Multiple shock fronts in RBS 797: the Chandra window on shock heating in galaxy clusters

Using $\sim$427 ks of Chandra observations, we present a study of shock heating and ICM cooling in the galaxy cluster RBS 797. We discover three nested pairs of weak shocks at roughly 50 kpc, 80 kpc and 130 kpc from the center. The total energy associated with the shocks is $\sim6\times10^{61}$ erg, with the central AGN driving a pair of weak shocks every 20-30 Myr with a power $P_{sh}\approx10^{46}$ erg s$^{-1}$. Based on its morphology and age ($\sim$30 Myr), the inner cocoon shock is associated with the four equidistant X-ray cavities previously discovered. From the thermodynamic analysis of the inner 30 kpc, we find evidence for ICM condensation into colder gas between and behind the X-ray cavities. The total AGN mechanical power (cavities and shocks) of $3.4\times10^{46}$ erg s$^{-1}$ can balance the ICM radiative losses, estimated as $L_{cool} = 2.3\times10^{45}$ erg s$^{-1}$. By building plots of $P_{cav}$ vs. $L_{cool}$, $P_{shock}$ vs. $L_{cool}$ and $P_{tot}$ vs. $L_{cool}$ for RBS 797 and 14 other galaxy clusters, groups and elliptical galaxies where both cavities and shocks are detected, we verify that the most powerful outbursts are found in the strongest cooling systems. Ultimately, we observe that the mechanical power of the AGN exceeds the gas radiative losses by a factor that is different for FR I and FR II radio galaxies, being less than a few tens for FR Is (as RBS 797) and more than roughly a hundred for FR IIs.