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 v 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.