Dynamical Instability of Multi-planet Systems and Free-floating Planets

TL;DR

This study uses numerical simulations to explore how multi-planet systems become dynamically unstable, leading to planet ejections and the formation of free-floating planets, especially highlighting the role of cold Jupiters.

Contribution

It provides new insights into the timescales and conditions under which planets are ejected, emphasizing the impact of cold Jupiters on super-Earth ejections and system stability.

Findings

Ejection timescales depend on the semimajor axis of the innermost planet.

Cold Jupiters increase the likelihood of super-Earth ejections.

Most ejected super-Earths have velocities below 6 km/s.

Abstract

The ejection of planets by the instability of planetary systems is a potential source of free-floating planets. We numerically simulate multi-planet systems to study the evolution process, the properties of surviving systems, and the statistics of ejected planets. For systems with only super-Earth planets, we find that the time (in units of the orbital period $P_{1}$ of the innermost planet) for the system to lose the first planet by collision or ejection increases with the semimajor axis of the innermost planet. In contrast, the time (in units of $P_{1}$) for the first close encounter between two planets is identical. These two timescales also depend differently on the orbital spacing between the planets. Most systems with only super-Earths do not have planets ejected. In systems with super-Earths and a cold Jupiter, we discover that a cold Jupiter significantly increases the probability of ejection of the super-Earths by close encounters. Of 38\% of ejected super-Earths, most velocities relative to their parent stars are smaller than $6\ \mathrm{km\ s^{-1}}$. We conservatively estimate that more than 86\% of the surviving two-planet systems in the super-Earths plus cold Jupiter sample are long-term stable by using empirical criteria. Most super-Earths in the remaining two-planet systems are on highly elliptical but stable orbits and have migrated inwards compared with their initial states.