Predicting planets in known extrasolar planetary systems. I. Test particle simulations

Recent work has suggested that many planetary systems lie near instability. If all systems are near instability, then at least one additional planet must exist in stable regions of well-separated extrasolar planetary systems to push these systems to the edge of stability. We examine the known systems by placing massless test particles in between the planets and integrating for 1-10 million yr. We find that some systems, HD 168443 and HD 74156, eject nearly all test particles within 2 million yr. However, we find that HD 37124, HD 38529, and 55 Cnc have large contiguous regions in which particles survive for 10 million yr. These three systems, therefore, seem the most likely candidates for additional companions. Furthermore, HD 74156 and HD 168443 must be complete; therefore radial velocity surveys should only focus on detecting more distant companions. We also find that several systems show stable regions that only exist at nonzero eccentricities.