We presentPhantom, a fast, parallel, modular, and low-memory smoothed particle hydrodynamics and magnetohydrodynamics code developed over the last decade for astrophysical applications in three dimensions. The code has been developed with a focus on stellar, galactic, planetary, and high energy astrophysics, and has already been used widely for studies of accretion discs and turbulence, from the birth of planets to how black holes accrete. Here we describe and test the core algorithms as well as modules for magnetohydrodynamics, self-gravity, sink particles, dust–gas mixtures, H₂chemistry, physical viscosity, external forces including numerous galactic potentials, Lense–Thirring precession, Poynting–Robertson drag, and stochastic turbulent driving.Phantomis hereby made publicly available.

Rings are the most frequently revealed substructure in Atacama Large Millimeter/submillimeter Array (ALMA) dust observations of protoplanetary disks, but their origin is still hotly debated. In this paper, we identify dust substructures in 12 disks and measure their properties to investigate how they form. This subsample of disks is selected from a high-resolution (∼0.″12) ALMA 1.33 mm survey of 32 disks in the Taurus star-forming region, which was designed to cover a wide range of brightness and to be unbiased to previously known substructures. While axisymmetric rings and gaps are common within our sample, spiral patterns and high-contrast azimuthal asymmetries are not detected. Fits of disk models to the visibilities lead to estimates of the location and shape of gaps and rings, the flux in each disk component, and the size of the disk. The dust substructures occur across a wide range of stellar mass and disk brightness. Disks with multiple rings tend to be more massive and more extended. The correlation between gap locations and widths, the intensity contrast between rings and gaps, and the separations of rings and gaps could all be explained if most gaps are opened by low-mass planets (super-Earths and Neptunes) in the condition of low disk turbulence (α = 10⁻⁴). The gap locations are not well correlated with the expected locations of CO and N₂ ice lines, so condensation fronts are unlikely to be a universal mechanism to create gaps and rings, though they may play a role in some cases.

We explain the axisymmetric gaps seen in recent long-baseline observations of the HL Tau protoplanetary disc with the Atacama Large Millimetre/Submillimetre Array (ALMA) as being due to the different response of gas and dust to embedded planets in protoplanetary discs. We perform global, three-dimensional dusty smoothed particle hydrodynamics calculations of multiple planets embedded in dust/gas discs which successfully reproduce most of the structures seen in the ALMA image. We find a best match to the observations using three embedded planets with masses of 0.2, 0.27 and 0.55 M_J in the three main gaps observed by ALMA, though there remain uncertainties in the exact planet masses from the disc model.

We present a high-resolution (∼0.″12, ∼16 au, mean sensitivity of 50 μJy beam⁻¹ at 225 GHz) snapshot survey of 32 protoplanetary disks around young stars with spectral type earlier than M3 in the Taurus star-forming region using the Atacama Large Millimeter Array. This sample includes most mid-infrared excess members that were not previously imaged at high spatial resolution, excluding close binaries and objects with high extinction, thereby providing a more representative look at disk properties at 1–2 Myr. Our 1.3 mm continuum maps reveal 12 disks with prominent dust gaps and rings, 2 of which are around primary stars in wide binaries, and 20 disks with no resolved features at the observed resolution (hereafter smooth disks), 8 of which are around the primary star in wide binaries. The smooth disks were classified based on their lack of resolved substructures, but their most prominent property is that they are all compact with small effective emission radii (R _eff,95% ≲ 50 au). In contrast, all disks with R _eff,95% of at least 55 au in our sample show detectable substructures. Nevertheless, their inner emission cores (inside the resolved gaps) have similar peak brightness, power-law profiles, and transition radii to the compact smooth disks, so the primary difference between these two categories is the lack of outer substructures in the latter. These compact disks may lose their outer disk through fast radial drift without dust trapping, or they might be born with small sizes. The compact dust disks, as well as the inner disk cores of extended ring disks, that look smooth at the current resolution will likely show small-scale or low-contrast substructures at higher resolution. The correlation between disk size and disk luminosity correlation demonstrates that some of the compact disks are optically thick at millimeter wavelengths.