Hydrodynamics of embedded planets' first atmospheres - III. The role of radiation transport for super-Earth planets

The population of close-in super-Earths, with gas mass fractions of up to 10% represents a challenge for planet formation theory: how did they avoid runaway gas accretion and collapsing to hot Jupiters despite their core masses being in the critical range of $M_\mathrm{c} \simeq 10 M_\mathrm{\oplus}$? Previous three-dimensional (3D) hydrodynamical simulations indicate that atmospheres of low-mass planets cannot be considered isolated from the protoplanetary disc, contrary to what is assumed in 1D-evolutionary calculations. This finding is referred to as the recycling hypothesis. In this Paper we investigate the recycling hypothesis for super-Earth planets, accounting for realistic 3D radiation hydrodynamics. Also, we conduct a direct comparison in terms of the evolution of the entropy between 1D and 3D geometries. We clearly see that 3D atmospheres maintain higher entropy: although gas in the atmosphere loses entropy through radiative cooling, the advection of high entropy gas from the disc into the Bondi/Hill sphere slows down Kelvin-Helmholtz contraction, potentially arresting envelope growth at a sub-critical gas mass fraction. Recycling, therefore, operates vigorously, in line with results by previous studies. However, we also identify an "inner core" -- in size $\approx$ 25% of the Bondi radius -- where streamlines are more circular and entropies are much lower than in the outer atmosphere. Future studies at higher resolutions are needed to assess whether this region can become hydrodynamically-isolated on long time-scales.Comment: 16 pages, 12 figures, accepted for publication at MNRA

Torque wiggles -- a robust feature of the global disc-planet interaction

Gravitational coupling between planets and protoplanetary discs is responsible for many important phenomena such as planet migration and gap formation. The key quantitative characteristics of this coupling is the excitation torque density -- the torque (per unit radius) imparted on the disc by planetary gravity. Recent global simulations and linear calculations found an intricate pattern of low-amplitude, quasi-periodic oscillations in the global radial distribution of torque density in the outer disc, which we call torque wiggles. Here we show that torque wiggles are a robust outcome of global disc-planet interaction and exist despite the variation of disc parameters and thermodynamic assumptions (including $\beta$-cooling). They result from coupling of the planetary potential to the planet-driven density wave freely propagating in the disc. We developed analytical theory of this phenomenon based on approximate self-similarity of the planet-driven density waves in the outer disc. We used it, together with linear calculations and simulations, to show that (a) the radial periodicity of the wiggles is determined by the global shape of the planet-driven density wave (its wrapping in the disc) and (b) the sharp features in the torque density distribution result from constructive interference of different azimuthal (Fourier) torque contributions at radii where the planetary wake crosses the star-planet line. In the linear regime the torque wiggles represent a weak effect, affecting the total (integrated) torque by only a few per cent. However, their significance should increase in the non-linear regime, when a gap (or a cavity) forms around the perturber's orbit.Comment: 19 pages, 15 figures, submitted to MNRA

Planetary population synthesis

In stellar astrophysics, the technique of population synthesis has been successfully used for several decades. For planets, it is in contrast still a young method which only became important in recent years because of the rapid increase of the number of known extrasolar planets, and the associated growth of statistical observational constraints. With planetary population synthesis, the theory of planet formation and evolution can be put to the test against these constraints. In this review of planetary population synthesis, we first briefly list key observational constraints. Then, the work flow in the method and its two main components are presented, namely global end-to-end models that predict planetary system properties directly from protoplanetary disk properties and probability distributions for these initial conditions. An overview of various population synthesis models in the literature is given. The sub-models for the physical processes considered in global models are described: the evolution of the protoplanetary disk, the planets' accretion of solids and gas, orbital migration, and N-body interactions among concurrently growing protoplanets. Next, typical population synthesis results are illustrated in the form of new syntheses obtained with the latest generation of the Bern model. Planetary formation tracks, the distribution of planets in the mass-distance and radius-distance plane, the planetary mass function, and the distributions of planetary radii, semimajor axes, and luminosities are shown, linked to underlying physical processes, and compared with their observational counterparts. We finish by highlighting the most important predictions made by population synthesis models and discuss the lessons learned from these predictions - both those later observationally confirmed and those rejected.Comment: 47 pages, 12 figures. Invited review accepted for publication in the 'Handbook of Exoplanets', planet formation section, section editor: Ralph Pudritz, Springer reference works, Juan Antonio Belmonte and Hans Deeg, Ed

Hydrodynamics of embedded planets' first atmospheres - III. The role of radiation transport for super-Earth planets

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Formation of a planetary Laplace resonance through migration in an eccentric disk

Context. Orbital mean motion resonances in planetary systems originate from dissipative processes in disk-planet interactions that lead to orbital migration. In multi-planet systems that host giant planets, the perturbation of the protoplanetary disk strongly affects the migration of companion planets. Aims. By studying the well-characterized resonant planetary system around GJ 876 we aim to explore which effects shape disk-driven migration in such a multi-planet system to form resonant chains. Methods. We modelled the orbital migration of three planets embedded in a protoplanetary disk using two-dimensional locally isothermal hydrodynamical simulations. In order to explore the effect of several disk characteristics, we performed a parameter study by varying the disk thickness, α viscosity, mass as well as the initial position of the planets. Moreover, we have carefully analysed and compared simulations with various boundary conditions at the disk’s inner rim. Results. We find that due to the high masses of the giant planets in this system, substantial eccentricity can be excited in the disk. This results in large variations of the torque acting on the outer lower mass planet, which we attribute to a shift of Lindblad and corotation resonances as it approaches the eccentric gap that the giants create. Depending on disk parameters, the migration of the outer planet can be stopped at the gap edge in a non-resonant state. In other models, the outer planet is able to open a partial gap and to circularize the disk again, later entering a 2:1 resonance with the most massive planet in the system to complete the observed 4:2:1 Laplace resonance. Conclusions. Disk-mediated interactions between planets due to spiral waves and excitation of disk eccentricity by massive planets cause deviations from smooth inward migration of exterior lower mass planets. Self-consistent modelling of the disk-driven migration of multi-planet systems is thus mandatory. Constraints can be placed on the properties of the disk during the migration phase, based on the observed resonant state of the system. Our results are compatible with a late migration of the outermost planet into the resonant chain, when the giant planet pair already is in resonance