  In a previous work, we have shown that the formation of the Fermi bubbles can
be due to the interaction between winds launched from the hot accretion flow in
Sgr A* and the interstellar medium (ISM). In that work, we focus only on the
morphology. In this paper we continue our study by calculating the gamma-ray
radiation. Some cosmic ray protons (CRp) and electrons must be contained in the
winds, which are likely formed by physical processes such as magnetic
reconnection. We have performed MHD simulations to study the spatial
distribution of CRp, considering the advection and diffusion of CRp in the
presence of magnetic field. We find that a permeated zone is formed just
outside of the contact discontinuity between winds and ISM, where the
collisions between CRp and thermal nuclei mainly occur. The decay of neutral
pions generated in the collisions, combined with the inverse Compton scattering
of background soft photons by the secondary leptons generated in the collisions
and primary CR electrons can well explain the observed gamma-ray spectral
energy distribution. Other features such as the uniform surface brightness
along the latitude and the boundary width of the bubbles are also explained.
The advantage of this accretion wind model is that the adopted wind properties
come from the detailed small scale MHD numerical simulation of accretion flows
and the value of mass accretion rate has independent observational evidences.
The success of the model suggests that we may seriously consider the
possibility that cavities and bubbles observed in other contexts such as galaxy
clusters may be formed by winds rather than jets.
