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

The Milagro telescope monitors the northern sky for 100 GeV to 100 TeV transient emission through continuous very high energy wide-field observations. The large effective area and ~100 GeV energy threshold of Milagro allow it to detect very high energy (VHE) gamma-ray burst emission with much higher sensitivity than previous instruments and a fluence sensitivity at VHE energies comparable to that of dedicated gamma-ray burst satellites at keV to MeV energies. Even in the absence of a positive detection, VHE observations can place important constraints on gamma-ray burst (GRB) progenitor and emission models. We present limits on the VHE flux of 40 s -- 3 h duration transients nearby to earth, as well as sensitivity distributions which 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 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 gamma-ray bursts for any GRB emission and progenitor model.