  Distant powerful radio-loud active galactic nuclei (RLAGN) tend to reside in
dense environments and are commonly found in proto-clusters at z > 1.3. We
examine whether this occurs because RLAGN are hosted by massive galaxies, which
preferentially reside in rich environments. We compare the environments of
powerful RLAGN at 1.3 < z < 3.2 from the CARLA survey to a sample of
radio-quiet galaxies matched in mass and redshift. We find the environments of
RLAGN are significantly denser than those of radio-quiet galaxies, implying
that not more than 50% of massive galaxies in this epoch can host powerful
radio-loud jets. This is not an observational selection effect as we find no
evidence to suggest it is easier to observe the radio emission when the galaxy
resides in a dense environment. We therefore suggest that the dense Mpc-scale
environment fosters the formation of a radio-jet from an AGN. We show that the
number density of potential RLAGN host galaxies is consistent with every >
10^14 solar mass cluster having experienced powerful radio-loud feedback of
duration ~60 Myr during 1.3 < z < 3.2. This feedback could heat the
intracluster medium to the extent of 0.5-1 keV per gas particle, which could
limit the amount of gas available for further star formation in the
proto-cluster galaxies.
