Polarized Infrared Emission by Polycyclic Aromatic Hydrocarbons resulting from Anisotropic Illumination

The strong infrared emission features at 3.3, 6.2, 7.7, 8.6, 11.3 and 12.7 µm have been attributed to vibrational modes in planar Polycyclic Aromatic Hydrocarbons (PAHs) (e.g., Leger & Puget 1984;Allamandola et al. 1985). Additional strong features at 16.4 and ∼ 17 µm (e.g., Smith et al. 2007) have also been attributed to PAHs, although the identification is less certain. Leger (1988) noted that a planar PAH molecule may emit partially polarized light if anisotropically illuminated by a source of UV photons. The basic reasons are the following: i ) UV absorption is favored if the molecule faces the illuminating source; ii ) spinning of the molecule around its angular momentum preserves some memory of the illumination direction; iii ) the vibrational dipoles responsible for the IR emission features oscillate either perpendicular or parallel to the molecular plane. In particular, the C-H stretching mode (3.3 µm) and the in-plane C-H bending mode (8.6 µm) oscillate parallel to the grain plane, whereas the out-of-plane C-H bending mode (11.3 and 12.7 µm) oscillates perpendicular to the molecular plane. The strong emission features at 6.2 and 7.7 µm are believed to arise from in-plane C-C stretching and bending modes. In-plane modes (3.3, 6.2, 7.7, 8.6 µm) and out-of-plane modes (11.3, 12.7 µm) should exhibit orthogonal polarization angles (Leger 1988), and their electric field vector should be respectively perpendicular and parallel to the plane-of-sky projection of the illumination direction. Sellgren et al. (1988) have searched for linear polarization of the 3.3 and 11.3 µm emission features in a variety Electronic address: lsironi@astro.princeton.edu; draine@astro.princeton.edu of astronomical sources where PAH emission is observed offset from the illuminating source. Their upper limits on the degree of polarization are of the order a few percent. At one position on the Orion Bar they measure a linear polarization of 0.86 ± 0.28 % in the 3.3 µm feature, with the polarization angle consistent with being orthogonal to the line between the nebula and the star, as predicted by Leger (1988). However, as we show below, the polarization they report for the 3.3 µm feature is much larger than expected.

In this work we present analytic formulae for the degree of polarization of the PAH emission features, when the emitting grains are anisotropically illuminated. We model PAH molecules as planar disks with in-plane and out-of-plane vibrational dipoles. We extend the calculations by Leger (1988) to allow for an arbitrary degree of disalignment between the molecule’s principal axis of inertia â1 (perpendicular to the molecular plane) and its angular momentum J. We discuss both the case of a point-like illuminating source, which may be applied to reflection nebulae like the Orion Bar, and of an extended source (e.g., a disk galaxy), which may be relevant for dust above NGC 891 or M82. The level of polarization is sensitive to the angle between the line of sight and the illumination direction, and to the degree of alignment between â1 and J. Measurements of the degree of polarization can therefore provide insight into the rotational dynamics of PAHs.

This work is organized as follows: in §2 we describe our model for UV absorption and polarized IR emission by PAH molecules, commenting on uncertainties regarding the alignment of â1 with J; in §3 we present our results, both for a star-like illuminating source and for an extended galactic disk. The reader interested primarily in the observational implications of our work may wish to skip §2 and §3 and proceed directly to §4, where we summarize our findings and discuss how future polarization measurements may constrain the geometrical and rotational properties of PAHs.

As discussed by Leger (1988), planar PAH molecules may emit partially polarized light as a result of anisotropic illumination by a source of UV photons. UV absorption is favored if the molecular plane is perpendicular to the illumination direction. Following UV absorption, in-plane and out-of-plane vibrational modes are excited, producing the observed IR emission features.

The grain angular momentum J stays approximately constant during the whole process of UV absorption and IR emission (Leger 1988): first, the angular momentum contributed by the absorbed UV photon or removed via vibrational IR emission or rotational radio emission is small compared to the mean angular momentum of interstellar PAHs; secondly, collisions of the emitting grain with interstellar atoms or ions hardly occur during the few seconds of IR emission; finally, Larmor precession of J around the interstellar magnetic field takes much longer than the IR emission burst (Rouan et al. 1992). With J conserved, some memory of the source direction is retained and the IR emission bands will be partially polarized.

We adopt the system of coordinates used by Leger (1988) to specify the illumination geometry and the orientation of the emitting mole

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