The statistical mechanics of planet orbits

TL;DR

This paper introduces a statistical model for the distribution of planetary orbits after the giant-impact phase of planet formation, predicting eccentricities and orbital spacing consistent with simulations and observations.

Contribution

It presents an analytic, phase-space-based model that describes the orbital distribution of planets post-formation using a single parameter, the dynamical temperature.

Findings

Model predictions match N-body simulation results.

Distribution of semimajor axis differences aligns with Kepler data.

The approach may extend to giant planet orbital evolution.

Abstract

The final "giant-impact" phase of terrestrial planet formation is believed to begin with a large number of planetary "embryos" on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities until their orbits cross and they collide and merge; through this process the number of surviving bodies declines until the system contains a small number of planets on well-separated, stable orbits. In this paper we explore a simple statistical model for the orbit distribution of planets formed by this process, based on the sheared-sheet approximation and the ansatz that the planets explore uniformly all of the stable region of phase space. The model provides analytic predictions for the distribution of eccentricities and semimajor axis differences, correlations between orbital elements of nearby planets, and the complete N-planet distribution function, in terms of a single parameter, the "dynamical temperature", that is determined by the planetary masses. The predicted properties are generally consistent with N-body simulations of the giant-impact phase and with the distribution of semimajor axis differences in the Kepler catalog of extrasolar planets. A similar model may apply to the orbits of giant planets if these orbits are determined mainly by dynamical evolution after the planets have formed and the gas disk has disappeared.