Studies of regular and random magnetic fields in the ISM: statistics of   polarization vectors and the Chandrasekhar-Fermi technique
  Polarimetry is extensively used as a tool to trace the interstellar magnetic field projected on the plane of sky. Moreover, it is also possible to estimate the magnetic field intensity from polarimetric maps based on the Chandrasekhar-Fermi method. In this work, we present results for turbulent, isothermal, 3-D simulations of sub/supersonic and sub/super-Alfvenic cases. With the cubes, assuming perfect grain alignment, we created synthetic polarimetric maps for different orientations of the mean magnetic field with respect to the line of sight (LOS). We show that the dispersion of the polarization angle depends on the angle of the mean magnetic field regarding the LOS and on the Alfvenic Mach number. However, the second order structure function of the polarization angle follows the relation $SF \propto l^{\alpha}$, $\alpha$ being dependent exclusively on the Alfvenic Mach number. The results show an anti-correlation between the polarization degree and the column density, with exponent $\gamma \sim -0.5$, in agreement with observations, which is explained by the increase in the dispersion of the polarization angle along the LOS within denser regions. However, this effect was observed exclusively on supersonic, but sub-Alfvenic, simulations. For the super-Alfvenic, and the subsonic model, the polarization degree showed to be intependent on the column density. Our major quantitative result is a generalized equation for the CF method, which allowed us to determine the magnetic field strength from the polarization maps with errors $< 20%$. We also account for the role of observational resolution on the CF method. 
D. Falceta-Goncalves (NAT-Unicsul, UW-Madison), A. Lazarian   (UW-Madison), G. Kowal (UW-Madison)