The Secular Dynamics of TNOs and Planet Nine Interactions

Abstract: The existence of Planet Nine has been suggested to explain the pericenter clustering of extreme trans-Neptunian objects (TNOs). However, the underlying dynamics involving Planet Nine, test particles and Neptune is rich, and it remains unclear which dynamical processes lead to the alignment and how they depends on the properties of Planet Nine. Here, we investigate the secular interactions between an eccentric outer perturber and TNOs starting in a near-coplanar configuration. We find that a large number of TNOs could survive outside of mean motion resonances at 4Gyr, which differs from previous results obtained in the exact coplanar case with Neptune being treated as a quadrupole potential. In addition, secular dynamics leads to the orbital clustering seen in N-body simulations. We find that a near coplanar Planet Nine can flip TNO orbital planes, and when this happens, the geometrical longitudes of pericenter of the TNOs librate around $180<sup>\circ$ during the flip. Orbital precession caused by the inner giant planets can suppress the flips while keeping the longitude of pericenter librating when $30\lesssim r_p \lesssim 80$ AU $&amp;$ $a\gtrsim 250$ AU. This results in the alignment of the pericenter of the low inclination TNOs ($i \lesssim 40<sup>\circ$). We find the anti-aligned population and the flipped orbits could be produced by an eccentric ($e_9 \gtrsim 0.4$) outer planet of $\sim 10M_{\oplus}$ in a wide $a_9 \gtrsim 400 \sim 800$ AU orbit. Future surveys on the high inclination TNOs will help further constrain the properties of possible outer planets.