Modeling 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 UV background radiation.
In this paper, we develop a simple phenomenological model for the number and
redshift distribution of gamma-ray bursts that can be seen at GeV energies with
the Fermi satellite and 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 LAT 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.
