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

Abstract

The polarimetric observations on the protoplanetary disk around HL Tau have shown the scattering-induced polarization at ALMA Band 7, which indicates that the maximum dust size is $\sim 100\mu \mathrm{m}$, while the Spectral Energy Distribution (SED) has suggested that the maximum dust size is $\sim$ mm. 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, longer observing wavelength traces more interior layer 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 mm-sized grains for a broad range of turbulence strength, while $160\mu \mathrm{m}$-sized grains can explain barely only if the turbulence strength parameter ${\alpha }_{\mathrm{t}}$ is lower than $10^{-5}$. We also find that the observed polarization fraction can be potentially explained with the maximum dust size of $1\mathrm{mm}$ if ${\alpha }_{\mathrm{t}}\lesssim 10^{-5}$, although models with $160\mu \mathrm{m}$-sized grains are also acceptable. However, if the maximum dust size is $\sim 3\mathrm{mm}$, the simulated polarization fraction is too low to explain the observations even if the turbulence strength is extremely small, indicating the maximum dust size of $\lesssim 1$ mm. The degeneracy between 100 $\mu \mathrm{m}$-sized and mm-sized grains can be solved by improving the ALMA calibration accuracy or polarimetric observations at (sub-)cm wavelengths.

13 pages, 11 figures. Accepted for publication in ApJ

References in corpus (18)

• Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations
• One Solution to the Mass Budget Problem for Planet Formation: Optically Thick Disks with Dust Scattering
• Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics
• The Radial Distribution of Dust Particles in the HL Tau Disk from ALMA and VLA Observations
• The evidence of radio polarization induced by the radiative grain alignment and self-scattering of dust grains in a protoplanetary disk
• The anomalously low (sub)millimeter spectral indices of some protoplanetary disks may be explained by dust self-scattering
• ALMA Reveals Transition of Polarization Pattern with Wavelength in HL Tau's Disk
• Radiation Hydrodynamical Turbulence In Protoplanetary Disks: Numerical Models and Observational Constraints
• Gas and dust dynamics in starlight-heated protoplanetary disks
• Dust settling against hydrodynamic turbulence in protoplanetary discs
• Nonsticky Ice at the Origin of the Uniformly Polarized Submillimeter Emission from the HL Tau Disk
• On the accuracy of the ALMA flux calibration in the time domain and across spectral windows
• Intrinsic polarisation of elongated porous dust grains
• Solving grain size inconsistency between ALMA polarization and VLA continuum in the Ophiuchus IRS 48 protoplanetary disk
• Self-scattering of non-spherical dust grains
• Polarized emission by aligned grains in the Mie regime : application to protoplanetary disks observed by ALMA
• Modeling of the ALMA HL Tau Polarization by Mixture of Grain Alignment and Self-scattering
• Self-scattering in protoplanetary disks with dust settling

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