The duration photon energy relation of gamma-ray bursts and its interpretations

Fenimore et al. have recently presented a very tight correlation between the spectral and the temporal structure in gamma-ray bursts (GRBs). In particular, they discovered that the durations of the constituent subpulses which make up the time profile of a given GRB have a well-defined power-law dependence of index similar or equal to 0.45 on the energy E of the observed photons. In this paper we present two simple models which can account in a straightforward fashion for the observed correlation. These models involve (1) the impulsive injection of a population of relativistic electrons and their subsequent cooling by synchrotron radiation, and (2) The impulsive injection of monoenergetic high-energy photons in a medium of Thompson depth tau(T) similar to 5 and their subsequent downgrading in energy due to electron scattering. We present arguments for distinguishing between these two models from the existing data.