  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.
