Cosmic ray confinement in fossil cluster bubbles

Most cool core clusters of galaxies possess active galactic nuclei (AGN) in their centres. These AGN inflate buoyant bubbles containing non-thermal radio-emitting particles. If such bubbles efficiently confine cosmic rays (CRs) then this could explain 'radio relics' seen far from cluster centres. We simulate the diffusion of CRs from buoyant bubbles inflated by AGN. Our simulations include the effects of the anisotropic particle diffusion introduced by magnetic fields. Our models are consistent with the X-ray morphology of AGN bubbles, with disruption being suppressed by the magnetic draping effect. We conclude that for such magnetic field topologies, a substantial fraction of CRs can be confined inside the bubbles on buoyant rise time-scales even when the parallel diffusivity coefficient is very large. For isotropic diffusion at a comparable level, CRs would leak out of the bubbles too rapidly to be consistent with radio observations. Thus, the long confinement times associated with the magnetic suppression of CRs diffusion can explain the presence of radio relics. We show that the partial escape of CRs is mostly confined to the wake of the rising bubbles and speculate that this effect could: (i) account for the excitation of the H alpha filaments trailing behind the bubbles in the Perseus cluster, (ii) inject entropy into the metal-enriched material being lifted by the bubbles and, thus, help to displace it permanently from the cluster centre and (iii) produce observable gamma-rays via the interaction of the diffusing CRs with the thermal intracluster medium.