The New Generation Planetary Population Synthesis (NGPPS): I. Bern global model of planet formation and evolution, model tests, and emerging planetary systems

Context. The explosion of observational data on exoplanets gives many constraints on theoretical models of planet formation and evolution. Observational data probe very large areas of the parameter space and many different planet properties. Aims. Comparing theoretical models with observations allows one to take a key step forward towards understanding planetary systems. It however requires a model able to (i) predict all the necessary observable quantities (not only masses and orbits, but also radii, luminosities, magnitudes, or evaporation rates) and (ii) address the large range in relevant planetary masses (from Mars mass to super-Jupiters) and distances (from stellar-grazing to wide orbits). Methods. We have developed a combined global end-to-end planetary formation and evolution model, the Generation III Bern model, based on the core accretion paradigm. This model solves as directly as possible the underlying differential equations for the structure and evolution of the gas disc, the dynamical state of the planetesimals, the internal structure of the planets yielding their planetesimal and gas accretion rates, disc-driven orbital migration, and the gravitational interaction of concurrently forming planets via a full N-body calculation. Importantly, the model also follows the long-term evolution of the planets on gigayear timescales after formation including the effects of cooling and contraction, atmospheric escape, bloating, and stellar tides. Results. To test the model, we compared it with classical scenarios of Solar System formation. For the terrestrial planets, we find that we obtain a giant impact phase of protoplanet-protoplanet collisions provided enough embryos (~100) are initially emplaced in the disc. For the giant planets, we find that Jupiter-mass planets must accrete their core shortly before the dispersal of the gas disc to prevent strong inward migration that would bring them to the inner edge of the disc. Regarding the emergence of entire planetary systems, many aspects can be understood with the comparison of the timescales of growth and migration, the capture into resonances, and the consequences of large-scale dynamical instabilities caused by the gravitational interactions of protoplanets, including the situation when a second core starts runaway gas accretion. Conclusions. The Generation III Bern model provides one of the most comprehensive global end-to-end models of planetary system formation and evolution developed so far, linking a multitude of crucial physical processes self-consistently. The model can form planetary systems with a wide range of properties. We find that systems with only terrestrial planets are often well-ordered (in period, mass, and radius), while giant-planet bearing systems show no such similarity. In a series of papers, the model will be used to perform extensive planetary population syntheses, putting the current theoretical understanding of planet formation and evolution to the observational test.