Detailed radial scale height profile of dust grains as probed by dust self-scattering in HL Tau

The vertical settling of dust grains in a circumstellar disk, characterized by their scale height, is a pivotal process in the formation of planets. This study offers in-depth analysis and modeling of the radial scale height profile of dust grains in the HL Tau system, leveraging high-resolution polarization observations. We resolve the inner disk's polarization, revealing a significant near-far side asymmetry, with the near side being markedly brighter than the far side in polarized intensity. This asymmetry is attributed to a geometrically thick inner dust disk, suggesting a large aspect ratio of $H/R \ge 0.15$. The first ring at 20 au exhibits an azimuthal contrast, with polarization enhanced along the minor axis, indicating a moderately thick dust ring with $H/R \approx 0.1$. The absence of the near-far side asymmetry at larger scales implies a thin dust layer, with $H/R < 0.05$. Taken together, these findings depict a disk with a turbulent inner region and a settled outer disk, requiring a variable turbulence model with $\alpha$ increasing from $10^{-5}$ at 100 au to $10^{-2.5}$ at 20 au. This research sheds light on dust settling and turbulence levels within protoplanetary disks, providing valuable insights into the mechanisms of planet formation.