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The azimuthal polarization patterns observed in some protoplanetary disks byALMA at millimeter wavelength have raised doubts about their being produced bydust grains aligned with the magnetic field lines. These conclusions were basedon the calculations of dust polarized emission in the Rayleigh regime, i.e. forgrain sizes much smaller than the wavelength. However, the grain size in suchdisks is estimated to be typically in the range 0.1 - 1 mm from independentobservations. We study the dust polarization properties of aligned grains inemission in the Mie regime, i.e. when the mean grain size approches thewavelength. Using the T-MATRIX and DustEM codes, we compute the spectraldependence of the polarization fraction in emission for grains in perfectspinning alignment, for various grain size distributions of weakly-elongatedoblate and prolate grains of astrosilicate composition, with a mean sizeranging from 10 {\mu}m to 1 mm. In the submillimeter and millimeter wavelengthrange, the polarization by B-field aligned grains becomes negative for grainslarger than ~ 250 {\mu}m, meaning that the polarization vector becomes parallelto the B-field. The transition from the positive to the negative polarizationoccurs at a wavelength {\lambda} ~ 1 mm. The regime of negative polarizationdoes not exist for grains smaller than ~ 100 {\mu}m. When using realistic grainsize distributions for disks with grains up to the submillimeter sizes, thepolarization direction of thermal emission by aligned grains is shown to beparallel to the direction of the magnetic field over a significant fraction ofthe wavelengths typically used to observe young protoplanetary disks. Thisproperty may explain the peculiar azimuthal orientation of the polarizationvectors in some of the disks observed with ALMA and attest of the conservedability of dust polarized emission to trace the magnetic field in disks.

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