Millimeter-wave Polarization Due to Grain Alignment by the Gas Flow in Protoplanetary Disks

Dust grains emit intrinsic polarized emission if they are elongated and aligned in the same direction. The direction of the grain alignment is determined by external forces, such as magnetic fields, radiation, and gas flow against the dust grains. In this Letter, we apply the concept of the grain alignment by gas flow, which is called mechanical alignment, to the situation of a protoplanetary disk. We assume that grains have a certain helicity, which results in the alignment with the minor axis parallel to the grain velocity against the ambient disk gas and discuss the morphology of polarization vectors in a protoplanetary disk. We find that the direction of the polarization vectors depends on the Stokes number, which denotes how well grains are coupled to the gas. If the Stokes number is less than unity, the orientation of polarization is in the azimuthal direction because the dust velocity against the gas is in the radial direction. If the Stokes number is as large as unity, the polarization vectors show a leading spiral pattern because the radial and azimuthal components of the gas velocity against the dust grains are comparable. This suggests that if the observed polarization vectors show a leading spiral pattern, it would indicate that the Stokes number of dust grains is around unity, which is presumably radially drifting.