Spectral cutoffs of Fermi-LAT GRBs 080916C and 090926A

It is expected that there should be a spectral cutoff at the high energy end of emission from a prompt gamma-ray burst (GRB), due to, e.g. γγ absorption and/or a high energy cutoff in the electron distribution. We analyze the spectral data of Fermi-LAT detected GRBs 080916C and 090926A, aiming at locating the spectral cutoff. By assuming that the prompt GRB spectrum at the high energy end is a power law with an exponential cutoff, our analysis finds that the cutoff energy E_cutoff depends on the photon index β and the cutoff occurs at very high energy, E_cutoff = 161⁺⁵³³₋₉₅ GeV in GRB 080916C and E_cutoff ≳ 100 GeV (for β ≈ −2.3) in GRB 090926A. Such high energy photons, if they exist, may disfavor the synchrotron origin and need alternative generation mechanisms.