PROPERTIES OF INTERSTELLAR TURBULENCE FROM GRADIENTS OF LINEAR 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 (vertical bar del P vertical bar) for both observational data from a test image of the SouthernGalactic Plane Survey (SGPS) and isothermal three-dimensional simulations of MHD turbulence. Visually, in both observations and simulations, a complex network of filamentary structures is seen. Our analysis shows that the filaments in vertical bar del P vertical bar can be produced both by interacting shocks and random fluctuations characterizing the non-differentiable field of MHD turbulence. The latter dominates for subsonic turbulence, while the former is only present in supersonic turbulence. We show that supersonic and subsonic turbulence exhibit different distributions as well as different morphologies in themaps of vertical bar del P vertical bar. Particularly, filaments produced by shocks show a characteristic "double jump" profile at the sites of shock fronts resulting from delta function-like increases in the density and/or magnetic field, while those produced by subsonic turbulence show a single jump profile. In order to quantitatively characterize these differences, we use the topology tool known as the genus curve as well as the probability distribution function moments of the image distribution. We find that higher values for the moments correspond to cases of vertical bar del P vertical bar with larger sonic Mach numbers. The genus analysis of the supersonic simulations of vertical bar del P vertical bar reveals a "swiss cheese" topology, while the subsonic cases have characteristics of a "clump" topology. Based on the analysis of the genus and the higher order moments, the SGPS test region data have a distribution and morphology that match subsonic-to transonic-type turbulence, which confirms what is now expected for the warm ionized medium.