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 \gg 1 ) , which characterizes a turbulent field dominated region , or small ( \eta \lesssim 0.2 ) , 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 - 2 m } , 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 .