Multi-wavelength Emission from the Fermi Bubble II. Secondary Electrons
  and the Hadronic Model of the Bubble
  We analyse the origin of the gamma-ray flux from the Fermi Bubbles (FBs) in
the framework of the hadronic model in which gamma-rays are produced by
collisions of relativistic protons with the protons of background plasma in the
Galactic halo. It is assumed in this model that the observed radio emission
from the FBs is due to synchrotron radiation of secondary electrons produced by
$pp$ collisions. However, if these electrons loose their energy by the
synchrotron and inverse-Compton, the spectrum of secondary electrons is too
soft, and an additional arbitrary component of primary electrons is necessary
in order to reproduce the radio data. Thus, a mixture of the hadronic and
leptonic models is required for the observed radio flux. It was shown that if
the spectrum of primary electrons is $\propto E_e^{-2}$, the permitted range of
the magnetic field strength is within 2 - 7 $\mu$G region. The fraction of
gamma-rays produced by $pp$ collisions can reach about 80% of the total
gamma-ray flux from the FBs. If magnetic field is <2 $\mu$G or >7 $\mu$G the
model is unable to reproduce the data. Alternatively, the electrons in the FBs
may lose their energy by adiabatic energy losses if there is a strong plasma
outflow in the GC. Then, the pure hadronic model is able to reproduce
characteristics of the radio and gamma-ray flux from the FBs. However, in this
case the required magnetic field strength in the FBs and the power of CR
sources are much higher than those followed from observations.
