2012ApJ...752..132P

Previous studies have found that the width of the gamma-ray burst (GRB) pulse is energy dependent and that it decreases as a power-law function with increasing photon energy. In this work we have investigated the relation between the energy dependence of the pulse and the so-called Band spectrum by using a sample including 51 well-separated fast rise and exponential decay long-duration GRB pulses observed by BATSE (Burst and Transient Source Experiment on the Compton Gamma Ray Observatory). We first decompose these pulses into rise and decay phases and find that the rise widths and the decay widths also behave as a power-law function with photon energy. Then we investigate statistically the relations between the three power-law indices of the rise, decay, and total width of the pulse (denoted as δ_r, δ_d , and δ_w, respectively) and the three Band spectral parameters, high-energy index (α), low-energy index (β), and peak energy (E_p ). It is found that (1) α is strongly correlated with δ_w and δ_d but seems uncorrelated with δ_r; (2) β is weakly correlated with the three power-law indices, and (3) E_p does not show evident correlations with the three power-law indices. We further investigate the origin of δ_d-α and δ_w-α. We show that the curvature effect and the intrinsic Band spectrum could naturally lead to the energy dependence of the GRB pulse width and also the δ_d-α and δ_w-α correlations. Our results hold so long as the shell emitting gamma rays has a curved surface and the intrinsic spectrum is a Band spectrum or broken power law. The strong δ_d-α correlation and inapparent correlations between δ_r and the three Band spectral parameters also suggest that the rise and decay phases of the GRB pulses have different origins.