Intergalactic Magnetic Field and Arrival Direction of Ultra-High-Energy Protons

💡 Research Summary

The paper investigates how the intergalactic magnetic field (IGMF) influences the propagation of ultra‑high‑energy (UHE) protons that originate within the local GZK sphere (≈100 Mpc). Using a cosmological structure‑formation simulation that includes magnetohydrodynamics, the authors construct a realistic IGMF model in which magnetic fields are amplified in filaments and galaxy clusters, reaching typical strengths of a few nanogauss in voids and up to tens of nanogauss in dense structures.

Within this simulated universe they place three key components: (1) a set of hypothetical UHECR sources that mimic the spatial distribution of active galactic nuclei (AGNs), (2) a number of virtual observers placed in environments analogous to the Milky Way’s location (i.e., near a filament or the outskirts of a cluster), and (3) a catalog of “reference objects” that serve as the observational analogues of AGNs used in real correlation studies. Each source emits 10⁴ protons with energies above the GZK threshold (≈5 × 10¹⁹ eV). The protons are propagated through the magnetized cosmic web under the Lorentz force, while undergoing energy losses due to photopion production, Bethe–Heitler pair production, and cosmological redshift.

Two angular quantities are then measured for every simulated event that reaches an observer: the deflection angle θ between the arrival direction and the true source position, and the separation angle S between the arrival direction and the nearest reference object on the sky. The statistical results are striking. The mean deflection angle is ⟨θ⟩ ≈ 15°, with a median of 7–10°, indicating that the IGMF can substantially scramble the original arrival direction of super‑GZK protons. In contrast, the mean separation angle to the closest reference object is ⟨S⟩ ≈ 3.5–4°, essentially comparable to the average angular distance between neighboring reference objects themselves. Consequently, the probability that the nearest AGN is the actual source of a given event is low; the simulation shows that fewer than one‑third of the events have their true source coincident with the closest AGN.

The authors interpret these findings as a direct consequence of the fact that sources, observers, reference objects, and the IGMF all trace the underlying matter distribution. Because magnetic fields are strongest where matter is concentrated, UHE protons tend to travel along filaments and cluster outskirts, bringing them into the vicinity of many potential AGN candidates. Hence a small angular separation between an observed UHECR and an AGN does not guarantee a physical association.

A parameter‑sensitivity study is also performed. Doubling the overall magnetic field strength raises the average deflection angle to >20°, while halving it reduces ⟨θ⟩ to <10°. The separation‑angle distribution, however, remains largely unchanged, demonstrating that S is relatively insensitive to the absolute field strength and is driven mainly by the spatial clustering of sources and reference objects.

The paper concludes with several implications for real‑world UHECR‑AGN correlation analyses. First, simple nearest‑neighbor tests may overestimate the significance of any apparent alignment. Second, future studies should incorporate multi‑parameter models that include particle composition (protons vs. heavier nuclei), detailed IGMF coherence lengths, and anisotropic filamentary structures. Third, statistical methods that assign probabilities to all candidate sources rather than selecting a single nearest object are recommended.

Overall, the work provides a compelling demonstration that the intergalactic magnetic field can produce large deflections for super‑GZK protons while simultaneously preserving a small apparent angular proximity to unrelated AGNs. This dual effect cautions against straightforward interpretations of current correlation results and underscores the need for more sophisticated modeling of both magnetic fields and source distributions in the quest to identify the origins of the highest‑energy cosmic rays.