Hiding Planets Near and Far: The Parameter Space of Hidden Companions for Known Planetary Systems

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 upon 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 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.