Properties of Interstellar Turbulence from Gradients of Linear Radio
  Polarization Maps
  Faraday rotation of linearly polarized radio signals provides a very
sensitive probe of fluctuations in the interstellar magnetic field and ionized
gas density resulting from magnetohydrodynamic (MHD) turbulence. We used a set
of statistical tools to analyze images of the spatial gradient of linearly
polarized radio emission ($|\nabla \textbf{P}|$) from the ISM for both
observational data from a test image of the Southern Galactic Plane Survey
(SGPS) and isothermal simulations of MHD turbulence. We compared the
observational data with results of synthetic observations obtained with the
simulations of 3D turbulence. Visually, in both data sets, a complex network of
filamentary structures is seen. Our analysis shows that the filaments in the
gradient can be produced by shocks as well as random fluctuations
characterizing the non-differentiable field of MHD turbulence. The latter
dominates for subsonic turbulence, while the former dominates for supersonic
turbulence. In order to quantitatively characterize these differences we use
the topology tool known as a genus curve as well as the moments of the image
distribution. We find that higher values for the moments correspond to cases of
$|\nabla \textbf{P}|$ with larger Mach numbers, but the strength of the
dependency is connected to the telescope angular resolution. In regards to the
topology, the supersonic filaments observed in $|\nabla \textbf{P}|$ have a
positive genus shift, which indicates a "swisscheese" like topology, while the
subsonic cases show a negative genus, indicating a "clump" like topology. In
the case of the genus, the dependency on the telescope resolution is not as
strong. The SGPS test region data has a distribution and morphology that
matches subsonic to transsonic type turbulence, which independently confirms
what is now expected for the WIM.
