Scattering-produced (sub)millimetre polarization in inclined discs: Optical depth effects, near-far side asymmetry and dust settling

Disc polarization at (sub)millimetre 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 discs through a combination of analytical illustration, approximate semi-analytical modelling using formal solution to the radiative transfer equation, and Monte Carlo simulations.We find that the near-side of the disc is significantly brighter in polarized intensity than the far-side, provided that the disc is optically thick and that the scattering grains have yet to settle to the mid-plane. This asymmetry is the consequence of a simple geometric effect: the near-side of the disc 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 disc. As such, it opens an exciting new window on dust settling. We find anecdotal evidence from dust continuum imaging of edge-on discs that large grains are not yet settled in the youngest (Class 0) discs, but become more so in older discs. This trend is corroborated by the polarization data in inclined discs showing that younger discs 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.