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Recent (sub)millimeter polarization observations of protoplanetary disks reveal toroidally aligned, effectively prolate dust grains large enough (at least ~100 $\mu$m) to efficiently scatter millimeter 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 center of mass is offset from its geometric center, 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 center in the flow direction relative to its center of mass. Assuming specular reflection and subsonic flow, we derive an analytical equation of motion for spheroids where the center of mass can be shifted away from the spheroid's geometric center. We show that a prolate or an oblate grain can be aligned with the long axis parallel to the gas flow when the center of mass is shifted along that axis. Both scenarios can explain the required effectively prolate grains inferred from observations. Application to a simple disk model shows that the alignment timescales are shorter than or comparable to the orbital time. The grain alignment direction in a disk depends on the disk (sub-)structure and grain Stokes number (St) with azimuthal alignment for large St grains in sub-Keplerian smooth gas disks and for small St grains near the gas pressure extrema, such as rings and gaps., Comment: 21 pages, 12 figures, accepted by MNRAS

Millimeter and sub-millimeter 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 870 $\mu$m 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 870 $\mu$m 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 200 $\mu$m and high optical depth. In MWC 480, we can also reproduce features (1) and (2) with a model containing large grains ($a_{max}$ = 490 $\mu$m ) near the disk midplane and small grains ($a_{max}$ = 140 $\mu$m) above and below the midplane., Comment: 22 pages, 12 figures

Polarization is a unique tool to study the properties of dust grains of protoplanetary disks and detail the initial conditions of planet formation. 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 $\lambda$. The polarization morphology at Band 7 is predominantly parallel to the disk minor axis but appears azimuthally oriented at Band 3, with the morphology at Band 6 in between the two. We present new ~0.2" (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 disk with the most complete wavelength coverage in dust polarization. The polarization patterns at Bands 4 and 5 continue to follow the morphological transition with wavelength previously identified in Bands 3, 6, and 7. Based on the azimuthal variation, we decompose the polarization into contributions from scattering ($s$) and thermal emission ($t$). We find that $s$ decreases slowly with increasing $\lambda$, and $t$ increases more rapidly with $\lambda$ which are expected from optical depth effects of toroidally aligned, scattering prolate grains. The relatively weak $\lambda$ dependence of $s$ is consistent with large, porous grains. The sparse polarization detections from the Q-band image are also consistent with toroidally aligned prolate grains., Comment: 22 pages, 13 figures, submitted to MNRAS

While magnetic fields likely play an important role in driving the evolution of protoplanetary disks through angular momentum transport, observational evidence of magnetic fields has only been found in a small number of disks. Although dust continuum linear polarization has been detected in an increasing number of disks, its pattern is more consistent with that from dust scattering than from magnetically aligned grains in the vast majority of cases. Continuum linear polarization from dust grains aligned to a magnetic field can reveal information about the magnetic field's direction, but not its strength. On the other hand, observations of circular polarization in molecular lines produced by Zeeman splitting offer a direct measure of the line-of-sight magnetic field strength in disks. We present upper limits on the net toroidal and vertical magnetic field strengths in the protoplanetary disk AS 209 derived from Zeeman splitting observations of the CN 2-1 line. The 3$\sigma$ upper limit on the net line-of-sight magnetic field strength in AS 209 is 5.0 mG on the redshifted side of the disk and 4.2 mG on the blueshifted side of the disk. Given the disk's inclination angle, we set a 3$\sigma$ upper limit on the net toroidal magnetic field strength of 8.7 and 7.3 mG for the red and blue sides of the disk, respectively, and 6.2 and 5.2 mG on the net vertical magnetic field on the red and blue sides of the disk. If magnetic disk winds are a significant mechanism of angular momentum transport in the disk, magnetic fields of a strength close to the upper limits would be sufficient to drive accretion at the rate previously inferred for regions near the protostar., Comment: June 22, 2021: Corrected disk size scale bar in Figures 1, 2 and 5. Corrected percent polarization scale bar label in Figure 5