Spatial dependence of the break in the energy spectrum of cosmic rays in the new anisotropic diffusion approach

Abstract

At present, there is no consensus on whether the spectral break in the cosmic-ray flux of all elements around 4 PeV is a general characteristic of the Milky Way or is determined by a combination of factors that significantly affect the energy position of the knee. We argue that considering the anisotropic propagation of cosmic rays within a realistically modeled Galactic magnetic field enables an accurate description of the spectral break without invoking a source-related cutoff energy, and naturally predicts a spatial dependence of this phenomenon. To demonstrate this, we constructed a 3D diffusion propagation model with a diffusion tensor within a two-component magnetic field and determined both the local cosmic-ray spectrum and the spectra for specific regions of the Milky Way. We found that the spectral break is well reproduced by the energy dependence of the diffusion tensor components and appears at different energies in various regions of the Galaxy due to the inclusion of the turbulent component of the magnetic field. Furthermore, the spectral slope is determined by the degree of anisotropy in cosmic-ray diffusion. The model is based on the calculation of the diffusion tensor components using the trajectory method and on the direct solution of the stationary diffusion equation with a fully anisotropic diffusion tensor that includes all nine components in the global Galactic coordinate system, accounting for off-diagonal terms arising from the projection of locally field-aligned diffusion. We calculated the integral flux of diffuse gamma rays in the inner and outer regions of the Galaxy based on the cosmic-ray proton and nuclei spectra obtained within our model, which features a spatially dependent position of the knee. The resulting spectral shape of the diffuse gamma-ray flux is consistent with experimental data from LHAASO and Fermi-LAT.