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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.

 

We describe the first grid-based simulations of the polar alignment of a circumbinary disc. We simulate the evolution of an inclined disc around an eccentric binary using the grid-based code athena++ . The use of a grid-based numerical code allows us to explore lower disc viscosities than have been examined in previous studies. We find that the disc aligns to a polar orientation when the α viscosity is high, while discs with lower viscosity nodally precess with little alignment over 1000 binary orbital periods. The time-scales for polar alignment and disc precession are compared as a function of disc viscosity, and are found to be in agreement with previous studies. At very low disc viscosities (e.g. α = 10−5), anticyclonic vortices are observed along the inner edge of the disc. These vortices can persist for thousands of binary orbits, creating azimuthally localized overdensities and multiple pairs of spiral arms. The vortex is formed at ∼3–4 times the binary semimajor axis, close to the inner edge of the disc, and orbits at roughly the local Keplerian speed. The presence of a vortex in the disc may play an important role in the evolution of circumbinary systems, such as driving episodic accretion and accelerating the formation of polar circumbinary planets.

 

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.

 

Spirals in protoplanetary discs have been used to locate the potential planet in discs. Since only the spiral shape from a circularly orbiting perturber is known, most previous works assume that the planet is in a circular orbit. We develop a simple semi-analytical method to calculate the shape of the spirals launched by an eccentric planet. We assume that the planet emits wavelets during its orbit, and the wave fronts of these propagating wavelets form the spirals. The resulting spiral shape from this simple method agrees with numerical simulations exceptionally well. The spirals excited by an eccentric planet can detach from the planet, bifurcate, or even cross each other, which are all reproduced by this simple method. The spiral’s bifurcation point corresponds to the wavelet that is emitted when the planet’s radial speed reaches the disc’s sound speed. Multiple spirals can be excited by an eccentric planet (more than five spirals when e ≳ 0.2). The pitch angle and pattern speed are different between different spirals and can vary significantly across one spiral. The spiral wakes launched by high-mass eccentric planets steepen to spiral shocks and the crossing of spiral shocks leads to distorted or broken spirals. With the same mass, a more eccentric planet launches weaker spirals and induces a shallower gap over a long period of time. The observed unusually large/small pitch angles of some spirals, the irregular multiple spirals, and the different pattern speeds between different spirals may suggest the existence of eccentric perturbers in protoplanetary discs.

 

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 Giant planets have been discovered at large separations from the central star. Moreover, a striking number of young circumstellar disks have gas and/or dust gaps at large orbital separations, potentially driven by embedded planetary objects. To form massive planets at large orbital separations through core accretion within the disk lifetime, however, an early solid body to seed pebble and gas accretion is desirable. Young protoplanetary disks are likely self-gravitating, and these gravitoturbulent disks may efficiently concentrate solid material at the midplane driven by spiral waves. We run 3D local hydrodynamical simulations of gravitoturbulent disks with Lagrangian dust particles to determine whether particle and gas self-gravity can lead to the formation of dense solid bodies, seeding later planet formation. When self-gravity between dust particles is included, solids of size St = 0.1–1 concentrate within the gravitoturbulent spiral features and collapse under their own self-gravity into dense clumps up to several M ⊕ in mass at wide orbits. Simulations with dust that drift most efficiently, St = 1, form the most massive clouds of particles, while simulations with smaller dust particles, St = 0.1, have clumps with masses an order of magnitude lower. When the effect of dust backreaction onto the gas is included, dust clumps become smaller by a factor of a few but more numerous. The existence of large solid bodies at an early stage of the disk can accelerate the planet formation process, particularly at wide orbital separations, and potentially explain planets distant from the central stars and young protoplanetary disks with substructures. 

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. 

ABSTRACT The streaming instability is a fundamental process that can drive dust–gas dynamics and ultimately planetesimal formation in protoplanetary discs. As a linear instability, it has been shown that its growth with a distribution of dust sizes can be classified into two distinct regimes, fast- and slow-growth, depending on the dust-size distribution and the total dust-to-gas density ratio ϵ. Using numerical simulations of an unstratified disc, we bring three cases in different regimes into non-linear saturation. We find that the saturation states of the two fast-growth cases are similar to its single-species counterparts. The one with maximum dimensionless stopping time τs,max = 0.1 and ϵ = 2 drives turbulent vertical dust–gas vortices, while the other with τs,max = 2 and ϵ = 0.2 leads to radial traffic jams and filamentary structures of dust particles. The dust density distribution for the former is flat in low densities, while the one for the latter has a low-end cut-off. By contrast, the one slow-growth case results in a virtually quiescent state. Moreover, we find that in the fast-growth regime, significant dust segregation by size occurs, with large particles moving towards dense regions while small particles remain in the diffuse regions, and the mean radial drift of each dust species is appreciably altered from the (initial) drag-force equilibrium. The former effect may skew the spectral index derived from multiwavelength observations and change the initial size distribution of a pebble cloud for planetesimal formation. The latter along with turbulent diffusion may influence the radial transport and mixing of solid materials in young protoplanetary discs. 

ABSTRACT The core accretion model of giant planet formation has been challenged by the discovery of recycling flows between the planetary envelope and the disc that can slow or stall envelope accretion. We carry out 3D radiation hydrodynamic simulations with an updated opacity compilation to model the proto-Jupiter’s envelope. To isolate the 3D effects of convection and recycling, we simulate both isolated spherical envelopes and envelopes embedded in discs. The envelopes are heated at given rates to achieve steady states, enabling comparisons with 1D models. We vary envelope properties to obtain both radiative and convective solutions. Using a passive scalar, we observe significant mass recycling on the orbital time-scale. For a radiative envelope, recycling can only penetrate from the disc surface until ∼0.1–0.2 planetary Hill radii, while for a convective envelope, the convective motion can ‘dredge up’ the deeper part of the envelope so that the entire convective envelope is recycled efficiently. This recycling, however, has only limited effects on the envelopes’ thermal structure. The radiative envelope embedded in the disc has identical structure as the isolated envelope. The convective envelope has a slightly higher density when it is embedded in the disc. We introduce a modified 1D approach which can fully reproduce our 3D simulations. With our updated opacity and 1D model, we recompute Jupiter’s envelope accretion with a 10 M⊕ core, and the time-scale to runaway accretion is shorter than the disc lifetime as in prior studies. Finally, we discuss the implications of the efficient recycling on the observed chemical abundances of the planetary atmosphere (especially for super-Earths and mini-Neptunes).