Statistical study of turbulence from polarized synchrotron emission

When turbulent motions perturb magnetic field lines and produce magnetic fluctuations, the perturbations leave imprints of turbulence statistics on magnetic field. Observation of synchrotron radiation is one of the easiest ways to study turbulent magnetic field. Therefore, we study statistical properties of synchrotron polarization emitted from media with magnetohydrodynamic (MHD) turbulence, using both synthetic and MHD turbulence simulation data. First, we obtain the spatial spectrum and its derivative with respect to wavelength of synchrotron polarization arising from both synchrotron radiation and Faraday rotation. The study of spatial spectrum shows how the spectrum is affected by Faraday rotation and how we can recover the statistics of underlying turbulent magnetic field as well as turbulent density of electrons from interferometric observations that incorporate the effects of noise and finite telescopic beam size. Second, we study quadrupole ratio to quantitatively describe the degree of anisotropy introduced by magnetic field in the presence of MHD turbulence. We consider the case that the synchrotron emission and Faraday rotation are spatially separated, as well as the situation that the sources of the synchrotron radiation and thermal electrons causing Faraday rotation exist in the same region. In this study, we demonstrate that the spectrum and quadrupole ratio of synchrotron polarization can be very informative tools to get detailed information about the statistical properties of MHD turbulence from radio observations of diffuse synchrotron polarization.