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

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.