Constraining the source properties of individual Terrestrial Gamma-ray Flashes

We report on the spectral analysis of two individual Terrestrial Gamma-ray Flashes (TGFS) observed with the Fermi Gamma- ray Burst Monitor (GBM). The large GBM sample provides some events suitable for individual spectral analysis: sufficiently bright, localized by ground-based radio, and with the gamma rays reaching a detector unobstructed. We account for the low counts in individual TGFS by using Poisson likelihood, and we also consider instrumental effects. The data are fit with models obtained from Monte Carlo simulations of the large scale Relativistic Runaway Electron Avalanche (RREA) model, including propagation through the atmosphere. Two beaming geometries were considered: In one, the photons retain the intrinsic distribution from scattering (narrow), and in the other, the photons are smeared into a wider beam (wide). Large-scale RREA models can accommodate both narrow and wide beams, with narrow beams suggest large-scale RREA in organized electric fields while wide beams may imply converging or diverging electric fields. Wide beams are also consistent with acceleration in the electric fields of lightning leaders, but the TGFS that favor narrow beam models appear inconsistent with some lightning leader models. (author)