Recovering 3D Magnetic Turbulence from Single-frequency Faraday Screens

Abstract Statistics of polarized synchrotron radiation carry information about the properties of the underlying turbulence. We consider a setup in which synchrotron radiation is emitted in a distant volume and then passes through a turbulent screen that induces Faraday rotation. Using both MHD simulations and synthetic turbulence spectra, we explore the spectrum of observed polarization directions measured at a single frequency as a diagnostic for recovering the statistics of turbulence in both the emitting region and the Faraday rotation volume. We compare these results with our analytical expectations. In doing so, we compare the directional spectrum with the wavelength-derivative diagnostic explored earlier by Lazarian & Pogosyan. We demonstrate that the directional spectrum exhibits greater sensitivity to the turbulence in the Faraday rotation volume. We provide an observer-friendly criterion to determine whether it samples turbulence in the synchrotron-emitting region or in the Faraday rotation region. These results open a practical pathway for extracting turbulence statistics from existing and forthcoming single-band radio polarimetry.