SIMBAD references

Ultra-high-energy (UHE) cosmic rays (CRs) of energies ∼(10¹⁸-10²⁰) eV, accelerated in violent astrophysical environments, interact with cosmic background radiation fields via photo-hadronic processes, leading to strong attenuation. Typically, the Universe would become "opaque" to UHE CRs after several tens of megaparsecs, setting the boundary of the Greisen-Zatsepin-Kuz'min (GZK) horizon. In this work, we investigate the contribution of sources beyond the conventional GZK horizon to the UHE CR flux observed on Earth, when photospallation of the heavy nuclear CRs is taken into account. We demonstrate that this contribution is substantial, despite the strong attenuation of UHE CRs. A significant consequence is the emergence of an isotropic background component in the observed flux of UHE CRs, coexisting with the anisotropic foreground component that is associated with nearby sources. Multi-particle CR horizons, which evolve over redshift, are determined by the CR nuclear composition. Thus, they are dependent on the source populations and source evolutionary histories.