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Dynamical instabilities among giant planets are thought to be nearly ubiquitous and culminate in the ejection of one or more planets into interstellar space. Here, we perform N -body simulations of dynamical instabilities while accounting for torques from the galactic tidal field. We find that a fraction of planets that would otherwise have been ejected are instead trapped on very wide orbits analogous to those of Oort cloud comets. The fraction of ejected planets that are trapped ranges from 1 to 10 per cent, depending on the initial planetary mass distribution. The local galactic density has a modest effect on the trapping efficiency and the orbital radii of trapped planets. The majority of Oort cloud planets survive for Gyr time-scales. Taking into account the demographics of exoplanets, we estimate that one in every 200–3000 stars could host an Oort cloud planet. This value is likely an overestimate, as we do not account for instabilities that take place at early enough times to be affected by their host stars' birth cluster or planet stripping from passing stars. If the Solar system's dynamical instability happened after birth cluster dissolution, there is a ∼7 per cent chance that an ice giant was captured in the Sun's Oort cloud. [ABSTRACT FROM AUTHOR]

In co-orbital planetary systems, two or more planets share the same orbit around their star. Here we test the dynamical stability of co-orbital rings of planets perturbed by outside forces. We test two setups: (i) 'stationary' rings of planets that, when unperturbed, remain equally spaced along their orbit and (ii) horseshoe constellation systems, in which planets are continually undergoing horseshoe librations with their immediate neighbours. We show that a single rogue planet crossing the planets' orbit more massive than a few lunar masses (⁠|$0.01\!-\!0.04 {\rm \, M_\oplus }\!\!$|) systematically disrupts a co-orbital ring of 6, 9, 18, or 42 Earth-mass planets located at 1 au. Stationary rings are more resistant to perturbations than horseshoe constellations, yet when perturbed they can transform into stable horseshoe constellation systems. Given sufficient time, any co-orbital ring system will be perturbed into either becoming a horseshoe constellation or complete destabilization. [ABSTRACT FROM AUTHOR]

Co-orbital systems contain two or more bodies sharing the same orbit around a planet or star. The best-known flavours of co-orbital systems are tadpoles (in which two bodies' angular separations oscillate about the L4/L5 Lagrange points 60° apart) and horseshoes (with two bodies periodically exchanging orbital energy to trace out a horseshoe shape in a co-rotating frame). Here, we use N -body simulations to explore the parameter space of many-planet horseshoe systems. We show that up to 24 equal-mass, Earth-mass planets can share the same orbit at 1 au, following a complex pattern in which neighbouring planets undergo horseshoe oscillations. We explore the dynamics of horseshoe constellations, and show that they can remain stable for billions of years and even persist through their stars' post-main sequence evolution. With sufficient observations, they can be identified through their large-amplitude, correlated transit timing variations. Given their longevity and exotic orbital architectures, horseshoe constellations may represent potential SETI beacons. [ABSTRACT FROM AUTHOR]

Observations of the population of cold Jupiter planets (r >1 AU) show that nearly all of these planets orbit their host star on eccentric orbits. For planets up to a few Jupiter masses, eccentric orbits are thought to be the outcome of planet–planet scattering events taking place after gas dispersal. We simulated the growth of planets via pebble and gas accretion as well as the migration of multiple planetary embryos in their gas disc. We then followed the long-term dynamical evolution of our formed planetary system up to 100 Myr after gas disc dispersal. We investigated the importance of the initial number of protoplanetary embryos and different damping rates of eccentricity and inclination during the gas phase for the final configuration of our planetary systems. We constrained our model by comparing the final dynamical structure of our simulated planetary systems to that of observed exoplanet systems. Our results show that the initial number of planetary embryos has only a minor impact on the final orbital eccentricity distribution of the giant planets, as long as the damping of eccentricity and inclination is efficient. If the damping is inefficient (slow), systems with a larger initial number of embryos harbour larger average eccentricities. In addition, for slow damping rates, we observe that scattering events are already common during the gas disc phase and that the giant planets that formed in these simulations match the observed giant planet eccentricity distribution best. These simulations also show that massive giant planets (above Jupiter mass) on eccentric orbits are less likely to host inner super-Earths as they get lost during the scattering phase, while systems with less massive giant planets on nearly circular orbits should harbour systems of inner super-Earths. Finally, our simulations predict that giant planets are not single, on average, but they live in multi-planet systems. [ABSTRACT FROM AUTHOR]

Protoplanetary discs are thought to be truncated at orbital periods of around 10 d. Therefore, the origin of rocky short-period planets with P < 10 d is a puzzle. We propose that many of these planets may form through the Type-I migration of planets locked into a chain of mutual mean motion resonances. We ran N -body simulations of planetary embryos embedded in a protoplanetary disc. The embryos experienced gravitational scatterings, collisions, disc torques, and dampening of orbital eccentricity and inclination. We then modelled Kepler observations of these planets using a forward model of both the transit probability and the detection efficiency of the Kepler pipeline. We found that planets become locked into long chains of mean motion resonances that migrate in unison. When the chain reaches the edge of the disc, the inner planets are pushed past the edge due to the disc torques acting on the planets farther out in the chain. Our simulated systems successfully reproduce the observed period distribution of short-period Kepler planets between 1 and 2 R ⊕. However, we obtain fewer closely packed short-period planets than in the Kepler sample. Our results provide valuable insight into the planet formation process, and suggests that resonance locks, migration, and dynamical instabilities play important roles in the formation and evolution of close-in small exoplanets. [ABSTRACT FROM AUTHOR]

Super-Earths – planets with sizes between the Earth and Neptune – are found in tighter orbits than that of the Earth around more than one third of main sequence stars. It has been proposed that super-Earths are scaled-up terrestrial planets that also formed similarly, through mutual accretion of planetary embryos, but in discs much denser than the solar protoplanetary disc. We argue instead that terrestrial planets and super-Earths have two clearly distinct formation pathways that are regulated by the pebble reservoir of the disc. Through numerical integrations, which combine pebble accretion and N-body gravity between embryos, we show that a difference of a factor of two in the pebble mass flux is enough to change the evolution from the terrestrial to the super-Earth growth mode. If the pebble mass flux is small, then the initial embryos within the ice line grow slowly and do not migrate substantially, resulting in a widely spaced population of approximately Mars-mass embryos when the gas disc dissipates. Subsequently, without gas being present, the embryos become unstable due to mutual gravitational interactions and a small number of terrestrial planets are formed by mutual collisions. The final terrestrial planets are at most five Earth masses. Instead, if the pebble mass flux is high, then the initial embryos within the ice line rapidly become sufficiently massive to migrate through the gas disc. Embryos concentrate at the inner edge of the disc and growth accelerates through mutual merging. This leads to the formation of a system of closely spaced super-Earths in the five to twenty Earth-mass range, bounded by the pebble isolation mass. Generally, instabilities of these super-Earth systems after the disappearance of the gas disc trigger additional merging events and dislodge the system from resonant chains. Therefore, the key difference between the two growth modes is whether embryos grow fast enough to undergo significant migration. The terrestrial growth mode produces small rocky planets on wider orbits like those in the solar system whereas the super-Earth growth mode produces planets in short-period orbits inside 1 AU, with masses larger than the Earth that should be surrounded by a primordial H/He atmosphere, unless subsequently lost by stellar irradiation. The pebble flux – which controls the transition between the two growth modes – may be regulated by the initial reservoir of solids in the disc or the presence of more distant giant planets that can halt the radial flow of pebbles. [ABSTRACT FROM AUTHOR]

Recent observations have found a valley in the size distribution of close-in super-Earths that is interpreted as a signpost that close-in super-Earths are mostly rocky in composition. However, new models predict that planetesimals should first form at the water ice line such that close-in planets are expected to have a significant water ice component. Here we investigate the water contents of super-Earths by studying the interplay between pebble accretion, planet migration and disc evolution. Planets' compositions are determined by their position relative to different condensation fronts (ice lines) throughout their growth. Migration plays a key role. Assuming that planetesimals start at or exterior to the water ice line (r > rH2O $r>r_{\textrm{H}_2\textrm{O}}$ r > r H 2 O ), inward migration causes planets to leave the source region of icy pebbles and therefore to have lower final water contents than in discs with either outward migration or no migration. The water ice line itself moves inward as the disc evolves, and delivers water as it sweeps across planets that formed dry. The relative speed and direction of planet migration and inward drift of the water ice line is thus central in determining planets' water contents. If planet formation starts at the water ice line, this implies that hot close-in super-Earths (r < 0.3 AU) with water contents of a few percent are a signpost of inward planet migration during the early gas phase. Hot super-Earths with larger water ice contents on the other hand, experienced outward migration at the water ice line and only migrated inwards after their formation was complete either because they become too massive to be contained in the region of outward migration or in chains of resonant planets. Measuring the water ice content of hot super-Earths may thus constrain their migration history. [ABSTRACT FROM AUTHOR]

Giant planets migrate though the protoplanetary disc as they grow their solid core and attract their gaseous envelope. Previously, we have studied the growth and migration of an isolated planet in an evolving disc. Here, we generalise such models to include the mutual gravitational interaction between a high number of growing planetary bodies. We have investigated how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that Jupiter-like planets in orbits outside the water ice line originate from embryos starting out at 20–40 AU when using nominal type-I and type-II migration rates and a pebble flux of approximately 100–200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 30 AU migrate into the inner system (rP < 1AU). There they form super-Earths or hot and warm gas giants, producing systems that are inconsistent with the configuration of the solar system, but consistent with some exoplanetary systems. We also explored slower migration rates which allow the formation of gas giants from embryos originating from the 5–10 AU region, which are stranded exterior to 1 AU at the end of the gas-disc phase. These giant planets can also form in discs with lower pebbles fluxes (50–100 Earth masses per Myr). We identify a pebble flux threshold below which migration dominates and moves the planetary core to the inner disc, where the pebble isolation mass is too low for the planet to accrete gas efficiently. In our model, giant planet growth requires a sufficiently high pebble flux to enable growth to out-compete migration. An even higher pebble flux produces systems with multiple gas giants. We show that planetary embryos starting interior to 5 AU do not grow into gas giants, even if migration is slow and the pebble flux is large. These embryos instead grow to just a few Earth masses, the mass regime of super-Earths. This stunted growth is caused by the low pebble isolation mass in the inner disc and is therefore independent of the pebble flux. Additionally, we show that the long-term evolution of our formed planetary systems can naturally produce systems with inner super-Earths and outer gas giants as well as systems of giant planets on very eccentric orbits. [ABSTRACT FROM AUTHOR]

A leading model for the origin of super-Earths proposes that planetary embryos migrate inward and pile up on close-in orbits. As large embryos are thought to preferentially form beyond the snowline, this naively predicts that most super-Earths should be very water-rich. Here we show that the shortest period planets formed in the migration model are often purely rocky. The inward migration of icy embryos through the terrestrial zone accelerates the growth of rocky planets via resonant shepherding. We illustrate this process with a simulation that provided a match to the Kepler-36 system of two planets on close orbits with very different densities. In the simulation, two super-Earths formed in a Kepler-36-like configuration; the inner planet was pure rock while the outer one was ice-rich. We conclude from a suite of simulations that the feeding zones of close-in super-Earths are likely to be broad and disconnected from their final orbital radii. [ABSTRACT FROM AUTHOR]

The planetary building blocks that formed in the terrestrial planet region were likely very dry, yet water is comparatively abundant on Earth. Here we review the various mechanisms proposed for the origin of water on the terrestrial planets. Various in-situ mechanisms have been suggested, which allow for the incorporation of water into the local planetesimals in the terrestrial planet region or into the planets themselves from local sources, although all of those mechanisms have difficulties. Comets have also been proposed as a source, although there may be problems fitting isotopic constraints, and the delivery efficiency is very low, such that it may be difficult to deliver even a single Earth ocean of water this way. The most promising route for water delivery is the accretion of material from beyond the snow line, similar to carbonaceous chondrites, that is scattered into the terrestrial planet region as the planets are growing. Two main scenarios are discussed in detail. First is the classical scenario in which the giant planets begin roughly in their final locations and the disk of planetesimals and embryos in the terrestrial planet region extends all the way into the outer asteroid belt region. Second is the Grand Tack scenario, where early inward and outward migration of the giant planets implants material from beyond the snow line into the asteroid belt and terrestrial planet region, where it can be accreted by the growing planets. Sufficient water is delivered to the terrestrial planets in both scenarios. While the Grand Tack scenario provides a better fit to most constraints, namely the small mass of Mars, planets may form too fast in the nominal case discussed here. This discrepancy may be reduced as a wider range of initial conditions is explored. Finally, we discuss several more recent models that may have important implications for water delivery to the terrestrial planets. [ABSTRACT FROM AUTHOR]

'Hot super-Earths' (or 'mini-Neptunes') between one and four times Earth's size with period shorter than 100 d orbit 30-50 per cent of Sun-like stars. Their orbital configuration - measured as the period ratio distribution of adjacent planets in multiplanet systems - is a strong constraint for formation models. Here, we use N-body simulations with synthetic forces from an underlying evolving gaseous disc to model the formation and long-term dynamical evolution of super-Earth systems. While the gas disc is present, planetary embryos grow and migrate inward to form a resonant chain anchored at the inner edge of the disc. These resonant chains are far more compact than the observed super-Earth systems. Once the gas dissipates, resonant chains may become dynamically unstable. They undergo a phase of giant impacts that spreads the systems out. Disc turbulence has no measurable effect on the outcome. Our simulations match observations if a small fraction of resonant chains remain stable, while most super-Earths undergo a late dynamical instability. Our statistical analysis restricts the contribution of stable systems to less than 25 per cent. Our results also suggest that the large fraction of observed single-planet systems does not necessarily imply any dichotomy in the architecture of planetary systems. Finally, we use the low abundance of resonances in Kepler data to argue that, in reality, the survival of resonant chains happens likely only in ~5 per cent of the cases. This leads to a mystery: in our simulations only 50-60 per cent of resonant chains became unstable, whereas at least 75 per cent (and probably 90-95 per cent) must be unstable to match observations. [ABSTRACT FROM AUTHOR]

Jupiter's core is generally assumed to have formed beyond the snow line. Here we consider an alternative scenario, that Jupiter's core may have accumulated in the innermost parts of the protoplanetary disk. A growing body of research suggests that small particles ("pebbles") continually drift inward through the disk. If a fraction of drifting pebbles is trapped at the inner edge of the disk a several Earth-mass core can quickly grow. Subsequently, the core may migrate outward beyond the snow line via planet-disk interactions. Of course, to reach the outer Solar System Jupiter's core must traverse the terrestrial planet-forming region. We use N-body simulations including synthetic forces from an underlying gaseous disk to study how the outward migration of Jupiter's core sculpts the terrestrial zone. If the outward migration is fast (τmig ~ 104 years), the core simply migrates past resident planetesimals and planetary embryos. However, if its migration is slower (τmig ~ 105 years) the core removes solids from the inner disk by shepherding objects in mean motion resonances. In many cases the disk interior to 0.5-1 AU is cleared of embryos and most planetesimals. By generating a mass deficit close to the Sun, the outward migration of Jupiter's core may thus explain the absence of terrestrial planets closer than Mercury. Jupiter's migrating core often stimulates the growth of another large (~Earth-mass) core -- that may provide a seed for Saturn's core -- trapped in exterior resonance. The migrating core also may transport a fraction of terrestrial planetesimals, such as the putative parent bodies of iron meteorites, to the asteroid belt. [ABSTRACT FROM AUTHOR]