We perform a comprehensive stacking analysis of data collected by the Fermi Large Area Telescope (LAT) of gamma-ray bursts (GRB) localized by the Swift spacecraft, which were not detected by the LAT but which fell within the instruments field of view at the time of trigger. We examine a total of 79 GRBs by comparing the observed counts over a range of time intervals to that expected from designated background orbits, as well as by using a joint likelihood technique to model the expected distribution of stacked counts. We find strong evidence for subthreshold emission at MeV to GeV energies using both techniques. This observed excess is detected during intervals that include and exceed the durations typically characterizing the prompt emission observed at keV energies and lasts at least 2700 s after the co-aligned burst trigger. By utilizing a novel cumulative likelihood analysis, we find that although a bursts prompt gamma-ray and afterglow X-ray flux both correlate with the strength of the subthreshold emission, the X-ray afterglow flux measured by Swifts X-ray Telescope (XRT) at 11 hr post trigger correlates far more significantly. Overall, the extended nature of the subthreshold emission and its connection to the bursts afterglow brightness lend further support to the external forward shock origin of the late-time emission detected by the LAT. These results suggest that the extended high-energy emission observed by the LAT may be a relatively common feature but remains undetected in a majority of bursts owing to instrumental threshold effects.
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