Coupled time-dependent proton acceleration and leptonic-hadronic radiation in turbulent supermassive black hole coronae

Turbulent coronae of supermassive black holes can accelerate nonthermal particles to high energies and produce observable radiation, but capturing this process is challenging due to comparable timescales of acceleration, cooling, and the development of cascades. We present a time-dependent numerical framework that self-consistently couples proton acceleration—modeled by the Fokker-Planck equation—with leptonic-hadronic radiation. For the neutrino-emitting Seyfert galaxy NGC 1068, we reproduce the neutrino spectrum observed by IceCube while satisfying gamma-ray constraints. We also consider a transient corona scenario, potentially emerging in tidal disruption events like AT 2019dsg, and show that cascade feedback on proton cooling can impact proton acceleration and radiation processes in weaker coronae, producing delayed optical or ultraviolet, x-ray, and neutrino emissions of O ( 100 d ) . This flexible tool efficiently models multimessenger signals from both steady and transient astrophysical sources, providing insights in combining particle acceleration and radiation mechanisms.