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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.

 

Observations of substructure in protoplanetary disks have largely been limited to the brightest and largest disks, excluding the abundant population of compact disks, which are likely sites of planet formation. Here, we reanalyze ∼0.″1, 1.33 mm Atacama Large Millimeter/submillimeter Array (ALMA) continuum observations of 12 compact protoplanetary disks in the Taurus star-forming region. By fitting visibilities directly, we identify substructures in six of the 12 compact disks. We then compare the substructures identified in the full Taurus sample of 24 disks in single-star systems and the ALMA DSHARP survey, differentiating between compact (R_eff,90%< 50 au) and extended (R_eff,90%≥50 au) disk sources. We find that substructures are detected at nearly all radii in both small and large disks. Tentatively, we find fewer wide gaps in intermediate-sized disks withR_eff,90%between 30 and 90 au. We perform a series of planet–disk interaction simulations to constrain the sensitivity of our visibility-fitting approach. Under the assumption of planet–disk interaction, we use the gap widths and common disk parameters to calculate potential planet masses within the Taurus sample. We find that the young planet occurrence rate peaks near Neptune masses, similar to the DSHARP sample. For 0.01M_J/M_⊙≲M_p/M_*≲0.1M_J/M_⊙, the rate is 17.4% ± 8.3%; for 0.1M_J/M_⊙≲M_p/M_*≲1M_J/M_⊙, it is 27.8% ± 8.3%. Both of them are consistent with microlensing surveys. For gas giants more massive than 5M_J, the occurrence rate is 4.2% ± 4.2%, consistent with direct imaging surveys.

 

Abstract Rings and gaps are ubiquitous in protoplanetary disks. Larger dust grains will concentrate in gaseous rings more compactly due to stronger aerodynamic drag. However, the effects of dust concentration on the ring’s thermal structure have not been explored. Using MCRT simulations, we self-consistently construct ring models by iterating the ring’s thermal structure, hydrostatic equilibrium, and dust concentration. We set up rings with two dust populations having different settling and radial concentration due to their different sizes. We find two mechanisms that can lead to temperature dips around the ring. When the disk is optically thick, the temperature drops outside the ring, which is the shadowing effect found in previous studies adopting a single-dust population in the disk. When the disk is optically thin, a second mechanism due to excess cooling of big grains is found. Big grains cool more efficiently, which leads to a moderate temperature dip within the ring where big dust resides. This dip is close to the center of the ring. Such a temperature dip within the ring can lead to particle pileup outside the ring and feedback to the dust distribution and thermal structure. We couple the MCRT calculations with a 1D dust evolution model and show that the ring evolves to a different shape and may even separate to several rings. Overall, dust concentration within rings has moderate effects on the disk’s thermal structure, and a self-consistent model is crucial not only for protoplanetary disk observations but also for planetesimal and planet formation studies. 

We developed convolutional neural networks (CNNs) to rapidly and directly infer the planet mass from radio dust continuum images. Substructures induced by young planets in protoplanetary discs can be used to infer the potential young planets’ properties. Hydrodynamical simulations have been used to study the relationships between the planet’s properties and these disc features. However, these attempts either fine-tuned numerical simulations to fit one protoplanetary disc at a time, which was time consuming, or azimuthally averaged simulation results to derive some linear relationships between the gap width/depth and the planet mass, which lost information on asymmetric features in discs. To cope with these disadvantages, we developed Planet Gap neural Networks (PGNets) to infer the planet mass from two-dimensional images. We first fit the gridded data in Zhang et al. as a classification problem. Then, we quadrupled the data set by running additional simulations with near-randomly sampled parameters, and derived the planet mass and disc viscosity together as a regression problem. The classification approach can reach an accuracy of 92 per cent, whereas the regression approach can reach 1σ as 0.16 dex for planet mass and 0.23 dex for disc viscosity. We can reproduce the degeneracy scaling α ∝ $M_\mathrm{ p}^3$ found in the linear fitting method, which means that the CNN method can even be used to find degeneracy relationship. The gradient-weighted class activation mapping effectively confirms that PGNets use proper disc features to constrain the planet mass. We provide programs for PGNets and the traditional fitting method from Zhang et al., and discuss each method’s advantages and disadvantages.

 

ABSTRACT We have carried out 2D hydrodynamical simulations to study the effects of disc self-gravity and radiative cooling on the formation of gaps and spirals. (1) With disc self-gravity included, we find stronger, more tightly wound spirals and deeper gaps in more massive discs. The deeper gaps are due to the larger Angular Momentum Flux (AMF) of the waves excited in more massive discs, as expected from the linear theory. The position of the secondary gap does not change, provided that the disc is not extremely massive (Q ≳ 2). (2) With radiative cooling included, the excited spirals become monotonically more open (less tightly wound) as the disc’s cooling time-scale increases. On the other hand, the amplitude and strength of the spirals decrease when the cooling time increases from a small value to ∼1/Ω, but then the amplitude starts to increase again when the cooling time continues to increase. This indicates that radiative dissipation becomes important for waves with Tcool ∼ 1. Consequently, the induced primary gap is narrower and the secondary gap becomes significantly shallower when the cooling time becomes ∼1/Ω. When the secondary gap is present, the position of it moves to the inner disc from the fast cooling cases to the slow cooling cases. The dependence of gap properties on the cooling time-scale (e.g. in AS 209) provides a new way to constrain the disc optical depth and thus disc surface density.