The Effects of Disc Self-Gravity and Radiative Cooling on the Formation of Gaps and Spirals by Young Planets

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

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.Comment: 39 pages, 18 figures, 1 table, accepted to be published in The Astrophysical Journa

One Solution to the Mass Budget Problem for Planet Formation: Optically Thick Disks with Dust Scattering

Atacama Large Millimeter Array (ALMA) surveys have suggested that the dust in Class II disks may not be enough to explain the averaged solid mass in exoplanets, under the assumption that the mm disk continuum emission is optically thin. This optically thin assumption seems to be supported by recent Disk Substructures at High Angular Resolution Project (DSHARP) observations where the measured optical depths are mostly less than one. However, we point out that dust scattering can considerably reduce the emission from an optically thick region. If that scattering is ignored, an optically thick disk with scattering can be misidentified as an optically thin disk. Dust scattering in more inclined disks can reduce the intensity even further, making the disk look even fainter. The measured optical depth of ~0.6 in several DSHARP disks can be naturally explained by optically thick dust with an albedo of ~0.9 at 1.25 mm. Using the DSHARP opacity, this albedo corresponds to a dust population with the maximum grain size (s max) of 0.1–1 mm. For optically thick scattering disks, the measured spectral index α can be either larger or smaller than 2 depending on whether the dust albedo increases or decreases with wavelength. We describe how this optically thick scattering scenario could explain the observed scaling between submm continuum sizes and luminosities, and might help ease the tension between the dust size constraints from polarization and dust continuum measurements. We suggest that a significant amount of disk mass can be hidden from ALMA observations and longer wavelength observations (e.g., Very Large Array or Square Kilometre Array) are desired to probe the dust mass in disks

The Disk Substructures at High Angular Resolution Project (DSHARP). IV. Characterizing Substructures and Interactions in Disks around Multiple Star Systems

To characterize the substructures induced in protoplanetary disks by the interaction between stars in multiple systems, we study the 1.25 mm continuum and the 12CO(J = 2–1) spectral line emission of the triple systems HT Lup and AS 205, at scales of ≈5 au, as part of the Disk Substructures at High Angular Resolution Project (DSHARP). In the continuum emission, we find two symmetric spiral arms in the disk around AS 205 N, with a pitch angle of 14°, while the southern component AS 205 S, itself a spectroscopic binary, is surrounded by a compact inner disk and a bright ring at a radius of 34 au. The 12CO line exhibits clear signatures of tidal interactions, with spiral arms, extended arc-like emission, and high velocity gas, possible evidence of a recent close encounter between the disks in the AS 205 system, as these features are predicted by hydrodynamic simulations of flyby encounters. In the HT Lup system, we detect continuum emission from all three components. The primary disk, HT Lup A, also shows a two-armed symmetric spiral structure with a pitch angle of 4°, while HT Lup B and C, located at 25 and 434 au in projected separation from HT Lup A, are barely resolved with ~5 and ~10 au in diameter, respectively. The gas kinematics for the closest pair indicates a different sense of rotation for each disk, which could be explained by either a counter rotation of the two disks in different, close to parallel, planes, or by a projection effect of these disks with a close to 90° misalignment between them

The Disk Substructures at High Angular Resolution Project (DSHARP). VI. Dust Trapping in Thin-ringed Protoplanetary Disks

A large fraction of the protoplanetary disks observed with ALMA display multiple well-defined and nearly perfectly circular rings in the continuum, in many cases with substantial peak-to-valley contrast. The DSHARP campaign shows that several of these rings are very narrow in radial extent. In this Letter we test the hypothesis that these dust rings are caused by dust trapping in radial pressure bumps, and if confirmed, put constraints on the physics of the dust trapping mechanism. We model this process analytically in 1D, assuming axisymmetry. By comparing this model to the data, we find that all rings are consistent with dust trapping. Based on a plausible model of the dust temperature we find that several rings are narrower than the pressure scale height, providing strong evidence for dust trapping. The rings have peak absorption optical depth in the range between 0.2 and 0.5. The dust masses stored in each of these rings is of the order of tens of Earth masses, though much ambiguity remains due to the uncertainty of the dust opacities. The dust rings are dense enough to potentially trigger the streaming instability, but our analysis cannot give proof of this mechanism actually operating. Our results show, however, that the combination of very low and very large grains can be excluded by the data for all the rings studied in this Letter

The Disk Substructures at High Angular Resolution Project (DSHARP). III. Spiral Structures in the Millimeter Continuum of the Elias 27, IM Lup, and WaOph 6 Disks

We present an analysis of Atacama Large Millimeter/submillimeter Array 1.25 mm continuum observations of spiral structures in three protoplanetary disks from the Disk Substructures at High Angular Resolution Project. See full text for full abstract

The Disk Substructures at High Angular Resolution Project (DSHARP). VII. The Planet–Disk Interactions Interpretation

The Disk Substructures at High Angular Resolution Project (DSHARP) provides a large sample of protoplanetary disks with substructures that could be induced by young forming planets. To explore the properties of planets that may be responsible for these substructures, we systematically carry out a grid of 2D hydrodynamical simulations, including both gas and dust components. We present the resulting gas structures, including the relationship between the planet mass, as well as (1) the gaseous gap depth/width and (2) the sub/super-Keplerian motion across the gap. We then compute dust continuum intensity maps at the frequency of the DSHARP observations. We provide the relationship between the planet mass, as well as (1) the depth/width of the gaps at millimeter intensity maps, (2) the gap edge ellipticity and asymmetry, and (3) the position of secondary gaps induced by the planet. With these relationships, we lay out the procedure to constrain the planet mass using gap properties, and study the potential planets in the DSHARP disks. We highlight the excellent agreement between observations and simulations for AS 209 and the detectability of the young solar system analog. Finally, under the assumption that the detected gaps are induced by young planets, we characterize the young planet population in the planet mass–semimajor axis diagram. We find that the occurrence rate for \u3e5 M J planets beyond 5–10 au is consistent with direct imaging constraints. Disk substructures allow us to probe a wide-orbit planet population (Neptune to Jupiter mass planets beyond 10 au) that is not accessible to other planet searching techniques

The Disk Substructures at High Angular Resolution Program (DSHARP). VIII. The Rich Ringed Substructures in the AS 209 Disk

The Disk Substructures at High Angular Resolution Program (DSHARP). VIII. The Rich Ringed Substructures in the AS 209 Dis