Radio measurements with the LOFAR telescope of the atmospheric depth of shower maximum, XmaxX_{\mathrm{max}}, of cosmic-ray air showers between 101710^{17} and 1017.510^{17.5} eV revealed a light-mass (proton-plus-helium) fraction of roughly 80%, far above what a single Galactic population with a rigidity-limited (momentum-per-unit-charge-limited) cutoff predicts at these energies and in conflict with the below-30% light fraction inferred by KASCADE-Grande from ground-level muon/electron ratios. The source paper (Buitink et al., Nature 531, 70 (2016)) left open the astrophysical origin of this component -- a second Galactic population from extreme accelerators (Wolf-Rayet star explosions into their stellar winds, past Galactic gamma-ray bursts, or reacceleration at the Galactic wind termination shock) versus an extragalactic component already significant below 1017.510^{17.5} eV -- together with the hadronic-interaction-model systematics that block identification of individual elemental abundances and the cross-observable composition discrepancy. A decade of follow-up has confirmed the light component with better-controlled systematics, quantified and largely removed the atmospheric-refractivity contribution, and codified the muon-modeling problem, but the origin question and the XmaxX_{\mathrm{max}}-versus-muon composition tension remain open.

Background

Cosmic rays are atomic nuclei (mostly protons and helium) accelerated by astrophysical sources, arriving at Earth with energies up to beyond 102010^{20} eV. The all-particle energy spectrum steepens at the 'knee' near 3×10153\times10^{15} eV, shows a further mild steepening called the 'second knee' near 101710^{17} eV, and hardens at the 'ankle' near 4×10184\times10^{18} eV. Galactic accelerators such as supernova remnants are generally held to supply the flux below the knee; where the Galactic component ends and an extragalactic component takes over -- somewhere between the second knee and the ankle -- is a central open question, because it determines what the ankle feature itself means and which sources are the most extreme particle accelerators the Galaxy contains.

A primary cosmic ray entering the atmosphere initiates a cascade of secondary particles, an extensive air shower. The standard mass-sensitive observable is the atmospheric depth of the shower maximum, XmaxX_{\mathrm{max}} (expressed in g/cm2^2 of atmosphere traversed): lighter primaries penetrate deeper on average, with the mean XmaxX_{\mathrm{max}} shifting approximately proportionally to ln⁡A\ln A for primary mass number AA. XmaxX_{\mathrm{max}} can be measured by imaging fluorescence or Cherenkov light along the shower, or by recording the radio emission -- produced mainly by the deflection of shower charged particles in Earth's magnetic field plus a negative charge excess in the shower front -- with antenna arrays and fitting the two-dimensional radio footprint with microscopic Monte Carlo simulations (the CoREAS plugin of the CORSIKA air-shower code). Alternatively, composition can be inferred without XmaxX_{\mathrm{max}} from the ratio of electrons to muons among particles reaching a ground detector array: heavier primaries yield relatively more muons. The radio method, pioneered with the LOFAR radio telescope in the Netherlands (triggered by its co-located particle-detector array LORA), achieves per-event XmaxX_{\mathrm{max}} resolutions of about 17-20 g/cm2^2 with nearly 100% duty cycle.

Interpreting any of these observables requires models of the hadronic interactions inside the shower, in a forward-production kinematic region not directly measured at accelerators. The post-LHC event generators QGSJETII.04, EPOS-LHC, and Sibyll 2.x differ in predicted mean XmaxX_{\mathrm{max}} by 15-20 g/cm2^2 -- the same size as the separation between neighboring light elements such as proton-deuterium or helium-beryllium -- so elemental fractions derived from XmaxX_{\mathrm{max}} carry an irreducible model dependence. On the muon side, simulations underpredict the number of muons measured at ground level (the 'muon puzzle', established by combined analyses of several air-shower experiments), so muon-based composition inferences are similarly model-biased.

If the knee is the cutoff of the ordinary Galactic population, scaled in rigidity (particle momentum per unit charge, so that each nucleus's spectrum cuts off at an energy proportional to its charge), that population should be iron-dominated by 101710^{17} eV. The LOFAR measurement instead found a mixed composition with a light fraction near 80% at 101710^{17}-1017.510^{17.5} eV. Such a component requires either a second, extremely energetic Galactic population -- candidates discussed in the source paper include explosions of Wolf-Rayet stars (hot, massive stars that shed their outer layers as dense stellar winds) into those winds, past Galactic gamma-ray bursts, and reacceleration at the termination shock of the Galactic wind (the shock where the Galaxy's outflowing hot plasma meets the intergalactic medium), collectively termed 'Galactic exatrons' -- or an extragalactic component already significant below 1017.510^{17.5} eV. The latter option would move the Galactic-to-extragalactic transition below the ankle and would require the ankle to arise from pair-production losses of extragalactic protons on the cosmic microwave background; this explanation strictly requires a proton-dominated flux and is therefore in tension with the measured light-element mixture, though not excluded. In apparent conflict with both LOFAR and Pierre Auger Observatory composition results, KASCADE-Grande reported from muon/electron ratios a light (proton+helium) fraction below 30% at 3×10173\times10^{17} eV, alongside an ankle-like hardening of the light-element spectrum at 1017.110^{17.1} eV.

Problem Statement

Identify the origin of the large light-mass component of cosmic rays at 101710^{17}-1017.510^{17.5} eV: determine whether the light component is (a) a second Galactic population produced by extreme accelerators -- Wolf-Rayet star explosions into their stellar winds, past Galactic gamma-ray bursts, or reacceleration at the Galactic wind termination shock -- or (b) an extragalactic component already significant below 1017.510^{17.5} eV; in case (b), establish the corresponding interpretation of the second knee and of the ankle.

Discriminants on which the candidate scenarios differ, as discussed in the literature, include elemental fractions (in particular the hydrogen-to-helium ratio), the energy dependence of the light fraction across the 101610^{16}-101810^{18} eV transition range, and the associated spectral features (the second knee near 101710^{17} eV and the light-element hardening at 1017.110^{17.1} eV); anisotropy constraints have also been considered.

The origin question is entangled with the composition measurements on which it relies. KASCADE-Grande inferred from muon/electron ratios a light (proton+helium) fraction below 30% at 3×10173\times10^{17} eV, and the source paper notes that inaccurate predictions of muon production or of mean XmaxX_{\mathrm{max}} can be the cause of this discrepancy. The XmaxX_{\mathrm{max}}-based light fraction is itself energy-window and model dependent: the 2016 LOFAR fit found roughly 80% proton-plus-helium in 101710^{17}-1017.510^{17.5} eV, while the updated four-element fit over the broader 1016.810^{16.8}-1018.310^{18.3} eV window gives 23-39% depending on the hadronic interaction model. A proposed origin must account for these composition measurements together with their hadronic-model systematics.

References

  1. S. Buitink et al. (LOFAR Collaboration), A large light-mass component of cosmic rays at 10^{17}-10^{17.5} electronvolts from radio observations, Nature 531, 70-73 (2016), doi:10.1038/nature16976, arXiv:1603.01594, https://arxiv.org/abs/1603.01594
  2. A. Corstanje et al. (LOFAR Collaboration), Depth of shower maximum and mass composition of cosmic rays from 50 PeV to 2 EeV measured with the LOFAR radio telescope, Phys. Rev. D 103, 102006 (2021), doi:10.1103/PhysRevD.103.102006, arXiv:2103.12549, https://arxiv.org/abs/2103.12549
  3. A. Corstanje et al., The effect of the atmospheric refractive index on the radio signal of extensive air showers, Astropart. Phys. 89, 23 (2017), doi:10.1016/j.astropartphys.2017.01.009, arXiv:1701.07338, https://arxiv.org/abs/1701.07338
  4. P. Mitra et al., Reconstructing air shower parameters with LOFAR using event specific GDAS atmosphere, Astropart. Phys. 123, 102470 (2020), doi:10.1016/j.astropartphys.2020.102470, arXiv:2006.02228, https://arxiv.org/abs/2006.02228
  5. S. Thoudam et al., Cosmic-ray energy spectrum and composition up to the ankle: the case for a second Galactic component, Astron. Astrophys. 595, A33 (2016), doi:10.1051/0004-6361/201628894, arXiv:1605.03111, https://arxiv.org/abs/1605.03111
  6. J. Albrecht et al., The Muon Puzzle in cosmic-ray induced air showers and its connection to the Large Hadron Collider, Astrophys. Space Sci. 367, 27 (2022), doi:10.1007/s10509-022-04054-5, arXiv:2105.06148, https://arxiv.org/abs/2105.06148
  7. W. D. Apel et al. (KASCADE-Grande Collaboration), Ankle-like Feature in the Energy Spectrum of Light Elements of Cosmic Rays Observed with KASCADE-Grande, Phys. Rev. D 87, 081101(R) (2013), doi:10.1103/PhysRevD.87.081101, arXiv:1304.7114, https://arxiv.org/abs/1304.7114
  8. A. Abdul Halim et al. (Pierre Auger Collaboration), Radio Measurements of the Depth of Air-Shower Maximum at the Pierre Auger Observatory, Phys. Rev. D 109, 022002 (2024), doi:10.1103/PhysRevD.109.022002, arXiv:2310.19966, https://arxiv.org/abs/2310.19966
  9. A. Abdul Halim et al. (Pierre Auger Collaboration), Demonstrating Agreement between Radio and Fluorescence Measurements of the Depth of Maximum of Extensive Air Showers at the Pierre Auger Observatory, Phys. Rev. Lett. 132, 021001 (2024), doi:10.1103/PhysRevLett.132.021001, arXiv:2310.19963, https://arxiv.org/abs/2310.19963
  10. A. Corstanje et al., Origins of Cosmic Rays in the Galactic-extragalactic Transition Energy Range (2026), arXiv:2606.27270, https://arxiv.org/abs/2606.27270
  11. S. Buitink et al., Anomalous Air Showers and What They Reveal About Hadronic Interactions and Cosmic-ray Masses (2026), arXiv:2607.00135, https://arxiv.org/abs/2607.00135