K. S. Cheng, D. O. Chernyshov, V. A. Dogiel, C. M. Ko, W. H. Ip, Y. Wang
The {\it Fermi} Large Area Telescope has recently discovered two giant
gamma-ray bubbles which extend north and south of the Galactic center with
diameters and heights of the order of $H\sim 10$ kpc. We suggest that the
periodic star capture processes by the Galactic supermassive black hole Sgr
A$^*$, with a capture rate of $\tau_{\rm cap}^{-1}\sim 3\times 10^{-5}$
yr$^{-1}$ and an energy release of $W\sim 3\times 10^{52}$ erg per capture, can
result in hot plasma injecting into the Galactic halo at a wind velocity of
$u\sim 10^8$ cm s$^{-1}$. 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 $E> 10^{15}$
eV, 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 $D_B\sim 3\times 10^{30}$ cm$^2$ s$^{-1}$, we can
reproduce the spectral index of the spectrum beyond the knee and within. 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.
View original:
http://arxiv.org/abs/1111.5127
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