Explaining the Knee by Cosmic Ray Escape from the Galaxy [HEAP]


We study the escape of cosmic rays (CRs) with energies between $E/Z=10^{14}$ eV and $10^{17}$ eV from our Galaxy, calculating the trajectories of individual CRs in recent models of the regular and turbulent Galactic magnetic field. Determining the average grammage $X(E)$ traversed by CRs, we find a knee-like structure of $X(E)$ around $E/Z=$ few $\times 10^{15}$ eV for a coherence length $l_{\rm c} \simeq 5$ pc of the turbulent field. The resulting change in the slope of $X(E)$ is sufficiently strong to explain the proton knee observed by KASCADE: Thus the knee may, in this regard, be entirely explained by CR leakage from the Milky Way, rendering additional effects unnecessary. We find that the decrease of $X(E)$ slows down around $E/Z \simeq 10^{16}$ eV in a model with a weak turbulent magnetic field, in agreement with the energy dependence of the proton flux as determined by KASCADE-Grande.

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G. Giacinti, M. Kachelriess and D. Semikoz
Fri, 14 Mar 14