Modeling High-Energy Gamma-Rays from the Fermi Bubbles
In 2010, the Fermi Bubbles were discovered at the galactic center of the Milky Way. These giant gamma-ray structures, extending 55° in galactic latitude and 20°-30° in galactic longitude, were not predicted. We wish to develop a model for the gamma-ray emission of the Fermi Bubbles. To do so, we assume that second order Fermi acceleration is responsible for the high-energy emission of the bubbles. Second order Fermi acceleration requires charged particles and irregular magnetic fields{ both of which are present in the disk of the Milky Way galaxy. By solving the steady-state case of the transport equation, I compute the proton spectrum due to second order Fermi acceleration. I compare the analytical solutions of the proton spectrum to a numerical solution. I find that the numerical solution to the transport equation converges to the analytical solution in all cases. The gamma-ray spectrum due to proton-proton interaction is compared to Fermi Bubble data (from Ackermann et al. 2014), and I find that second order Fermi acceleration is a good fit for the gamma-ray spectrum of the Fermi Bubbles at low energies with an injection source term of S = 1.5 × 10 -10 GeV -1 cm -3 yr -1 . I find that a non-steady-state solution to the gamma-ray spectrum with an injection source term of S = 2 × 10 -10 GeV -1 cm -3 yr -1 matches the bubble data at high energies.