Millimeter-wave polarization of protoplanetary disks due to dust scattering

TL;DR

This paper introduces a method using millimeter-wave polarization observations to constrain dust grain sizes in protoplanetary disks, leveraging self-scattering effects and radiative transfer modeling to interpret polarization patterns.

Contribution

It presents a novel approach to determine grain sizes in disks through polarization measurements, highlighting the wavelength dependence and spatial polarization patterns.

Findings

Polarization degree can reach up to 2.5% at 870 μm.

Polarization vectors show radial and azimuthal patterns in different disk regions.

Maximum polarization occurs when grain size is about λ/2π.

Abstract

We present a new method to constrain the grain size in protoplanetary disks with polarization observations at millimeter wavelengths. If dust grains are grown to the size comparable to the wavelengths, the dust grains are expected to have a large scattering opacity and thus the continuum emission is expected to be polarized due to self-scattering. We perform 3D radiative transfer calculations to estimate the polarization degree for the protoplanetary disks having radial Gaussian-like dust surface density distributions, which have been recently discovered. The maximum grain size is set to be $100 {\rm~\mu m}$ and the observing wavelength to be 870 ${\rm \mu m}$. We find that the polarization degree is as high as 2.5 % with a subarcsec spatial resolution, which is likely to be detected with near-future ALMA observations. The emission is polarized due to scattering of anisotropic continuum emission. The map of the polarization degree shows a double peaked distribution and the polarization vectors are in the radial direction in the inner ring and in the azimuthal direction in the outer ring. We also find the wavelength dependence of the polarization degree: the polarization degree is the highest if dust grains have a maximum size of $a_{\rm max}\sim\lambda/2\pi$, where $\lambda$ is the observing wavelength. Hence, multi-wave and spatially resolved polarization observations toward protoplanetary disks enable us to put a constraint on the grain size. The constraint on the grain size from polarization observations is independent of or may be even stronger than that from the opacity index.