Theoretical models of planetary system formation: mass vs semi-major axis

TL;DR

This paper models the formation of planetary systems by simulating multiple planets interacting within a protoplanetary disc, revealing how competition and gravitational effects influence planetary masses and orbits.

Contribution

It introduces a new N-body simulation approach that incorporates competition, gravitational interactions, and damping effects to better understand planetary system formation.

Findings

Planet masses and semi-major axes are significantly affected by planetary interactions.

Competition for accretion alters the final planetary mass distribution.

Gravitational interactions influence orbital configurations and system architecture.

Abstract

Planet formation models have been developed during the last years in order to try to reproduce the observations of both the solar system, and the extrasolar planets. Some of these models have partially succeeded, focussing however on massive planets, and for the sake of simplicity excluding planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of both radial velocity, transit and direct imaging surveys, seems to be even more pronounced for low mass planets. These new observations require the improvement of planet formation models, including new physics, and considering the formation of systems. In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals, and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc, and show the effect, in terms of global architecture and composition of this multiplicity. We use a N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. We show that the masses and semi-major axis of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping.