Gamma rays from Fermi bubbles as due to diffusive injection of Galactic cosmic rays

Recent detailed analysis of the Fermi-LAT data has discovered two giant γ-ray emission regions, the so-called Fermi bubbles, extending up to ~50° in Galactic latitude above and below the Galactic center with a width of ~40° in longitude. The origin of the γ-ray emission is not clearly understood. Here, we discuss the possibility that the γ-rays can be the result of diffusive injection of Galactic cosmic-ray protons during their propagation through the Galaxy. In the model, we consider that the bubbles are slowly expanding, and cosmic rays undergo much slower diffusion inside the bubbles than in the averaged Galaxy. Moreover, we consider that cosmic rays inside the bubbles suffer losses from adiabatic expansion, and also from inelastic collisions with the bubble plasma producing pion-decay γ rays. We show that this simple model can explain some of the important properties of Fermi bubbles such as the measured γ-ray intensity profile, the energy spectrum and the measured luminosity.