Prompt γ-ray and early afterglow emission in the external shock model

We describe our attempt to determine if γ-ray burst (GRB) and afterglow emissions could both arise in external shocks for simple GRBs – bursts consisting of just a few peaks in their light curves. We calculate peak flux and peak frequency during the γ-ray burst for 10 well-observed bursts using the same set of parameters that are determined from modelling afterglow emissions. We find the γ-ray emission properties for 970508 (which had a single-peak light curve) fit nicely with the extrapolation of its afterglow data, and therefore this burst was probably 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 ∼102 than the afterglow value at ∼1 d. 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 two of these parameters, and is smaller 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 γ-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. We have also calculated emission from the reverse shock for these ten bursts and find the flux in the optical band for more than half of these bursts to be between 9th and 12th magnitude at the deceleration time if the reverse shock microphysics parameters are the same as those found from afterglow modelling and the deceleration time is of the order of the burst duration. However, the cooling frequency in the reverse shock for most of these bursts is below the optical band, and therefore the observed flux decays rapidly with time (as ∼t−3) and is unobservable after a few deceleration times. It is also possible that the deceleration time is much larger than the burst duration, in which case we expect weak reverse shock emission.