Statistical Assessment of Shapes and Magnetic Field Orientations in
  Molecular Clouds through Polarization Observations
  We present a novel statistical analysis aimed at deriving the intrinsic
shapes and magnetic field orientations of molecular clouds using dust emission
and polarization observations by the Hertz polarimeter. Our observables are the
aspect ratio of the projected plane-of-the-sky cloud image, and the angle
between the mean direction of the plane-of-the-sky component of the magnetic
field and the short axis of the cloud image. To overcome projection effects due
to the unknown orientation of the line-of-sight, we combine observations from
24 clouds, assuming that line-of-sight orientations are random and all are
equally probable. Through a weighted least-squares analysis, we find that the
best-fit intrinsic cloud shape describing our sample is an oblate disk with
only small degrees of triaxiality. The best-fit intrinsic magnetic field
orientation is close to the direction of the shortest cloud axis, with small
(~24 deg) deviations toward the long/middle cloud axes. However, due to the
small number of observed clouds, the power of our analysis to reject
alternative configurations is limited.
