Planetary population synthesis and the emergence of four classes of planetary system architectures

Planetary population synthesis is a helpful tool to understand the physics of planetary system formation. It builds on a global model, meaning that the model has to include a multitude of physical processes. The outcome can be statistically compared with exoplanet observations. Here, we review the population synthesis method and then use one population computed using the Generation III Bern model to explore how different planetary system architectures emerge and which conditions lead to their formation. The emerging systems can be classified into four main architectures: Class I of near in situ compositionally ordered terrestrial and ice planets, Class II of migrated sub-Neptunes, Class III of mixed low-mass and giant planets, broadly similar to the Solar System, and Class IV of dynamically active giants without inner low-mass planets. These four classes exhibit distinct typical formation pathways and are characterised by certain mass scales. We find that Class I forms from the local accretion of planetesimals followed by a giant impact phase, and the final planet masses correspond to what is expected from such a scenario, the 'Goldreich mass'. Class II, the migrated sub-Neptune systems form when planets reach the 'equality mass' where accretion and migration timescales are comparable before the dispersal of the gas disc, but not large enough to allow for rapid gas accretion. Giant planets form when the 'equality mass' allows for gas accretion to proceed while the planet is migrating, i.e. when the critical core mass is reached. The main discriminant of the four classes is the initial mass of solids in the disc, with contributions from the lifetime and mass of the gas disc. The distinction between mixed Class III systems and Class IV dynamically active giants is in part due to the stochastic nature of dynamical interactions, such as scatterings between giant planets, rather than the initial conditions only. The breakdown of system into classes allows to better interpret the outcome of a complex model and understand which physical processes are dominant. Comparison with observations reveals differences to the actual population, pointing at limitation of theoretical understanding. For example, the overrepresentation of synthetic super-Earths and sub-Neptunes in Class I systems causes these planets to be found at lower metallicities than in observations.