On the Shapes of Interstellar Grains: Modeling Extinction and
  Polarization by Spheroids and Continuous Distributions of Ellipsoids
  Although interstellar grains are known to be aspherical, their actual shapes
remain poorly constrained. We assess whether three continuous distributions of
ellipsoidal shapes from the literature are suitable for describing the shapes
of interstellar grains. Randomly-selected shapes from each distribution are
shown as illustrations. The often-used Bohren-Huffman CDE includes a very large
fraction of extreme shapes: fully 10% of random draws have axial ratio $a_3/a_1
> 19.7$, and 5% have $a_3/a_1 > 33$. The CDE2 distribution includes a much
smaller fraction of extreme shapes, and appears to be more realistic. For each
of the three CDEs considered, we derive shape-averaged cross sections for
extinction and polarization in the Rayleigh limit. Finally, we describe a
method for "synthesizing" a dielectric function for an assumed shape or shape
distribution if the actual absorption cross sections per grain volume in the
Rayleigh limit are known from observations. This synthetic dielectric function
predicts the wavelength dependence of polarization, which can then be compared
to observations to constrain the grain shape.
