Radio sources in galaxy clusters:: Radial distribution, and 1.4 Ghz and K-band bivariate luminosity function

We present a statistical study of several fundamental properties of radio sources in nearby clusters (z <= 0.2), including the radial distribution within clusters, the radio luminosity function (RLF), and the fraction of galaxies that is radio active ( radio active fraction, RAF). The analysis is carried out for a sample of 573 clusters detected in the X-ray and also observed at 1.4 GHz in the NRAO VLA Sky Survey. The X-ray data are used to locate the cluster center and estimate cluster mass. In addition, near-IR data from the Two Micron All-Sky Survey are used to identify the brightest cluster galaxies (BCGs) and to construct the K-band luminosity function. Our main results include ( 1) The surface density profile of radio-loud active galactic nuclei (AGNs) is much more concentrated than that of all galaxies and can be described by the Navarro, Frenk, & White profile with concentration similar to 25. More powerful radio sources are more concentrated than the weaker ones. ( 2) A comparison of the RLFs in the clusters and in the field shows that the cluster AGN number density is about 5700 times higher, corresponding to a factor of 6.8 higher probability of a galaxy being radio active in the cluster than in the field. We suggest that about 40% -50% of radio-loud AGNs in clusters may reside in low-mass galaxies (M-K greater than or similar to - 23); if an equivalent population exists in the field, the RLFs in the two environments can be brought into better agreement. The strongest support for the existence of this low-mass population comes from their spatial distribution and RLF. ( 3) The RAFs of cluster galaxies of different stellar mass are estimated directly. About 5% of galaxies more luminous than the characteristic luminosity (M-K <= M-K* approximate to -24) host radio-loud AGNs. The RAF for BCGs is > 30%, and depends on the cluster mass. Compared to the field population, cluster galaxies have 5-10 times higher RAF. Combining the AGN RLF and spatial distribution within clusters, we estimate that they may inject an energy of similar to 0.13 keV per particle to the intracluster medium near the cluster center. We also investigate the degree of contamination by cluster radio sources on the yields of Sunyaev-Zel'dovich effect (SZE) cluster surveys. Under our simple model extrapolating to higher frequency, we estimate that as many as 10% of clusters detected at 150 GHz may host AGNs whose flux is comparable to the cluster SZE signal. The fraction is expected to be much higher at lower frequency.