Stochasticity & Predictability in Terrestrial Planet Formation

TL;DR

This study uses numerical simulations to demonstrate that terrestrial planet formation is highly chaotic, making individual system predictions unreliable, but allowing statistical insights into planetary system properties influenced by initial conditions and giant planet configurations.

Contribution

It reveals the chaotic nature of terrestrial planet formation and analyzes how initial conditions and giant planet orbits influence the resulting planetary systems, providing a statistical framework.

Findings

Chaotic evolution causes large variability in planetary configurations.

Giant planet eccentricity affects the number and mass of terrestrial planets.

Outer system edges are determined by the $ u_6$ resonance location.

Abstract

Terrestrial planets are thought to be the result of a vast number of gravitational interactions and collisions between smaller bodies. We use numerical simulations to show that practically identical initial conditions result in a wide array of final planetary configurations. This is a result of the chaotic evolution of trajectories which are highly sensitive to minuscule displacements. We determine that differences between systems evolved from virtually identical initial conditions can be larger than the differences between systems evolved from very different initial conditions. This implies that individual simulations lack predictive power. For example, there is not a reproducible mapping between the initial and final surface density profiles. However, some key global properties can still be extracted if the statistical spread across many simulations is considered. Based on these spreads, we explore the collisional growth and orbital properties of terrestrial planets which assemble from different initial conditions (we vary the initial planetesimal distribution, planetesimal masses, and giant planet orbits). Confirming past work, we find that the resulting planetary systems are sculpted by sweeping secular resonances. Configurations with giant planets on eccentric orbits produce fewer and more massive terrestrial planets on tighter orbits than those with giants on circular orbits. This is further enhanced if the initial mass distribution is biased to the inner regions. In all cases, the outer edge of the system is set by the final location of the $\nu_6$ resonance and we find that the mass distribution peaks at the $\nu_5$ resonance. Using existing observations, we find that extrasolar systems follow similar trends. Although differences between our numerical modelling and exoplanetary systems remain, we suggest that CoRoT-7, HD 20003, and HD 20781 may host undetected giant planets.