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 spectrums 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 $sim 1.3times 10^6 L_{odot}$ at the frequency 5 GHz (radio band), of $sim 1.1times 10^6 L_{odot}$ at $4.3times10^{14}$ Hz (R band, corresponding to the absolute magnitude -10.4), and of $sim 1.5times 10^{7} L_{odot}$ at $2.4times10^{17}$ Hz (soft X-ray, 0.5 -- 2.0 keV band).
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