High-energy neutrino emission associated with gravitational-wave signals: effects of cocoon photons and constraints on late-time emission

We investigate prospects for the detection of high-energy neutrinos produced in the prolonged jets of short gamma-ray bursts (sGRBs). The X-ray lightcurves of sGRBs show extended emission components lasting for 100-1000 seconds, which are considered to be produced by prolonged engine activity. Jets by prolonged engine activity should interact with photons in the cocoon formed by the jet propagation inside the ejecta of neutron star mergers. We calculate neutrino emission from jets by prolonged engine activity, taking account of the interaction between photons provided from the cocoon and cosmic rays accelerated in the jets. We find that IceCube-Gen2, a future neutrino telescope, with the second-generation gravitational wave detectors will probably be able to observe neutrino signals associated with gravitational waves with around 10 years of operation, regardless of the assumed value of the Lorentz factor of the jets. Neutrino observations may enable us to constrain the dissipation region of the jets. We apply this model to GRB 211211A, a peculiar long GRB whose origin may be a binary neutron-star merger. Our model predicts that IceCube is unlikely to detect any associated neutrino, but a few similar events will be able to put a meaningful constraint on the physical quantities of the prolonged engine activities.