The "Supercritical Pile" Model of GRB: Thresholds, Polarization, Time Lags

Abstract

The essence of the ``Supercritical Pile'' model is a process for converting the energy stored in the relativistic protons of a Relativistic Blast Wave (RBW) of Lorentz factor $\Gamma$ into electron -- positron pairs of similar Lorentz factor, while at the same time emitting most of the GRB luminosity at an energy $E_p \simeq 1$ MeV. This is achieved by scattering the synchrotron radiation emitted by the RBW in an upstream located ``mirror'' and then re-intercepting it by the RBW. The repeated scatterings of radiation between the RBW and the ``mirror'', along with the threshold of the pair production reaction $p \gamma \to p e^-e^+$, lead to a maximum in the GRB luminosity at an energy $E_p \simeq 1$ MeV, {\sl independent of the value of $\Gamma$}. Furthermore, the same threshold implies that the prompt $\gamma-$ray emission is only possible for $\Gamma$ larger than a minimum value, thereby providing a ``natural'' account for the termination of this stage of the GRB as the RBW slows down. Within this model the $\gamma-$ray ($E \sim 100$ keV -- 1 MeV) emission process is due to Inverse Compton scattering and it is thus expected to be highly polarized if viewed at angles $\theta \simeq 1/\Gamma$ to the RBW's direction of motion. Finally, the model also predicts lags in the light curves of the lower energy photons with respect to those of higher energy; these are of purely kinematic origin and of magnitude $\Delta t \simeq 10^{-2}$ s, in agreement with observation.