Polarization Gradient Study of Interstellar Medium Turbulence Using the Canadian Galactic Plane Survey

We have investigated the magneto-ionic turbulence in the interstellar medium through spatial gradients of the complex radio polarization vector in the Canadian Galactic Plane Survey (CGPS). The CGPS data cover 1300 square degrees, over the range , , with an extension to in the range , and arcminute resolution at 1420 MHz. Previous studies found a correlation between the skewness and kurtosis of the polarization gradient and the Mach number of the turbulence, or assumed this correlation to deduce the Mach number of an observed turbulent region. We present polarization gradient images of the entire CGPS data set, and analyze the dependence of these images on angular resolution. The polarization gradients are filamentary, and the length of these filaments is largest toward the Galactic anti-center, with the smallest toward the inner Galaxy. This may imply that small-scale turbulence is stronger in the inner Galaxy, or that we observe more distant features at low Galactic longitudes. For every resolution studied, the skewness of the polarization gradient is influenced by the edges of bright polarization gradient regions, which are not related to the turbulence revealed by the polarization gradients. We also find that the skewness of the polarization gradient is sensitive to the size of the box used to calculate the skewness, but insensitive to Galactic longitude, implying that the skewness only probes the number and magnitude of the inhomogeneities within the box. We conclude that the skewness and kurtosis of the polarization gradient are not ideal statistics for probing natural magneto-ionic turbulence.