Third Integral of Motion for High-velocity Stars

Abstract

SEVERAL attempts have been made in recent years to establish whether models of the galactic mass distribution admit a third isolating integral of motion for stellar orbits in addition to the well-known integrals of energy and angular momentum^1–4. Although the various investigators concerned are in agreement that orbits of the solar type are non-ergodic, the issue is not so clear-cut for the high-velocity stars. The current lively interest in violent events connected with galactic nuclei has given rise to the idea⁵ that stars in almost radial orbits may have been expelled from the central region of the Galaxy, and the present investigation was undertaken in order to study the behaviour of such orbits. It will later be argued that this special case does not restrict the validity of the results as applied to the high-velocity stars so long as one is considering orbits or very low angular momentum.