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

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 (HSC) 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 multi-pulse light curves from slowly expanding regions ($u_{\rm exp}\lesssim 0.01 c)$ 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 $\sim 1$ MeV ($\sim 1$ GeV) for maximum proton energies $\sim 1-10$ PeV ($1-10$ EeV) assuming a jet Lorentz factor 100. Peak $\gamma$-ray luminosities are in the range $10^{49}-10^{52}$ erg s$^{-1}$, with the MeV-peaked spectra being $\sim 100-300$ times more luminous than their GeV-peaked analogues. HSC bursts peaking in the MeV are also copious $\sim 10$ TeV neutrino emitters, with an all-flavour fluence $\sim 10\%$ of the $\gamma$-ray one. The hypothesis that typical long-duration GRBs are powered by HSC could be tested in the near future with more sensitive neutrino telescopes like IceCube-Gen2.