2005ApJ...632.1008Q

We study in detail how the pulse width of gamma-ray bursts is related to energy under the assumption that the sources concerned are in the fireball stage. Due to the Doppler effect of fireballs, there exists a power-law relationship between the two quantities within a limited range of frequency. The power-law range and power-law index depend strongly on the observed peak energy E_pas well as the rest-frame radiation form, and the upper and lower limits of the power-law range can be determined by E_p. It is found that within the same power-law range, the ratio of the FWHM of the rising portion to that of the decaying phase of the pulses is also related to energy in the form of power laws. A plateau/power law/plateau feature is observed in the two relationships. In the case of an obvious softening of the rest-frame spectrum, the two power-law relationships also exist, but the feature evolves to a peaked one. Predictions of the relationships in the energy range covering both the BATSE and Swift bands for a typical hard burst and a typical soft one are made. A sample of FRED (fast rise and exponential decay) pulse bursts shows that 27 out of the 28 sources belong to either the plateau/power law/plateau feature class or to the peaked feature group, suggesting that the effect concerned is indeed important for most of the sources of the sample. Among these bursts, many might undergo an obvious softening evolution of the rest-frame spectrum.