Semi-analytical model for the dynamical evolution of planetary systems via giant impacts

In the standard model of terrestrial planet formation, planets are formed through giant impacts of planetary embryos after the dispersal of the protoplanetary gas disc. Traditionally, $N$-body simulations have been used to investigate this process. However, they are computationally too expensive to generate sufficient planetary populations for statistical comparisons with observational data. A previous study introduced a semi-analytical model that incorporates the orbital and accretionary evolution of planets due to giant impacts and gravitational scattering. This model succeeded in reproducing the statistical features of planets in $N$-body simulations near 1 au around solar-mass stars. However, this model is not applicable to close-in regions (around 0.1 au) or low-mass stars because the dynamical evolution of planetary systems depends on the orbital radius and stellar mass. This study presents a new semi-analytical model applicable to close-in orbits around stars of various masses, validated through comparison with $N$-body simulations. The model accurately predicts the final distributions of planetary mass, semi-major axis, and eccentricity for the wide ranges of orbital radius, initial planetary mass, and stellar mass, with significantly reduced computation time compared to $N$-body simulations. By integrating this model with other planet-forming processes, a computationally low-cost planetary population synthesis model can be developed.