Escape model for Galactic cosmic rays and an early extragalactic transition

We show that the cosmic ray (CR) knee can be entirely explained by energy-dependent CR leakage from the Milky Way, with an excellent fit to all existing data. We test this hypothesis calculating the trajectories of individual CRs in the Galactic magnetic field. We find that the CR escape time $\tau_{\rm esc}(E)$ exhibits a knee-like structure around $E/Z={\rm few}\times 10^{15}$ eV for small coherence lengths and strengths of the turbulent magnetic field. The resulting intensities for different groups of nuclei are consistent with the ones determined by KASCADE and KASCADE-Grande, using simple power-laws as injection spectra. The transition from Galactic to extragalactic CRs is terminated at $\approx 2\times 10^{18}$ eV, while extragalactic CRs contribute sizeable to the subdominant proton flux already for $\gtrsim 2\times 10^{16}$ eV. The natural source of extragalactic CRs in the intermediate energy region up to the ankle are in this model normal and starburst galaxies. The escape model provides a good fit to $\ln(A)$ data; it predicts that the phase of the CR dipole varies strongly in the energy range between $1\times 10^{17}$ and $3\times 10^{18}$ eV, while our estimate for the dipole magnitude is consistent with observations.