Investigating binary-neutron-star mergers as production sites of high-energy neutrinos

The end state of binary-neutron-star (BNS) mergers can manifest conditions to produce high-energy neutrinos. Inspired by the event GW170817, detected in gravitational waves and in optical/infrared emission, we investigate a scenario in which cosmic-ray (CR) particles are accelerated, in a population of BNS mergers, in the energy range that might contribute from the \textit{knee} to the \textit{ankle} of the CR measured spectrum. By taking into account the measured thermal and non-thermal energy density of the photon fields in the source environment as a function of the time after the merger, we model the CR interactions and the consequent neutrino production. We propagate the escaped CR and neutrino fluxes through the extragalactic space and compare the expected diffuse fluxes to the experimental data and current limits. Depending on the CR spectral and composition parameters at acceleration, and on the possible contribution to the \textit{sub-ankle} CR flux, we discuss the predicted diffuse neutrino flux associated to this class of astrophysical objects, as a function of the details of the photon field characterizing the merger stage, including its evolution in time. We constrain the fraction of accelerated baryons in the source site given the BNS merger rate per volume, taking into account at the same time the constraints from the measured CR and neutrino fluxes.