Impact of Differential Dust Settling on the SED and Polarization: Application to the Inner Region of the HL Tau Disk

The polarimetric observations of the protoplanetary disk around HL Tau have shown the scattering-induced polarization at ALMA Band 7, which indicates that the maximum dust size is ∼100 μm, while the spectral energy distribution (SED) has suggested that the maximum dust size is approximately a millimeter. To solve the contradiction, we investigate the impact of differential settling of dust grains on the SED and polarization. If the disk is optically thick, a longer observing wavelength traces more interior layers, which would be dominated by larger grains. We find that the SED of the center part of the HL Tau disk can be explained with millimeter-sized grains for a broad range of turbulence strength, while 160 μm–sized grains cannot be explained unless the turbulence strength parameter α _t is lower than 10⁻⁵. We also find that the observed polarization fraction can be potentially explained with a maximum dust size of 1 mm if α _t ≲ 10⁻⁵, although models with 160 μm–sized grains are also acceptable. However, if the maximum dust size is ∼3 mm, the simulated polarization fraction is too low to explain the observations even if the turbulence strength is extremely small, indicating a maximum dust size of ≲1 mm. The degeneracy between 100 μm– and millimeter-sized grains can be solved by improving the ALMA calibration accuracy or polarimetric observations at (sub)centimeter wavelengths.