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 ${53^{\circ}}\leq{\ell}\leq{192^{\circ}}$,
${-3^{\circ}}\leq{b}\leq{5^{\circ}}$ with an extension to ${b}={17.5^{\circ}}$
in the range ${101^{\circ}}\leq{\ell}\leq{116^{\circ}}$, 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 dataset, and analyze the dependence of these images on angular
resolution. The polarization gradients are filamentary, and the length of these
filaments is largest towards the Galactic anti-center, and smallest towards 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.
