Porous Dust Particles in Protoplanetary Disks: Application to the HL Tau Disk

Dust particle sizes constrained from dust continuum and polarization observations by radio interferometry are inconsistent by at least an order of magnitude. Motivated by porous dust observed in small Solar System bodies (e.g., from the Rosetta mission), we explore how the dust particle's porosity affects the estimated particle sizes from these two methods. Porous particles have lower refractive indices, which affect both opacity and polarization fraction. With weaker Mie interference patterns, the porous particles have lower opacity at mm wavelengths than the compact particles if the particle size exceeds several hundred microns. Consequently, the inferred dust mass using porous particles can be up to a factor of six higher. The most significant difference between compact and porous particles is their scattering properties. The porous particles have a wider range of particle sizes with high linear polarization from dust self-scattering, allowing mm-cm-sized particles to explain polarization observations. With a Bayesian approach, we use porous particles to fit HL Tau disk's multi-wavelength continuum and mm-polarization observations from ALMA and VLA. The moderately porous particles with sizes from 1 mm-1 m can explain both continuum and polarization observations, especially in the region between 20-60 au. If the particles 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 particle's porosity and size.