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Recent ground- and space-based observations show that stars with multiple planets are common in the Galaxy. Most of these observational methods are biased toward detecting large planets near to their host stars. Because of these observational biases, these systems can hide small, close-in planets or far-orbiting (big or small) companions. These planets can still exert dynamical influence on known planets and have such influence exerted on them in turn. In certain configurations, this influence can destabilize the system; in others, the star’s gravitational influence can instead further stabilize the system. For example, in systems with planets close to the host star, effects arising from general relativity can help to stabilize the configuration. We derive criteria for hidden planets orbiting both beyond and within known planets that quantify how strongly general relativistic effects can stabilize systems that would otherwise be unstable. As a proof of concept, we investigate the several planets in a system based on Kepler-56 and show that the outermost planet will not disrupt the system even at high eccentricities, and we show that an Earth-radius planet could be stable within this system if it orbits below 0.08 au. Furthermore, we provide specific predictions to known observed systems by constraining the parameter space of possible hidden planets.

 

Abstract Multiplanetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai–Lidov mechanism. However, the star–planet and the planet–planet interactions can help stabilize the system. In this work, we extend the previous stability criterion that only considered the companion–planet and planet–planet interactions by also accounting for short-range forces or effects, specifically, relativistic precession induced by the host star. A general analytical stability criterion is developed for planetary systems with N inner planets and a relatively distant inclined perturber by comparing precession rates of relevant dynamical effects. Furthermore, we demonstrate as examples that in systems with two and three inner planets, the analytical criterion is consistent with numerical simulations using a combination of Gauss’s averaging method and direct N -body integration. Finally, the criterion is applied to observed systems, constraining the orbital parameter space of a possible undiscovered companion. This new stability criterion extends the parameter space in which an inclined companion of multiplanet systems can inhabit.