Estimate of the source parameters of terrestrial gamma-ray flashes observed at low-Earth-orbit satellites

A special attention has been paid in the past decades to studies of terrestrial gamma-ray flashes (TGFs) observed above active thunderstorms. The physical mechanism of the TGF generation and its source location in the atmosphere have not been firmly established. A numerical modelling, such as Monte Carlo simulation, is commonly used to analyze the problem having regard to the complexity of basic electrodynamic and transport equations. Here, in contrast to previous numerical studies, we have constructed a suitably idealized analytical model of a point source of gamma-rays in a vertically inhomogeneous atmosphere. An energy-distribution of gamma photons is assumed to be determined by the energy spectrum of electron bremsstrahlung resulted from the relativistic runaway electron avalanche in a strong electric field. The absorption of photon energy due to photoelectric effect, Compton scattering and the electron-positron pair production have been accounted for approximately with an effective coefficient of energy absorption. A photon mean free path in the atmosphere is assumed to be dependent on its energy and altitude. A spatiotemporal distribution of gamma-ray flux density and photon fluence at a low-Earth orbit (LEO) are estimated as functions of the TGF source altitude, total number of photons emitted by the source, and other parameters. The model matches the LEO observations indicating that the TGF source is located at an altitude about 10 - 14 km. The same model can be applied for the description of the recently found downward-directed TGF detected by the large-area Telescope Array cosmic ray observatory.