2005MNRAS.364.1343D

We extend our earlier work on cluster cores with distinct radio bubbles, adding more active bubbles, i.e. those with GHz radio emission, to our sample and also investigating `ghost bubbles', i.e. those without GHz radio emission. 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. Constraints on the ages of the active bubbles confirm that the ratio of the energy factor, k, to the volume filling factor, f, lies within the range 1 ≲k/f≲ 1000. On the assumption that there is pressure equilibrium between the radio-emitting plasma and the surrounding thermal X-ray gas, none of the radio lobes has equipartition between the relativistic particles and the magnetic field. A Monte Carlo simulation of the data led to the conclusion that there are not enough bubbles present in the current sample to be able to determine the shape of the population. An analysis of the ghost bubbles in our sample showed that on the whole they have higher upper limits on k/f than the active bubbles, especially when compared with those in the same cluster. A study of the Brightest 55 (B55) cluster sample shows that 17, possibly 20, clusters required some form of heating as they have a short central cooling time, t_cool≤ 3Gyr, and a large central temperature drop, T_centre/T_outer< 1/2. Of these, between 12 (70 per cent) and 15 (75 per cent) contain bubbles. This indicates that the duty cycle of bubbles is large in such clusters and that they can play a major role in the heating process.