Limits on Very High Energy Emission from Gamma-Ray Bursts with the Milagro Observatory

The Milagro telescope monitors the northern sky for 100 GeV-100 TeV transient emission through continuous very high energy (VHE) wide-field observations. The large effective area and ~100 GeV energy threshold of Milagro allow it to detect VHE gamma-ray burst (GRB) emission with much higher sensitivity than previous instruments and a fluence sensitivity at VHE energies comparable to that of dedicated GRB satellites at keV-MeV energies. Even in the absence of a positive detection, VHE observations can place important constraints on GRB progenitor and emission models. We present limits on the VHE flux of 40 s-3 hr duration transients near Earth as well as sensitivity distributions that have been corrected for gamma-ray absorption by extragalactic background light and cosmological effects. The sensitivity distributions suggest that the typical intrinsic VHE fluence of GRBs is similar to or weaker than the keV-MeV emission, and we demonstrate how these sensitivity distributions may be used to place observational constraints on the absolute VHE luminosity of GRBs for any GRB emission and progenitor model.