Gamma-ray Burst Peak Duration as a Function of Energy

Gamma-ray burst time histories often consist of many peaks. These peaks tend to be narrower at higher energy. If gamma-ray bursts are cos-mological, the energy dependence of gamma-ray burst time scales must be understood in order to correct the time scale dependence due to the expansion of the universe. By using the average autocorrelation function and the average pulse width, we show that the narrowing with energy follows, quite well, a power law. The power law index is-0.4. This is the rst quantitative relationship between temporal and spectral structure in gamma-ray bursts. It is unclear what physics causes this relationship. The average au-tocorrelation has a universal shape such that one energy range scales linearly with time into all other energy ranges. This shape is approximately the sum 1 of two exponential.