On the prevalence of radio-loud active galactic nuclei in brightest cluster galaxies: implications for AGN heating of cooling flows

The prevalence of radio-loud active galactic nucleus (AGN) activity in present-day massive haloes is determined using a sample of 625 nearby groups and clusters selected from the Sloan Digital Sky Survey. Brightest group and cluster galaxies (BCGs) are more likely to host a radio-loud AGN than other galaxies of the same stellar mass (by below a factor of 2 at a stellar mass of similar to 5 x 10(11) M-circle dot, but rising to over an order of magnitude below 10(11) M-circle dot). The distribution of radio luminosities for BCGs does not depend on mass, however, and is similar to that of field galaxies of the same stellar mass. Neither the radio-loud fraction nor the radio luminosity distribution of BCGs depends strongly on the velocity dispersion of the host cluster. The radio-AGN fraction is also studied as a function of distance from the cluster centre. Only within 0.2r(200) do cluster galaxies exhibit an enhanced likelihood of radio-loud AGN activity, which approaches that of the BCGs. In contrast to the radio properties, the fraction of galaxies with optical emission-line AGN activity is suppressed within r(200) in groups and clusters, decreasing monotonically towards the cluster centre. It is argued that the radio-loud AGN properties of both BCGs and non-BCGs can naturally be explained if this activity is fuelled by cooling from hot gas surrounding the galaxy. Using observational estimates of the mechanical output of the radio jets, the time-averaged energy output associated with recurrent radio source activity is estimated for all group and cluster galaxies. Within the cooling radius of the cluster, the radio-mode heating associated with the BCG dominates over that of all other galaxies combined. The scaling between total radio-AGN energy output and cluster velocity dispersion is observed to be considerably shallower than the similar to sigma(4)(v) scaling of the radiative cooling rate. Thus, unless either the mechanical-to-radio luminosity ratio or the efficiency of converting AGN mechanical energy into heating increases by 2-3 orders of magnitude between groups and rich clusters, radio-mode heating will not balance radiative cooling in systems of all masses. In groups, radio-AGN heating probably overcompensates the radiative cooling losses, and this may account for the observed entropy floor in these systems. In the most massive clusters, an additional heating process (most likely thermal conduction) may be required to supplement the AGN heating.