Hidden planetary friends: on the stability of two-planet systems in the presence of a distant, inclined companion

Abstract

Recent observational campaigns have shown that multiplanet 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 both secularly and with N-body simulations. 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-56, Kepler-448, Kepler-88, Kepler-109, and Kepler-36 systems.