Annu. Rev. Astron. Astrophys. 1990. 28: 37-70
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5.1 Continuum Polarization

5.1.1 Optical and NIR The empirical wavelength dependence of optical/NIR polarization (151a) follows ``Serkowski's Law'', i.e. p(lambda) / p(lambdamax) = exp[-K ln2(lambda / lambdamax)], where lambdamax is the wavelength of the maximum polarizarion p(lambdamax). The quantity K was originally taken to be 1.15, but an improved fit (170) is K = -0.10 + 1.86lambdamax. This law is entirely empirical, and it would be important to determine deviations at large |ln(lambda / lambdamax)|. Salient features of the optical polarization law are:

1. The averaged value of lambdamax is 0.55 µm (151a), with extremes from about 0.34 µm to about 1 µm. The values of lambdamax, determined by a least-squares fitting to Serkowski's law rather than a direct search for the maximum, depend mainly upon the observations at extreme wavelengths.

2. The polarization typically rises with wavelength through the ground-based UV to a maximum in the optical and then falls slowly through the NIR. Such behavior bears little resemblance to the extinction law, which keeps rising monotonically, except for the bump, towards shorter wavelengths throughout the observable UV. The grains responsible for the extinction in the ground-based UV do not participate in polarization because they are not elongated and/or not aligned.

3. The value of lambdamax is almost proportional to RV (25, 167, 168), although there is more scatter in the relationship than for the extinction laws. To a large extent, optical polarization measurements can substitute for NIR extinction in obtaining RV.

4. The polarization law p(lambda) varies as p(lambda) propto lambda-1.8 for both diffuse dust and outer-cloud dust in the range 0.9 µm < lambda < 5 µm (108). The polarization law exponent is less well determined than for extinction, varying between -1.5 and -2.0 for various samples, but it is certainly similar to the value for extinction (-1.7 - -1.8; see Section 2.1.3). Note that this relation involves the absolute polarization, not relative to p(lambdamax). The optical p(lambda) does vary strongly with RV (see point 2 above), and the silicate feature has strong polarization which dominates for lambda > 5 µm. The independence of p(lambda) from RV again suggests that the size distribution of large grains is similar for clouds and the diffuse ISM.

5. The maximum value of p(lambdamax) / A(lambdamax) is about 0.03 mag-1, far less than from perfectly aligned spinning cylinders [0.22 mag-1 (111)]. This is interesting because the polarization direction closely follows the contours of the edges of several molecular clouds, presumably in regions where hydrogen changes its state from molecular to atomic relatively abruptly in space and perhaps in time. If the alignment mechanism keeps grains aligned under these adverse conditions, one would expect almost complete alignment when conditions are favorable, and a larger value of p(lambdamax) / A(lambdamax) than is observed, in directions where the line of sight is perpendicular to the field. Perhaps there are two or more separate types of grains, only some of which are aligned. Alternatively, all grains might be well aligned but have shapes that are less efficient than a spinning cylinder for producing polarization. A third possibility is that there is always a randomly oriented component to the field.

6. Polarization in the UV is unknown except for two stars (58). These limited data suggest that the bump is unpolarized. Upcoming observations from space (the WUPPE experiment on ASTRO missions) should provide many data. The polarization of the lambda2175 bump has been predicted if the bump is produced by aligned graphite (36).

An explanation for the form of the polarization law (111) assumes that grains can be aligned only if they contain one or more ``superparamagnetic'' particles (magnetite or other magnetic materials), which dissipate rotational energy as heat. Large grains are preferentially aligned because they are relatively likely to contain inclusions. Polarization is not specific to any particular grain model; if the large grains are aligned, and a model predicts the extinction correctly, it will do well for the polarization also.

5.1.2 FIR POLARIZATION Polarization is observed in the emission from grains deep within the Orion molecular cloud and Sgr A, near the galactic center (35, 72, 163). The direction of the FIR polarization is perpendicular to the optical, exactly as expected: light transmitted in the optical is polarized in the direction of smaller absorption. Emission, on the other hand, is largest in the direction of largest absorption.

Grain alignment is even more difficult for dense clouds than for the diffuse ISM (71). Alignment depends upon the grain being far from equilibrium with its surroundings, in which case there is no preferred axis by the equipartition of energy. Deep inside a cloud, a grain should come to thermal equilibrium with the dense surrounding gas. The fact that polarization is observed shows that the rotation of aligned grains within clouds is not thermalized; they are presumably kept spinning in a particular direction because of the ejection of particles (H2 after formation, or electrons) from particular sites (134), so the momentum of the ejected particles is not random. However, deep inside a cloud one would expect the gas impinging upon the grain to already be overwhelmingly H2. Probably there also needs to be an enhanced dissipation of energy by superparamagnetic inclusions in the grains.

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