On the Dynamics of the Inclination Instability

Understand

Axisymmetric disks of eccentric Kepler orbits are vulnerable to an instability which causes orbits to exponentially grow in inclination, decrease in eccentricity, and cluster in their angle of pericenter.

• Geometrically, the disk expands to a cone shape which is asymmetric about the mid-plane.
• In this paper, we describe how secular gravitational torques between individual orbits drive this "inclination instability".
• We derive growth timescales for a simple two-orbit model using a Gauss $N$-ring code, and generalize our result to larger $N$ systems with $N$-body simulations.