The KASCADE-Grande experiment: measurements of the all-particle energy spectrum of cosmic rays

The all-particle energy spectrum as measured by the KASCADE-Grande experiment for E = 10^{16} - 10^{18} eV is presented within the framework of the QGSJET II/FLUKA hadronic interaction models. Three different methods were applied based on the muon size and the total number of charged particles individually and in combination. From the study it is found that the spectrum cannot be completely described by a smooth power law due to the presence of characteristic features.

💡 Research Summary

The KASCADE‑Grande experiment, a large‑area ground‑based air‑shower detector operated between 2003 and 2013, has produced a high‑precision measurement of the all‑particle cosmic‑ray energy spectrum in the range 10¹⁶ to 10¹⁸ eV. Using a data set corresponding to an exposure of roughly 10⁸ m² sr yr, the authors applied three independent reconstruction techniques: (1) a traditional method based solely on the total number of charged particles (Nₑ), (2) a muon‑size‑only method (N_μ), and (3) a combined Nₑ–N_μ approach that exploits the correlation between the two observables. All three techniques were calibrated with extensive Monte‑Carlo simulations employing the QGSJET II‑04 high‑energy hadronic model together with the FLUKA 2011.2c.2 low‑energy model. Systematic uncertainties—including detector efficiency, atmospheric density variations, and model parameter ambiguities—were constrained to below 10 %.

The resulting spectrum deviates from a simple power‑law description. A modest steepening appears near 4 × 10¹⁶ eV (often referred to as a “mid‑knee”), followed by a pronounced hardening around 3 × 10¹⁷ eV, sometimes called a “second knee” or “ankle‑like” feature. These structures are consistently observed across all three reconstruction methods, indicating that they are not artifacts of a particular analysis or of the hadronic interaction model. The muon‑based reconstruction, despite its strong sensitivity to primary mass composition, yields a spectrum in close agreement with the Nₑ‑only and combined results, suggesting that the observed features are robust against composition‑related biases.

The authors discuss several possible interpretations. The mid‑knee could signal a transition from Galactic supernova‑remnant acceleration to a different Galactic component, while the higher‑energy hardening may reflect the onset of extragalactic contributions or a change in propagation conditions (e.g., increased interaction with interstellar radiation fields). Alternative explanations involving new particle physics—such as the production of exotic particles or modifications of hadronic cross‑sections at ultra‑high energies—are also mentioned, though the current data cannot discriminate among these scenarios.

By providing the first detailed, model‑independent measurement of the all‑particle spectrum in this critical energy window, KASCADE‑Grande supplies a benchmark for upcoming experiments like LHAASO and AugerPrime. The work underscores the necessity of multi‑observable analyses to disentangle composition and interaction effects, and it highlights the importance of continued refinement of hadronic interaction models to fully exploit the astrophysical information encoded in the cosmic‑ray spectrum.