The Fate of Dead Radio-loud Active Galactic Nuclei: A New Prediction of Long-lived Shell Emission

We examine the fate of a dead radio source in which jet injection from the central engine has stopped at an early stage of its evolution ($t = t_j \lesssim 10^5$ yr). To this aim, we theoretically evaluate the evolution of the emission from both the lobe and the shell, which are composed of shocked jet matter and a shocked ambient medium, respectively. Based on a simple dynamical model of expanding lobe and shell, we clarify how the broadband spectrum of each component evolves before and after the cessation of the jet activity. It is shown that the spectrum is strongly dominated by the lobe emission while the jet is active ($t \leq t_j$). On the other hand, once the jet activity has ceased ($t > t_j$), the lobe emission fades out rapidly, since fresh electrons are no longer supplied from the jet. Meanwhile, shell emission only shows a gradual decrease, since accelerated electrons are continuously supplied from the bow shock that is propagating into the ambient medium. As a result, overall emission from the shell overwhelms that from the lobe at wide range of frequencies from radio up to gamma-ray soon after the jet activity has ceased. Our result predicts a new class of dead radio sources that are dominated by shell emission. We suggest that the emission from the shell can be probed in particular at a radio wavelengths with the Square Kilometer Array (SKA) phase 1.