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ABSTRACT Recent (sub)millimetre polarization observations of protoplanetary discs reveal toroidally aligned, effectively prolate dust grains large enough (at least $$\sim 100$$\mu$$m) to efficiently scatter millimetre light. The alignment mechanism for these grains remains unclear. We explore the possibility that gas drag aligns grains through gas–dust relative motion when the grain’s centre of mass is offset from its geometric centre, analogous to a badminton birdie’s alignment in flight. A simple grain model of two non-identical spheres illustrates how a grain undergoes damped oscillations from flow-induced restoring torques which align its geometric centre in the flow direction relative to its centre of mass. Assuming specular reflection and subsonic flow, we derive an analytical equation of motion for spheroids where the centre of mass can be shifted away from the spheroid’s geometric centre. We show that a prolate or an oblate grain can be aligned with the long axis parallel to the gas flow when the centre of mass is shifted along that axis. Both scenarios can explain the required effectively prolate grains inferred from observations. Application to a simple disc model shows that the alignment time-scales are shorter than or comparable to the orbital time. The grain alignment direction in a disc depends on the disc (sub-)structure and grain Stokes number (St) with azimuthal alignment for large St grains in sub-Keplerian smooth gas discs and for small St grains near the gas pressure extrema, such as rings and gaps. 

Abstract Millimeter and submillimeter observations of continuum linear dust polarization provide insight into dust grain growth in protoplanetary disks, which are the progenitors of planetary systems. We present the results of the first survey of dust polarization in protoplanetary disks at 870μm and 3 mm. We find that protoplanetary disks in the same molecular cloud at similar evolutionary stages can exhibit different correlations between observing wavelength and polarization morphology and fraction. We explore possible origins for these differences in polarization, including differences in dust populations and protostar properties. For RY Tau and MWC 480, which are consistent with scattering at both wavelengths, we present models of the scattering polarization from several dust grain size distributions. These models aim to reproduce two features of the observational results for these disks: (1) both disks have an observable degree of polarization at both wavelengths; and (2) the polarization fraction is higher at 3 mm than at 870μm in the centers of the disks. For both disks, these features can be reproduced by a power-law distribution of spherical dust grains with a maximum radius of 200μm and high optical depth. In MWC 480, we can also reproduce features (1) and (2) with a model containing large grains (a_max= 490μm) near the disk midplane and small grains (a_max= 140μm) above and below the midplane. 

ABSTRACT Polarization is a unique tool to study the dust grains of protoplanetary discs. Polarization around HL Tau was previously imaged using the Atacama Large Millimeter/submillimeter Array (ALMA) at Bands 3 (3.1 mm), 6 (1.3 mm), and 7 (0.87 mm), showing that the polarization orientation changes across wavelength λ. Polarization at Band 7 is predominantly parallel to the disc minor axis but appears azimuthally oriented at Band 3, with the morphology at Band 6 in between the two. We present new ∼0.2 arcsec (29 au) polarization observations at Q-Band (7.0 mm) using the Karl G. Jansky Very Large Array (VLA) and at Bands 4 (2.1 mm), 5 (1.5 mm), and 7 using ALMA, consolidating HL Tau’s position as the protoplanetary disc with the most complete wavelength coverage in dust polarization. The polarization patterns at Bands 4 and 5 follow the previously identified morphological transition with wavelength. From the azimuthal variation, we decompose the polarization into contributions from scattering (s) and thermal emission (t). s decreases slowly with increasing λ, and t increases more rapidly which are expected from optical depth effects of toroidally aligned scattering prolate grains. The weak λ dependence of s is inconsistent with the simplest case of Rayleigh scattering by small grains in the optically thin limit but can be affected by factors such as optical depth, disc substructure, and dust porosity. The sparse polarization detections from the Q-band image are also consistent with toroidally aligned prolate grains.