High Frequency Cluster Radio Galaxies: Luminosity Functions and
  Implications for SZE Selected Cluster Samples
  We study the overdensity of point sources in the direction of X-ray-selected
galaxy clusters from the Meta-Catalog of X-ray detected Clusters of galaxies
(MCXC; $\langle z \rangle = 0.14$) at South Pole Telescope (SPT) and Sydney
University Molonglo Sky Survey (SUMSS) frequencies. Flux densities at 95, 150
and 220 GHz are extracted from the 2500 deg$^2$ SPT-SZ survey maps at the
locations of SUMSS sources, producing a multi-frequency catalog of radio
galaxies. In the direction of massive galaxy clusters, the radio galaxy flux
densities at 95 and 150 GHz are biased low by the cluster Sunyaev-Zel'dovich
Effect (SZE) signal, which is negative at these frequencies. We employ a
cluster SZE model to remove the expected flux bias and then study these
corrected source catalogs. We find that the high frequency radio galaxies are
centrally concentrated within the clusters and that their luminosity functions
(LFs) exhibit amplitudes that are characteristically an order of magnitude
lower than the cluster LF at 843 MHz. We use the 150 GHz LF to estimate the
impact of cluster radio galaxies on an SPT-SZ like survey. The radio galaxy
flux typically produces a small bias on the SZE signal and has negligible
impact on the observed scatter in the SZE mass-observable relation. If we
assume there is no redshift evolution in the radio galaxy LF then $1.8\pm0.7$
percent of the clusters would be lost from the sample. Allowing for redshift
evolution of the form $(1+z)^{2.5}$ increases the incompleteness to $5.6\pm1.0$
percent. Improved constraints on the evolution of the cluster radio galaxy LF
require a larger cluster sample extending to higher redshift.
