stars don't orbit at their guiding radii!

A subject of conversation all week has been about stellar orbits in the Milky Way disk, driven by some visualizations made by Adrian Price-Whelan (Flatiron). We often describe the azimuthal action or the z component of the angular momentum (L_Z or J_Phi) of a disk star in terms of the guiding radius, or the radius of a circular orbit of the same azimuthal action. The idea is: If the star has radial action, it will oscillate around the guiding radius as it orbits. Wrong!! If the vertical action is comparable to or larger than the radial action (and that’s typical), the star will orbit outside the guiding radius, always. The trivial picture is simply incorrect.