NASA's Kepler mission discovered ∼ 700 planets in multi-planet systems containing 3 or more transiting bodies, many of which are super-Earths and mini-Neptunes in compact configurations. Using N-body simulations, we examine the in situ, final stage assembly of multi-planet systems via the collisional accretion of protoplanets. Our initial conditions are constructed using a subset of the Kepler 5-planet systems as templates. Two different prescriptions for treating planetary collisions are adopted. The simulations address numerous questions: do the results depend on the accretion prescription?; do the resulting systems resemble the Kepler systems, and do they reproduce the observed distribution of planetary multiplicities when synthetically observed?; do collisions lead to significant modification of protoplanet compositions, or to stripping of gaseous envelopes?; do the eccentricity distributions agree with those inferred for the Kepler planets? We find the accretion prescription is unimportant in determining the outcomes. The final planetary systems look broadly similar to the Kepler templates adopted, but the observed distributions of planetary multiplicities or eccentricities are not reproduced, because scattering does not excite the systems sufficiently. In addition, we find that ∼ 1% of our final systems contain a co-orbital planet pair in horseshoe or tadpole orbits. Post-processing the collision outcomes suggests they would not significantly change the ice fractions of initially ice-rich protoplanets, but significant stripping of gaseous envelopes appears likely. Hence, it may be difficult to reconcile the observation that many low mass Kepler planets have H/He envelopes with an in situ formation scenario that involves giant impacts after dispersal of the gas disc.

Observations have confirmed the existence of multiple-planet systems containing a hot Jupiter and smaller planetary companions. Examples include WASP-47, Kepler-730, and TOI-1130. We examine the plausibility of forming such systems in situ using N-body simulations that include a realistic treatment of collisions, an evolving protoplanetary disc and eccentricity/inclination damping of planetary embryos. Initial conditions are constructed using two different models for the core of the giant planet: a ‘seed-model’ and an ‘equal-mass-model’. The former has a more massive protoplanet placed among multiple small embryos in a compact configuration. The latter consists only of equal-mass embryos. Simulations of the seed-model lead to the formation of systems containing a hot Jupiter and super-Earths. The evolution consistently follows four distinct phases: early giant impacts; runaway gas accretion onto the seed protoplanet; disc damping-dominated evolution of the embryos orbiting exterior to the giant; a late chaotic phase after dispersal of the gas disc. Approximately 1% of the equal-mass simulations form a giant and follow the same four-phase evolution. Synthetic transit observations of the equal-mass simulations provide an occurrence rate of 0.26% for systems containing a hot Jupiter and an inner super-Earth, similar to the 0.2% occurrence rate from actual transit surveys, but simulated hot Jupiters are rarely detected as single transiting planets, in disagreement with observations. A subset of our simulations form two close-in giants, similar to the WASP-148 system. The scenario explored here provides a viable pathway for forming systems with unusual architectures, but does not apply to the majority of hot Jupiters.

Approximately half of the planets discovered by NASA’s Kepler mission are in systems where just a single planet transits its host star, and the remaining planets are observed to be in multi-planet systems. Recent analyses have reported a dichotomy in the eccentricity distribution displayed by systems where a single planet transits compared with that displayed by the multi-planet systems. Using N-body simulations, we examine the hypothesis that this dichotomy has arisen because inner systems of super-Earths are frequently accompanied by outer systems of giant planets that can become dynamically unstable and perturb the inner systems. Our initial conditions are constructed using a subset of the known Kepler five-planet systems as templates for the inner systems, and systems of outer giant planets with masses between those of Neptune and Saturn that are centred on orbital radii 2 ≤ ap ≤ 10 au. The parameters of the outer systems are chosen so that they are always below an assumed radial velocity detection threshold of 3 m s−1. The results show an inverse relation between the mean eccentricities and the multiplicites of the systems. Performing synthetic transit observation of the final systems reveals dichotomies in both the eccentricity and multiplicity distributions that are close to being in agreement with the Kepler data. Hence, understanding the observed orbital and physical properties of the compact systems of super-Earths discovered by Kepler may require holistic modelling that couples the dynamics of both inner and outer systems of planets during and after the epoch of formation.