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.
