We present a statistical study of several fundamental properties of radio sources in nearby clusters ( z \leq 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 profile with concentration \sim 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 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 } \gtrsim - 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 } \leq M _ { K* } \approx - 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 \sim 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 .