Proton Acceleration by Collisionless Shocks in Supermassive Black Hole Coronae: Implications for High-Energy Neutrinos

Recent observations by the IceCube Neutrino Observatory have revealed a significant excess of high-energy neutrinos from nearby Seyfert galaxies, such as NGC~1068, without a corresponding flux of high-energy gamma-rays. This suggests that neutrinos are produced via hadronic interactions in a region opaque to gamma-rays, likely a hot corona surrounding the central supermassive black hole. However, the mechanism responsible for accelerating the parent protons to the required energies ($\sim 100$ TeV) remains an open question. In this study, we investigate diffusive shock acceleration (DSA) in active galactic nucleus (AGN) coronae using a suite of one-dimensional Particle-in-cell (PIC) simulations spanning a broad range of plasma parameters. We find that DSA is a robust and efficient mechanism for proton acceleration, consistently channeling approximately 10\% of the shock's kinetic energy into non-thermal ions, even for shocks with sonic Mach number as low as $ M_s \approx 2$. In contrast, the efficiency of electron acceleration is highly variable and less efficient ($