Interplay among Cooling, AGN Feedback and Anisotropic Conduction in the
  Cool Cores of Galaxy Clusters
  Feedback from the active galactic nuclei (AGN) is one of the most promising
heating mechanisms to circumvent the cooling-flow problem in galaxy clusters.
However, the role of thermal conduction remains unclear. Previous studies have
shown that anisotropic thermal conduction in cluster cool cores (CC) could
drive the heat-flux driven buoyancy instabilities (HBI) that re-orient the
field lines in the azimuthal directions and isolate the cores from conductive
heating from the outskirts. However, how the AGN interacts with the HBI is
still unknown. To understand these interwined processes, we perform the first
3D magnetohydrodynamic (MHD) simulations of isolated CC clusters that include
anisotropic conduction, radiative cooling, and AGN feedback. We find that: (1)
For realistic magnetic field strengths in clusters, magnetic tension can
suppress a significant portion of HBI-unstable modes and thus the HBI is either
completely inhibited or significantly impaired, depending on the unknown
magnetic field coherence length. (2) Turbulence driven by AGN jets can
effectively randomize magnetic field lines and sustain conductivity at ~1/3 of
the Spitzer value; however, the AGN-driven turbulence is not volume-filling.
(3) Conductive heating within the cores could contribute to ~10% of the
radiative losses in Perseus-like clusters and up to ~50% for clusters twice the
mass of Perseus. (4) Thermal conduction has various impacts on the AGN activity
and ICM properties for the hottest clusters, which may be searched by future
observations to constrain the level of conductivity in clusters. The
distribution of cold gas and the implications are also discussed.
