Relationship between width of pulses and Lorentz factor expected from the light curve of fireball sources

Time profiles of many gamma-ray bursts consist of distinct pulses, which provides a possibility of characterizing the temporal structure of these bursts. We employ a simple model of highly symmetric fireballs to analyse the effect of the expansion speed on the light curve arising from different forms of local pulses. The relationship between the ratio r of the FWHM width of the rising phase of the light curve to that of the decaying phase and the Lorentz factor is investigated. The analysis shows that, when the rest frame radiation form is ignored, temporal profiles of the light curve arising from pulses of fireballs will not be affected by the expansion speed (that is, r is almost a constant) as long as the fireball expands relativistically. When the rest frame radiation form is taken into account, there will be a break in the curves of r −log Γ. The location of the break depends mainly on the adopted value of the rest frame peak frequency ν 0,p . One would reach almost the same result when a jet is considered. In addition, we utilize a sample of 48 individual GRB pulses to check the relationship between the ratio r and the expansion speed Γ. We find no significant correlation between them and this is consistent with the theoretical analysis.