2020ApJ...889...15Y

Spatially resolved (sub)millimeter polarization has been detected by Atacama Large Millimeter/submillimeter Array in an increasing number of disks. The majority of the observations show polarization patterns consistent with self scattering, especially at Band 7. The inferred sizes of the grains are typically of order 100 µm, which is very different from the millimeter size commonly inferred from the dust opacity index β. In an effort to resolve this discrepancy, we first introduce the so-called "Coplanar Isotropic Radiation Field" approximation, which enables the computation of the (signed) polarization fraction semianalytically. With an oft-adopted dust composition, we find that models with big dust grains produce very small polarization with reversed orientation, which has not been observed. The semianalytic results are validated through Monte Carlo radiative transfer simulations. In these models, the "correct" polarization orientation and the small β index are mutually exclusive. To resolve this tension, we explore a wide range of dust models, parameterized by their complex refractive indices m = n + ik. We find that both the fraction and the orientation of the polarization depend on the refractive index in a complex way, and this dependence is mapped out on an n-k plane for a representative 3 mm size distribution and wavelength of 870 µm. In particular, 3 mm-sized refractory organics grains produce reversed polarization, whereas grains made of absorptive carbonaceous materials produce a percent-level, nonreversed polarization; the latter may alleviate the aforementioned tension in grain size estimates. We conclude that scattering-induced polarization has the potential to also probe the grain compositions.