On the Dynamics of the Inclination Instability

Author
Abstract
<p>Axisymmetric disks of eccentric\&nbsp;<em>Kepler</em>\&nbsp;orbits are vulnerable to an instability that 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 that 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\&nbsp;N-ring code, and generalize our result to larger\&nbsp;N\&nbsp;systems with\&nbsp;N-body simulations. We find that two-body relaxation slows the growth of the instability at low\&nbsp;N\&nbsp;and that angular phase coverage of orbits in the disk is important at higher\&nbsp;N. As N\textrightarrow$\infty$\&nbsp;, the e-folding timescale converges to that expected from secular theory.</p>
Year of Publication
2018
Journal
The Astronomical Journal
Volume
156
Date Published
2018-09
URL
http://iopscience.iop.org/article/10.3847/1538-3881/aad95c/pdf
DOI
10.3847/1538-3881/aad95c
JILA PI
Journal Article