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 $E/Z={10}^{14}\mathrm{eV}$ and ${10}^{17}\mathrm{eV}$ propagating them in the regular and turbulent Galactic magnetic field. We find a knee-like structure of the CR escape time ${\tau }_{\text{esc}}(E)$ around $E/Z=\text{few}\times {10}^{15}\mathrm{eV}$ for a coherence length $l_{\mathrm{c}}\simeq 2\mathrm{pc}$ of the turbulent field, while the decrease of ${\tau }_{\text{esc}}(E)$ slows down around $E/Z\simeq {10}^{16}\mathrm{eV}$ 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.

• Received 16 June 2014

DOI:https://doi.org/10.1103/PhysRevD.90.041302