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On the astrophysical origin of cosmic rays: Constraining the Ultra-High-Energy Cosmic Ray Horizon through Nearby Galaxy Distributions

By comparing Pierre Auger Observatory data with nearby galaxy distributions while accounting for Galactic magnetic deflections, this study demonstrates that the observed anisotropy of ultra-high-energy cosmic rays above 8 EeV is primarily driven by sources within approximately 50–60 Mpc.

Original authors: F. Dávila-Kurbán, F. Duplancic, D. Garcia Lambas

Published 2026-07-27

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CC BY 4.0

Original authors: F. Dávila-Kurbán, F. Duplancic, D. Garcia Lambas

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, chaotic pinball machine. Instead of metal balls, the table is filled with invisible, high-speed particles called cosmic rays. These aren't your average dust motes; they are atomic nuclei traveling at nearly the speed of light, carrying enough energy to power a city for a day in a single, tiny particle. Scientists call the most energetic ones "Ultra-High-Energy Cosmic Rays" (UHECRs). The big mystery is: where do they come from? Are they born in our own Milky Way galaxy, or do they travel from distant, violent events in the deep cosmos?

The problem is that these particles are terrible at keeping a straight line. As they zoom through space, they get bumped and pushed by invisible magnetic fields, much like a hiker trying to walk in a straight line through a dense, swirling fog. This makes it nearly impossible to look at where a particle hits Earth and simply draw a line back to its home. However, there is a rule of the universe called the "GZK limit." Think of it as a cosmic speed bump. If these particles travel too far (more than a few hundred million light-years), they crash into background light and lose their energy. This means that if we see a super-fast particle, it must have come from a relatively nearby neighborhood, not from the far edges of the universe. The big question for scientists is: just how "nearby" is nearby? Is it the whole local group of galaxies, or just the ones right next door?

This paper sets out to solve that specific puzzle by playing a game of "connect the dots" between the sky and the ground. The researchers took a map of the most energetic cosmic rays hitting Earth and compared it to a massive catalog of nearby galaxies. They wanted to see if the cosmic rays were pointing toward specific clusters of galaxies, and if so, how far away those galaxies could be before the connection disappeared.

The team used a clever trick to handle the "fog" of magnetic fields. They knew that the Milky Way's magnetic field acts like a giant, invisible lens that bends the paths of these particles. So, they didn't just look at the raw data; they simulated how the magnetic field would twist the paths of particles coming from different directions. They then weighted their galaxy data, giving more importance to galaxies in areas where the magnetic field is less likely to scramble the signal.

Here is what they found: The cosmic rays are definitely pointing toward a specific direction in the sky, and that direction lines up best with the distribution of galaxies that are very close to us. Specifically, the connection is strongest for galaxies within a distance of about 60 million parsecs (or roughly 200 million light-years, corresponding to a speed of 4,000 km/s). When they looked at galaxies further away than this "horizon," the cosmic rays stopped pointing in their direction. The signal from distant galaxies faded away, suggesting that the super-fast particles we see today are almost entirely generated by sources in our immediate cosmic neighborhood.

The study also confirmed that the magnetic fields of our galaxy play a huge role. When the researchers accounted for how the Milky Way's magnetic field bends the particles, the link between the cosmic rays and the nearby galaxies became more than twice as strong. This suggests that while the magnetic fields scramble the signal, they don't destroy it entirely; the "fingerprint" of the nearby universe is still clearly visible if you know how to look for it.

In short, the paper suggests that the most energetic particles in the universe are local celebrities. They aren't traveling from the farthest reaches of the cosmos; they are likely being born in the violent engines of galaxies just a few hundred million light-years away. The universe has a "local horizon" for these particles, and thanks to this study, we have a much better idea of where to look for their origins.

Technical Summary: Constraining the Ultra-High-Energy Cosmic Ray Horizon through Nearby Galaxy Distributions

Problem Statement
The origin of Ultra-High-Energy Cosmic Rays (UHECRs) with energies $E \ge 8$ EeV remains a central open problem in astroparticle physics. While observational evidence suggests an extragalactic origin, tracking these particles to their sources is complicated by significant deflections from Galactic and extragalactic magnetic fields. Furthermore, the Greisen–Zatsepin–Kuzmin (GZK) effect imposes an energy-dependent horizon, limiting the propagation distance of UHECRs. Although a large-scale dipolar anisotropy in UHECR arrival directions has been detected by the Pierre Auger Observatory, the effective spatial scale over which the local large-scale structure contributes to this anisotropy is poorly constrained. Current studies often suffer from observational biases, such as magnitude limits in galaxy catalogues that underrepresent faint galaxies at greater distances, potentially obscuring the true relationship between UHECRs and their source distributions.

Methodology
This work employs a multi-faceted statistical approach to constrain the UHECR propagation horizon by correlating UHECR arrival directions with the distribution of nearby galaxies.

Data Selection:
- UHECR Data: The study utilizes all-sky flux maps from the Pierre Auger Observatory for energies $E \ge 8$ EeV, covering approximately 85% of the celestial sphere ( $-90^\circ < \delta < 45^\circ$ ).
- Galaxy Catalogue: The analysis uses the GLADE+ catalogue, a homogenized, all-sky compilation of $\sim 23$ million sources. To mitigate distance- and luminosity-dependent selection biases, a Volume-Limited Sample (GLADE+VLS) was constructed. This sample includes galaxies with an absolute B-band magnitude $M_B < -18$ within a radial velocity range of $1200 < cz < 10000$ km s $^{-1}$ (corresponding to luminosity distances of $\sim 18$ to $150$ Mpc). The sample excludes the Galactic plane (Zone of Avoidance) and regions with declinations $> 45^\circ$ to match the Auger sky coverage.
Dipole Analysis:
- The authors performed a Rayleigh analysis on the right ascension of the galaxy samples to calculate the dipole amplitude and phase.
- This was conducted in successive radial velocity slices to investigate the evolution of the galaxy dipole relative to the UHECR dipole reported by the Auger Collaboration.
Angular Cross-Correlation:
- An angular cross-correlation function, $w(\theta)$ , was calculated between the discrete galaxy positions and the continuous Auger flux map using the TreeCorr estimator.
- The analysis was stratified by distance, dividing the GLADE+VLS into three bins: $1200-4000$, $4000-7000$, and $7000-10000$ km s $^{-1}$ .
Magnetic Deflection Modeling:
- To account for the smearing of UHECR trajectories by the Galactic Magnetic Field (GMF), the study employed the Unger & Farrar (2024) GMF model.
- Backtracking simulations were performed using the CRPropa 3 framework for a representative rigidity of $R = 5$ EV (covering light-to-intermediate mass nuclei).
- A weighting scheme was applied to the cross-correlation estimator, where each galaxy was weighted by the inverse of the squared angular deflection area ( $w_i \propto \theta_i^{-2}$ ) predicted by the GMF model. This effectively down-weights sources in regions of high magnetic distortion.
- Robustness checks were performed using alternative rigidities ( $R=2, 8$ EV) and alternative GMF models (JF12, KST24).

Key Results

Dipole Alignment: The angular separation between the galaxy dipole and the Auger UHECR dipole is minimized for the nearest galaxy population ( $cz \lesssim 4000$ km s $^{-1}$ , or $\lesssim 60$ Mpc). In this range, the galaxy dipole amplitude is also maximal. As the distance increases beyond this threshold, the dipole alignment weakens significantly, and the amplitude decreases.
Distance Dependence of Correlation: The angular cross-correlation signal between galaxies and UHECRs is dominated by the nearest galaxy bin ($cz < 4000$ km s $^{-1}$ ). The correlation amplitude drops rapidly for intermediate and distant bins, indicating that the observed anisotropy is driven primarily by the local large-scale structure.
Impact of Magnetic Deflections: Incorporating GMF deflection weights into the correlation analysis enhances the correlation amplitude by more than a factor of two compared to the unweighted case. This suggests that magnetic deflections play a critical role in shaping the observed anisotropy and that correcting for them reveals a stronger underlying physical association between UHECRs and nearby matter.
Robustness: The results remain consistent across different rigidity values ( $R=2, 5, 8$ EV) and different GMF models (UF23, JF12, KST24), confirming that the enhancement of the correlation signal is a robust feature of the analysis.

Significance and Conclusions
The paper concludes that the large-scale anisotropy of UHECRs with $E \ge 8$ EeV is primarily driven by sources within a characteristic distance of $\sim 50-60$ Mpc. This scale is consistent with theoretical expectations derived from GZK energy losses and magnetic deflections.

The study demonstrates that the observed UHECR anisotropy retains a measurable imprint of the nearby extragalactic matter distribution. By utilizing volume-limited galaxy samples and accounting for Galactic magnetic deflections, the authors provide an observational determination of the effective UHECR source horizon. The findings reinforce the interpretation that the UHECR flux suppression and anisotropy are linked to the local Universe, rather than being solely intrinsic properties of the sources or effects of distant propagation. The work establishes a framework for future studies to further constrain the astrophysical nature of UHECR progenitors by applying similar cross-correlation techniques to specific galaxy populations.

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