Relaxation of time-variable neutron-loaded relativistic jets across the photosphere and their GeV-TeV neutrino counterparts

Abstract

Both observational and theoretical studies indicate that the central engine of a gamma-ray burst (GRB) is intrinsically time-variable, implying jet inhomogeneity. A jet with an inhomogeneous Lorentz factor distribution develops internal shocks both below and above the photosphere, relaxing toward homologous expansion. Below the photosphere, neutrons, whose mean free paths are much longer than those of charged particles, play an essential role in the dissipation process. Using neutron-inclusive shell simulations with initial conditions based on the collapsar scenario, we link the statistical inhomogeneity of the jet at the breakout of the progenitor to the dissipation that occurs inside and outside the photosphere, and calculate the GeV-TeV neutrino counterpart originated from inelastic neutron-proton interactions consistently with the prompt gamma-ray emission. We find that the peak energy of the GeV-TeV neutrinos is in 10-30 GeV irrespective to the baryon loading factor of the jet, with the high-energy tail extending into the TeV range as the amplitude of the time variability becomes stronger. When gamma-ray emission is efficient as in typical GRBs (i.e., the gamma-ray radiation efficiency with respect to the total jet power is approximately 100%, the radiative efficiency of GeV-TeV neutrinos remains 0.1-10%. By contrast, when the gamma-ray radiation efficiency is relatively low (< 10%) for jets where a large fraction of the energy is dissipated below the photosphere, the neutrino efficiency can increase up to 20%. This suggests that GRBs with relatively low gamma-ray luminosities, as well as X-ray-rich transients, can be promising targets for ongoing and future GeV-TeV neutrino transient searches.