The gamma-ray burst rate at high photon energies

Some gamma-ray burst (GRB) spectra exhibit high-energy tails with the highest photon energy detected at 18 GeV. The spectral slope of the high-energy tails is sufficiently flat in vF(v) to consider the possibility of their detection at still higher energies. We calculate how many bursts can reasonably be expected above a given energy threshold for a cosmological distribution of bursts satisfying the observed apparent brightness distribution. The crucial point is that the gamma-ray absorption by pair production in the intergalactic diffuse radiation field eliminates bursts from beyond the gamma-ray horizon tau(gamma gamma) similar to 1, thus drastically reducing the number of bursts at high energies. Our results are consistent with the nondetection of bursts by current experiments in the 100 GeV to 100 TeV energy range, For the earthbound detector array MILAGRO, we predict a maximal GRB rate of similar to 10 events per year. The Whipple Observatory can detect, under favorable conditions, similar to 1 event per year. The event rate for the HEGRA array is similar to 0.01 per year. Detection of significantly higher rates of bursts would severely challenge cosmological burst scenarios.