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Prompt Gamma-ray and Early Afterglow Emission in the External Shock Model

We describe our attempt to determine if gamma-ray burst (GRB) and afterglow emissions could both arise in external shocks for simple GRBs--bursts consisting of just a few peaks in their lightcurves. We calculate peak flux and peak frequency during the gamma-ray burst for ten well observed bursts using the same set of parameters that are determined from modeling afterglow emissions. We find the gamma-ray emission properties for 970508 (which had a single peak lightcurve) fit nicely with the extrapolation of its afterglow data, and therefore this burst was likely produced in the external shock. One can explain two other bursts in this sample as forward shock synchrotron emission provided that the magnetic field parameter during the burst is close to equipartition, and larger by a factor of 100 than the afterglow value at ~1 day. The remaining seven bursts cannot be explained in the external shock model even if we allow the energy fraction in electrons and magnetic field and the density of the surrounding medium to take on any physically permitted value; the peak of the spectrum is above the cooling frequency, therefore the peak flux is independent of the latter of these two parameters, and is too small by about an order of magnitude than the observed values. We have also considered inverse-Compton scattering in forward and reverse shock regions and find that it can explain the gamma-ray emission for a few bursts, but requires the density to be 1--2 orders of magnitude larger than a typical Wolf-Rayet star wind and much larger than permitted by late afterglow observations. [Abridged]