Ultra high-energy cosmic rays from beyond the Greisen-Zatsepin-Kuz'min
  horizon
  Ultra-high-energy (UHE) cosmic rays (CRs) of energies $\sim
(10^{18}-10^{20})~{\rm eV}$, 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 Mpc, 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 photo-spallation of the heavy nuclear CRs is taken into
account. We demonstrate 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 are 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.
