The New Generation Planetary Population Synthesis (NGPPS): II. Planetary population of solar-like stars and overview of statistical results

Context. Planetary formation and evolution is a combination of multiple interlinked processes. Constraining the mechanisms observationally requires statistical comparison to a large diversity of planetary systems. Aims. We want to understand global observable consequences of different physical processes (accretion, migration, and interactions) and initial properties (like disc masses and metallicities) on the demographics of the planetary population. We also want to study the convergence of our scheme with respect to one initial condition, the initial number of planetary embryo in each disc. Methods. We selected distributions of initial conditions that are representative of known protoplanetary discs. Then, we used the Generation III Bern model to perform planetary population synthesis. We synthesise five populations with each a different initial number of Moon-mass embryos per disc: 1, 10, 20, 50, and 100. The last is our nominal population consisting of 1000 stars (systems) that was used for an extensive statistical analysis of planetary systems around 1 Mpdbl stars. Results. The properties of giant planets do not change much as long as there are at least ten embryos in each system. The study of giants can thus be done with simulations requiring less computational resources. For inner terrestrial planets, only the 100-embryos population is able to attain the giant-impact stage. In that population, each planetary system contains, on average, eight planets more massive than 1 Mpdbl. The fraction of systems with giants planets at all orbital distances is 18%, but only 1.6% are at >10 au. Systems with giants contain on average 1.6 such planets. The planetary mass function varies as M-2 between 5 and 50 Mpdbl. Both at lower and higher masses, it follows approximately M-1. The frequency of terrestrial and super-Earth planets peaks at a stellar [Fe/H] of -0.2 and 0.0, respectively, being limited at lower [Fe/H] by a lack of building blocks, and by (for them) detrimental growth of more massive dynamically active planets at higher [Fe/H]. The frequency of more massive planets (Neptunian, giants) increases monotonically with [Fe/H]. The fast migration of planets in the 5-50 Mpdbl range is reduced by the presence of multiple lower-mass inner planets in the multi-embryos populations. To assess the impact of parameters and model assumptions, we also study two non-nominal populations: insitu formation without gas-driven migration, and a different initial planetesimal surface density. Conclusions. We present one of the most comprehensive simulations of (exo)planetary system formation and evolution to date. For observations, the syntheses provides a large data set to search for comparison synthetic planetary systems that show how these systems have come into existence. The systems, including their full formation and evolution tracks are available online. For theory, they provide the framework to observationally test the global statistical consequences of theoretical models for specific physical processes. This is an important ingredient towards the development of a standard model of planetary formation and evolution.