Studying the Properties of Compressible Magnetohydrodynamic Turbulence Using Synchrotron Fluctuation Statistics

Abstract

We study the observable properties of compressible magnetohydrodynamic (MHD) turbulence covering different turbulence regimes, based on synthetic synchrotron observations arising from 3D MHD numerical simulations. Using the synchrotron emissivity and intensity, we first explore how the cosmic-ray spectral indices affect the measurements of the turbulence properties by employing normalized correlation functions. We then study how the anisotropy of the synchrotron total and polarization intensities arising from the three fundamental MHD modes varies with the viewing angle, i.e., the angle between the mean magnetic field and the line of sight. We employ the ratio of the quadrupole moment to the monopole moment (QM) for this purpose. Our numerical results demonstrate that: (1) the two-point correlation function of synchrotron statistics for the arbitrary cosmic-ray spectral index is related to the special case of the magnetic field index γ = 2, in agreement with the analytical formulae provided by Lazarian & Pogosyan; (2) the anisotropy of the synchrotron total and polarization intensities arising from the Alfvén and slow modes increases with the increase of the viewing angle, while that of fast mode remains almost unchanged with the viewing angle; and (3) the analytical formulae of the synchrotron intensities for studying turbulence can be applied to describe the statistics of the polarization intensities, and the QM can be successfully used to recover the turbulence anisotropy. This study validates the analytical approach of Lazarian & Pogosyan and opens up a way of studying turbulence from observations.