Hadronic supercriticality as a trigger for GRB emission

TL;DR

This paper investigates a hadronic model for gamma-ray burst emission, showing that supercritical energy transfer from protons to photons and neutrinos can produce observed spectra with high efficiency, under certain conditions.

Contribution

It introduces a minimal-parameter hadronic model demonstrating supercriticality as a trigger for GRB emission, supported by analytical and numerical analysis.

Findings

Supercriticality occurs when proton injection compactness exceeds a critical value.

Photon spectra become Band-like due to Comptonization in supercritical conditions.

Energy transfer efficiency to gamma-rays and neutrinos reaches approximately 30%.

Abstract

We explore a one-zone hadronic model that may be able to reproduce $\gamma$-ray burst (GRB) prompt emission with a minimum of free parameters. Assuming only that GRBs are efficient high-energy proton accelerators and without the presence of an ab initio photon field, we investigate the conditions under which the system becomes supercritical, i.e. there is a fast, non-linear transfer of energy from protons to secondary particles initiated by the spontaneous quenching of proton-produced $\gamma$-rays. We first show analytically that the transition to supercriticality occurs whenever the proton injection compactness exceeds a critical value, which favours high proton injection luminosities and a wide range of bulk Lorentz factors. The properties of supercriticality are then studied with a time-dependent numerical code that solves concurrently the coupled equations of proton, photon, electron, neutron and neutrino distributions. For conditions that drive the system deep into the supercriticality we find that the photon spectra obtain a Band-like shape due to Comptonization by cooled pairs and that the energy transfer efficiency from protons to $\gamma$-rays and neutrinos is high reaching $\sim 0.3$. Although some questions concerning its full adaptability to the GRB prompt emission remain open, supercriticality is found to be a promising process in that regard.