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# Circular polarization of starlight

The circular polarization of starlight has been observed to be a function of the linear polarization of starlight.

Starlight becomes partially linearly polarized by scattering from elongated interstellar dust grains whose long axes tend to be oriented perpendicular to the galactic magnetic field. According to the Davis-Greenstein mechanism, the grains spin rapidly with their rotation axis along the magnetic field. Light polarized along the direction of the magnetic field perpendicular to the line of sight is transmitted, while light polarized in the plane defined by the rotating grain is blocked. Thus the polarization direction can be used to map out the galactic magnetic field. The degree of polarization is on the order of 1.5% for stars at 1000 parsecs distance.[1]

Normally, a much smaller fraction of circular polarization is found in starlight. Serkowski, Mathewson and Ford[2] measured the polarization of 180 stars in UBVR filters. They found a maximum fractional circular polarization of $q = 6 \times 10^{-4}$, in the R filter.

The explanation is that the interstellar medium is optically thin. Starlight traveling through a kiloparsec column undergoes about a magnitude of extinction, so that the optical depth ~ 1. An optical depth of 1 corresponds to a mean free path, which is the distance, on average that a photon travels before scattering from a dust grain. So on average, a starlight photon is scattered from a single interstellar grain; multiple scattering (which produces circular polarization) is much less likely. Observationally,[1] the linear polarization fraction p ~ 0.015 from a single scattering; circular polarization from multiple scattering goes as p2, so we expect a circularly polarized fraction of $q \sim 2 \times 10^{-4}$.

Light from early-type stars has very little intrinsic polarization. Kemp et al [3] measured the optical polarization of the Sun at sensitivity of $3 \ times 10^{-7}$; they found upper limits of 10 − 6 for both p (fraction of linear polarization) and q (fraction of circular polarization).

The interstellar medium can produce circularly polarized (CP) light from unpolarized light by sequential scattering from elongated interstellar grains aligned in different directions. One possibility is twisted grain alignment along the line of sight due to variation in the galactic magnetic field; another is the line of sight passes through multiple clouds. For these mechanisms the maximum expected CP fraction is q˜p2, where p is the fraction of linearly polarized (LP) light. Kemp & Wolstencroft [4] found CP in six early-type stars (no intrinsic polarization), which they were able to attribute to the first mechanism mentioned above. In all cases, q˜10 − 4 in blue light.

Martin[5] showed that the interstellar medium can convert LP light to CP by scattering from partially aligned interstellar grains having a complex index of refraction. This effect was observed for light from the Crab Nebula by Martin, Illing and Angel.[6]

An optically thick circumstellar environment can potentially produce much larger CP than the interstellar medium. Martin[7] suggested that LP light can become CP near a star by multiple scattering in an optically thick asymmetric circumstellar dust cloud. This mechanism was invoked by Bastien, Robert and Nadeau,[8] to explain the CP measured in 6 T-Tauri stars at a wavelength of 768 nm. They found a maximum CP of $q \sim 7 \times 10^{-4}$. Serkowski[9] measured CP of $q = 7 \times 10^{-3}$ for the red supergiant NML Cygni and $q = 2 \times 10^{-3}$ in the long period variable M star VY Canis Majoris in the H band, ascribing the CP to multiple scattering in circumstellar envelopes. Chrysostomou et al[10] found CP with q of up to 0.17 in the Orion OMC-1 star-forming region, and explained it by reflection of starlight from aligned oblate grains in the dusty nebula.

Circular polarization of zodiacal light and Milky Way diffuse galactic light was measured at wavelength of 550 nm by Wolstencroft and Kemp.[11] They found values of $q \sim 5 \times 10^{-3}$, which is higher than for ordinary stars, presumably because of multiple scattering from dust grains.

## References

1. ^ a b Fosalba (2002). "{{{title}}}". ApJ 564: 722.
2. ^ Serkowski; Mathewson and Ford (1975). "{{{title}}}". ApJ 196: 261.
3. ^ Kemp; et al (1987). "{{{title}}}". Nature 326: 270.
4. ^ Kemp; Wolstencroft (1972). "{{{title}}}". ApJ 176: L115.
5. ^ Martin (1972). "{{{title}}}". MNRAS 159: 179.
6. ^ Martin; Illing and Angel (1972). "{{{title}}}". MNRAS 159: 191.
7. ^ Martin 1972
8. ^ Bastein; Robert and Nadeau (1989). "{{{title}}}". ApJ 339: 1089.
9. ^ Serkowski (1973). "{{{title}}}". ApJ 179: L101.
10. ^ Chrysostomou; et al (2000). "{{{title}}}". MNRAS 312: 103.
11. ^ Wolstencroft; Kemp (1972). "{{{title}}}". ApJ 177: L137.