THE CAPTURE AND ESCAPE OF STARS

The shape of galaxies depends on their orbital populations. These popu lations change through capture into and escape from resonance. Capture problems fall into distinct cases depending upon the shape of the pot ential well. To visualize the effective potential well for orbital cap ture, a diagrammatic approach to the resonant perturbation theory of B orn is presented. These diagrams we call equiaction sections. To illus trate their use, we present examples drawn from both galactic and Sola r system dynamics. The probability of capture for generic shapes of th e potential well is calculated. A number of predictions are made. Firs t, there are barred galaxies that possess two outer rings of gas and s tars (type R(1)R(2)) We show how to relate changes in the pattern spee d and amplitude of the bar to the strength of the two rings. Secondly, under certain conditions, small disturbances can lead to dramatic cha nges in orbital shape. This can be exploited as a mechanism to pump co unter-rotating stars and gas into the nuclei of disc galaxies. Tidal r esonant forcing of highly inclined orbits around a central mass causes a substantial increase in the likelihood of collision. Thirdly, the a ngular momentum of a potential well is changed by the passage of stars across or capture into the well. This can lead to the creation of hol es, notches and high-velocity tails in the stellar distribution functi on, whose form we explicitly calculate.