Modeling of the ALMA HL Tau Polarization by Mixture of Grain Alignment and Self-scattering

Dust polarization at (sub)millimeter wavelengths has been observed for many protoplanetary disks. Theoretically, multiple origins potentially contribute to the polarized emission but it is still uncertain what mechanism is dominant in disk millimeter polarization. To quantitatively address the origin, we perform radiative transfer calculations of the mixture of alignment and self-scattering induced polarization to reproduce the 3.1 mm polarization of the HL Tau disk, which shows azimuthal pattern in polarization vectors. We find that a mixture of the grain alignment and self-scattering is essential to reproduce the HL Tau 3.1 mm polarization properties. Our model shows that the polarization of the HL Tau at 3.1 mm can be decomposed to be the combination of the self-scattering parallel to the minor axis and the alignment-induced polarization parallel to the major axis, with the orders of $sim 0.5%$ fraction for each component. This slightly eases the tight constraints on the grain size of $sim 70~{rm~mu m}$ to be $sim 130 {rm~mu m}$ in the previous studies but further modeling is needed. In addition, the grain alignment model requires effectively prolate grains but the physics to reproduce it in protoplanetary disks is still a mystery.