Free-floating Planets Produced by Planet-Planet Scatterings: Ejection Velocity and Survival Rate of Their Moons

TL;DR

This study examines how free-floating planets are ejected from multi-planet systems and assesses whether their moons can remain bound after ejection, providing analytical and simulation-based insights into their velocities and moon survival rates.

Contribution

It introduces an analytical framework for ejection velocities, identifies minimum planetary masses for ejection, and evaluates moon survival probabilities post-ejection.

Findings

Ejection velocity scales with planetary mass and initial orbit.

A minimum planetary mass is required for successful ejection.

Moons can survive ejection if their orbits are sufficiently close to the host planet.

Abstract

The discovery of numerous free-floating planets (FFPs) has intensified interest in their origins and dynamical histories. A leading formation mechanism is planet-planet scatterings in unstable multi-planetary systems, which can naturally lead to planetary ejections. If these planets originally host moons, it remains an open question whether such satellites can remain gravitationally bound to FFPs after ejection. In this work, we investigate both the ejection velocity of FFPs produced by planet-planet scatterings and the survival rate of their potential moons; we estimate the latter by determining the statistics of the minimum planet-planet distance prior to planet ejection, and comparing it to the initial orbital radius of the moon relative to its host planet. Using the circular restricted three-body framework, we derive an analytical boundary for the ejection velocity based on Jacobi energy conservation, which agrees with the results of integrations. We also identify a minimum planetary mass required for successful ejection. For two-planet systems with finite planetary masses, we use simulations and analytical arguments to determine how the ejection velocity scales with the planetary mass and initial semi-major axis. We contrast our results to the ejection of planets around binaries in unstable orbits. Extending our analysis to three-planet systems yields similar results, reinforcing the robustness of our conclusions. These findings offer insights into the property of FFPs and inform future efforts to search for exomoons around them.