  In the external shock model, gamma-ray burst (GRB) emissions are produced by
the energization and deceleration of a thin relativistic blast wave due to its
interactions with the circumburst medium (CBM). We study the physical
properties of an analytic function which describes temporally-evolving GRB
spectra in the limit of a smooth CBM with density n(x)\propto x^(-\eta), where
x is the radial coordinate. The hard-to-soft spectral evolution and the
intensity-hardness correlation of GRB peaks are reproduced. We predict that (1)
GRB peaks are aligned at high photon energies and lag at low energies according
to a simple rule; that (2) temporal indices at the leading edge of a GRB peak
display a well-defined shift with photon energy; and that (3) the change in the
spectral index values between the leading and trailing edges of a GRB peak
decreases at higher photon energies. The reason that GRBs are usually detected
with vF_v peaks in the 50 keV - several MeV range for detectors which trigger
on peak flux over a fixed time interval is shown to be a consequence of the
inverse correlation of peak flux and duration of the radiation emitted by
decelerating blast waves.

Astrophysics