Gamma-Ray Burst Spectra and Light Curves as Signatures of a Relativistically Expanding Plasma

Abstract

Several patterns have been discovered in how some spectral characteristics change during the decaying phase of long (> few s.) GRB pulses. We compare these observed signatures with those expected from a relativistically expanding shell. Within the internal shock model and assuming a short cooling time, we show that the angular dependence in arrival time can explain the general characteristics of long GRB pulses. This includes the pulse shape, with a fast rise and a slower decay, ~ (1+t/tau)^2, and the spectral evolution, which can be described by the hardness-intensity correlation (HIC), with the intensity being proportional to the square of the hardness. A variation of the relevant time scales involved (the angular spreading and the dynamic) can explain the broad, observed dispersion of the HIC index. Reasonable estimates of physical parameters lead to situations where the HIC relation deviates from a pure power law; features that are indeed present in the observations. Depending on the relative values of the rise and decay times of the intrinsic light curve, the spectral/temporal behavior, as seen by an observer, will produce hard-to-soft or tracking pulses. The observed spectrum is a superposition of many intrinsic spectra arriving from different parts of the shell with varying spectral shifts. Therefore, it will be broader than the emitted spectrum and its spectral parameters could have complex relations with the intrinsic ones. Furthermore, we show that the softening of the low-energy power-law index, that has been observed in some pulses, can be explained by geometric effects and does not need to be an intrinsic behavior.