Cool core cycles: Cold gas and AGN jet feedback in cluster cores

Using high-resolution 3-D and 2-D (axisymmetric) hydrodynamic simulations in spherical geometry, we study the evolution of cool cluster cores heated by feedback-driven bipolar active galactic nuclei (AGN) jets. Condensation of cold gas, and the consequent enhanced accretion, is required for AGN feedback to balance radiative cooling with reasonable efficiencies, and to match the observed cool core properties. A feedback efficiency (mechanical luminosity $\approx \epsilon \dot{M}_{\rm acc} c^2$; where $\dot{M}_{\rm acc}$ is the mass accretion rate at 1 kpc) as small as $5 \times 10^{-5}$ is sufficient to reduce the cooling/accretion rate by $\sim 10$ compared to a pure cooling flow. This value is smaller compared to the ones considered earlier, and is consistent with the jet efficiency and the fact that only a small fraction of gas at 1 kpc is accreted on to the supermassive black hole (SMBH). We find hysteresis cycles in all our simulations with cold mode feedback: {\em condensation} of cold gas when the ratio of the cooling-time to the free-fall time ($t_{\rm cool}/t_{\rm ff}$) is $\lesssim 10$ leads to a sudden enhancement in the accretion rate; a large accretion rate causes strong jets and {\em overheating} of the hot ICM such that $t_{\rm cool}/t_{\rm ff} > 10$; further condensation of cold gas is suppressed and the accretion rate falls, leading to slow cooling of the core and condensation of cold gas, restarting the cycle. Therefore, there is a spread in core properties, such as the jet power, accretion rate, for the same value of core entropy or $t_{\rm cool}/t_{\rm ff}$. A fewer number of cycles are observed for higher efficiencies and for lower mass halos because the core is overheated to a longer cooling time. The 3-D simulations show the formation of a few-kpc scale, rotationally-supported, massive ($\sim 10^{11} M_\odot$) cold gas torus. (abstract abridged)