The Fermi Bubble as a source of cosmic rays in the energy range >10 ¹⁵eV

The Fermi Large Area Telescope has recently discovered two giant gamma-ray bubbles that extend north and south of the Galactic center with diameters and heights of the order of H 10kpc. We suggest that the periodic star capture processes by the Galactic supermassive black hole Sgr A*, with a capture rate of τ^-1_cap 3 × 10^-5yr ^-1 and an energy release of W 3 × 10⁵²erg per capture, can result in hot plasma injecting into the Galactic halo at a wind velocity of u 10⁸cms^-1. The periodic injection of hot plasma can produce a series of shocks. Energetic protons in the bubble are re-accelerated when they interact with these shocks. We show that for energy larger than E > 10¹⁵eV, the acceleration process can be better described by the stochastic second-order Fermi acceleration. We propose that hadronic cosmic rays (CRs) within the "knee" of the observed CR spectrum are produced by Galactic supernova remnants distributed in the Galactic disk. Re-acceleration of these particles in the Fermi Bubble produces CRs beyond the knee. With a mean CR diffusion coefficient in this energy range in the bubble D_B 3 × 10³⁰cm²s^-1, we can reproduce the spectral index of the spectrum beyond the knee and within it. The conversion efficiency from shock energy of the bubble into CR energy is about 10%. This model provides a natural explanation of the observed CR flux, spectral indices, and matching of spectra at the knee.