Hadronic supercriticality in spherically expanding sources: application to GRB prompt emission

Abstract

ABSTRACT Relativistic hadronic plasmas can become, under certain conditions, supercritical, abruptly and efficiently releasing the energy stored in protons through photon outbursts. Past studies have tried to relate the features of such hadronic supercriticalities (HSCs) to the phenomenology of gamma-ray burst (GRB) prompt emission. In this work we investigate, for the first time, HSC in adiabatically expanding sources. We examine the conditions required to trigger HSC, study the role of expansion velocity, and discuss our results in relation to GRB prompt emission. We find multipulse light curves from slowly expanding regions (≲ 0.01c) that are a manifestation of the natural HSC quasi-periodicity, while single-pulse light curves with a fast rise and slow decay are found for higher velocities. The formation of the photon spectrum is governed by an in-source electromagnetic cascade. The peak photon energy is approximately $1 \cdot \frac{\Gamma }{100} \frac{1+z}{3}$ MeV for maximum proton energies $(1-10) \cdot \frac{\Gamma }{100} \frac{1+z}{3}$ PeV, while the peak γ-ray luminosities are in the range $(10^{49}-10^{52}) \cdot (\frac{\Gamma }{100})^4$ erg s−1. HSC bursts peaking in the MeV energy band are also copious neutrino emitters with peak energies $\sim 10 \cdot \frac{\Gamma }{100} \frac{1+z}{3}$ TeV and an all-flavour neutrino fluence $\sim 10~{{\ \rm per\ cent}}$ of the γ-ray one. The hypothesis that long-duration GRBs are powered by HSCs could be applied therefore only to the most luminous GRBs observed assuming bulk Lorentz factors Γ ≤ 100.