realizations of the evolving EBL. We also discuss the bright Fermi GRB 080916C in the context of this model. We find that the Large Area Telescope on Fermi can be expected to see a small number of photons above 10 GeV each year from distant GRBs. Annual results for ground-based instruments like MAGIC are highly variable due to the low duty cycle and sky coverage of the telescope. However, successfully viewing a bright or intermediate GRB from the ground could provide hundreds of photons from high redshift, which would almost certainly be extremely useful in constraining both GRB physics and the high-redshift EBL.