  We study the polarized infrared emission by Polycyclic Aromatic Hydrocarbons
(PAHs), when anisotropically illuminated by UV photons. PAH molecules are
modeled as planar disks with in-plane and out-of-plane vibrational dipoles. As
first pointed out by Leger (1988), infrared emission features resulting from
in-plane and out-of-plane modes should have orthogonal polarization directions.
We show analytically how the degree of polarization depends on the viewing
geometry and the molecule's internal alignment between principal axis of
inertia and angular momentum, which gets worse after photon absorption. Longer
wavelength features, emitted after better internal alignment is recovered,
should be more strongly polarized. The degree of polarization for
uni-directional illumination (e.g., by a star) is larger than for diffuse
illumination (e.g., by a disk galaxy), all else being equal. For PAHs in the
Cold Neutral Medium, the predicted polarization is probably too small to
distinguish from the contribution of linear dichroism by aligned foreground
dust. The level of polarization predicted for PAH emission from the Orion Bar
is only ~0.06% at 3.3 microns; Sellgren et al. (1988) report a much larger
value, 0.86+-0.28%, which suggests that the smallest PAHs may have moderately
suprathermal rotation rates. Future observations of (or upper limits on) the
degree of polarization for the Orion Bar or for dust above edge-on galaxies
(e.g., NGC 891 or M82) may constrain the internal alignment of emitting PAHs,
thus providing clues to their rotational dynamics.
