Apsidal behavior among planetary orbits: Testing the planet-planet scattering model

Planets in extrasolar systems tend to interact such that their orbits lie near a boundary between apsidal libration and circulation, a "separatrix," with one eccentricity periodically reaching near zero. One explanation, applied to the nu And system, assumed three original planets on circular orbits. One is ejected, leaving the other two with near-separatrix behavior. We test that model by integrating hundreds of hypothetical, unstable planetary systems that eject a planet. We find that the probability that the remaining planets exhibit near- separatrix motion is small (< 5% compared with nearly 50% of observed systems). Moreover, while observed librating systems are evenly divided between aligned and antialigned pericenter longitudes, the scattering model strongly favors alignment. Alternative scattering theories are proposed, which may provide a more satisfactory fit with observed systems.