The Dielectric Function of "Astrodust" and Predictions for Polarization in the 3.4$\mu$m and 10$\mu$m Features

The dielectric function of interstellar dust material is modeled using observations of extinction and polarization in the infrared, together with estimates for the mass of interstellar dust. The "astrodust" material is assumed to be a mix of amorphous silicates and other materials, including hydrocarbons producing an absorption feature at 3.4$\mu$m. The detailed shape of the 10$\mu$m polarization profile depends on the assumed porosity and grain shape, but the 10$\mu$m spectropolarimetric data are not yet good enough to clearly favor one shape over another, nor to constrain the porosity. The expected 3.4$\mu$m feature polarization is consistent with existing upper limits, provided the 3.4$\mu$m absorption is preferentially located in grain surface layers; a separate population of non-aligned carbonaceous grains is not required. We predict the 3.4$\mu$m polarization feature to be $(\Delta p)_{3.4\mu{\rm m}}/p(10\mu{\rm m})\approx 0.016$, just below current upper limits. Polarization by the same grains at submm wavelengths is also calculated.