Trapped orbits and solar-neighbourhood kinematics

TL;DR

This paper investigates how resonant trapping of stars affects local stellar kinematics, using torus mapping to analyze the distribution of stars in velocity space and assessing pattern speeds of the galactic bar.

Contribution

It introduces a quantitative measure for violations of Jeans' theorem in resonant trapping and applies it to determine the likely pattern speed of the galactic bar.

Findings

Trapping at corotation is favored with pattern speeds 33-36 /Gyr.

Outer Lindblad resonance trapping is disfavored.

Velocity space structure varies rapidly around the Sun, consistent with corotation trapping.

Abstract

Torus mapping yields constants of motion for stars trapped at a resonance. Each such constant of motion yields a system of contours in velocity space at the Sun and neighbouring points. If Jeans' theorem applied to resonantly trapped orbits, the density of stars in velocity space would be equal at all intersections of any two contours. A quantitative measure of the violation of this principal is defined and used to assess various pattern speeds for a model of the bar recently fitted to observations of interstellar gas. Trapping at corotation of a bar with pattern speed in the range 33-36 /Gyr is favoured and trapping at the outer Lindblad resonance is disfavoured. As one moves around the Sun the structure of velocity space varies quite rapidly, both as regards the observed star density and the zones of trapped orbits. The data seem consistent with trapping at corotation.