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Insights on the mass composition of ultrahigh-energy cosmic rays from small-scale anisotropy with large-scale structure simulations

Ryo Higuchi

Eiji Kido

Shigehiro Nagataki

  • Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan and Astrophysical Big Bang Laboratory (ABBL), RIKEN Pioneering Research Institute (PRI), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

  • Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan, Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China, and Astrophysical Big Bang Laboratory (ABBL), RIKEN Pioneering Research Institute (PRI), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

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Phys. Rev. D 114, 083040 – Published 22 October, 2026

DOI: https://doi.org/10.1103/llkm-59qr

Abstract

Ultrahigh-energy cosmic rays (UHECRs) with energies above 100 EeV provide important clues to the most energetic processes in the Universe. At the highest energies, it is expected that UHECRs originate only from nearby sources because of energy losses during propagation. In such a regime, small-scale anisotropies in arrival directions could appear if the magnetic deflections in cosmic magnetic fields are sufficiently small, for example, for a limited fraction of UHECRs with relatively low electric charge. Using the Pierre Auger Observatory open data, we confirm that for events with energies above 100 EeV, there is no significant small-scale anisotropy within 3°, indicating an almost isotropic sky distribution. To interpret this observation, we consider that heavier nuclei have higher photodisintegration thresholds due to their smaller Lorentz factors, resulting in longer propagation lengths. When combined with the nearly homogeneous distribution of galaxies at such distances, this can naturally explain the absence of anisotropies even above 100 EeV. Based on this idea, we perform mock observations of UHECRs above 100 EeV assuming pure-proton, iron, and uranium compositions. We predict the expected UHECR distributions using the Millennium Run semianalytic galaxy catalog and turbulent extragalactic magnetic fields. By varying the source density ρsource and magnetic field strength α, we evaluate the anisotropy for each case. Without magnetic fields, the observed isotropy above 100 EeV excludes the pure-proton and pure-iron cases. The pure-uranium case can reproduce the observed isotropy when the source density is high and the magnetic field is turbulent. When the turbulent field is strong, both the iron and uranium cases remain consistent with the data, whereas almost no parameter set can explain the observation for a pure-proton composition. Our results constrain the possible combinations of source density and magnetic field strength across different UHECR compositions and provide a framework for interpreting future anisotropy measurements at the highest energies.

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Phys. Rev. D 114, 083040– Published 22 October, 2026
  • Received 20 November 2025
  • Accepted 22 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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