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 with energyby a power-law. We wonder if the power-law index $\alpha$ is related with thecorresponding local pulse width $FWHM_0$. Seven FRED (fast rise and exponentialdecay) pulse GRBs are employed to study this issue, where six of them wereinterpreted recently by the relativistic curvature effect (the Doppler effectof fireballs) and the corresponding local pulses were intensely studied. Aregression analysis shows an anti-correlation between $log \alpha$ and $logFWHM_0$ with a slope of $-0.37\pm0.13$. This suggests that, for the class ofthe GRB pulses which are consequences of the curvature effect, the differenceof the local pulse width might lead to the variation of the power law index,where the smaller the width the larger the value of $\alpha$. Since the numberof sources employed in this analysis is small, our result is only a preliminaryone which needs to be confirmed by larger samples.Comment: 14 pages, 2 figures. accepted by ApJ