The Massive and Distant Clusters of WISE Survey IV: The Distribution of
  Active Galactic Nuclei in Galaxy Clusters at $z\sim1$
  We present an analysis of the radial distribution of Active Galactic Nuclei
(AGN) in $2300$ galaxy clusters from the Massive and Distant Clusters of {\it
WISE} Survey (MaDCoWS). MaDCoWS provides the largest coverage of the
extragalactic sky for a cluster sample at $z\sim1$. We use literature catalogs
of AGN selected via optical, mid-infrared (MIR), and radio data, and by
optical-to-MIR (OIR) color. Stacking the radial distribution of AGN within the
$6\arcmin$ of the centers of MaDCoWS galaxy clusters, we find a distinct
overdensity of AGN within $1\arcmin$ of the galaxy cluster center for AGN of
all selection methods. The fraction of red galaxies that host AGN as a function
of clustercentric distance is, however, dependent on the AGN selection. The
fraction of red galaxies in cluster environments that host AGN selected by
optical signatures or blue OIR color is at a deficit compared to the field,
while MIR-selected and red OIR color AGN are enhanced in the centers of
clusters when compared to field levels. The radio-selected AGN fraction is more
than $2.5$ times that of the field, implying that the centers of clusters are
conducive to the triggering of radio emission in AGN. We do not find a
statistically significant change in the AGN fraction as a function of cluster
richness. We also investigate the correlation of central radio activity with
other AGN in galaxy clusters. Clusters with radio activity have more central
AGN than radio-inactive clusters, implying that central cluster radio activity
and AGN triggering may be linked.
