The duty cycle of radio-mode feedback in complete samples of clusters
  The Chandra X-ray Observatory has revealed X-ray bubbles in the intracluster
medium (ICM) of many nearby cooling flow clusters. The bubbles trace feedback
that is thought to couple the central active galactic nucleus (AGN) to the ICM,
helping to stabilize cooling flows and govern the evolution of massive
galaxies. However, the prevalence and duty cycle of such AGN outbursts is not
well understood. To this end, we study how cooling is balanced by bubble
heating for complete samples of clusters (the Brightest 55 clusters of
galaxies, hereafter B55, and the HIghest X-ray FLUx Galaxy Cluster Sample,
HIFLUGCS). We find that the radio luminosity of the central galaxy only exceeds
2.5 x 10^30 erg s^-1 Hz^-1 in cooling flow clusters. This result implies a
connection between the central radio source and the ICM, as expected if AGN
feedback is operating. Additionally, we find a duty cycle for radio mode
feedback, the fraction of time that a system possesses bubbles inflated by its
central radio source, of > 69 per cent for B55 and > 63 per cent for HIFLUGCS.
These duty cycles are lower limits since some bubbles are likely missed in
existing images. We used simulations to constrain the bubble power that might
be present and remain undetected in the cooling flow systems without detected
bubbles. Among theses systems, almost all could have significant bubble power.
Therefore, our results imply that the duty cycle of AGN outbursts with the
potential to heat the gas significantly in cooling flow clusters is at least 60
per cent and could approach 100 per cent.
