Actions of highly eccentric orbits

Abstract

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 Staeckel potential, there is a critical value I_{3crit}(E) of the third integral I_3 below which I_3 does not contribute to the centrifugal barrier. An orbit is of box or loop type according as its value of I_3 is smaller or greater than I_{3crit}. We give algorithms for determining I_{3crit}(E) and the critical action Jzcrit below which orbits in any given potential are boxes. It is hard to compute the actions and especially the frequencies of orbits that have Jz ~ Jzcrit using the Staeckel Fudge. A modification of the Fudge that alleviates the problem is described.

9 pages 14 figures submitted to MNRAS

References in corpus (14)

• A Universal Density Profile from Hierarchical Clustering
• AGAMA: Action-based galaxy modelling architecture
• A direct dynamical measurement of the Milky Way's disk surface density profile, disk scale length, and dark matter profile at 4 kpc < R < 9 kpc
• Proper motions and dynamics of the Milky Way globular cluster system from Gaia DR2
• Actions for axisymmetric potentials
• The GALAH survey and Gaia DR2: dissecting the stellar disc's phase space by age, action, chemistry and location
• The origin of the Gaia phase-plane spiral
• Dynamical modeling of tidal streams
• Galactic seismology: the evolving "phase spiral" after the Sagittarius dwarf impact
• More dynamical models of our Galaxy
• Stream-orbit misalignment II: A new algorithm to constrain the Galactic potential
• Actions, angles and frequencies for numerically integrated orbits
• Torus mapper: a code for dynamical models of galaxies
• Modelling the Milky Way's globular cluster system