Lognormal distributions in gamma-ray bursts and cosmic lightning

The results obtained with the Burst and Transient Experiment (BATSE) on the Compton Gamma Ray Observatory (CGRO) show that the durations of gamma-ray bursts (GRB'bs) are consistent with two populations. We report here our attempts to fit lognormal distributions to various properties of GRBs. In particular, it is shown that the two populations are well fitted by lognormal distributions. Furthermore, the separations in time between the pulses of emission in long-duration, intense GRBs are also consistent with a lognormal distribution. This fingerprint of the emission process can be used to test the hypothesis of a cosmological origin for faint GRBs. The integral number versus peak flux distribution can be fitted by a truncated lognormal distribution, or by functions consisting of a single lognormal distribution with a power-law tail of slope - 1.5. The lognormal properties of GRBs are similar to terrestrial lightning, and suggest that relativistic discharges between regions of charge separation may be the emission mechanism responsible for GRBs originating in the Solar system, the Galaxy or at cosmological distances.