A volume-limited sample of X-ray galaxy groups and clusters - II. X-ray
  cavity dynamics
  We present the results of our study of a volume-limited sample (z <= 0.071)
of 101 X-ray galaxy groups and clusters, in which we explore the X-ray cavity
energetics. Out of the 101 sources in our parent sample, X-ray cavities are
found in 30 of them, all of which have a central cooling time of less than3
Gyr. New X-ray cavities are detected in three sources. We focus on the subset
of sources that have a central cooling time of less than 3 Gyr, whose active
galactic nucleus (AGN) duty cycle is approximately 61 percent (30/49). This
rises to over 80 percent for a central cooling time of less than 0.5 Gyr. When
projection effects and central radio source detection rates are considered, the
actual duty cycle is probably much higher. In addition, we show that data
quality strongly affects the detection rates of X-ray cavities. After
calculating the cooling luminosity and cavity powers of each source with
cavities, it is evident that the bubbling process induced by the central AGN
has to be, on average, continuous, to offset cooling. We find that the radius
of the cavities, r, loosely depends on the ambient gas temperature as T^0.5,
above about 1.5 keV, with much more scatter below that temperature. Finally, we
show that, at a given location in a group or cluster, larger bubbles travel
faster than smaller ones. This means that the bubbles seen at larger distances
from cluster cores could be the result of the merging of several smaller
bubbles, produced in separate AGN cycles.
