We present Phantom, 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, H2 chemistry, physical viscosity, external forces including numerous galactic potentials, Lense-Thirring precession, Poynting-Robertson drag and stochastic turbulent driving. Phantom is hereby made publicly available.

We investigate the properties of circumplanetary discs formed in three‐dimensional, self‐gravitating radiation hydrodynamical models of gas accretion by protoplanets. We determine disc sizes, scaleheights, and density and temperature profiles for different protoplanet masses, in solar nebulae of differing grain opacities. We find that the analytical prediction of circumplanetary disc radii in an evacuated gap (RHill/3) from Quillen & Trilling yields a good estimate for discs formed by high‐mass protoplanets. The radial density profiles of the circumplanetary discs may be described by power laws between r−2 and r−3/2. We find no evidence for the ring‐like density enhancements that have been found in some previous models of circumplanetary discs. Temperature profiles follow a ∼r−7/10 power law regardless of protoplanet mass or nebula grain opacity. The discs invariably have large scaleheights (H/r > 0.2), making them thick in comparison with their encompassing circumstellar discs, and they show no flaring.

We present results from three‐dimensional, self‐gravitating radiation hydrodynamical models of gas accretion by planetary cores. In some cases, the accretion flow is resolved down to the surface of the solid core – the first time such simulations have been performed. We investigate the dependence of the gas accretion rate upon the planetary core mass, and the surface density and opacity of the encompassing protoplanetary disc. Accretion of planetesimals is neglected. We find that high‐mass protoplanets are surrounded by thick circumplanetary discs during their gas accretion phase but, contrary to locally isothermal calculations, discs do not form around accreting protoplanets with masses ≲ when radiation hydrodynamical simulations are performed, even if the grain opacity is reduced from interstellar values by a factor of 100. We find that the opacity of the gas plays a large role in determining the accretion rates for low‐mass planetary cores. For example, reducing the opacities from interstellar values by a factor of 100 leads to roughly an order of magnitude increase in the accretion rates for protoplanets. The dependence on opacity becomes less important in determining the accretion rate for more massive cores where gravity dominates the effects of thermal support and the protoplanet is essentially accreting at the runaway rate. Increasing the core mass from 10 to 100 M increases the accretion rate by a factor of ≈50 for interstellar opacities. Beyond , the ability of the protoplanetary disc to supply material to the accreting protoplanet limits the accretion rate, independent of the opacity. Finally, for low‐mass planetary cores (≲), we obtain accretion rates that are in agreement with previous one‐dimensional quasi‐static models. This indicates that three‐dimensional hydrodynamical effects may not significantly alter the gas accretion time‐scales that have been obtained from quasi‐static models.

We have performed three‐dimensional two‐fluid (gas–dust) hydrodynamical models of circumstellar discs with embedded protoplanets (3–333 M⊕) and small solid bodies (radii 10 cm to 10 m). We find that high‐mass planets (≳ Saturn mass) open sufficiently deep gaps in the gas disc such that the density maximum at the outer edge of the gap can very efficiently trap metre‐sized solid bodies. This allows the accumulation of solids at the outer edge of the gap as solids from large radii spiral inwards to the trapping region. This process of accumulation occurs fastest for those bodies that spiral inwards most rapidly, typically metre‐sized boulders, whilst smaller and larger objects will not migrate sufficiently rapidly in the discs lifetime to benefit from the process. Around a Jupiter mass planet we find that bound clumps of solid material, as large as several Earth masses, may form, potentially collapsing under self‐gravity to form planets or planetesimals. These results are in agreement with Lyra et al., supporting their finding that the formation of a second generation of planetesimals or of terrestrial mass planets may be triggered by the presence of a high‐mass planet.