Hidden Planetary Friends: On the Stability Of 2-Planet Systems in the Presence of a Distant, Inclined Companion

TL;DR

This paper investigates the stability of two-planet systems influenced by distant inclined companions, deriving an analytic criterion that aligns with numerical simulations and predicting conditions for planetary companions in specific Kepler systems.

Contribution

The authors develop a new stability criterion for two-planet systems with distant inclined companions, validated by numerical simulations and applied to known Kepler systems.

Findings

Derived an analytic stability criterion based on companion's separation and eccentricity.

Validated the criterion through numerical integration of system ensembles.

Predicted parameter space for planetary companions in several Kepler systems.

Abstract

Recent observational campaigns have shown that multi-planet systems seem to be abundant in our Galaxy. Moreover, it seems that these systems might have distant companions, either planets, brown-dwarfs or other stellar objects. These companions might be inclined with respect to the inner planets, and could potentially excite the eccentricities of the inner planets through the Eccentric Kozai-Lidov mechanism. These eccentricity excitations could perhaps cause the inner orbits to cross, disrupting the inner system. We study the stability of two-planet systems in the presence of a distant, inclined, giant planet. Specifically, we derive a stability criterion, which depends on the companion's separation and eccentricity. We show that our analytic criterion agrees with the results obtained from numerically integrating an ensemble of systems. Finally, as a potential proof-of-concept, we provide a set of predictions for the parameter space that allows the existence of planetary companions for the Kepler-419, Kepler-56, Kepler-448, Kepler-88, Kepler-109, and Kepler-36 systems.