Redshift evolution of the 1.4 GHz volume averaged radio luminosity
  function in clusters of galaxies
  By cross-correlating large samples of galaxy clusters with publicly available
radio source catalogs, we construct the volume-averaged radio luminosity
function (RLF) in clusters of galaxies, and investigate its dependence on
cluster redshift and mass. In addition, we determine the correlation between
the cluster mass and the radio luminosity of the brightest source within 50 kpc
from the cluster center. We use two cluster samples: the optically selected
maxBCG cluster catalog and a composite sample of X-ray selected clusters. The
radio data come from the VLA NVSS and FIRST surveys. We use scaling relations
to estimate cluster masses and radii to get robust estimates of cluster
volumes. We determine the projected radial distribution of sources, for which
we find no dependence on luminosity or cluster mass. Background and foreground
sources are statistically accounted for, and we account for confusion of radio
sources by adaptively degrading the resolution of the radio source surveys. We
determine the redshift evolution of the RLF under the assumption that its
overall shape does not change with redshift. Our results are consistent with a
pure luminosity evolution of the RLF in the range 0.1 < z < 0.3 from the
optical cluster sample. The X-ray sample extends to higher redshift and yields
results also consistent with a pure luminosity evolution. We find no direct
evidence of a dependence of the RLF on cluster mass from the present data,
although the data are consistent with the most luminous sources only being
found in high-mass systems.
