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Compton scattering in terrestrial gamma-ray flashes detected with the Fermi gamma-ray burst monitor

Terrestrial gamma-ray flashes (TGFs) are short intense flashes of gamma rays associated with lightning activity in thunderstorms. Using Monte Carlo simulations of the relativistic runaway electron avalanche (RREA) process, theoretical predictions for the temporal and spectral evolution of TGFs are compared to observations made with the Gamma-ray Burst Monitor (GBM) on board the Fermi Gamma-ray Space Telescope. Assuming a single source altitude of 15 km, a comparison of simulations to data is performed for a range of empirically chosen source electron variation time scales. The data exhibit a clear softening with increased source distance, in qualitative agreement with theoretical predictions. The simulated spectra follow this trend in the data, but tend to underestimate the observed hardness. Such a discrepancy may imply that the basic RREA model is not sufficient. Alternatively, a TGF beam that is tilted with respect to the zenith could produce an evolution with source distance that is compatible with the data. Based on these results, we propose that the source electron distributions of TGFs observed by GBM vary on time scales of at least tens of microseconds, with an upper limit of approx. 100 microseconds.