Ultra-High-energy Cosmic Rays from beyond the Greisen–Zatsepin–Kuz’min Horizon

Abstract

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.

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

“…Figure 3 shows the UHE CR spectrum at 𝑧 = 0 in the case of the four source population models in the left panel. Data obtained by the Pierre Auger Observatory [20] are included for comparison (for more detailed comparisons with data, see [8]). In the right panel of Figure 3, the fractional contribution from sources above a given redshift, 𝑓 CR (> 𝑧), for the four source models is shown.…”

“…The CMB permeates the Universe and provides a strong target field to drive the interactions described in section 2.1. Additionally, the EBL can also act to attenuate more massive UHE CRs with energies slightly lower than those principally affected by the CMBs [8,18]. The EBL is comprised of radiation emitted from astrophysical objects [for an overview, see 19].…”

Effects of large-scale magnetic fields on the observed composition of ultrahigh-energy cosmic rays

“…We consider four UHE CR source population models, specified over a redshift range from z min ¼ 0 to z max ¼ 3. For each model, the source number density in redshift space, composition, and injected CR energy spectra follows the same parametrization as in [11]. We summarize the source population models and the corresponding parametrizations as follows.…”

“…UHE CRs could originate from more distant source populations located beyond their photopion horizon (e.g., [10,11]). Their residual "background" contribution can be used to study possible source population distributions over redshift because the cumulative effect of photospallation as the CR ensemble propagates modifies its arrival composition on Earth.…”

“…It is also the first to assess the effects of an inhomogeneous IGMF on CR propagation and whether or not it can unambiguously be discerned in the observed CR spectrum and composition on Earth. The assumptions and methodology in our previous work [11] 4 are adopted here, with, in addition, the treatment of the effects brought about by IGMFs.…”