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 centre. However, if fields are not re-randomised, anisotropic thermal conduction drives the heat buoyancy instability (HBI) which re-orients magnetic field lines and shuts off radial heat fluxes. We revisit the efficiency of thermal conduction under the influence of spin-driven active galactic nuclei (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 intracluster medium if central AGN are the sole source of turbulence. Whistler-wave-driven saturation of thermal conduction reduces the magnitude of the HBI, but does not prevent it.