Fermi has discovered two giant gamma-ray-emitting bubbles that extend nearly 10 kpc in diameter. We propose that periodic star capture processes by the galactic supermassive black hole, Sgr A*, with a capture rate $<10^{-5}$ yr$^{-1}$ and energy release $sim 10^{52}$ erg per one capture can produce shocks in the halo, which accelerate electrons to the energy ~ 1 TeV. These electrons generate radio emission via synchrotron radiation, and gamma-rays via inverse Compton scattering with the relic and the galactic soft photons. Estimates of the diffusion coefficient from the observed gamma-ray flux explains consistently the necessary maximum energy of electrons and sharp edges of the bubble.
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