Average properties of the time behaviour of gamma-ray bursts

The average peak-aligned profile of all bursts detected by BATSE with sufficient data quality has a simple ``stretched'' exponential shape, F ~ exp[-(t/t_0)^{1/3}], where $t$ is the time measured from the time for the peak flux of the event, and $t_0$ is a time constant. We study the behaviour of $t_0$ of both the post-peak and the pre-peak slopes of the average time profile as a function of the peak brightness range of the burst sample. We found that the post-peak slope shows time dilation when comparing bright and dim bursts, while the pre-peak slope hardly changes. Thus dimmer bursts have a different shape -- they are more asymmetric. This shape-brightness correlation is observed at a 99.6% confidence level. Such a correlation has a natural explanation within the pulse avalanche model, which is briefly described. Complex events, consisting of many pulses are more symmetric and are intrinsically brighter. Bursts consisting of one or a few pulses are intrinsically weaker and more asymmetric. For such a correlation to be observable requires that the luminosity distance distribution of GRBs to be different from a power-law.