Precise Measurement of Cosmic Ray Light and Helium Spectra above 0.1 Peta-electron-Volt

TL;DR

This work delivers a precise measurement of the cosmic-ray light component and, by subtraction, the helium energy spectrum in the knee region using the LHAASO KM2A-WFCTA hybrid system with a consistent energy scale. By exploiting a light-component selection and a robust energy-reconstruction framework, the authors extract a helium spectrum that exhibits a pronounced hardening at $E_h$ and a knee at $E_k$, aligning with multi-species rigidity considerations yet revealing complex, non-monotonic dominance transitions with energy. The analysis includes iterative refinements of the proton spectrum via an $H/He$ method, comprehensive systematic assessments across hadronic-interaction models, and the development of updated composition models to reduce model-dependent uncertainties. These results imply multiple Galactic CR source populations and provide stringent constraints on hadronic interactions, propagation, and acceleration scenarios in the knee energy range.

Abstract

We report a measurement of the cosmic ray helium energy spectrum in the energy interval 0.16 -- 13 PeV, derived by subtracting the proton spectrum from the light component (proton and helium) spectrum obtained with observations made by the Large High Altitude Air Shower Observatory (LHAASO) under a consistent energy scale. The helium spectrum shows a significant hardening centered at $E \simeq$ 1.1 PeV, followed by a softening at $\sim$ 7 PeV, indicating the appearance of a helium `knee'. Comparing the proton and helium spectra in the LHAASO energy range reveals some remarkable facts. In the lower part of this range, in contrast to the behavior at lower energies, the helium spectrum is significantly softer than the proton spectrum. This results in protons overtaking helium nuclei and becoming the largest cosmic ray component at $E \simeq$ 0.7 PeV. A second crossing of the two spectra is observed at $E \simeq$ 5 PeV, above the proton knee, when helium nuclei overtake protons to become the largest cosmic ray component again. These results have important implications for our understanding of the Galactic cosmic ray sources.

Figures (21)

• Figure 1: ( A): Inset panel: Comparison of $P_{\mu e}$ distributions between LHAASO experimental data (black dots) and simulations using the GSF-LHAASO composition model: total component (red solid line), light component (purple solid line), and heavy component (blue dashed line). The region between the vertical solid and dashed lines indicates the $P_{\mu e}$ selection range for identifying light component showers. All displayed simulation results use the EPOS-LHC hadronic interaction model. Main panel: Purity ($\epsilon$) versus efficiency ($\eta$) for light component at $\log_{10}(E/\text{PeV}) \in [0.2, 0.4]$ under two composition selection cuts. ( B): Light component selection efficiency $\eta$ (black triangles) and purity $\epsilon$ (red circles), heavy component selection efficiency $\eta^{H}$ (pink inverted triangles), and the relative variation in H/He ($\xi_{R} = \frac{(\text{H/He})^{after~cuts}}{(\text{H/He})^{before~cuts}}\times 100$) (blue circles) are shown as functions of cosmic ray energy. The three gray dashed lines correspond to y-axis values of 20, 60, and 100 (bottom to top), provided for reference.
• Figure 2: ( A): The energy spectrum of the light component ($\Phi_{L}$), together with the proton spectrum ($\Phi_{p}$) and the helium spectrum ($\Phi_{He}=\Phi_{L}-\Phi_{p}$), is plotted as a function of energy after normalization by multiplication with $E^{2.75}$. The proton energy spectrum is updated through iterations described in the text. The shaded bands indicate the systematic uncertainty estimated with the EPOS--LHC hadronic interaction model, while the error bars represent statistical uncertainties. The red line depicts the fitting result of the helium spectrum with the EPOS--LHC interaction model. Eq. \ref{['for:fit3']}, a combination of 3 power-law functional forms, is used in the fitting procedure. All parameters and uncertainties are available in Supplemental Material Helium. This fit is conducted over the energy range of 0.3 to 13 PeV. The dashed red line extends the function to lower energies with a simple extrapolation. The first three points are found to deviate from the extended function by 41.7$\sigma$, 10.7$\sigma$, and 0.7$\sigma$, respectively. ( B): (Upper): Helium spectra based on different hadronic interaction models are presented as a function of energy after being multiplied by $E^{2.75}$. (Bottom): Spectral indices of helium energy spectra for different hadronic interaction models, plotted as a function of energy. Each index was fitted using a single power-law function with three adjacent points. Error bars show fitting uncertainties.
• Figure 3: ( A): Energy spectra of helium (blue solid geometries) and protons (red hollow geometries), scaled by $E^{2.75}$, as a function of kinetic energy. Error bars denote statistical uncertainties. For comparison, the helium spectrum includes data from AMS-02 AMS:2021nhj, NUCLEON Gorbunov:2018stf, DAMPE Alemanno:2021gpb, CREAM-III Yoon:2017qjx, CALET CALET:2023nif, IceTop IceCube:2019hmk, and KASCADE KASCADE:2005ynk. Proton spectra measurements from AMS-02 AMS:2021nhj, DAMPE DAMPE:2019gys, and LHAASO are also shown, along with the all-particle spectrum from LHAASO LHAASO:2024knt. A comparison of the energy spectra, which includes systematic uncertainties, is provided in the Supplemental Material Helium. ( B): Proton to helium flux ratio (H/He) as a function of kinetic energy, with statistical uncertainties. Gray points: AMS-02 measurements (proton data interpolated from Ref. AMS:2021nhj). Blue points: DAMPE measurements (helium data interpolated from Ref. Alemanno:2021gpb). Gray line: reference ratio of 1.0 (equal proton and helium fluxes).
• Figure 4: ( A): Rigidity spectra from LHAASO for helium (black circles) and protons (red circles) scaled by $R^{2.75}$. Error bars indicate statistical uncertainties. For comparison, proton and helium spectra from AMS-02 AMS:2021nhj and DAMPE Alemanno:2021gpbDAMPE:2019gys are shown. ( B): The ratio of proton to helium flux (H/He) as a function of rigidity, with statistical uncertainties. Gray points: AMS-02 measurements AMS:2021nhj. Blue points: DAMPE measurements (helium data interpolated from Ref. Alemanno:2021gpb).
• Figure S1: The red squares and blue dots indicate the operational electromagnetic detectors (EDs) and muon detectors (MDs) of KM2A, respectively. The black dots represent the telescopes of WFCTA. The central green squares delineate the region of the WCDA. The red solid lines delineate the area for selecting the reconstructed shower core. The area enclosed by the black lines represents the throwing area for the shower core in the simulation. This picture is from Ref. LHAASO:2025byy.