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Abstract 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 millimeter 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 millimeter- to centimeter-sized particles to explain polarization observations. With a Bayesian approach, we use porous particles to fit HL Tau disk’s multiwavelength continuum and millimeter-polarization observations from the Atacama Large Millimeter/submillimeter Array (ALMA) and the Very Large Array (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 and 60 au. If the particles in HL Tau are porous, the porosity should be from 70%–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. 

ABSTRACT Despite many methods developed to find young massive planets in protoplanetary discs, it is challenging to directly detect low-mass planets that are embedded in discs. On the other hand, the core-accretion theory suggests that there could be a large population of embedded low-mass young planets at the Kelvin-Helmholtz (KH) contraction phase. We adopt both 1D models and 3D simulations to calculate the envelopes around low-mass cores (several to tens of M⊕) with different luminosities, and derive their thermal fluxes at radio wavelengths. We find that, when the background disc is optically thin at radio wavelengths, radio observations can see through the disc and probe the denser envelope within the planet’s Hill sphere. When the optically thin disc is observed with the resolution reaching one disc scale height, the radio thermal flux from the planetary envelope around a 10 M⊕ core is more than 10 per cent higher than the flux from the background disc. The emitting region can be extended and elongated. Finally, our model suggests that the au-scale clump at 52 au in the TW Hydrae disc revealed by ALMA is consistent with the envelope of an embedded 10–20 M⊕ planet, which can explain the detected flux, the spectral index dip, and the tentative spirals. The observation is also consistent with the planet undergoing pebble accretion. Future ALMA and ngVLA observations may directly reveal more such low-mass planets, enabling us to study core growth and even reconstruct the planet formation history using the embedded ‘protoplanet’ population.