Polarized emission by aligned grains in the Mie regime: Application to protoplanetary disks observed by ALMA

Abstract

Context. The azimuthal polarization patterns observed in some protoplanetary disks by the Atacama Large Millimetre Array (ALMA) at millimeter wavelengths have raised doubts about whether they are truly produced by dust grains that are aligned with the magnetic field lines. These conclusions were based on the calculations of dust polarized emission in the Rayleigh regime, that is, for grain sizes that are much smaller than the wavelength. However, the grain size in such disks is typically estimated to be in the range of 0.1−1 mm from independent observations. Aims. We study the dust polarization properties of aligned grains in emission in the Mie regime, that is, when the mean grain size approaches the wavelength. Methods. By using the T-MATRIX and DustEM codes, we computed the spectral dependence of the polarization fraction in emission for grains in perfect spinning alignment for various grain size distributions. We restricted our study to weakly-elongated oblate and prolate grains of astrosilicate composition that have a mean size ranging from 10 μm to 1 mm. Results. In the submillimeter and millimeter wavelength range, the polarization by B-field aligned grains becomes negative for grains larger than ∼250 μm, meaning that the polarization vector becomes parallel to the B-field. The transition from the positive to the negative polarization occurs at a wavelength of λ ∼ 1 mm. The regime of negative polarization does not exist for grains that are smaller than ∼100 μm. Conclusions. When using realistic grain size distributions for disks with grains up to the submillimeter sizes, the polarization direction of thermal emission by aligned grains is shown to be parallel to the direction of the magnetic field over a significant fraction of the wavelengths typically used to observe young protoplanetary disks. This property may explain the peculiar azimuthal orientation of the polarization vectors in some of the disks observed with ALMA and attest to the conserved ability of dust polarized emission to trace the magnetic field in disks.