Explaining the Spectra of Cosmic Ray Groups above the Knee by Escape from the Galaxy

Abstract

We investigate the possibility that the cosmic ray (CR) knee is entirely explained by the energy-dependent CR leakage from the Milky Way. We test this hypothesis calculating the trajectories of individual CRs with energies between $E/Z=10^{14}$ eV and $10^{17}$ eV propagating them in the regular and turbulent Galactic magnetic field. We find a knee-like structure of the CR escape time $\tau_{\rm esc}(E)$ around $E/Z={\rm few}\times 10^{15}$ eV for a coherence length $l_{\rm c} \simeq 2$ pc of the turbulent field, while the decrease of $\tau_{\rm esc}(E)$ slows down around $E/Z\simeq 10^{16}$ eV in models with a weak turbulent magnetic field. Assuming that the injection spectra of CR nuclei are power-laws, the resulting CR intensities in such a turbulence are consistent with the energy spectra of CR nuclei determined by KASCADE and KASCADE-Grande. We calculate the resulting CR dipole anisotropy as well as the source rate in this model.