Gamma-ray burst spectra and light curves as signatures of a relativistically expanding plasma

Temporal and spectral characteristics of prompt emission of gamma-ray burst (GRB) pulses are the primary observations for constraining the energizing and emission mechanisms. In spite of very complex temporal behavior of the GRBs, several patterns have been discovered in how some spectral characteristics change during the decaying phase of individual, well-defined long (greater than a few seconds) pulses. In this paper we compare these observed signatures with those expected from a relativistically expanding, shock-heated, and radiation-emitting plasma shell. Within the internal shock model and assuming a short cooling time, we show that the angular dependence in arrival time from a spherical expanding shell can explain the general characteristics of some well-defined long GRB pulses. This includes the pulse shape, with a fast rise and a slower decay, proportional to(1 + t/tau)(2), where tau is a time constant, 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 measured by the value of the peak, e. g., E(p) of the nuF(nu) spectrum. 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 the hard-to-soft evolution and the so-called tracking pulses. In our model the observed spectrum is a superposition of many intrinsic spectra arriving from different parts of the fireball 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.