Validating scattering-induced (sub)millimetre disc polarization through the spectral index, wavelength-dependent polarization pattern, and polarization spectrum: the case of HD 163296

A number of young circumstellar discs show strikingly ordered (sub)millimetre polarization orientations along the minor axis, which is strong evidence for polarization due to scattering by ∼0.1 mm-sized grains. To test this mechanism further, we model the ALMA dust continuum and polarization data of HD 163296 using radmc-3d. We find that scattering by grains with a maximum size of 90 μm simultaneously reproduces the polarization observed at Band 7 and the unusually low spectral index (α ∼ 1.5) between Bands 7 and 6 in the optically thick inner disc as a result of more efficient scattering at the shorter wavelength. The low spectral index of ∼2.5 inferred for the optically thin gaps is reproduced by the same grains, as a result of telescope beam averaging of the gaps (with an intrinsic α ∼ 4) and their adjacent optically thick rings (where α ≲ 2). The tension between the grain sizes inferred from polarization and spectral index disappears because the low α values do not require large mm-sized grains. In addition, the polarization fraction has a unique azimuthal variation: higher along the major axis than the minor axis in the gaps, but vice versa in the rings. We find a rapidly declining polarization spectrum (with p ∝ λ^-3 approximately) in the gaps, which becomes flattened or even inverted towards short wavelengths in the optically thick rings. These contrasting behaviours in the rings and gaps provide further tests for scattering-induced polarization via resolved multiwavelength observations.