Polarized emission by aligned grains in the Mie regime : application to
  protoplanetary disks observed by ALMA
  The azimuthal polarization patterns observed in some protoplanetary disks by
ALMA at millimeter wavelength have raised doubts about their being produced by
dust grains aligned with the magnetic field lines. These conclusions were based
on the calculations of dust polarized emission in the Rayleigh regime, i.e. for
grain sizes much smaller than the wavelength. However, the grain size in such
disks is estimated to be typically in the range 0.1 - 1 mm from independent
observations. We study the dust polarization properties of aligned grains in
emission in the Mie regime, i.e. when the mean grain size approches the
wavelength. Using the T-MATRIX and DustEM codes, we compute the spectral
dependence of the polarization fraction in emission for grains in perfect
spinning alignment, for various grain size distributions of weakly-elongated
oblate and prolate grains of astrosilicate composition, with a mean size
ranging from 10 {\mu}m to 1 mm. In the submillimeter and millimeter wavelength
range, the polarization by B-field aligned grains becomes negative for grains
larger than ~ 250 {\mu}m, meaning that the polarization vector becomes parallel
to the B-field. The transition from the positive to the negative polarization
occurs at a wavelength {\lambda} ~ 1 mm. The regime of negative polarization
does not exist for grains smaller than ~ 100 {\mu}m. 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 of the conserved
ability of dust polarized emission to trace the magnetic field in disks.
