Quantitative Theory of Grain Alignment: Probing Grain Environment and Grain Composition

Polarization of starlight arising from aligned dust was discovered accidentally approximately 60 years ago (Hall 1949, Hiltner 1949). This gave rise to attempts to explain the alignment. In the years that followed various interactions from paramagnetic relaxation (Davis & Greenstein 1951) and streaming of grains (Gold 1951) to interaction with cosmic rays (Salpeter & Wickramasinghe 1969) and photons (Harwit 1970) have been explored. Many key insights into the dynamics of grains are associated with Lyman Spitzer and Edward Purcell who addressed the problem of grain alignment on a number of occasions1 . While we can refer the reader interested in the history of ideas on grain alignment to a review in Lazarian (2003), in this short publication we concentrate on the modern quantitative understanding of grain alignment. 2 Several mechanisms were proposed and elaborated to various degree (see Lazarian 2007 for a review), including the "textbook solution", namely, the paramagnetic Davis-Greenstein (1951) mechanism, which matured through intensive work since its introduction (e.g. Jones & Spitzer 1967, Purcell 1979, Spitzer & McGlynn 1979, Mathis 1986, Roberge et al. 1993, Lazarian 1997, Roberge & Lazarian 1999). The mechanical stochastic alignment was pioneered by Gold (1951), who concluded that supersonic flows should align grains rotating thermally. Further advancement of the mechanical alignment mechanism (e.g. Lazarian 1994Lazarian , 1995a) ) allowed one to extend the range of applicability of the mechanism, but left it as an auxiliary process, nevertheless. The major problem was that even the favorite alignment mechanism, the paramagnetic one, experienced severe problems explaining observational data.

I feel that the attempts to solve the problem for spheres and spheroids, reminiscent of a theorist’s favorite “spherical cow”, were the major stumbling block for understanding of grain alignment. The first attempt to consider something which is not symmetric but has net helicity was a ground-breaking study by Dolginov & Mytrophanov (1976). The authors considered there a grain that has different cross-sections for the extinction of the right-and left-polarized photons and predicted that such a grain was bound to spin up and get aligned when subjected to the anisotropic external radiative field.

The study by Dolginov & Mytrophanov (1976) had several deficiencies, however. First of all, it did not provide clear recipes about calculating the amplitude of radiative torques. In addition, the functional dependences of the torques calculated there were incorrect (Hoang & Lazarian 2009). One way or another, the work was mostly ignored for another 20 years until it attracted attention of Bruce Draine, who modified his publicly available DDSCAT code to calculate radiative torques acting on irregular grains. This resulted in the explosion of interest to radiative torques. Empirical studies in Draine (1996), Draine & Weingartner (1996, 1997), Weingartner & Draine (2003) demonstrated that the magnitude of torques is substantial for irregular shapes studied. After that it became impossible to ignore the radiative torque alignment. Later, the spin-up of grains by radiative torques was demonstrated in laboratory conditions (Abbas et al. 2004).

The initial work on radiative torque alignment did not provide quantitative predictions for the grain alignment degree. The multi-parameter space presented by grain alignment induced by radiative torques (henceforth RATs) posed an insurmountable problem for the “brute force” numerical approach. At the same time, both the interpretation and modeling of polarization call for simple recipes to parameterize effects of grain alignment. This is not feasible with numerical calculations which suggest that RATs depend on grain shape, grain size, radiation spectrum, grain composition, and the angle between the radiation direction and the magnetic field. Consequently, the important empirical studies above had limited predictive powers and were used to demonstrated the radiative torque effects sometimes using one grain shape, one grain size, one wavelength of light, and one direction of the light beam with respect to the magnetic field.

The quantitative stage of radiative torque studies required theoretical models describing radiative torques. In Lazarian & Hoang (2007a) we proposed a simple model of RATs which allowed a good analytical description of the align-Figure 1.

A model of a “helical” grain, that consists of a spheroidal body with a mirror at an angle α attached to it (α is chosen to be π/4 in the standard LH07 model). The “scattering coordinate system” which illustrates the definition of torque components: a 1 is directed along the maximal inertia axis of the grain; k is the direction of radiation. The projections of normalized radiative torques Q e1 , Q e2 and Q e3 are calculated in this reference frame. From Lazarian & Hoang 2007a. ment. This model was elaborated and extended in Lazar

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