On the conservation of the vertical action on galactic disks

We employ high-resolution N-body simulations of isolated spiral galaxy models, from low-amplitude, multi-armed galaxies to Milky Way-like disks, to estimate the vertical action of ensembles of stars in an axisymmetric potential. In the multi-armed galaxy the low-amplitude arms represent tiny perturbations of the potential, hence the vertical action for a set of stars is conserved, although after several orbital periods of revolution the conservation degrades significantly. For a Milky Way-like galaxy with vigorous spiral activity and the formation of a bar, our results show that the potential is far from steady, implying that the action is not a constant of motion. Furthermore, because of the presence of high-amplitude arms and the bar, considerable in-plane and vertical heating occurs that forces stars to deviate from near-circular orbits, reducing the degree at which the actions are conserved for individual stars, in agreement with previous results, but also for ensembles of stars. If confirmed, this result has several implications, including the assertion that the thick disk of our Galaxy forms by radial migration of stars, under the assumption of the conservation of the action describing the vertical motion of stars.