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

TL;DR

This work develops a time-variable, neutron-loaded jet model for GRBs within the collapsar framework, implementing a shell-based treatment that includes sub-photospheric neutron physics, neutron–proton decoupling, photospheric emission, and shell collisions. By simulating energy dissipation across the photosphere and beyond, the authors compute GeV–TeV neutrino spectra via Geant4 and connect the variability imprint at breakout to the resulting photon and neutrino outputs. They find that neutrinos peak at $E_\nu\sim10$–$30$ GeV with a TeV tail when variability is strong, and neutrino efficiency can reach up to $\sim20\%$ in certain low-$\langle\eta_{\rm ini}\rangle$ regimes, while typical GRBs favor photon-dominated dissipation with $0.1$–$10\%$ neutrino efficiency. The results imply that relatively gamma-ray-faint GRBs and X-ray-rich transients could be favorable targets for upcoming GeV–TeV neutrino searches, and they emphasize an anti-correlation between photon and neutrino outputs across the jet's evolution.

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.

Figures (7)

• Figure 1: Energy dissipation by photon radiation (upper panel) and neutrino radiation (lower panel) and their dependence on the radius for a time-variable neutron-loaded jet with $A = 1$, $\delta t = 10\,\mathrm{ms}$, $\left< \eta_\mathrm{ini} \right> = 200$, and $L_\mathrm{j, iso} = 3.5\times 10^{52}\,\mathrm{erg\,s^{-1}}$.
• Figure 2: Same as Fig. \ref{['fig:FiducialEneOut']}, but for the case $A = 2$, $\delta t = 1\,\mathrm{ms}$, and $\left< \eta_\mathrm{ini} \right> = 800$, that yields one of the most efficient photon emission.
• Figure 3: Same as Fig. \ref{['fig:FiducialEneOut']}, but the case with $A = 2$, $\delta t = 1\,\mathrm{ms}$, and $\left< \eta_\mathrm{ini} \right> = 50$, that yields the most efficient neutrino emission.
• Figure 4: Photon radiation efficiency versus neutrino radiation efficiency, and their dependence on the properties of a time-variable, neutron-loaded jet. The isotropic luminosity and duration of the jet are fixed to be $L_\mathrm{j, iso} = 3.5\times 10^{52}\,\mathrm{erg\,s^{-1}}$, and $\Delta t = 20\,\mathrm{s}$ respectively.
• Figure 5: GeV-TeV neutrino counterparts of time-variable neutron-loaded jets with various statistical inhomogeneity. The isotropic luminosity and duration of the jet, and the luminosity distance are fixed to be $L_\mathrm{j, iso} = 3.5\times 10^{52}\,\mathrm{erg\,s^{-1}}$, $\Delta t = 20\,\mathrm{s}$, and $d_\mathrm{L} = 100\,\mathrm{Mpc}$, respectively. The black dotted lines represent the IceCube templates for neutrinos from collision scenario, where the relative Lorentz factor is fixed to $\Gamma_\mathrm{rel}\sim2$Murase2022IceCubeCollab2023.