Does HL Tau Disk Polarization in ALMA Band 3 Come from Radiatively Aligned Grains?

Disk polarization in (sub)millimeter dust continuum is a rapidly growing field in the ALMA era. It opens up the exciting possibility of detecting and characterizing magnetic fields and grain growth in disks around young stellar objects. However, to use polarization for probing the disk properties, its production mechanism must be ascertained first. To date, the conventional mechanism involving magnetically aligned grains fails to explain the polarization patterns detected in most disks. This is especially true for the inclined disk of HL Tau in ALMA Band 3 (wavelength $\sim 3$ mm), which has an elliptical polarization pattern. The elliptical pattern was taken as evidence for polarized emission by dust grains aligned with their long axes perpendicular the direction of the radiative flux. We show that the radiatively aligned grains produce a circular, rather than elliptical, polarization pattern even in inclined disks such as HL Tau. An elliptical polarization pattern can be produced if the grains are aligned aerodynamically by the difference in rotation speed between the dust and gas through the Gold mechanism. However, a strong azimuthal variation in polarized intensity is expected for both the radiative and aerodynamic alignment, but not observed in the HL Tau disk in ALMA Band 3. We conclude that neither of these two mechanisms alone can explain the data and the origin of the 3 mm polarization remains a mystery. We speculate that this mystery may be resolved by a combination of both direct emission and scattering by aerodynamically aligned grains.