Joint Constraint on the Propagation Origin of the Cosmic-Ray Spectral Knee from Energy Spectrum and Anisotropy Observations

Abstract The origin mechanism of the cosmic-ray knee region remains an unresolved mystery, with acceleration, interaction, and propagation models drawing significant attention. The latest experimental observations of the PeV total spectrum, composition energy spectrum, and anisotropy—particularly the precise measurements of the proton spectrum by the LHAASO experiment—have provided crucial breakthroughs in uncovering its origin. Based on the latest LHAASO measurements of the proton energy spectrum, combined with cosmic-ray spectral and anisotropy data, this study proposes that the spectral index variation in the knee region arises from changes in the propagation coefficient. By introducing a knee position <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">knee</mml:mi> </mml:mrow> </mml:msub> </mml:math> and an index variation δ knee , we construct a rigidity-dependent double-power-law diffusion model to reproduce the knee-region spectral structure. Through modifications to the diffusion coefficient, we successfully replicate the observed knee-region spectral structure in the LHAASO proton spectrum and calculate the corresponding anisotropy. Under current data and model dependencies, a joint analysis of the energy spectrum and anisotropy does not support the propagation-origin model of the cosmic-ray knee at a 95% confidence level. We hope that future LHAASO experiments will provide precise measurements of the energy spectra and anisotropies of various nuclei in the knee region, thereby offering a definitive test of the propagation model as the origin mechanism of the knee-region spectral structure.