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