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 } _ { acc } c ^ { 2 } ; where \dot { M } _ { acc } is the mass accretion rate at 1 kpc ) as small as 6 \times 10 ^ { -5 } is sufficient to reduce the cooling/accretion rate by \sim 10 compared to a pure cooling flow in clusters ( with M _ { 200 } \lesssim 7 \times 10 ^ { 14 } M _ { \odot } ) .
This value is much 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 ) .
The feedback efficiency in earlier works was so high that the cluster core reached equilibrium in a hot state without much precipitation , unlike what is observed in cool-core clusters .
We find hysteresis cycles in all our simulations with cold mode feedback : condensation of cold gas when the ratio of the cooling-time to the free-fall time ( t _ { cool } / t _ { ff } ) is \lesssim 10 leads to a sudden enhancement in the accretion rate ; a large accretion rate causes strong jets and overheating of the hot ICM such that t _ { cool } / t _ { 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 _ { cool } / t _ { 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 .
Since the torus gas is not accreted on to the SMBH , it is largely decoupled from the feedback cycle .
The radially dominant cold gas ( T < 5 \times 10 ^ { 4 } K ; |v _ { r } | > |v _ { \phi } | ) consists of fast cold gas uplifted by AGN jets and freely-infalling cold gas condensing out of the core .
The radially dominant cold gas extends out to 25 kpc for the fiducial run ( halo mass 7 \times 10 ^ { 14 } { M } _ { \odot } and feedback efficiency 6 \times 10 ^ { -5 } ) , with the average mass inflow rate dominating the outflow rate by a factor of \approx 2 .
We compare our simulation results with recent observations .