We present the statistics of the ratio, ${mathrm R}$, between the prompt and afterglow plateau fluxes of GRB. This we define as the ratio between the mean prompt energy flux in the {em Swift} BAT and the {em Swift} XRT, immediately following the stee
p transition between these two states and the beginning of the afterglow stage referred to as the plateau. Like the distribution of other GRB observables, the histogram of ${mathrm R}$ is close to log-normal, with maximum at ${mathrm R = R}_{rm m} simeq 2,000$, FWHM of about 2 decades and with the entire distribution spanning about 6 decades in the value of ${mathrm R}$. We note that the peak of the distribution is close to the proton-to-electron mass ratio $({mathrm R}_{rm m} simeq m_p/m_e = 1836)$, as proposed by us earlier, on the basis of a specific model for the conversion of the GRB blast wave kinetic energy into radiation, before any similar analysis were made. It therefore appears that, in addition to the values of the energy of peak luminosity ${E_{rm pk}sim m_{e} c^2}$, GRB present us with one more quantity with an apparently characteristic value. The fact that the values of both these quantities (i.e. $E_{rm pk}$ and ${mathrm R}$) comply with those implied by the same specific model devised to account for an altogether different issue, namely the efficient conversion of the GRB blast wave kinetic energy into radiation, argues favorably for its underlying assumptions.
We examine the prompt and afterglow emission within the context of the Supercritical Pile model for GRBs. For this we have performed self-consistent calculations, by solving three time-dependent kinetic equations for protons, electrons and photons in
addition to the usual mass and energy conservation equations. We follow the evolution of the RBW as it sweeps up circumstellar matter and assume that the swept-up electrons and protons have energies equal to the Lorentz factor of the flow. While the electrons radiate their energies through synchrotron and inverse Compton radiation on short timescales, the protons, at least initially, start accumulating without any dissipation. As the accumulated mass of relativistic protons increases, however, they can become supercritical to the `proton-photon pair-production - synchrotron radiation network, and, as a consequence, they transfer explosively their stored energy to secondary electron-positron pairs and radiation. This results in a burst which has many features similar to the ones observed in GRB prompt emission. We have included in our calculations the radiation drag force exerted on the flow from the scattered radiation of the prompt emission on the circumstellar material. We find that this can decelerate the flow on timescales which are much faster than the ones related to the usual adiabatic/radiative ones. As a result the emission exhibits a steep drop just after the prompt phase, in agreement with the Swift afterglow observations.
