Description
Polarimetric observations of protoplanetary disks at millimeter wavelengths have been dramatically developing with ALMA. One of the most dominant mechanisms is the self-scattering of thermal dust emission, but there are contributions of intrinsic polarization of elongated dust grains and it requires modeling approach to discuss its scientific implications. In this talk, We first quickly review the possible mechanisms that may produce the millimeter polarization, and then pick up the HL Tau disk to demonstrate interpretations. We found that self-scattering dominates the 0.88 mm wavelengths but alignment due to gas flow may dominate at 3.1 mm wavelengths. This indicates the grain size to be an order of 100 micron, which is inconsistent with the millimeter size inferred from spectral index analyses. We also discuss the possible contamination of self-scattering at long wavelengths as well as the effects of turbulent mixing.