Search for Relativistic Curvature Effects in Gamma-Ray Burst Pulses

Abstract

We analyze the time profiles of individual gamma-ray burst (GRB) pulses, that are longer than 2 s, by modelling them with analytical functions that are based empirical descriptions of GRB spectral evolution. These analytical profiles are independent of the emission mechanism and can be used to model both the rise and decay profiles Using this method, we have studied a sample of 77 individual GRB pulses, allowing us to examine the fluence, pulse width, asymmetry, and rise and decay power-law distributions. We find that the rise phase is best modelled with a power law of average index $r = 1.31 \pm 0.11$ and that the average decay phase has an index o.f $d = 2.39 \pm 0.12$. We also find that the ratio between the rise and decay times (the pulse asymmetry) exhibited by the GRB pulse shape has an average value of 0.47 which varies little from pulse to pulse and is independent of pulse duration or intensity. We compare these parameters with those predicted to occur if individual pulse shapes are created purely by relativistic curvature effects in the context of the fireball model, a process that makes specific predictions about the shape of GRB pulses. The decay index distribution obtained from our sample shows that the average GRB pulse fades faster than the value predicted by curvature effects, with only 39% of our sample being consistent with the curvature model. We discuss several refinements of the relativistic curvature scenario that could naturally account for these observed deviations.