We extend our earlier work on cluster cores with distinct radio bubbles , adding more active bubbles , i.e .
those with { \thinspace GHz } radio emission , to our sample , and also investigating “ ghost bubbles , ” i.e .
those without { \thinspace GHz } radio emission .
We have determined k , which is the ratio of the total particle energy to that of the electrons radiating between 10 { \thinspace MHz } and 10 { \thinspace 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 \lesssim k / f \lesssim 1000 .
In 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 to those in the same cluster .
A study of the Brightest 55 cluster sample shows that 17 , possibly 20 , clusters required some form of heating as they have a short central cooling time , t _ { cool } \leq 3 \thinspace Gyr , 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 .