The "Supercritical Pile" Model for GRB: Getting the nu F_{nu} peak at 1 MeV

Abstract

We propose that the internal energy of the GRB blast waves, thought to be stored in the form of relativistic protons co-moving with the blast wave, is converted explosively (i.e. on light crossing time scales) into relativistic electrons of the same Lorentz factor, which are responsible for the production of observed prompt gamma-ray emission of the burst. This conversion is the result of the combined effects of the reflection of photons produced within the flow by upstream located matter, their re-interception by the blast wave and their eventual conversion into e^+e^--pairs in interactions with the relativistic protons of the blast wave (via the p gamma --> p e^+e^- reaction). This entire procedure is contingent on two conditions on the relativistic protons: a kinematic one imposed by the threshold of the p gamma --> e^+e^- reaction and a dynamic one related to the column density of the post shock matter to the same process. This latter condition is in essence identical to that of the criticality of a nuclear pile, hence the terminology. It is argued that the properties of relativistic blast waves operating under these conditions are consistent with GRB phenomenology, including the recently found correlation between quiescence periods and subsequent flare fluence. Furthermore, it is shown that, when operating near threshold, the resulting GRB spectrum produces its peak luminosity at an energy (in the lab frame) E ~= m_ec^2, thereby providing an answer to this outstanding question of GRBs.