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, 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 NVSS. K-band data from the 2MASS are used to identify the brightest cluster galaxies (BCGs), and to construct the K-band LF. Our main results include: (1) The surface density profile of radio-loud AGNs is much more concentrated than that of all galaxies, and can be described by the NFW profile with concentration ~ 25. (2) A comparison of the RLFs in the clusters and in the field shows that the cluster AGN number density is about 5,700 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>-23). (3) The RAFs of cluster galaxies of different stellar mass are estimated. About 5% of galaxies more luminous than the characteristic luminosity (M_K<M_*~-24) host radio-loud AGNs. The RAF for BCGs is >30%, and depends on the cluster mass. Compare 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 ~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 SZE cluster surveys, and estimate that as many as 10% of clusters detected at 150 GHz may host AGNs whose flux is comparable to the cluster SZE signal. (abridged)