Cosmic-Ray Mass Composition around the Knee via Principal Component Analysis

TL;DR

This study uses Principal Component Analysis (PCA) on four extensive air shower observables from KASCADE, namely $LCm$, $N_\mu$, $N_e$, and $Age$, to reconstruct the mass composition of cosmic rays around the knee for five primaries ($p$, He, C, Si, Fe) in $\lg(E/\mathrm{eV})\in [15.0,16.0]$. By projecting MC simulations with three hadronic models onto the first two PCs (PCA0, PCA1) and fitting the resulting 2D distributions to the experimental data, the authors obtain energy-dependent primary fractions with minimal model dependence; the inferred $\langle \ln(A) \rangle$ agrees well with LHAASO--KM2A and the GSF model, showing a decline in the light component and a slight rise in heavy components near the knee. The analysis demonstrates that a multi-observable PCA approach can robustly extract composition information from EAS data and provides a cross-check against data-driven composition models. These results enhance our understanding of CR origin and propagation around the knee and offer a model-insensitive benchmark for future studies.

Abstract

In this paper, we apply Principal Component Analysis (PCA) to experimental data recorded by the KASCADE experiment to reconstruct the mass composition of cosmic rays around the \textit{knee} region. A set of four extensive air shower parameters sensitive to the primary particle mass ($LCm$, $N_μ$, $N_{e}$, and lateral shower $age$) was considered, whose coordinates were transformed into a new orthogonal basis that maximally captures the data variance. Based on the experimental distributions of the first two principal components (PCA0 vs.\ PCA1) and full Monte Carlo simulations of the KASCADE array considering five types of primary particles (p, He, C, Si, and Fe) and three hadronic interaction models (EPOS-LHC, QGSjet-II-04, and SIBYLL~2.3d), we obtained the evolution of the abundance of each primary species as a function of energy, as well as the evolution of the mean logarithmic mass with energy. We found that the reconstruction of the mass composition resulting from this comprehensive analysis significantly reduces dependence on the hadronic interaction model used in the simulation process, even though the initial input parameters are model-dependent. Moreover, the results support the idea that around the \textit{knee} region, the abundance of the light component (protons) decreases, while the heavy component shows a slight increase. The evolution of $\langle \ln (A) \rangle$ as a function of energy derived from this analysis shows excellent agreement with recent results from the LHAASO--KM2A experiment and aligns very well with the predictions of the data-driven GSF model.

Figures (8)

• Figure 1: The $LCm^{-1}$ distributions in the energy range $\lg(E/\mathrm{eV}) = [15.4 - 15.6]$ and $\lg(E/\mathrm{eV}) = [15.6 - 15.8]$ for proton (left) and Fe (right) induced showers as predicted by the three hadronic interaction models. Bottom plots display the ratio between each pair of two distributions: EPOS-LHC - QGSjet-II-04 (red), EPOS-LHC - SIBYLL 2.3d (blue) and QGSjet-II-04 - SIBYLL 2.3d (green).
• Figure 2: The $N_{\mu}$ distributions in the energy range $\lg(E/\mathrm{eV}) = [15.4 - 15.6]$ and $\lg(E/\mathrm{eV}) = [15.6 - 15.8]$ for proton (left) and Fe (right) induced showers as predicted by the three hadronic interaction models. Bottom plots display the ratio between each pair of two distributions: EPOS-LHC - QGSjet-II-04 (red), EPOS-LHC - SIBYLL 2.3d (blue) and QGSjet-II-04 - SIBYLL 2.3d (green).
• Figure 3: The $N_{e}^{-1}$ distributions in the energy range $\lg(E/\mathrm{eV}) = [15.4 - 15.6]$ and $\lg(E/\mathrm{eV}) = [15.6 - 15.8]$ for proton (left) and Si (right) induced showers as predicted by the three hadronic interaction models. Bottom plots display the ratio between each pair of two distributions: EPOS-LHC - QGSjet-II-04 (red), EPOS-LHC - SIBYLL 2.3d (blue) and QGSjet-II-04 - SIBYLL 2.3d (green).
• Figure 4: The distributions of $Age$ parameter in the energy range $\lg(E/\mathrm{eV}) = [15.4 - 15.6]$ and $\lg(E/\mathrm{eV}) = [15.6 - 15.8]$ for He (left) and Fe (right) induced showers as predicted by the three hadronic interaction models. Bottom plots display the ratio between each pair of two distributions: EPOS-LHC - QGSjet-II-04 (red), EPOS-LHC - SIBYLL 2.3d (blue) and QGSjet-II-04 - SIBYLL 2.3d (green).
• Figure 5: The distributions of PCA0 for proton induced showers (left) and PCA1 for iron induced showers (right) in the energy range $\lg(E/\mathrm{eV}) = [15.4 - 15.6]$ and $\lg(E/\mathrm{eV}) = [15.6 - 15.8]$ for three hadronic interaction models. Bottom plots display the ratio between each pair of two distributions: EPOS-LHC - QGSjet-II-04 (red), EPOS-LHC - SIBYLL 2.3d (blue) and QGSjet-II-04 - SIBYLL 2.3d (green).