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

Aims. We present a detailed analysis of jet activity in the radio galaxy 3C 348 at the center of the galaxy cluster Hercules A. We aim to investigate the jet-driven shock fronts, the radio-faint X-ray cavities, the eastern jet, and the presence of extended inverse Compton (IC) X-ray emission from the radio lobes. Methods. We used archival Chandra observations to investigate surface brightness profiles extracted in several directions and to measure the spectral properties of the hot gas and of the nonthermal emission from the radio jet and lobes. Results. We detect two pairs of shock fronts: 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 M = 1.65 +/- 0.05 and M = 1.9 +/- 0.3, respectively. Together, they form a complete cocoon surrounding 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, which are misaligned from the main lobes and each approximately 100 kpc wide and 40-60 Myr old. A backflow from the radio lobes might explain why the cavities appear to be dynamically younger than the surrounding cocoon shock front. We also detect nonthermal 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 active galactic nucleus and can be accounted for by an IC model with mild Doppler boosting (delta similar to 2.7). A synchrotron model could explain the observed radio-to-X-ray spectrum only for very high Lorentz factors gamma >= 10(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 +/- 1.4 (statistical) +/- 1.3 (systematic) nJy. A thermal model is unlikely, as it would require an unrealistically high temperature, density, and pressure for the gas in the lobes, along with 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 +/- 3 mu G in the lobes.