Origination of gamma-ray burst pulses associated with the Doppler effect of spherical fireballs or uniform jet

Abstract

Ryde and Petrosian have pointed out that the rise phases of gamma-ray burst (GRB) pulses originate from the widths of the intrinsic pulses and their decay phases are determined by the curvature effect of the expanding fireball surface based on their simplified formula. In this paper we investigate in detail the issue based on the formula in Ref. [20], which is derived based on a model of highly symmetric expanding fireballs, where the Doppler effect is the key factor to be concerned about, and no terms are omitted in their derivation. Our analyses show that the decay phases of the observed pulses originate from the contributions from both the curvature effect of the expanding fireball and the two timescales of the local pulses, and the rise phases of the observed pulses only come from the two timescales of the local pulses. Associated with a local pulse with both rise and decay portions, the light curve of GRBs in the rise portion is expected to undergo a concave phase and then a convex one, whereas that in the decay portion is expected to evolve by an opposite process. And the ratio of the concave timescale to the convex one in the rise phase of the observed pulse linearly increases with the ratio of the rising timescale to the decay one of the local pulse (rrd), whereas the ratio of the convex timescale to the concave timescale in its decay phase linearly decreases with rrd. The two correlations are independent of the local pulse forms and the rest-frame radiation forms. But the different forms of local pulses and the different values of rrd gives rise to the diversity of the light curve pulse shapes. We test a sample of 86 GRB pulses detected by the BATSE instrument on board the Compton Gamma Ray Observatory and find that the characteristics do exist in the light curve of GRBs.