The External Shock Model of Gamma-Ray Bursts: Three Predictions and a Paradox Resolved

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Abstract
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.

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