Constraining Radio Mode Feedback in Galaxy Clusters with the Cluster
  Radio AGN Properties to z$\sim$1
  We study the properties of the Sydney University Molonglo Sky Survey (SUMSS)
843~MHz radio AGN population in galaxy clusters from two large catalogs created
using the Dark Energy Survey (DES): $\sim$11,800 optically selected RM-Y3 and
$\sim$1,000 X-ray selected MARD-Y3 clusters. We show that cluster radio loud
AGN are highly concentrated around cluster centers to $z\sim1$. We measure the
halo occupation number for cluster radio AGN above a threshold luminosity,
finding that the number of radio AGN per cluster increases with cluster halo
mass as $N\propto M^{1.2\pm0.1}$ ($N\propto M^{0.68\pm0.34}$) for the RM-Y3
(MARD-Y3) sample. Together, these results indicate that radio mode feedback is
favoured in more massive galaxy clusters. Using optical counterparts for these
sources, we demonstrate weak redshift evolution in the host broad band colors
and the radio luminosity at fixed host galaxy stellar mass. We use the redshift
evolution in radio luminosity to break the degeneracy between density and
luminosity evolution scenarios in the redshift trend of the radio AGN
luminosity function (LF). The LF exhibits a redshift trend of the form
$(1+z)^\gamma$ in density and luminosity, respectively, of $\gamma_{\rm
D}=3.0\pm0.4$ and $\gamma_{\rm P}=0.21\pm0.15$ in the RM-Y3 sample, and
$\gamma_{\rm D}=2.6\pm0.7$ and $\gamma_{\rm P}=0.31\pm0.15$ in MARD-Y3. We
discuss the physical drivers of radio mode feedback in cluster AGN, and we use
the cluster radio galaxy LF to estimate the average radio-mode feedback energy
as a function of cluster mass and redshift and compare it to the core
($<0.1R_{500}$) X-ray radiative losses for clusters at $z<1$.
