2005ApJ...631L..25J

The FWHM of gamma-ray burst (GRB) pulses is known to be related to energy by a power law. We wonder if the power-law index α is related to the corresponding local pulse width FWHM₀. Seven FRED (fast rise, exponential decay) pulse GRBs are employed to study this issue; six of them were interpreted recently by the relativistic curvature effect (the Doppler effect of fireballs), and the corresponding local pulses were intensely studied. A regression analysis shows an anticorrelation between logα and logFWHM₀with a slope of -0.37±0.13. This suggests that, for the class of the GRB pulses that are the consequence of the curvature effect, the difference in the local pulse width might lead to a variation in the power-law index, in which the smaller the width, the larger the value of α. Since the number of sources employed in this analysis is small, our result is only a preliminary one that needs to be confirmed by larger samples.