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.
