A Simple Energy-Dependent Model for GRB Pulses with Interesting Physical Implications

Abstract

A simple mathematical model for GRB pulses is postulated in both time and energy. The model breaks GRB pulses up into component functions, one general light curve function exclusively in the time dimension and four component functions exclusively in the energy dimension. Each component function of energy is effectively orthogonal to the other energy-component functions. The model is a good statistical fit to several of the most fluent separable GRB pulses known. Even without theoretical interpretation, the model may be immediately useful for fitting prompt emission from GRB pulses across energy channels with a minimal number of free parameters, sometimes far fewer than freshly fitting a GRB pulse in every energy band separately. Some theoretical implications of the model might be particularly interesting, however, as the temporal component (e.g. the shape of the light curve) is well characterized mathematically by the well known Planck distribution.