The all-particle cosmic-ray energy spectrum steepens at the knee, measured by LHAASO-KM2A at 3.67 ± 0.05 ± 0.15 PeV with a spectral-index change of about 0.39, accompanied by a mean logarithmic mass that falls to near helium and then rises. The 2024 measurement suggested, but could not prove, that the knee is a light-component cutoff, and identified the decomposition of the all-particle spectrum into single-element or narrow-group spectra as its outstanding task. Subsequent LHAASO hybrid measurements (2025–2026) directly measured the proton spectrum (0.15–12 PeV, knee near 3.3 PeV) and the helium spectrum (0.16–13 PeV, knee near 7 PeV), largely establishing the light-component interpretation. The surviving problem is to complete the decomposition: measure the heavy-group spectra (CNO, Mg–Al–Si, and Fe — the carbon–nitrogen–oxygen, magnesium–aluminium–silicon, and iron mass groups) across the knee with comparable precision and quantified hadronic-model dependence, demonstrate closure of the full set of group spectra on the all-particle flux and mean logarithmic mass, and determine which physical scenario — rigidity-dependent source cutoffs with population spread, a change in propagation, or the emergence of a new PeV component — accounts for the knee's position, sharpness, and index change.

Background

Cosmic rays are relativistic atomic nuclei (and electrons) arriving at Earth from astrophysical sources; their combined flux as a function of energy per nucleus is the all-particle energy spectrum. Above ~10^14 eV the flux is too low for direct detection by instruments on satellites or balloons, so it is measured indirectly: a primary nucleus strikes the atmosphere and triggers an extensive air shower (EAS), a cascade of secondary particles, whose electrons/photons and muons at ground level and Cherenkov light emitted along the shower front sample the primary's energy and mass. LHAASO (Large High Altitude Air Shower Observatory), at 4410 m in Sichuan, China, includes KM2A (a square-kilometer array of electromagnetic-particle and muon detectors) and WFCTA (a wide-field Cherenkov telescope array); operating both together ('hybrid' mode) adds a measurement of the shower-development profile that enables event-by-event discrimination of the primary's mass group. Interpreting shower observables requires high-energy hadronic interaction models such as EPOS-LHC, QGSJETII-04, and SIBYLL-2.3d — simulation codes for nucleus–nucleus collisions at energies beyond accelerator fixed-target reach — whose residual differences propagate into composition inferences. A standard composition summary is the mean logarithmic mass ⟨ln⁡A⟩\langle\ln A\rangle, where AA is the primary mass number (1 for protons, 4 for helium, 56 for iron). The most prominent feature of the all-particle spectrum is the knee, a steepening from index ~ −2.74 to ~ −3.13 discovered in 1958; whether it marks the maximum energy of Galactic accelerators (supernova remnants and other 'PeVatrons', sources reaching peta-electronvolt energies), a change in cosmic-ray propagation, or the transition between source populations has remained unsettled for over six decades. LHAASO-KM2A (Phys. Rev. Lett. 132, 131002 (2024)) measured the all-particle spectrum and ⟨ln⁡A⟩\langle\ln A\rangle from 0.3 to 30 PeV using a composition-insensitive energy estimator, and found ⟨ln⁡A⟩\langle\ln A\rangle decreasing toward helium below the knee and rising above it, suggesting the first cutoff is due to light components — but with ~6% model-driven variation in ⟨ln⁡A⟩\langle\ln A\rangle and no elemental decomposition. In 2025–2026, LHAASO hybrid KM2A+WFCTA measurements delivered high-purity proton (0.15–12 PeV) and helium (0.16–13 PeV) spectra, revealing a proton knee at ~3.3 PeV and a helium knee at ~7 PeV, and refuting the hypothesis that protons are only accelerated to ~0.1 PeV so that the knee must be heavy-nucleus dominated. The spectra of the heavy mass groups — CNO (carbon–nitrogen–oxygen), Mg–Al–Si (magnesium–aluminium–silicon), and Fe (iron) — across the knee remain unmeasured at comparable precision, and the astrophysical interpretation of the observed structures is described in the newest primary literature as 'a very open problem'.

Problem Statement

Complete the elemental decomposition of the cosmic-ray spectrum across the knee and use it to determine the physical origin of the knee. Concretely, with the proton spectrum (0.15–12 PeV, knee ≈ 3.3 PeV) and helium spectrum (0.16–13 PeV, knee ≈ 7 PeV) now measured by LHAASO: (i) determine the energy spectra of the remaining heavy mass groups — at minimum the CNO (carbon–nitrogen–oxygen), Mg–Al–Si (magnesium–aluminium–silicon), and Fe (iron) groups — across the knee region (approximately 0.3–30 PeV, or the sub-range a stated technique validly covers), with statistical and systematic precision, and quantified hadronic-interaction-model dependence, comparable to the published proton and helium measurements; (ii) demonstrate quantitative closure of the decomposition: the sum of the group spectra must reproduce the measured all-particle energy spectrum, and the flux-weighted ⟨ln⁡A⟩\langle\ln A\rangle computed from the group spectra must reproduce the measured mean logarithmic mass, within stated uncertainties across the measured range; and (iii) establish whether the measured light-component cutoffs quantitatively account for the position, sharpness, and spectral-index change of the all-particle knee at 3.67 PeV, and determine which physical scenario the complete decomposition supports — rigidity-dependent source cutoffs (each nuclear species is accelerated only up to a maximum rigidity, the momentum per unit charge, so heavier nuclei cut off at proportionally higher energies; including the effect of source-to-source spread in that maximum), a change in propagation, the emergence of a new PeV component, or significant heavy-group contributions — ranking the scenarios by their discriminating observables, and support the attribution with at least one falsifiable observable that discriminates the supported scenario from the principal alternative (such as a predicted anisotropy or a secondary gamma-ray or neutrino signature).

References

  1. LHAASO Collaboration (Z. Cao, F. Aharonian, et al.), "Measurements of All-Particle Energy Spectrum and Mean Logarithmic Mass of Cosmic Rays from 0.3 to 30 PeV with LHAASO-KM2A", Physical Review Letters 132, 131002 (2024). DOI: 10.1103/PhysRevLett.132.131002; arXiv:2403.10010; https://arxiv.org/abs/2403.10010
  2. LHAASO Collaboration (Z. Cao, F. Aharonian, et al.), "Precise measurements of the cosmic ray proton energy spectrum in the "knee" region", Science Bulletin 70, 4173-4180 (2025). DOI: 10.1016/j.scib.2025.10.048; arXiv:2505.14447; https://arxiv.org/abs/2505.14447
  3. LHAASO Collaboration (Z. Cao, F. Aharonian, et al.), "Precise Measurement of the Cosmic Ray Helium Spectrum above 0.1 PeV", Physical Review Letters 136, 121001 (2026). DOI: 10.1103/d838-49gt; arXiv:2511.05013; https://arxiv.org/abs/2511.05013
  4. N. Arsene, "Cosmic-Ray Mass Composition around the Knee via Principal Component Analysis", The Astrophysical Journal 992, 135 (2025). DOI: 10.3847/1538-4357/ae09a9; arXiv:2507.01396; https://arxiv.org/abs/2507.01396
  5. H. He, H. Zhang, Q. Cheng, et al., "Unveiling the nature of the knee in the cosmic ray energy spectrum", preprint (2024). arXiv:2411.13793; https://arxiv.org/abs/2411.13793
  6. T. A. Dzhatdoev, A. A. Semenov, "Elemental cosmic ray spectra reveal two populations of Galactic sources and an immediate transition to an extragalactic component after the knee", preprint (2026). arXiv:2606.02748; https://arxiv.org/abs/2606.02748
  7. C. Evoli, "A Population View of the Cosmic-Ray Knee: The Role of Variance in Supernova Maximum Rigidities", Physics and the Cosmos (2026). DOI: 10.53941/pac.2026.100008; arXiv:2608.15892; https://arxiv.org/abs/2608.15892
  8. J. Zhao, J. Liu, "A new method for detecting heavy cosmic ray component above the knee region", Astroparticle Physics 175, 103180 (2026). DOI: 10.1016/j.astropartphys.2025.103180; https://doi.org/10.1016/j.astropartphys.2025.103180