Binary Neutron Star Mergers as Potential Sources for Ultra-High-Energy Cosmic Rays and High-Energy Neutrinos

Recent studies suggest that the most energetic cosmic rays, exceeding 100 EeV, may primarily consist of $r$-process nuclei. This highlights binary neutron star mergers and collapsars as promising sources of ultra-high-energy cosmic rays (UHECRs). Building on these insights, we examine the conditions that facilitate the efficient production of UHE $r$-process nuclei during the prompt radiation (PR), extended emission (EE), and plateau emission phases of short gamma-ray bursts (sGRBs) following neutron star mergers. Our study reveals that jets associated with the PR phase, characterized by typical bulk Lorentz factors ($\gtrsim 400-500$), dissipation radii, and magnetic field strengths, can accelerate $r$-process nuclei to energies $\gtrsim 100$ EeV while preserving them during propagation within the source. Additionally, we investigate the production of HE neutrinos from photomeson and hadronic interactions, as well as from the $β$ decay of accelerated $r$-process nuclei. We find that the HE neutrino fluxes from sGRBs, mainly produced via photomeson interactions, are significantly limited to preserve the accelerated heavy nuclei, leading to lower fluxes than the predictions without allowing for contributions to UHECRs. Our results suggest that sGRBs may potentially contribute to UHECRs during the PR phase and to HE neutrinos during the EE phase$-$a scenario that can be tested by future neutrino observatories.