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Previous studies have found that the width of gamma-ray burst (GRB) pulse isenergy dependent and that it decreases as a power-law function with increasingphoton energy. In this work we have investigated the relation between theenergy dependence of pulse and the so-called Band spectrum by using a sampleincluding 51 well-separated fast rise and exponential decay long-duration GRBpulses observed by BATSE (Burst and Transient Source Experiment on the ComptonGamma Ray Observatory). We first decompose these pulses into rise, and decayphases and find the rise widths, and the decay widths also behavior as apower-law function with photon energy. Then we investigate statistically therelations between the three power-law indices of the rise, decay and totalwidth of pulse (denoted as $\delta_r$, $\delta_d$ and $\delta_w$, respectively)and the three Band spectral parameters, high-energy index ($\alpha$),low-energy index ($\beta$) and peak energy ($E_p$). It is found that(1)$\alpha$ is strongly correlated with $\delta_w$ and $\delta_d$ but seemsuncorrelated with $\delta_r$; (2)$\beta$ is weakly correlated with the threepower-law indices and (3)$E_p$ does not show evident correlations with thethree power-law indices. We further investigate the origin of $\delta_d-\alpha$and $\delta_w-\alpha$. We show that the curvature effect and the intrinsic Bandspectrum could naturally lead to the energy dependence of GRB pulse width andalso the $\delta_d-\alpha$ and $\delta_w-\alpha$ correlations. Our resultswould hold so long as the shell emitting gamma rays has a curve surface and theintrinsic spectrum is a Band spectrum or broken power law. The strong$\delta_d-\alpha$ correlation and inapparent correlations between $\delta_r$and three Band spectral parameters also suggest that the rise and decay phasesof GRB pulses have different origins.

Energy-Dependent GRB Pulse Width due to the Curvature Effect and Intrinsic Band Spectrum