  The Gamma-ray Burst Monitor (GBM) on board the Fermi Gamma-ray Space
Telescope has triggered on over 300 terrestrial gamma-ray flashes (TGFs) since
its launch in June 2008. With 14 detectors, GBM collects on average ~100 counts
per triggered TGF, enabling unprecedented studies of the time profiles of TGFs.
Here we present the first rigorous analysis of the temporal properties of a
large sample of TGFs (278), including the distributions of the rise and fall
times of the individual pulses and their durations. A variety of time profiles
are observed with 19 of TGFs having multiple pulses separated in time and 31
clear cases of partially overlapping pulses. The effect of instrumental dead
time and pulse pileup on the temporal properties are also presented. As the
observed gamma ray pulse structure is representative of the electron flux at
the source, TGF pulse parameters are critical to distinguish between
relativistic feedback discharge and lightning leader models. We show that at
least 67% of TGFs at satellite altitudes are significantly asymmetric. For the
asymmetric pulses, the rise times are almost always shorter than the fall
times. Those which are not are consistent with statistical fluctuations. The
median rise time for asymmetric pulses is ~3 times shorter than for symmetric
pulses while their fall times are comparable. The asymmetric shapes observed
are consistent with the relativistic feedback discharge model when Compton
scattering of photons between the source and Fermi is included, and
instrumental effects are taken into account.
