Inferring magnetic field strengths in high-redshift lensing galaxies from Faraday rotation measure observations
Observations of Faraday rotation in the lensing galaxy of CLASS B1152+199 at z = 0.439 suggest that efficient dynamo mechanisms had already amplified galactic magnetic fields by this epoch. We assess the reliability of this method for deriving magnetic field strengths and the likelihood of observing similarly large Faraday rotation differences. We select 64 star-forming disk galaxies from the TNG50 cosmological magnetohydrodynamical simulation, matched to CLASS B1152+199 in mass and redshift, and forward model them using polarized radiative transfer with POLARIS and subsequent RM synthesis. TNG50 predicts characteristic large-scale field strengths of B$_0$ = 1.9-15.6 $μ$G for individual galaxies, while the combined sample yields B$_0$ = 10.3 $μ$G. Field strengths B$_{obs}$ inferred from the synthetic observations generally recover B$_0$ within a factor of three. B$_{obs}$ depends only weakly on the assumed magnetic field geometry, whereas galaxy inclination and beam depolarization have stronger effects. The differential rotation measure recovered from RM synthesis remains correlated with the directly integrated value, although beam depolarization systematically reduces its magnitude. Only 1.41% of directly integrated sightline pairs reproduce the observed $Δ$RM = 1040 $\pm$ 60 rad m$^{-2}$ of CLASS B1152+199, increasing to 3.16% for sightlines at galactocentric distances comparable to the observed 2.6 and 6.5 kpc. Differential Faraday rotation of gravitationally lensed sources therefore provides a robust probe of large-scale magnetic fields, while the large $Δ$RM of CLASS B1152+199 is relatively rare among the considered TNG50 analog galaxies.