Extension of an Exponential Light Curve GRB Pulse Model Across Energy Bands

Abstract

A simple mathematical model of GRB pulses in time, suggested in Norris et al. (2005), is extended across energy. For a class of isolated pulses, two of those parameters appear effectively independent of energy. Specifically, statistical fits indicate that pulse amplitude $A$ and pulse width $\tau$ are energy dependent, while pulse start time and pulse shape are effectively energy independent. These results bolster the Pulse Start and Pulse Scale conjectures of Nemiroff (2000) and add a new Pulse Shape conjecture which states that a class of pulses all have the same shape. The simple resulting pulse counts model is $P(t,E) = A(E) \ {\rm exp} (-t/\tau(E) - \tau(E)/t)$, where $t$ is the time since the start of the pulse. This pulse model is found to be an acceptable statistical fit to many of the fluent separable BATSE pulses listed in Norris et al. (2005). Even without theoretical interpretation, this cross-energy extension may be immediately useful for fitting prompt emission from GRB pulses across energy channels with a minimal number of free parameters.