Adiabatic evolution and capture into resonance: vertical heating of a growing stellar disc

Abstract

When a resonant island sweeps through the phase space of a stellar system adiabatically, it could leave behind a radically altered distribution. Nearly all orbits will, generically, pass through resonance; some of them could be captured, dragged along, and released elsewhere in phase space. Building on earlier work in Solar system dynamics, we give a general formulation of the changes induced in a collisionless stellar system by the passage of a resonant island. We derive equations of evolution for coarse-grained distribution functions (DFs). These equations satisfy an H-theorem; thus the microscopic evolution is mixing, and effectively irreversible. We then present an application of the phenomenon of capture into resonance to the problem of vertically heating a slowly growing stellar disc, such as the one recently considered by Sridhar & Touma. We construct a simple model of the growth of a galactic disc in the symmetry plane of an oblate halo. The (2:2) resonance we study is between vertical and epicyclic oscillations about the (mainly) circular motions of stars. As the disc grows more massive, resonant stars rise high, levitating as it were, by converting their radial actions into vertical actions; they can reach several kpc above the plane, corresponding to vertical velocities > 60 km s(-1). Levitation is a possible mechanism for making the thick disc of our Galaxy. We end with a comparison of the results from the simple model with the more realistic orbital computations of Sridhar & Touma.