Testing pulse density distribution for terrestrial gamma ray flashes

Abstract

AbstractMaximum likelihood fits for the time profiles of 51 terrestrial gamma ray flashes (from Compton Gamma Ray Observatory/Burst and Transient Source Experiment and Fermi Gamma‐Ray Space Telescope/Gamma‐Ray Burst Monitor) were calculated for five proposed probability densities. A lognormal distribution, which had been used by other researchers, was compared with piecewise Gaussian, piecewise exponential, inverse Gaussian, and Ornstein‐Uhlenbeck probability density functions. The piecewise Gaussian and piecewise exponential distributions are justified physically through assuming exponential growth and decay of the electron avalanches which result in the gamma ray bursts and are therefore highly relevant in this context. However, identifying the electron avalanche phenomenon as a form of stochastic exit time process, the inverse Gaussian and Ornstein‐Uhlenbeck are reasonable alternatives. Results of the maximum likelihood calculations indicate that the five probability densities fit the gamma ray pulse data equally well. By this comparison, our aim is to indicate to terrestrial gamma ray flash researchers these other at least equally valid distribution functions, which may give insights into the physical processes that the electrons (and the positrons) undergo in the gamma ray flashes.