Figure 2.12 Polarization of light by grain scattering. The incident radiation propagates along the direction n. That portion scattered into orthogonal directions s or s' is linearly polarized, while that in an arbitrary direction s'' is only partially polar-

If one rotates a polarizing Alter in front of a source, the received intensity at any wavelength varies from some lowest value Imin up to Imax. The orientation of the polarizer corresponding to Imax is the position angle of E, while the degree of polarization is defined to be

This quantity is a function of wavelength, since Q\sca generally decreases with A. Consequently, reflection nebulae appear bluer than their central stars. Values of P in the optical are typically a few percent in the reflection nebulae surrounding young stars, but can be as high as 0.2. Note that the change in polarization direction (i. e., the orientation of E) across such a nebula depends on the position of the star relative to the line of sight. In many cases, the pattern of E-vectors accurately locates an illuminating source that is too embedded for direct observation.

In the presence of a magnetic field, grains also polarize radiation through dichroic extinction. This phenomenon depends on the fact that the particles are not perfect spheres, but irregular structures that tend to rotate end over end, i. e., about their shortest principal axes. Grain material also has a small electric charge and is paramagnetic. Both features cause it to acquire a magnetic moment M that points along the instantaneous axis of rotation. Interaction with the ambient magnetic field then creates a torque M x B that gradually forces the grain's short axis to align with the field. Figure 2.13 illustrates this situation, for the case of an idealized, cylindrical grain.

Consider now unpolarized radiation that impinges on this rotating grain. The electric field is most effective in driving charges down the body's long axis, This direction therefore becomes the one of maximum absorption for the electromagnetic wave. As seen in Figure 2.13, the electric vector of the transmitted radiation lies along the ambient B. The reader may check that the effect is greatest when the propagation direction of the incident radiation is nearly orthogonal

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