On the Settling, Scattering, and Submillimeter Polarization of Dust in Planet-Forming Disks

Planet formation is a multi-stage process that requires the growth of dust grains from submicron-sized particles to planetary bodies thousands of kilometers in size. The mechanisms participating in this growth, such as dust coagulation and streaming instability, are intimately tied to the structure of protoplanetary disks and the properties of dust grains, including their size distribution. Observational constraints have become increasingly accessible with the advent of the Atacama Large Millimeter/submillimeter Array (ALMA) in recent years. This thesis undertakes a multifaceted exploration, addressing pivotal questions across three primary themes.

The first theme focuses on dust settling, which may serve as a prerequisite for triggering streaming instability by enhancing the midplane dust-to-gas ratio in the protoplanetary disks. Observing edge-on disks can place direct constraints on the vertical distribution of dust, and targeting young, embedded disks allows for the study of dust settling over time. Utilizing HH 212 mms and IRAS 04302+2247 as examples, this work demonstrates that the dust has not completely settled yet in these systems. Additionally, the edge-on view enables the study of the vertical temperature structure and places constraints on the long-uncertain dust opacity.

The second theme investigates the scattering of spherical and randomly aligned grains, which has been proposed as a potential source of the diverse (sub)millimeter wave continuum polarization detections in protoplanetary disks. Through 3D Monte Carlo radiation transfer simulations, this work demonstrates that dust scattering can self-consistently explain both the polarization and the spectral index observed in HD 163296, assuming spherical grains with sizes of approximately 100 micron. However, polarization also depends on grain shape, and by incorporating laboratory measurements of irregular grains much larger than the observing wavelength, a broader range of grain sizes is inferred, rather than a maximum size of 100 micron.

The third theme explores the interplay between aligned grains and scattering in producing polarized emission from protoplanetary disks. Starting in the limit without scattering, I explain how thermal polarization from aligned grains diminishes when optically thick and relates to the temperature gradient along the line of sight which is relevant for optically thick protoplanetary disks. In a unifying effort, I employ a plane-parallel slab model to calculate the scattering of aligned grains self-consistently, incorporating the T-matrix method to account for the scattering properties of ellipsoidal grains. Image simulations using scattering from toroidally aligned, prolate grains successfully explain the multiwavelength transition of polarization and the polarization image of HL Tau with unprecedented resolution (5 au), resolving the polarization pattern between the rings and gaps. Both experiments are connected simply by changes in the optical depth of scattering, aligned grains. Recognizing the numerical cost of self-consistent calculations of scattering by aligned grains, I propose an approximation to the azimuthal variation of the complete solution. Scattering predominantly produces polarization that is constant in azimuth, while thermal polarization depends on the viewing angle of an elongated grain around the azimuth. Applications of this approximation to protoplanetary disks allow for the decomposition of the two components and permit empirical measurements of the scattering spectrum which can constrain the sizes of grains.