Interstellar circular polarization and the dielectric nature of dust grains
The implications of the observed relationship between the wavelength dependence of interstellar circular and linear polarization were reexamined. Mie theory calculations for grains with various optical constants demonstrate that any population of grains which matches the observed wavelength dependence of linear polarization also yields the correct cross-over wavelength of circular polarization. The coincidence of the peak wavelength of linear polarization and the cross-over of circular polarization is therefore independent of the optical constants of the grains and cannot be used as a critical constraint on grain properties. The observed relationship instead reflects a more fundamental connection between linear and circular polarization which was derived from the Kramers-Kronig relations by Shapiro (1975). Numerical results fully support Shapiro's conclusions and demonstrate that the apparent upper limit on the visual absorptivity of polarizing grains deduced from earlier Mie theory calculations (Martin, 1972) was spurious and resulted from a violation of the Kramers-Kronig relations in the assumed optical constants of the particles. The Kramers-Kronig interpretation of circular polarization can be used to place constraints on linear polarization outside the wavelength range in which it was observed. This approach was used to show that the peak observed in the visual is likely to be the only significant feature in the linear polarization curve, which therefore appears to be well approximated at all wavelengths by the Serkowski formula. A synthesis of available laboratory data was used to analyze the properties of dielectric core-mantel grains as the source of visual extinction and polarization.