Physical implication of the Kocevski Ryde Liang pulse function of gamma ray bursts

In this paper, we contrast an empirical pulse function of gamma-ray bursts with a theoretical model in order to provide a physical explanation to the parameters of the KRL function and directly relate parameters in both models. We find the ratio of the rise index r to the decay index d, derived when fitted by the KRL function, increases quickly first and then remains nearly invariant with the relative width of local pulses when the width exceeds 2. The rise and decay times of pulses are found to be related to the Lorentz factor by a power law, where the power law index associated with the rise time is less than that of the decay time, and both are close to -2. In addition, the mean asymmetry shows a slight trend of decreasing with Lorentz factors. In plots of decay indices versus asymmetry, there is a descending phase and after this phase there is a rising portion. We find that these long bursts of the KRL sample are mainly associated with those light curves arising from co-moving pulses with the relative width being larger than 0.1. We show that the effect of the co-moving pulse shape on the KRL function parameters of the resulting pulses is considerable and can be distinguished by the decay index d when the relative co-moving pulse width is less than 2.