The Duration -- Photon Energy Relation of Gamma Ray Bursts and Its Interpretations

Fenimore et al. (1995) have recently presented a very tight correlation between the spectral and the temporal structure in Gamma Ray Bursts (hereafter 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 $\simeq 0.45$, on the energy $E$ of the observed photons. In this note we present two simple models which can account in a straightforward fashion for the observed correlation. These models involve: (a) The impulsive injection of a population of relativistic electrons and their subsequent cooling by synchrotron radiation. (b) The impulsive injection of monoenergetic high energy photons in a medium of Thompson depth $\tau_T \sim 5$ and their subsequent downgrading in energy due to electron scattering. We present arguments for distinguishing between these two models from the existing data.