Polarization of Dust Emission in Clumpy Molecular Clouds and Cores
  Grain alignment theory has reached the stage where quantitative predictions of the degree of alignment and its variations with optical depth are possible. With the goal of studying the effect of clumpiness on the sub-millimeter and far infrared polarization we computed the polarization due to alignment via radiative torques within clumpy models of cores and molecular clouds. Our models were based upon a highly inhomogeneous simulation of compressible magnetohydrodynamic turbulence. The P-I relations for our models reproduce those seen in observations. We show that the degree of polarization observed is extremely sensitive to the upper grain size cut-off, and is less sensitive to changes in the radiative anisotropy. Furthermore, despite a variety of dust temperatures along a single line of sight through our core and amongst dust grains of different sizes, the assumption of isothermality amongst the aligned grains does not introduce a significant error. Our calculations indicate that sub-mm polarization vectors can be reasonably good tracers for the underlying magnetic field structure, even for relatively dense clouds (A_V~10 to the cloud center).   The current predictive power of the grain alignment theory should motivate future polarization observations using the next generation of multi-wavelength sub-mm polarimeters such as those proposed for SOFIA. 
T. J. Bethell, A. Chepurnov, A. Lazarian, J. Kim