On the origin of high energy $\gamma$-rays from giant radio lobes of Centaurus A

Recently the Fermi LAT collaboration reported on the detection of high energy $\gamma$-ray signal from giant lobes of the radio galaxy Centaurus A. It is shown that if the $\gamma$-rays had originated from the inverse-Compton scattering of cosmic microwave background photons for the equipartition magnetic field of 2 $\mu G$, the Fermi LAT would not detect $\gamma$-rays from the lobes of Centaurus A.
However, the detected $\gamma$-rays may be produced in hadronic interactions, namely in interactions of high energy protons with low density plasma followed with the production of pions, the neutral component decaying into $2 \gamma$-quanta. In this article we study the hadronic origin of $\gamma$-rays, and estimate the total energy of protons assuming a power-law proton distribution with an exponential cut-off.