Fossil shell in 3C 84 as TeV $γ$-ray emitter and cosmic-ray accelerator

We explore physical properties of the shocked external medium (i.e., a shell) in 3C 84 associated with the recurrent radio lobe born around 1960. In the previous work of Ito et al., we investigated a dynamical and radiative evolution of such a shell after the central engine stops the jet launching and we found that a fossil shell emission overwhelms that of the rapidly fading radio lobe. We apply this model to 3C 84 and find the followings: (i) The fossil shell made of shocked diffuse ambient matter with the number density of 0.3 cm$^{-3}$ radiates bright Inverse-Compton (IC) emission with the seed photons of the radio emission from the central compact region and the IC emission is above the sensitivity threshold of the Cherenkov Telescope Array (CTA). (ii) When the fossil shell is produced in a geometrically thick ionized plasma with the number density of $10^{3}$ cm$^{-3}$ and the field strength in the shell may reach about 17 mG in the presence of magnetic fields amplification and the radio emission becomes comparable to the sensitivity of deep imaging VLBI observations. A possible production of ultra high energy cosmic-rays (UHECRs) in the dense shocked plasma is also argued.