Analysis of atmospheric gamma-ray flashes detected in near space with allowance for the transport of photons in the atmosphere

Monte Carlo simulations of transport of the bremsstrahlung produced by relativistic runaway electron avalanches are performed for altitudes up to the orbit altitudes where terrestrial gamma-ray flashes (TGFs) have been detected aboard satellites. The photon flux per runaway electron and angular distribution of photons on a hemisphere of radius similar to that of the satellite orbits are calculated as functions of the source altitude z. The calculations yield general results, which are recommended for use in TGF data analysis. The altitude z and polar angle are determined for which the calculated bremsstrahlung spectra and mean photon energies agree with TGF measurements. The correlation of TGFs with variations of the vertical dipole moment of a thundercloud is analyzed. We show that, in agreement with observations, the detected TGFs can be produced in the fields of thunderclouds with charges much smaller than 100 C and that TGFs are not necessarily correlated with the occurrence of blue jets and red sprites.