The true fluence distribution of terrestrial gamma flashes at satellite altitude

In this paper we use the fluence distributions observed by two different instruments, RHESSI and Fermi GBM, corrected for the effects of their different orbits, combined with their different daily TGF detection rates and their relative sensitivities to make an estimate of the true fluence distribution of TGFs as measured at satellite altitudes. The estimate is then used to calculate the dead-time loss for an average TGF measured by RHESSI. An independent estimate of RHESSI dead-time loss and true fluence distribution is obtained from a Monte Carlo (MC) simulation in order to evaluate the consistency of our results. The two methods give RHESSI dead-time losses of 24-26% for average fluence of 33-35 counts. Assuming a sharp cut-off the true TGF fluence distribution is found to follow a power law with lambda = 2.3 +/- 0.2 down to similar to 5/600 of the detection threshold of RHESSI. This corresponds to a lowest number of electrons produced in a TGF of similar to 10(14) and a global production rate within +/- 38 degrees latitude of 50000 TGFs/day or about 35 TGFs every minute, which is 2% of all IC lightning. If a more realistic distribution with a roll-off below 1/3 (or higher) of the RHESSI lower detection threshold with a true distribution with lambda <= 1.7 that corresponds to a source distribution with lambda <= 1.3 is considered, we can not rule out that all discharges produce TGFs. In that case the lowest number of total electrons produced in a TGF is similar to 10(12).