A Simple Law for the Average Time History of Gamma-Ray Bursts and Their Time Dilations

Individual gamma ray bursts (GRBs) have very diverse time behavior - from a single pulse to a long complex sequence of chaotic pulses of different timescales. I studied light curves of GRBs using data from the CGRO's BATSE experiment and found that the average post-peak time history for a sample of 460 bursts obeys an unique and simple analytical law: $I \sim \exp(-(t/t_0)^{1/3})$ where $t$ is time measured from the peak of the event and $t_0$ is a constant ranging from 0.3 sec for strong bursts to $\sim 1$ sec for weak bursts. The average peak aligned profile follows this law with good accuracy in the whole range availible for analysis (from fractions of a second to $\sim$ 150 seconds after the peak). Such a law with a single time constant characterising the overall sample of GRBs should have important physical meaning. The dependence of $t_0$ versus brightness of GRBs is presented. The fact that $t_0$ depends on the brightness apparantly confirms the recently discovered effect of time dilation of weak bursts which has a possible cosmological interpretation. The time dilation is detected at a confidence level of $7\sigma$ and it is slightly larger than was previously reported.