Scattering-Produced (Sub)millimeter Polarization in Inclined Disks: Optical Depth Effects, Near-Far Side Asymmetry, and Dust Settling

Disk polarization at (sub)millimeter wavelengths is being revolutionized by ALMA observationally, but its origin remains uncertain. Dust scattering was recently recognized as a potential contributor to polarization, although its basic properties have yet to be thoroughly explored. Here, we quantify the effects of optical depth on the scattering-induced polarization in inclined disks through a combination of analytical illustration, approximate semi-analytical modeling using formal solution to the radiative transfer equation, and Monte Carlo simulations. We find that the near-side of the disk is significantly brighter in polarized intensity than the far-side, provided that the disk is optically thick and that the scattering grains have yet to settle to the midplane. This asymmetry is the consequence of a simple geometric effect: the near-side of the disk surface is viewed more edge-on than the far-side. It is a robust signature that may be used to distinguish the scattering-induced polarization from that by other mechanisms, such as aligned grains. The asymmetry is weaker for a geometrically thinner dust disk. As such, it opens an exciting new window on dust settling. We find anecdotal evidence from dust continuum imaging of edge-on disks that large grains are not yet settled in the youngest (Class 0) disks, but become more so in older disks. This trend is corroborated by the polarization data in inclined disks showing that younger disks have more pronounced near-far side asymmetry and thus less grain settling. If confirmed, the trend would have far-reaching implications for grain evolution and, ultimately, the formation of planetesimals and planets.