Using the Starlight Polarization Efficiency Integral to Constrain Shapes and Porosities of Interstellar Grains

We have developed a new method for using the observed starlight polarization and polarized submillimeter emission to constrain the shapes and porosities of interstellar grains. We first present the modified picket-fence approximation and verify that it is sufficiently accurate for modeling starlight polarization. We then introduce the observed starlight polarization integral Π obs as a measure of the overall strength of the observed polarization of starlight, and the starlight polarization efficiency integral Φ to characterize the effectiveness of different grain types for producing polarization of starlight. The ratio Π obs /Φ determines the mass-weighted alignment 〈 f align 〉 of the grains. Approximating the aligned grains in the ISM as spheroids, we use Π obs /Φ to show that the observed starlight polarization constrains the grains to have a minimum degree of asphericity. For porosity  = 0 , the minimum axial ratio is ∼1.4 for oblate spheroids, or ∼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 submillimeter wavelengths but with further limits on shape and porosity. Porosities  ≳ 0.75 are ruled out. If interstellar grains can be approximated by “astrodust” spheroids, we predict the ratio of 10 μ m polarization to starlight polarization p V : p (10 μ m)/ p V = 0.219 ± 0.029. For Cyg OB2-12, we predict p (10 μ m) = (2.1 ± 0.3)%, which should be observable.