Sensitivity of Polarization to Grain Shape: I. Convex Shapes

Abstract

Aligned interstellar grains produce polarized extinction (observed at wavelengths from the far-ultraviolet to the mid-infrared), and polarized thermal emission (observed at far-infrared and submm wavelengths). The grains must be quite nonspherical, but the actual shapes are unknown. The \emph{relative} efficacy for aligned grains to produce polarization at optical vs.\ infrared wavelengths depends on particle shape. The discrete dipole approximation is used to calculate polarization cross sections for 20 different convex shapes, for wavelengths from $0.1\mu$m to $100\mu$m, and grain sizes $a_{\rm eff}$ from $0.05\mu$m to $0.3\mu$m. Spheroids, cylinders, square prisms, and triaxial ellipsoids are considered. Minimum aspect ratios required by the observed starlight polarization are determined. Some shapes can also be ruled out because they provide too little or too much polarization at far-infrared and sub-mm wavelengths. The ratio of $10\mu$m polarization to integrated optical polarization is almost independent of grain shape, varying by only $\pm8\%$ among the viable convex shapes; thus, at least for convex grains, uncertainties in grain shape cannot account for the discrepancy between predicted and observed 10$\mu$m polarization toward Cyg OB2-12.