Advanced Diagnostics for the Study of Linearly Polarized Emission. II: Application to Diffuse Interstellar Radio Synchrotron Emission.

Diagnostics of polarized emission provide us with valuable information on the Galactic magnetic field and the state of turbulence in the interstellar medium, which cannot be obtained from synchrotron intensity alone. In Paper I (Herron et al. 2017b), we derived polarization diagnostics that are rotationally and translationally invariant in the $Q$-$U$ plane, similar to the polarization gradient. In this paper, we apply these diagnostics to simulations of ideal magnetohydrodynamic turbulence that have a range of sonic and Alfv\'enic Mach numbers. We generate synthetic images of Stokes $Q$ and $U$ for these simulations, for the cases where the turbulence is illuminated from behind by uniform polarized emission, and where the polarized emission originates from within the turbulent volume. From these simulated images we calculate the polarization diagnostics derived in Paper I, for different lines of sight relative to the mean magnetic field, and for a range of frequencies. For all of our simulations, we find that the polarization gradient is very similar to the generalized polarization gradient, and that both trace spatial variations in the magnetoionic medium for the case where emission originates within the turbulent volume, provided that the medium is not supersonic. We propose a method for distinguishing the cases of emission coming from behind or within a turbulent, Faraday rotating medium, and a method to partly map the rotation measure of the observed region. We also speculate on statistics of these diagnostics that may allow us to constrain the physical properties of an observed turbulent region.