Porous Grains in Protoplanetary Disks: Application to the Outer Region of the HL Tau Disk

Shangjia Zhang, Zhaohuan Zhu, Takahiro Ueda, Akimasa Kataoka, Anibal Sierra, Carlos Carrasco-Gonzalez, Enrique Macias

Grain sizes constrained from dust continuum and polarization observations by radio interferometry are inconsistent by at least an order of magnitude. Motivated by porous grains observed in small Solar System bodies (e.g., from the Rosetta mission), we explore how the dust grain's porosity affects the estimated grain sizes from these two methods. Porous grains have lower refractive indices, which affect both opacity and polarization fraction. With weaker Mie interference patterns, the porous grains have lower opacity at mm wavelengths than the compact grains if the grain size exceeds several hundred micrometers. Consequently, the inferred dust mass using porous grains can be up to a factor of six higher. The most significant difference between compact and porous grains is their scattering properties. The porous grains have a wider range of grain sizes with high linear polarization from dust self-scattering, allowing mm-cm-sized grains to explain polarization observations.

With a Bayesian approach, we use porous grains to fit HL Tau disk's multi-wavelength continuum and mm-polarization observations from ALMA and VLA. The moderately porous grains with sizes from 1 mm-1 m can explain both continuum and polarization observations, especially in the region between 20-60 au. If the grains in HL Tau are porous, the porosity should be from 70% to 97% from current polarization observations. We also predict that future observations of the self-scattering linear polarization at longer wavelengths (e.g., ALMA B1 and ngVLA) have the potential to further constrain the grain porosity and size.