Actions of highly eccentric orbits

Journal article

The challenge presented by computing actions for eccentric orbits in axisymmetric potentials is discussed. In the limit of vanishing angular momentum about the potential’s symmetry axis, there is a clean distinction between box and loop orbits. We show that this distinction persists into the regime of non-zero angular momentum. In the case of a Stäckel potential, there is a critical value of the third integral below which does not contribute to the centrifugal barrier. An orbit is of box or loop type according as its value of is smaller or greater than . We give algorithms for determining and the critical action below which orbits in any given potential are boxes. It is hard to compute the actions and especially the frequencies of orbits that have using the Stäckel Fudge. A modification of the Fudge that alleviates the problem is described.

Authors: Wright, T; Binney, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Oxford University Press
• Journal: Monthly Notices of the Royal Astronomical Society
• Volume: 549
• Issue: 1
• Article number: stag839
• Publication date: 2026-05-06
• Acceptance date: 2026-04-30
• DOI: 10.1093/mnras/stag839
• EISSN: 1365-2966
• ISSN: 0035-8711
• Language: English
• Keywords: Galaxy: kinematics and dynamics; methods: numerical; galaxies: kinematics and dynamics