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. 
Blakesley Burkhart, A. Lazarian, B. M. Gaensler
astro-ph.GA