Probing UHECR sources - Constraints from cosmic-ray measurements

TL;DR

The paper addresses the origin of ultra-high-energy cosmic rays (UHECRs) by synthesizing spectrum, composition, and arrival-direction data from Auger and TA with improved Galactic and extragalactic magnetic-field models, focusing on features around the ankle at $10^{18.7}$ eV. A joint modeling framework ties source emission to a hard, mixed-composition injection with a Peters-cycle-like cutoff and explores mild source evolution and potential multiple extragalactic populations. Key findings favor an extragalactic, relatively dense source population with a roughly universal maximum rigidity, and they show that large-scale anisotropies, Cen A and SBG/AGN correlations, and very-high-energy events can be accommodated only within specific GMF/EGMF assumptions. The results constrain viable UHECR source classes, and point to a path forward with next-generation experiments and multi-messenger probes to resolve remaining questions.

Abstract

Ultra-high-energy cosmic rays (UHECRs) are the most energetic particles known - and yet their origin is still an open question. However, with the precision and accumulated statistics of the Pierre Auger Observatory and the Telescope Array, in combination with advancements in theory and modeling - e.g. of the Galactic magnetic field - it is now possible to set solid constraints on the sources of UHECRs. The spectrum and composition measurements above the ankle can be well described by a population of extragalactic, homogeneously distributed sources emitting mostly intermediate-mass nuclei. Using additionally the observed anisotropy in the arrival directions, namely the large-scale dipole >8 EeV as well as smaller-scale warmspots at higher energies, even more powerful constraints on the density and distribution of sources can be placed. Yet, open questions remain - like the striking similarity of the sources that is necessary to describe the rather pure mass composition above the ankle, or the origin of the highest energy events whose tracked back directions point towards voids. The current findings and possible interpretation of UHECR data will be presented in this review.

Figures (10)

• Figure 1: Measured (black markers) and modeled (colors) energy spectrum at Earth. Left for the "UFA"-model unger_origin_2015 with one Galactic (dashed) and one extragalactic mixed source population considering also in-source interactions. Right for a model with two extragalactic mixed populations without in-source interactions from the_pierre_auger_collaboration_a_abdul_halim_constraining_2023, where the bands indicate the size of the systematic uncertainties.
• Figure 2: Impact of the GMF on UHECRs, for details see text.
• Figure 3: Left: amplitude of the dipole moment as measured by Auger only abdul_halim_large-scale_2024 (red markers) and by the combined working group of Auger and TA rubtsov_update_2025 (blue markers). Right: angular power spectrum from the combined Auger+TA data set for the integrated bin corresponding to $E>8.53\,\mathrm{EeV}$ for Auger and $E>10\,\mathrm{EeV}$ for TA. The hatched region (red dashed line) corresponds to the gray solid region (red solid line) but neglecting the systematic uncertainty from the energy scale calibration. Only the dipole deviates from isotropic expectations. Both figures from rubtsov_update_2025.
• Figure 4: Measured dipole directions (left) and flux predicted for UHECR sources following the LSS (right).
• Figure 5: Contributions to the flux of different element groups and different distances for two energy thresholds, left for $E>8\,\mathrm{EeV}$ and right for $E>32\,\mathrm{EeV}$ predicted by the LSS-based model from bister_constraints_2024. The distances of dominant galaxy clusters are indicated at the top. Note that the plots have been split into the nearby (more anisotropic) part $<100\,\mathrm{Mpc}$, and the further away more isotropic part $>100\,\mathrm{Mpc}$, both displayed on linear scales.