Polarization-shape alignment of IllustrisTNG star-forming galaxies

In star-forming disk galaxies, the radio continuum emission ($1$-$10\,$GHz) powered by star formation has an integrated polarization direction imperfectly aligned with the apparent disk minor axis. This polarization-shape alignment effect was previously observed in a small sample of local spirals. If this is prevalent for disk galaxies out to cosmological redshifts, novel measurements of cosmic birefringence and cosmic shear will be enabled by leveraging radio continuum surveys synergized with galaxy shape measurements. We calculate the polarization-shape misalignment angle for star-forming galaxies in the \texttt{IllustrisTNG50} simulation at $0 < z < 2$, assuming that additional polarized radio emission from an AGN is negligible. The alignment found for $z=0$ is consistent with local spiral data, but significantly deteriorates as redshift increases. Moreover, it degrades toward lower frequencies due to internal Faraday depolarization. Thanks to cosmic redshifting, observing higher-$z$ galaxies at a fixed frequency greatly mitigates degradation due to reduced Faraday depolarization at the source-frame frequency. We present analytic fits to the non-Gaussian misalignment angle distribution, and evaluate Fisher information per galaxy for measuring cosmic birefringence. For observation at 4.8 GHz, the effective RMS misalignment angle $\sigma_{\alpha,{\rm eff}}$ is $18^\circ$, $23^\circ$ and $33^\circ$ at $z=0$, $1$ and $2$, respectively. Analyzing $N$ independent galaxies reduces the uncertainty on an isotropic cosmic birefringence signal to $\sigma_{\alpha,{\rm eff}}/\sqrt{N}$, providing competitive sensitivity once large samples are available. Our results motivate pilot observations to empirically characterize polarization-shape alignment, facilitate forecasts of cosmology and fundamental physics applications that exploit this effect.