The Massive and Distant Clusters of WISE Survey. VIII. Radio Activity in
  Massive Galaxy Clusters
  We present a study of the central radio activity of galaxy clusters at high
redshift. Using a large sample of galaxy clusters at $0.7<z<1.5$ from the
Massive and Distant Clusters of {\it WISE} Survey and the Faint Images of the
Radio Sky at Twenty-Centimeters $1.4$~GHz catalog, we measure the fraction of
clusters containing a radio source within the central $500$~kpc, which we term
the cluster radio-active fraction, and the fraction of cluster galaxies within
the central $500$~kpc exhibiting radio emission. We find tentative
($2.25\sigma$) evidence that the cluster radio-active fraction increases with
cluster richness, while the fraction of cluster galaxies that are
radio-luminous ($L_{1.4~\mathrm{GHz}}\geq10^{25}$~W~Hz$^{-1}$) does not
correlate with richness at a statistically significant level. Compared to that
calculated at $0 < z < 0.6$, the cluster radio-active fraction at $0 < z < 1.5$
increases by a factor of $10$. This fraction is also dependent on the radio
luminosity. Clusters at higher redshift are much more likely to host a radio
source of luminosity $L_{1.4~\mathrm{GHz}}\gtrsim10^{26}$~W~Hz$^{-1}$ than are
lower redshift clusters. We compare the fraction of radio-luminous cluster
galaxies to the fraction measured in a field environment. For $0.7<z<1.5$, we
find that both the cluster and field radio-luminous galaxy fraction increases
with stellar mass, regardless of environment, though at fixed stellar mass,
cluster galaxies are roughly $2$ times more likely to be radio-luminous than
field galaxies.
