The Fermi bubbles from stochastic acceleration of electrons in a
  Galactic outflow
  The discovery of the Fermi bubbles---a huge bilobular structure seen in GeV
gamma-rays above and below the Galactic center---implies the presence of a
large reservoir of high energy particles at $\sim 10 \, \text{kpc}$ from the
disk. The absence of evidence for a strong shock coinciding with the edge of
the bubbles, and constraints from multi-wavelength observations point towards
stochastic acceleration by turbulence as a likely mechanism of acceleration. We
have investigated the time-dependent acceleration of electrons in a large-scale
outflow from the Galactic centre. For the first time, we present a detailed
numerical solution of the particle kinetic equation that includes the
acceleration, transport and relevant energy loss processes. We also take into
account the addition of shock acceleration of electrons at the bubble's blast
wave. Fitting to the observed spectrum and surface brightness distribution of
the bubbles allows determining the transport coefficients, thereby shedding
light on the origin of the Fermi bubbles.
