  Active galactic nuclei (AGN) play an integral role in galaxy formation and
evolution by influencing galaxies and their environments through radio jet
feedback. Historically, interpreting observations of radio galaxies and
quantifying radio jet feedback has been challenging due to degeneracies between
their physical parameters. In particular, it is well-established that different
combinations of jet kinetic power and environment density can yield
indistinguishable radio continuum properties, including apparent size and
Stokes I luminosity. We present an approach to breaking this degeneracy by
probing the line-of-sight environment with Faraday rotation. We study this
effect in simulations of three-dimensional relativistic magnetohydrodynamic AGN
jets in idealised environments with turbulent magnetic fields. We generate
synthetic Stokes I emission and Faraday rotation measure (RM) maps, which
enable us to distinguish between our simulated sources. We find enhanced RMs
near the jet head and lobe edges and an RM reversal across the jet axis. We
show that increasing the environment density and the average cluster magnetic
field strength broadens the distribution of Faraday rotation measure values. We
study the depolarisation properties of our sources, finding that the hotspot
regions depolarise at lower frequencies than the lobes. We quantify the effect
of depolarisation on the RM distribution, finding that the frequency at which
the source is too depolarised to measure the RM distribution accurately is a
probe of environmental properties. This technique offers a range of new
opportunities for upcoming surveys, including probing radio galaxy environments
and determining more accurate estimates of the AGN feedback budget.
