Precise measurements of the cosmic ray proton energy spectrum in the "knee'' region

TL;DR

This study delivers a precise, high-purity measurement of the cosmic-ray proton energy spectrum from $\sim$0.16 to $12.6~\mathrm{PeV}$ using LHAASO's hybrid KM2A and WFCTA detectors. By combining muon content and Cherenkov-imaging features into a proton-selection framework, the authors achieve a proton sample with $\sim$89% purity and robust energy reconstruction, enabling a three-component spectral fit with a hardening near $E_{\mathrm{h}} \approx 0.34~\mathrm{PeV}$ and a knee at $E_{\mathrm{k}} \approx 3.3~\mathrm{PeV}$; this structure aligns with the all-particle knee and hints at a new Galactic CR component possibly linked to PeVatrons. The analysis rigorously accounts for systematics from hadronic-interaction models, composition, and environmental conditions, and compares results across multiple models (QGSJETII-04, EPOS-LHC, SIBYLL 2.3d). The findings provide crucial constraints on CR acceleration and propagation and support a scenario in which a fresh PeV-scale component emerges in the knee region, potentially connected to recently identified Galactic PeVatrons. Together with space-borne measurements, this work bridges a critical energy gap and informs models of Galactic CR origins and high-energy sources.

Abstract

We report the high-purity identification of cosmic-ray (CR) protons and a precise measurement of their energy spectrum from 0.15 to 12 PeV using the Large High Altitude Air Shower Observatory (LHAASO). Abundant event statistics, combined with the simultaneous detection of electrons/photons, muons, and Cherenkov light in air showers, enable spectroscopic measurements with statistical and systematic precision comparable to satellite data at lower energies. The proton spectrum shows significant hardening relative to low-energy extrapolations, culminating at 3 PeV, followed by sharp softening. This distinct spectral structure closely aligned with the knee in the all-particle spectrum points to the emergence of a new CR component at PeV energies that might be linked to the dozens of PeVatrons recently discovered by LHAASO, and offers crucial clues to the origin of Galactic cosmic rays.

Figures (20)

• Figure 1: Energy reconstruction, proton selection principle and performance. (a) The energy resolution functions for events with reconstructed energy from three energy bins. They are symmetric and well fitted with Gaussian functions, with the systematic bias less than 1% and $\sigma$-parameter $\sim$14% [$\log(E/\mathrm{PeV})$=$-0.8$ to $-0.7$], $\sim$10% [$\log(E/\mathrm{PeV})$=0.0 to 0.1] and $\sim$10% [$\log(E/\mathrm{PeV})$=1.0 to 1.1], respectively. (b) Simulated event distributions in the two-dimensional parameter space ($P_{\mathrm{\theta c}}$, $P_{\mathrm{\mu e}}$). $P_{\mathrm{\theta c}}$ is a component sensitive variable related to shower maximum measured by WFCTA, while $P_{\mathrm{\mu e}}$ is a component sensitive variable related to muon content measured by KM2A. For detailed descriptions, please refer to the following text and Supplementary material. Many proton events (red contours) are clearly separated from the other events (blue contours). The gray points show the scatter plot of the association between $P_{\mathrm{\theta c}}$ and $P_{\mathrm{\mu e}}$ for heavier components. The black solid line indicates the selection criterion for protons. The events to the lower right of the black line are those retained after selection. (c) Distributions of $P_{\mathrm{\theta c+\mu e}}$ for events with energy between 1.58 and 2.51 PeV. The experimental data (black dots) are shown together with simulated protons (pink histogram), helium (blue histogram), heavier components(green histogram), and their sum which is marked as MC (red histogram). The sum of the simulated events fits the data well. The simulation events are based on the EPOS-LHC model. The black line represents the proton selection criterion. It can be seen that, after selection, events heavier than helium (CNO+MgAlSi+Iron) are almost completely excluded, allowing the contamination of proton events to be neglected. (d) The corresponding selection efficiency of protons (black dots) and other components (blue squares), as well as the purity of protons (red dots), as a function of energy. The three dashed lines at 25% (black), 90%(red), and 3%(blue), serve as their reference values, respectively.
• Figure 2: CR proton energy spectrum measured by LHAASO. (a) The proton flux multiplied by $E^{2.75}$ as a function of energy. The error bars indicate the statistical uncertainties and the shaded band indicates the systematic uncertainties. EPOS-LHC is the hadronic interaction model used in the figure. The solid and dashed lines represent the best fitting results using Eq. (\ref{['formula:protonSpectrum-FitSBPL-maintext']}) for three power-law components and for two power-law components with an exponential cut-off feature, respectively. (b) The local spectral index as a function of energy. The spectral indices are obtained using adjacent three data points fitted with a power-law function form. This indicates a slight hardening with $\Delta\gamma\sim0.2$ and a gradual softening structure ("knee") with $\Delta\gamma\sim-1$.
• Figure 3: (a) CR proton spectrum from a few TeV to tens of PeV. The fluxes are multiplied by a factor of $E^{2.75}$, allowing a detailed comparison between measurements in entirely different energy domains. Proton spectra reported by the space-borne ISS-CREAM, DAMPE, CALET, and NUCLEON and ground-based GRAPES-3, ICETOP, and KASCADE detectors and the LHAASO all-particle spectrum are plotted together with the proton spectrum measured in this work by LHAASO. Here we show three proton energy spectra based on different hadronic models. All error bars represent the statistical errors. The shaded band represents the overall systematic uncertainty, excluding that introduced by the hadronic interaction models. The center of the shaded band corresponds to the results from the EPOS-LHC model. The systematic uncertainty introduced by the hadronic interaction models can be referenced by the differences among the three energy spectra. (b) To clearly see how those measurements are connected over a wider energy range starting from 1 GeV, the spectra by AMS-02, DAMPE and LHAASO (proton spectrum and all-particle spectrum) are plotted. AMS-02 and DAMPE have a good overlap around $10^{3}$ GeV, and the gap between DAMPE and LHAASO around 0.1 PeV should be covered by the two experiments shortly, allowing a complete description of the spectrum without suffering from a relative energy scale difference between experiments.
• Figure S1: (a) The core and direction of the shower are reconstructed with KM2A, while the shower detector plane SDP is reconstructed with WFCTA. (b) The resolutions of core, angular, telescope distance to the shower $R_\mathrm{p}$, and SDP as functions of the reconstruction energy are presented.
• Figure S2: LHAASO layout. (a): The WCDA is located at the center of the LHAASO detector array, surrounded by the KM2A array and 18 Cherenkov telescopes of WFCTA. The red solid line indicates the area for selecting the reconstructed shower core, while the black solid line represents the throwing area for the shower core in the simulation. The distance from the core selection area to the KM2A boundary exceeds 50 m, and the distance from the throwing area boundary to the core selection area is more than 30 m, ensuring accurate geometric reconstruction. (b): The colored dashed line represents the FoV of WFCTA. The red area represents the FoV used for selecting the centroid of the Cherenkov image in the analysis.