Inclination-induced polarization of scattered millimetre radiation from protoplanetary discs: the case of HL Tau

Spatially resolved polarized millimetre/submillimetre emission has been observed in the disc of HL Tau and two other young stellar objects. It is usually interpreted as coming from magnetically aligned grains, but can also be produced by dust scattering, as demonstrated explicitly by Kataoka et al. for face-on discs. We extend their work by including the polarization induced by disc inclination with respect to the line of sight. Using a physically motivated, semi-analytic model, we show that the polarization fraction of the scattered light increases with the inclination angle i, reaching 1/3 for edge-on discs. The inclination-induced polarization can easily dominate that intrinsic to the disc in the face-on view. It provides a natural explanation for the two main features of the polarization pattern observed in the tilted disc of HL Tau (i similar to 45 degrees): the polarized intensity concentrating in a region elongated more or less along the major axis, and polarization in this region roughly parallel to the minor axis. This broad agreement provides support to dust scattering as a viable mechanism for producing, at least in part, polarized millimetre radiation. In order to produce polarization at the observed level (similar to 1 per cent), the scattering grains must have grown to a maximum size of tens of microns. However, such grains may be too small to produce the opacity spectral index of beta less than or similar to 1 observed in HL Tau and other sources; another population of larger, millimetre/centimetre-sized, grains may be needed to explain the bulk of the unpolarized continuum emission.