Escape model for Galactic cosmic rays

Abstract

We show that the cosmic ray (CR) knee can be entirely explained by energy-dependent CR leak-age from the Milky Way, with an excellent fit to all existing data. We test this hypothesis cal-culating the trajectories of individual CRs in the Galacticmagnetic field. We find that the CRescape timeτesc(E)exhibits a knee-like structure aroundE/Z=few×1015eV for small coher-ence lengths and strengths of the turbulent magnetic field. The resulting intensities for differentgroups 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 isterminated at≈2×1018eV, while extragalactic CRs contribute significantly to thesubdominantproton flux already for>∼2×1016eV. The natural source of extragalactic CRs in the intermediateenergy region up to the ankle are in this model normal and starburst galaxies. The escape modelprovides a good fit to ln(A)data; it predicts that the phase of the CR dipole varies strongly inthe energy range between 1×1017and 3×1018eV, while our estimate for the dipole magnitudeis consistent with observations. aboveE>1014eV. Adding a single nearby source to this modelexplains moreover the dipole anisotropy below 1014eV, the specific slope of the locally measuredproton flux as well as of the antiproton and positron fluxes.