The minimum variability time-scale and its relation to pulse profiles of <i>Fermi</i> GRBs

Abstract We present a direct link between the minimum variability time-scales extracted through a wavelet decomposition and the rise times of the shortest pulses extracted via fits of 34 Fermi Gamma-ray Burst Monitor (GBM) Gamma-Ray Burst (GRB) light curves comprised of 379 pulses. Pulses used in this study were fitted with lognormal functions, whereas the wavelet technique used employs a multiresolution analysis that does not rely on identifying distinct pulses. By applying a corrective filter to published data fitted with pulses, we demonstrate agreement between these two independent techniques and offer a method for distinguishing signal from noise.