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

Abstract

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 time profiles of GRBs using data from the Compton Gamma Ray Observatory's Burst and Transient Source Experiment (BATSE) and found that the postpeak slope of the average peak-aligned time profile of GRBs obeys a unique and simple analytical law, I ~ exp [-(t/t0)1/3], where t is the time measured from the peak of the event and t0 is a constant ranging from 0.3 s for strong bursts to ~1 s for weak bursts. The average peak-aligned time profile follows this law with good accuracy in the whole time range available for analysis (from fractions of a second to ~120 s after the peak). Such a law (a stretched exponential) appears in processes associated with fractals (e.g., turbulence). The same analysis for solar flares gives a different shape for the average time profile. The dependence of t0 on the brightness of GRBs is presented. The time dilation of the dimmest GRBs relative to the brightest GRBs is at least a factor ~2 and possibly ~3. The statistics (600 GRBs), however, still does not allow us to rule out an intrinsic anticorrelation between intensity and duration of GRBs as a possible explanation of the effect. Probably, it is possible to confirm (or disprove) the cosmological origin of GRBs using the total existing statistics of strong bursts.