Auger searches cosmic-ray directions for patterns at different scales

Ultra-high-energy cosmic rays are extremely energetic particles detected through the showers of secondary particles they create in Earth’s atmosphere. Their arrival directions may help reveal where they came from, but a pattern on the sky is not, by itself, proof of a particular source.

In a Pierre Auger Collaboration preprint prepared for submission to JCAP, researchers analyze surface-detector data collected from 2004 through 2022. They consider events above 4 exaelectronvolts (EeV), where 1 EeV equals 10¹⁸ electronvolts. The reported total exposure is 123,000 km² sr yr: square kilometres multiplied by steradians (a measure of solid angle) and years. The paper’s submission note does not establish whether the work has been peer reviewed.

One framework for different-sized patterns

The researchers ask whether the arrival directions depart from what would be expected for an isotropic sky—that is, one with no preferred direction, accounting for the Observatory’s directional exposure. They model a possible excess with a von Mises–Fisher distribution, a mathematical profile defined on a sphere. By varying its concentration and position, they can test broad patterns as well as more localized excesses within the same framework.

The analysis uses standard energy bins and additional overlapping, or “sliding,” energy intervals. For each tested concentration, the team compares the strongest result in the data with results from 10,000 isotropic simulations. The paper’s isotropic probabilities are defined at a fixed concentration parameter, κ. They are not a single global probability corrected across the full scan of angular scales and energy intervals. When no simulation reaches a data result, the authors estimate the probability by extrapolating with a chi-squared distribution. These details matter when interpreting how unusual a feature is.

A broad pattern leads the results

In the standard energy bins, the most significant excess is a dipole-like modulation in the 8–16 EeV range. Its amplitude and direction are reported as compatible with earlier Pierre Auger findings. Broad excesses are also the most significant patterns in the standard bins above 8 EeV, and the fitted dipole amplitude increases with energy, consistent with the trend described in previous analyses.

At higher energies, the researchers report indications of an additional, more concentrated excess in the Centaurus region. In the standard bin above 32 EeV, this intermediate-scale feature appears alongside the broad modulation; its fitted Gaussian-equivalent width is about 16 degrees. In the overlapping-bin analysis, an intermediate-scale excess is also reported for 32–64 EeV. Above 40 EeV, it is the most significant configuration in that bin. Thus, which scale gives the strongest result depends on the chosen energy interval.

The team conducted a further simulation study focused specifically on the above-32 EeV bin. They modeled the broad excess and asked how often simulations would also produce an intermediate-scale excess meeting specified criteria: an isotropic probability below 6.1 × 10⁻³ and sufficient angular separation from the broad excess. They also tested the converse, modeling the intermediate-scale feature and checking for a sufficiently significant, separated broad excess. The authors report no evidence in these tests that either observed feature is simply a statistical fluctuation of the other. This is a result of that particular simulation procedure—not a general test of whether the patterns have physically independent origins.

What the patterns do—and do not—tell us

The Centaurus-region indication does not establish that Centaurus A, or any other named object, produced the particles. The authors discuss possible explanations, including contributions from a nearby dominant source together with more distant sources, or different cosmic-ray particle charges contributing to different patterns. These remain possibilities, not conclusions of the analysis. The paper suggests that future composition measurements, including those from AugerPrime, could help investigate them.

The authors also state that their analysis omits small time-dependent variations in array exposure and the effect of the array’s tilt; they estimate these would have minimal impact on the dipole amplitude. More broadly, the results depend on the model, energy intervals, and statistical tests used. The findings support a broad pattern compatible with previous Auger results and indications of a Centaurus-region excess at intermediate angular scales at high energies. They do not settle the origin of the cosmic rays. This account is based on the cited arXiv preprint, whose publication and peer-review status should be checked separately.