A New Method to Trace Three-dimensional Magnetic Field Structure within
  Molecular Clouds Using Dust Polarization
  The complete three-dimensional structure of the magnetic field within
molecular clouds has eluded determination despite its high value in determining
controlling factors in the star formation process, as it cannot be directly
probed observationally. Considering that inclination of the magnetic field
relative to the plane of sky is one of the major sources of depolarization of
thermal emission from dust in molecular clouds, we propose here a new method to
estimate the inclination angle of the cloud-scale magnetic field based on the
statistical properties of the observed polarization fraction. We test this
method using a series of Monte Carlo experiments, and find that the method
works well provided that deviations of magnetic field direction from the
averaged values are small. When applied to synthetic observations of numerical
simulations of star-forming clouds, our method gives fairly accurate
measurements of the mean magnetic field inclination angle (within
$10^\circ-25^\circ$), which can further be improved if we restrict our
technique to regions of low dispersion in polarization angles ${\cal S}$. We
tested our method on the BLASTPol polarimetric observations of the Vela C
molecular cloud complex, which suggests that the magnetic field of Vela C has a
high inclination angle ($\sim 60^\circ$), consistent with previous analyses.
