Cocoon shock, X-ray cavities and extended Inverse Compton emission in Hercules A: clues from Chandra observations

We present a detailed analysis of jet activity in the radio galaxy 3C348 at the center of the galaxy cluster Hercules A. We use archival Chandra data to investigate the jet-driven shock front, the radio-faint X-ray cavities, the eastern jet, and the presence of extended Inverse Compton (IC) X-ray emission from the radio lobes. We detect two pairs of shocks: one in the north-south direction at 150 kpc from the center, and another in the east-west direction at 280 kpc. These shocks have Mach numbers of $\mathcal{M} = 1.65\pm0.05$ and $\mathcal{M} = 1.9\pm0.3$, respectively. Together, they form a complete cocoon around the large radio lobes. Based on the distance of the shocks from the center, we estimate that the corresponding jet outburst is 90-150 Myr old. We confirm the presence of two radio-faint cavities within the cocoon, misaligned from the lobes, each $\sim$100 kpc wide and 40-60 Myr old. A backflow from the radio lobes might explain why the cavities are dynamically younger than the cocoon shock front. We also detect non-thermal X-ray emission from the eastern jet and from the large radio lobes. The X-ray emission from the jet is visible at 80 kpc from the AGN and can be accounted for by an IC model with a mild Doppler boosting ($\delta\sim2.7$). A synchrotron model could explain the radio-to-X-ray spectrum only for very high Lorentz factors $\gamma\geq10^{8}$ of the electrons in the jet. For the large radio lobes, we argue that the X-ray emission has an IC origin, with a 1 keV flux density of $21.7\pm1.4\text{(statistical)}\pm1.3\text{(systematic)}$ nJy. A thermal model is unlikely, as it would require unrealistically high gas temperature, density, and pressure, along with a strong depolarization of the radio lobes, which are instead highly polarized. The IC detection, combined with the synchrotron flux density, suggests a magnetic field of $12\pm3\mu$G in the lobes.