Particle Energies and Filling Fractions of Radio Bubbles in Cluster Cores

Using Chandra images of cluster cores with clear radio bubbles, we have determined k, which is the ratio of the total particle energy to that of the electrons radiating between 10 MHz and 10 GHz. Radiative and dynamical constraints on the bubbles indicate that the ratio of the energy factor, k, to the volume filling factor, f , lies within the range 1 . k/f . 1000. Assuming pressure equilibrium between the radio-emitting plasma and the surrounding Xray gas, none of the lobes have equipartition between relativistic particles and magnetic field. There is no evidence for any dependence of the upper limit of the k/f ratio on any physical parameter of the cluster or the radio source. The distribution of the upper limit on k/f appears to be bimodal, the value for some clusters being ∼ 3 and for the others ∼ 300. We show that this is may due to the composition of the jet which forms the bubbles, the variation in the volume filling fraction or variation in the amount of re-acceleration occurring in the bubble.