Galactic modulation of extragalactic cosmic rays: Possible origin of the   knee in the cosmic ray spectrum
  The existence of the spectral break around $\sim 3 \times 10^{15}$ eV in the cosmic ray spectrum (referred to as the `knee') is one of the biggest questions in cosmic ray astrophysics. At the same time, the origin of cosmic rays above the knee energies (between 10$^{15}$ and 10$^{18}$ eV) is also still unsettled. In this paper, we investigate how the hypothetical extragalactic CRs after modulated by the galactic wind contribute to the knee in the CR spectrum. We numerically calculate the modulated energy spectrum of the hypothetical cosmic rays coming into the galaxy from just outside of the ``galactic sphere'' where the galactic wind terminates. We show that the observed knee structure is reproduced well by a superposition of the modulated component and the galactic cosmic rays originating in supernova remnants. 
Hiroshi Muraishi, Shohei Yanagita and Tatsuo Yoshida