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.