Why ultra-high-energy cosmic rays may need metal-rich sources

Ultra-high-energy cosmic rays (UHECRs) are atomic nuclei with energies around or above 10¹⁸ electronvolts. Their mix of hydrogen, helium and heavier nuclei can help constrain where and how they are produced. But comparing that mix with lower-energy cosmic rays can mislead if the comparison is made at the same energy rather than at the same rigidity: a measure of how a charged particle responds to magnetic fields, determined by its energy divided by its electric charge.

Magnetic acceleration and confinement often depend on rigidity. A heavy nucleus and a proton at the same rigidity therefore have different energies. When their spectra have different slopes, comparing abundances at equal energy can understate the relative abundance of heavy nuclei. The authors argue that candidate source material should instead be compared at equal rigidity.

In this preprint, E. Podlesnyi, F. Oikonomou, D. Ehlert and M. Unger fit models to measurements from the Pierre Auger Observatory. They use the observed cosmic-ray energy spectrum and air-shower measurements, including the average depth at which a shower reaches its maximum and the spread in that depth. They also fit an inferred proton spectrum over a lower-energy range. To model changes during travel, they use CRPropa3 simulations that include energy losses and the breakup of heavier nuclei through interactions with background light.

The researchers infer the mix escaping the sources, then express abundances at a common rigidity. Their model includes five groups: hydrogen, helium, nitrogen-like nuclei, silicon-like nuclei and iron. They test different assumptions about how source populations change over cosmic time and check sensitivity to alternative models of particle interactions in air showers.

The analysis finds two broad types of fit. In one, much of the hydrogen detected at Earth is secondary: it comes from heavier nuclei breaking apart during intergalactic travel. In the other, primary hydrogen from the sources contributes alongside secondary protons. This second scenario allows the source hydrogen abundance to be comparable to that of Galactic cosmic rays. The available measurements and modeling uncertainties do not currently distinguish the two scenarios.

Both fits point to an excess of silicon- and iron-group nuclei compared with the Galactic cosmic-ray mixture used as a benchmark. Across the source-evolution scenarios considered, the authors report an inferred overall metal fraction at fixed rigidity at least about three times the Galactic value. In the more conservative fit, hydrogen and nitrogen-like abundances can be compatible with Galactic cosmic rays, while silicon and iron remain elevated. The paper reports that silicon abundance exceeds the Galactic value by more than an order of magnitude in the comparisons examined.

That finding does not identify the accelerators. The authors assess several proposed source models and find that, as published, none reproduces the full inferred composition. Some might be reconciled with it if additional processes—such as nuclei breaking apart inside sources—are included. The paper discusses possible contributions from stellar debris, white-dwarf disruptions and low-luminosity gamma-ray bursts, but leaves the origin of the heavy-element excess unresolved.

There are important caveats. Composition is inferred from air showers, not measured directly from the incoming nuclei. The inference depends on shower measurements and on models of high-energy particle interactions. The authors vary these assumptions and report that the heavy-element excess persists in the cases they test; that does not rule out every possible model or assumption. The comparison with Galactic cosmic rays also has uncertainty, and the analysis explores particular choices for source evolution and propagation. The authors note that other analyses of Auger data have not always required a silicon component.

This work is an arXiv preprint, so it should not be treated as established peer-reviewed consensus. The authors say the data are publicly available and that code to reproduce the results is planned for release upon manuscript acceptance. Future composition measurements and improved air-shower models could help distinguish the two fitted scenarios. For now, the study sharpens the puzzle: the modeled source material appears richer in heavy nuclei than Galactic cosmic rays, but what supplies that excess remains an open question.