The FWHM of local pulses and the corresponding power-law index of gamma-ray burst FRED pulses

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 a 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 and with a slope of -0.37 +/- 0.13. This suggests log a log FWHM0 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 a. 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.