A power-law relationship between the pulse width and energy of gamma-ray bursts (GRBs) has been found by many authors. Recently, under the assumption that the Doppler effect of the relativistically expanding fireball surface (or, in some papers, the curvature effect) is important, Qin et al. showed that, in most cases, this power-law relationship would exist in a certain energy range, and, within a similar range, a power-law relationship of an opposite trend between the ratio of the rising width to the decaying width and energy would be expected for the same burst. We check this prediction with two GRB samples that contain well-identified pulses. A power-law anticorrelation between the full pulse width and energy and a power-law correlation between the pulse-width ratio and energy are seen in the light curves of the majority (around 65 per cent) of bursts of the two samples within the energy range of BATSE, suggesting that these bursts probably arise from the emission associated with the shocks occurring on a relativistically expanding fireball surface. For the rest of the bursts, the relationships between these quantities had not been predicted previously. We propose considering other spectral evolutionary patterns or other radiation mechanisms such as a varying synchrotron or Comptonized spectrum to check whether the observed relationships for these bursts can also be accounted for by the Doppler model. In addition, we find that the upper limits of the width ratio for the two samples do not exceed 0.9, in agreement with what has previously been predicted by the Doppler model. The plateau/power law/plateau and the peaked features predicted and detected previously by Qin et al. are generally observed, with exceptions noticed only in a few cases. According to the distinct values of two power-law indices, α FWHM and α ratio , we divide the bursts into three subsets that are located in different areas of the α FWHM -α ratio plane. We suspect that different locations of (α FWHM , α ratio ) might correspond to different mechanisms.

Assuming an intrinsic 'Band' shape spectrum and an intrinsic energy-independent emission profile we have investigated the connection between the evolution of the rest-frame spectral parameters and the spectral lags measured in gamma-ray burst (GRB) pulses by using a pulse model. We first focus our attention on the evolution of the peak energy, E0,p, and neglect the effect of the curvature effect. It is found that the evolution of E0,p alone can produce the observed lags. When E0,p varies from hard to soft only the positive lags can be observed. The negative lags would occur in the case of E0,p varying from soft to hard. When the evolution of E0,p and the low-energy spectral index α0 varying from soft to hard then to soft we can find the aforesaid two sorts of lags. We then examine the combined case of the spectral evolution and the curvature effect of fireball and find the observed spectral lags would increase. A sample including 15 single pulses whose spectral evolution follows hard to soft has been investigated. All the lags of these pulses are positive, which is in good agreement with our theoretical predictions. Our analysis shows that only the intrinsic spectral evolution can produce the spectral lags and the observed lags should be contributed by the intrinsic spectral evolution and the curvature effect. But it is still unclear what cause the spectral evolution.

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We have investigated the evolution of observed spectral hardness E p (where E p is the maximum of the F spectrum) based on the model of highly symmetric expanding fireballs, where the Doppler effect of the expanding fireball surface is the key factor concerned, and find that the evolutionary curve of E p undergoes a drop to rise to decay evolution (the A, B, and C phases, respectively). The A phase peaks at the very onset of the corresponding light-curve pulse. Since the Doppler effect is less prominent in the B phase, corresponding to the rising portion of the pulse, the slope of the B phase reflects both the corresponding intrinsic spectral evolution and the shape of its local pulse. The C phase, corresponding to the decay portion of the pulse, where the Doppler effect dominates, always decreases monotonically and does not necessarily reflect the corresponding intrinsic spectral evolution. Investigation of a sample of 12 FRED pulses (their peak energy can be found in the work of Kaneko et al.) shows that the evolutionary characteristics of the fitted peak energy in the FRED pulses are in good agreement with our predictions.

In this paper we have analyzed the temporal and spectral behavior of 52 Fast Rise and Exponential Decay (FRED) pulses in 48 long-duration gamma-ray bursts (GRBs) observed by the CGRO/BATSE, using a pulse model with two shape parameters and the Band model with three shape parameters, respectively.It is found that these FRED pulses are distinguished both temporally and spectrally from those in long-lag pulses. Different from these long-lag pulses only one parameter pair indicates an evident correlation among the five parameters, which suggests that at least ∼4 parameters are needed to model burst temporal and spectral behavior. In addition, our studies reveal that these FRED pulses have correlated properties: (i) long-duration pulses have harder spectra and are less luminous than short-duration pulses; (ii) the more asymmetric the pulses are the steeper the evolutionary curves of the peak energy (E p ) in the νf ν spectrum within pulse decay phase are. Our statistical results give some constrains on the current GRB models.