The average temporal and spectral evolution of gamma-ray bursts

We have averaged bright BATSE bursts to uncover the average overall temporal and spectral evolution of gamma-ray bursts (GRBs). We align the temporal structure of each burst by setting its duration to a standard duration, which we call T-[DUR]. The observed average "aligned T-[Dur]" profile for 32 bright bursts with intermediate durations (16-40 s) has a sharp rise (within the first 20% of T-[Dur]) and then a linear decay. Exponentials and power laws do not fit this decay. In particular, the power law seen in the X-ray afterglow (proportional to T-1.4) is not observed during the bursts, implying that the X-ray afterglow is not just an extension of the average temporal evolution seen during the gamma-ray phase. The average burst spectrum has a low-energy slope of -1.03, a high-energy slope of -3.31, and a peak in the nu F-nu distribution at 390 keV. We determine the average spectral evolution. Remarkably, it is also a linear function, with the peak of the nu F-nu distribution given by similar to 680 - 600(T/T-[Dur]) keV. Since both the temporal profile and the peak energy are linear functions, on average, the peak energy is linearly proportional to the intensity. This behavior is inconsistent with the external shock model. The observed temporal and spectral evolution is also inconsistent with that expected from variations in just a Lorentz factor. Previously, trends have been reported for GRB evolution, but our results are quantitative relationships that models should attempt to explain.