The contribution of distant sources to the observed flux of ultra high-energy cosmic rays

TL;DR

This paper investigates how distant sources contribute to the observed ultra-high-energy cosmic ray flux, considering heavy nuclei and source evolution, revealing a significant isotropic component from beyond the GZK horizon.

Contribution

It demonstrates that distant sources can significantly contribute to UHE CRs, especially with heavy nuclei and evolving source populations, altering the expected flux composition.

Findings

Distant sources beyond the GZK horizon can contribute to UHE CRs.

Heavy nuclear CRs extend the effective horizon for cosmic rays.

An isotropic flux component naturally emerges from distant sources.

Abstract

Ultra-high-energy (UHE) cosmic rays (CRs) interact with cosmic background radiation through hadronic processes, and the Universe would become `opaque' to UHE CRs of energies $\sim$($10^{18}$- $10^{20}$) eV over about several tens of Mpc, setting the Greisen-Zatsepin-Kuz'min (GZK) horizon. We demonstrate that a non-negligible fraction of the UHE CRs arriving on Earth could originate from beyond the GZK horizon when heavy nuclear CRs, and the population and evolution of UHE CR sources are taken into account. We show how the multi-particle CR horizon is modified by different source populations, and discuss how this leads to the natural emergence of an isotropic flux component in the observed UHE CR background. This component would coexist with an anisotropic foreground component contributed by nearby sources within the GZK horizon.