Implications of a PeV neutrino spectral cut-off in gamma-ray burst models

Abstract

The recent discovery of extragalactic PeV neutrinos opens a new window to the exploration of cosmic-ray accelerators. The observed PeV neutrino flux is close to the Waxman-Bahcall upper bound implying that gamma-ray bursts (GRBs) may be the source of ultra-high energy cosmic rays (UHECRs). Starting with the assumption of the GRB-UHECR connection, we show using both analytical estimates and numerical simulations that the observed neutrinos can originate at the jet as a result of photopion interactions with the following implications: the neutrino spectra are predicted to have a cutoff at energy $\le 10$ PeV; the dissipation responsible for the GRB emission and cosmic-ray acceleration takes place at distances $r_{\rm diss} \approx 3 \times 10^{11}-3 \times 10^{13} \ {\rm cm}$ from the central engine; the Thomson optical depth at the dissipation region is $\tau_{\rm T} \sim 1$; the jet carries a substantial fraction of its energy in the form of Poynting flux at the dissipation region, and has a Lorentz factor $\Gamma \simeq 100-500$. The non-detection of $\sim$PeV neutrinos coincident with GRBs will indicate that GRBs are either poor cosmic accelerators or the dissipation takes place at small optical depths in the jet.