Spectral stellar dynamics - II. The action integrals

Open Access
Publisher Website
Google Scholar
Abstract
There are several reasons why one might wish to know the action integrals of orbits in galactic potentials. These include the capacity of action integrals to give a fair representation of the phase-space volume occupied by groups of orbits and the adiabatic invariance of these integrals. This paper shows how one may evaluate the actions of numerically integrated orbits in given potentials from the spectra of these orbits. In an inertial potential we find that the actions of loop and box orbits fit together to form a single continuum. Families of resonant loop and box orbits are associated with zones of missing actions in this continuum. The action integrals of loop and box orbits in a rotating bar do not fit together as in the inertial case. The action integrals of any orbit are accurately conserved during slow deformation of inertial and rotating potentials so long as the orbit does not switch from one orbital family to another. When an orbit does switch family, its actions usually change discontinuously no matter how slowly the potential is deformed. However, these changes are reversible if the potential is deformed sufficiently slowly. An important special case in which the actions do not change when an orbit switches between families, is that of changes between the loop and box families in an inertial bar. Possible applications of this technique to n-body models are discussed.

This publication has 0 references indexed in Scilit: