Multi-messenger constraints on transient accelerators of ultra-high energy cosmic rays

Abstract: The origin of ultra-high-energy cosmic rays (UHECRs) remains an open questions in astrophysics. We explore two primary scenarios for the distribution of UHECR sources, assuming that their production rate follows either the cosmic star-formation-rate or stellar-mass density. By jointly fitting the UHECR energy spectrum and mass composition measured by the Pierre Auger Observatory above the ankle (10^{18.7} eV), we derive constraints on the acceleration mechanisms, source energetics, and elemental abundances at escape. Using these constraints, we generate sky maps above 40 EeV based on a catalog of over 400,000 galaxies out to 350 Mpc, providing a near-infrared flux-limited sample that maps the two stellar-activity tracers across the full sky. A crucial factor in understanding UHECR propagation is the influence of large-scale cosmic structures, particularly galaxy clusters, the largest gravitationally bound systems in the Universe, which are filled with magnetized diffuse plasma. Intermittent sources hosted in galaxies within such structures, coupled with cosmic magnetic fields, shape the observed UHECR arrival directions and provide insights into the burst rate of the sources. We show that these environments can significantly impact UHECR transport, making them particularly opaque to heavy nuclei. Additionally, we compute the expected secondary neutrino and photon fluxes from UHECR interactions in these environments and compare them with current experimental limits, constraining the maximum energy that particles can achieve. Finally, we assess the compatibility of these constraints with astrophysical candidates, identifying long gamma-ray bursts as the most promising sources.