Synchrotron Emission from Elliptical Galaxies Consequent to AGN
  outbursts
  Both radiative and mechanical feedback from Active Galactic Nuclei have been
found to be important for the evolution of elliptical galaxies. We compute how
a shock may be driven from a central black hole into the gaseous envelope of an
elliptical galaxy by mechanical as well as radiative feedback (in the form of
nuclear winds) using high resolution 1-D hydrodynamical simulations. We
calculate the synchrotron emission from the electron cosmic rays accelerated by
the shocks (not the jets) in the central part of elliptical galaxies, and we
also study the synchrotron spectrum's evolution using the standard diffusive
shock acceleration mechanism, which is routinely applied to the scaled volume
case of supernova remnants. We find good agreement quantitatively between the
synchrotron radio emission produced via this mechanism with extant observations
of elliptical galaxies which are undergoing outbursts. Additionally, we also
find that synchrotron optical and X-ray emission can co-exist inside elliptical
galaxies during a certain phase of evolution subsequent to central outbursts.
In fact, our calculations predict a synchrotron luminosity of $\sim 1.3\times
10^6 L_{\odot}$ at the frequency 5 GHz (radio band), of $\sim 1.1\times 10^6
L_{\odot}$ at $4.3\times10^{14}$ Hz (R band, corresponding to the absolute
magnitude -10.4), and of $\sim 1.5\times 10^{7} L_{\odot}$ at
$2.4\times10^{17}$ Hz (soft X-ray, 0.5 -- 2.0 keV band).
