The external shock model of gamma-ray bursts:: Three predictions and a paradox resolved

In the external shock model, gamma-ray burst (GRB) emissions are produced by the energization and deceleration of a thin relativistic blast wave that interacts with the circumburst medium (CBM). We study the physical properties of an analytic function that describes temporally evolving GRB spectra in the limit of a smooth CBM with density n(x) proportional to 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 to several MeV range for detectors triggering on peak Aux over a fixed time interval is shown to be a consequence of the inverse cat-relation of the peak flux and the duration of the radiation emitted by decelerating blast waves.