AGN jets do not prevent the suppression of conduction by the heat buoyancy instability in simulated galaxy clusters

Centres of galaxy clusters must be efficiently reheated to avoid a cooling catastrophe. One potential reheating mechanism is anisotropic thermal conduction, which could transport thermal energy from intermediate radii to the cluster center. However, if fields are not re-randomised, anisotropic thermal conduction drives the heat buoyancy instability (HBI) which reorients magnetic field lines and shuts off radial heat fluxes. We revisit the efficiency of thermal conduction under the influence of spin-driven AGN jets in idealised magneto-hydrodynamical simulations with anisotropic thermal conduction. Despite the black hole spin's ability to regularly re-orientate the jet so that the jet-induced turbulence is driven in a quasi-isotropic fashion, the HBI remains efficient outside the central 50 kpc of the cluster, where the reservoir of heat is the largest. As a result, conduction plays no significant role in regulating the cooling of the intra-cluster medium if central active galactic nuclei are the sole source of turbulence. Whistler-wave driven saturation of thermal conduction reduces the magnitude of the HBI but does not prevent it.