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 b y the energization and deceleration of a thin relativistic blast wave that interacts with the circumburst medium (CBM). We study the physical properti es of an analytic function that describes temporally evolving GRB spectra i n the limit of a smooth CBM with density n(x) proportional to x(-eta), wher e x is the radial coordinate. The hard-to-soft spectral evolution and the i ntensity-hardness correlation of GRB peaks are reproduced. We predict that (1) GRB peaks are aligned at high photon energies and lag at low energies a ccording 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) t he change in the spectral index values between the leading and trailing edg es 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 fo r detectors triggering on peak Aux over a fixed time interval is shown to b e a consequence of the inverse cat-relation of the peak flux and the durati on of the radiation emitted by decelerating blast waves.