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

TL;DR

This paper introduces a new semi-analytical model for simulating the dynamical evolution of planetary systems via giant impacts, applicable to close-in orbits and various stellar masses, offering faster predictions than traditional N-body simulations.

Contribution

The study develops and validates a semi-analytical model that extends previous work to close-in planetary orbits and different stellar masses, enabling efficient planetary population synthesis.

Findings

Accurately predicts planetary mass, semi-major axis, and eccentricity distributions.

Validates the model against N-body simulations across various parameters.

Reduces computational time significantly compared to N-body methods.

Abstract

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.