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.