Studying Magnetohydrodynamic Turbulence with Synchrotron Polarization Dispersion

We test a new technique of studying magnetohydrodynamic (MHD) turbulence suggested by Lazarian \& Pogosyan, using synthetic synchrotron polarization observations. This paper focuses on a one-point statistics, which is termed the polarization frequency analysis, that is characterized by the variance of polarized emission as a function of the square of wavelengths along a single line of sight. We adopt a ratio $\eta$ of the standard deviation of the line-of-sight turbulent magnetic field to the line-of-sight mean magnetic field to depict the level of turbulence. When this ratio is either large ($\eta\gg1$), which characterizes a turbulent field dominated region, or small ($\eta\lesssim0.2$), which characterizes a mean field dominated region, we obtain the polarization variance $\left<P^2\right>\propto\lambda^{-2}$ and $\left<P^2\right>\propto\lambda^{-2-2m}$, respectively. At small $\eta$, i.e., the mean field dominated region, we successfully recover the turbulent spectral index by the polarization variance. We find that our simulations agree well with the theoretical prediction of Lazarian \& Pogosyan. With existing and upcoming data cubes from the Low-Frequency Array for Radio astronomy (LOFAR) and Square Kilometer Array (SKA), this new technique can be applied to study the magnetic turbulence in the Milky Way and other galaxies.