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.
