Probing Magnetic Fields in Protoplanetary Disk Atmospheres through Polarized Optical/IR Light Scattered by Aligned Grains

Magnetic fields play essential roles in protoplanetary disks. Magnetic fields in the disk atmosphere are of particular interest, as they are connected to the wind-launching mechanism. In this work, we study the polarization of the light scattered off of magnetically aligned grains in the disk atmosphere, focusing on the deviation of the polarization orientation from the canonical azimuthal direction, which may be detectable in near-IR polarimetry with instruments such as VLT/SPHERE. We show with a simple disk model that the polarization can even be oriented along the radial (rather than azimuthal) direction, especially in highly inclined disks with toroidally dominated magnetic fields. This polarization reversal is caused by the anisotropy in the polarizibility of aligned grains and is thus a telltale sign of such grains. We show that the near-IR light is scattered mostly by $\mu$m-sized grains or smaller at the $\tau=1$ surface and such grains can be magnetically aligned if they contain superparamagnetic inclusions. For comparison with observations, we generate synthetic maps of the ratios of $U_\phi/I$ and $Q_\phi/I$, which can be used to infer the existence of (magnetically) aligned grains through a negative $Q_\phi$ (polarization reversal) and/or a significant level of $U_\phi/I$. We show that two features observed in the existing data, an asymmetric distribution of $U_\phi$ with respect to the disk minor axis and a spatial distribution of $U_\phi$ that is predominantly positive or negative, are incompatible with scattering by spherical grains in an axisymmetric disk. They provide indirect evidences for scattering by aligned non-spherical grains.