Using the Starlight Polarization Efficiency Integral to Constrain Shapes
  and Porosities of Interstellar Grains
  We present a new method for using the observed starlight polarization and
polarized submm emission to constrain the shapes and porosities of interstellar
grains. We present the modified picket fence approximation (MPFA), and verify
that it is sufficiently accurate for modeling starlight polarization. We
introduce the starlight polarization integral $\Pi_{\rm obs}$ as a measure of
overall strength of the observed polarization of starlight, and the starlight
polarization efficiency integral $\Phi$ to characterize the effectiveness of
different grain types for producing polarization of starlight. The starlight
polarization integral $\Pi_{\rm obs}$ determines the mass-weighted alignment
$\langle f_{\rm align}\rangle$ of the grains. Approximating the aligned grains
in the interstellar medium as spheroids, we use $\Pi_{\rm obs}/\Phi$ to show
that the observed starlight polarization constrains the grains to have a
minimum degree of asphericity. For porosity ${\cal P}=0$, the minimum axial
ratio is $\sim$1.4 for oblate spheroids, or $\sim$1.8 for prolate spheroids. If
the grains are porous, more extreme axial ratios are required. The same grains
that produce the starlight polarization are able to provide the observed
polarized emission at submm wavelengths, but with further limits on shape and
porosity. Porosities ${\cal P}>0.75$ are ruled out. If interstellar grains can
be approximated by astrodust spheroids, we predict the ratio of 10$\mu{\rm m}$
polarization to starlight polarization $p_V$: $p(10\mu{\rm
m})/p_V=0.222\pm0.026$. For Cyg OB2-12 we predict $p(10\mu{\rm
m})=(2.1\pm0.3)\%$, which should be observable.
