Apsidal Clustering following the Inclination Instability

Disks of low-mass bodies on high-eccentricity orbits in near-Keplerian potentials can be dynamically unstable to buckling out of the plane. In this letter, we present $N$-body simulations of the long-term behavior of such a system, finding apsidal clustering of the orbits in the disk plane. The timescale over which the clustering is maintained increases with number of particles, suggesting that lopsided configurations are stable at large $N$. This discovery may explain the observed apsidal ($\varpi$) clustering of extreme trans-Neptunian Objects in the outer solar system.