Studying Anisotropy of Compressible Magnetohydrodynamic Turbulence by
  Synchrotron Polarization Intensity
  Based on statistical analysis of synchrotron polarization intensity, we study
the anisotropic properties of compressible magnetohydrodynamic (MHD)
turbulence. The second-order normalized structure function, quadrupole ratio
modulus and anisotropic coefficient are synergistically used to characterize
the anisotropy of the polarization intensity. On the basis of pre-decomposition
data cubes, we first explore the anisotropy of the polarization intensity in
different turbulence regimes and find that the most significant anisotropy
occurs in the sub-Alfv\'enic regime. Using post-decomposition data cubes in
this regime, we then study the anisotropy of the polarization intensity from
Alfv\'en, slow and fast modes. Statistics of polarization intensity from
Alfv\'en and slow modes demonstrate the significant anisotropy while statistics
of polarization intensity from fast modes show isotropic structures, which is
consistent with the earlier results provided in Cho & Lazarian (2002). As a
result, both quadrupole ratio modulus and anisotropic coefficient for
polarization intensities can quantitatively recover the anisotropy of
underlying compressible MHD turbulence. The synergistic use of the two methods
helps enhance the reliability of the magnetic field measurement.
