Circular polarization: change of sign

Traditionally, the main problem considered in connection with circular interstellar polarization is the meaning of the wavelength where $q(\lambda)$ changes the sign $\lambda_{\rm c}$. Its proximity to $\lambda_{\rm max}$ was treated as the indicator of the dielectric nature of interstellar grains. This feature was established by Martin ([1972]) in the first serious theoretical paper which accompanied the discovery of interstellar circular polarization. Martin ([1972], [1974]) found that the condition $\lambda_{\rm c} \approx \lambda_{\rm max}$ could be satisfied if the imaginary part of the refractive index is low at visible wavelengths ( ). However, Shapiro ([1975]) using DDA calculations for parallelepipeds of magnetite showed that a strongly absorbing conductor could reproduce this condition as well. Given conclusion is, possibly, not unquestionable because of doubt about the application of DDA to highly absorbing particles. Chlewicki and Greenberg ([1990]) reexamined the relationship between the interstellar linear and circular polarization on the basis of Kramers-Kronig relations. They concluded that the observed connection between $\lambda_{\rm c}$ and $\lambda_{\rm max}$ was reached independently of specific characteristics of grains, so long as they provide the ``correct''⁵ linear polarization. Note also that the shape effects for circular polarization were not analyzed: Martin ([1972], [1974]) considered infinite cylinders with PF orientation and $\alpha = 90\hbox{$^\circ$}$, Chlewicki and Greenberg ([1990]) performed calculations for infinite cylinders with PDG and IDG orientations and $\Omega=90\hbox{$^\circ$}$.

Calculations made for spheroidal particles show that the position where the circular polarization changes the sign shifts with variations of the particle inclination in the same manner as the position of $\lambda_{\rm max}$. This is clearly seen from Fig. 12 (right panels) where the efficiency factors are plotted for prolate spheroids with $a/b=2$: reduction of $\alpha$ leads to increase of the $x_V$ values where the circular polarization factors intersect the zero level. This means that the positions of both $\lambda_{\rm c}$ and $\lambda_{\rm max}$ should move to shorter wavelengths if the direction of alignment approaches the line of sight. Such a behaviour is seen in Fig. 19 (middle panel) for prolate spheroids while for oblate particles the displacement takes place in the opposite direction. Figure 19 (upper panel) also shows changes of circular polarization with wavelength for particles of astrosil and AC1. Comparison with the corresponding picture for linear polarization (Fig. 16, upper left panel) allows one to see an approximate coincidence of $\lambda_{\rm c}$ and $\lambda_{\rm max}$ for both dielectric and absorbing particles.

Figure 19: Wavelength dependence of the polarization factors for circular polarization. The corresponding factors for linear polarization are shown in Fig. 16 (upper and middle panels). On the lower panel, the wavelength dependence of the factors for linear $(Q^{\rm TM}_{\rm ext}-Q^{\rm TE}_{\rm ext})/2$ and circular $(Q^{\rm TM}_{\rm ext}-Q^{\rm TE}_{\rm ext}) (Q^{\rm TM}_{\rm p}-Q^{\rm TE}_{\rm p})$ polarization for prolate and oblate spheroids of magnetite (Fe$_3$O$_4$) is shown. The effects of variations of particle composition and shape are illustrated.

This is also demonstrated by Fig. 19 (lower panel) which shows the wavelength dependence of the factors of linear and circular polarization for particles of magnetite as was done by Shapiro ([1975]). We can confirm his conclusion about the proximity of $\lambda_{\rm c}$ and $\lambda_{\rm max}$ although the shape of curves for spheroids differs from that for parallelepipeds.

Finally, we can conclude that the wavelength where the interstellar circular polarization changes the sign and its coincidence with $\lambda_{\rm max}$ tell us almost nothing about the absorptive properties of interstellar grains but the dependence $q(\lambda)$ and the positions of their maxima/minima can serve for clearing up the dust properties. It is important that from the point of view of circular polarization there exists a large difference between prolate and oblate grains. The latter particles always produce much larger polarization (Fig. 19). Note also that the circular polarization observed for stars indicates the complex structure of interstellar magnetic fields in their directions and gives information on the birefringence in the dust cloud nearest to the observer.