Radial and vertical flows induced by galactic spiral arms: likely contributors to our 'wobbly Galaxy'

In an equilibrium axisymmetric galactic disc, the mean Galactocentric radial and vertical velocities are expected to be zero everywhere. In recent years, various large spectroscopic surveys have however shown that stars of the Milky Way disc exhibit non-zero mean velocities outside of the Galactic plane in both the Galactocentric radial and vertical velocity components. While radial velocity structures are commonly assumed to be associated with non-axisymmetric components of the potential such as spiral arms or bars, non-zero vertical velocity structures are usually attributed to excitations by external sources such as a passing satellite galaxy or a small dark matter substructure crossing the Galactic disc. Here, we use a three-dimensional test-particle simulation to show that the global stellar response to a spiral perturbation induces both a radial velocity flow and non-zero vertical motions. The resulting structure of the mean velocity field is qualitatively similar to what is observed across the Milky Way disc. We show that such a pattern also naturally emerges from an analytic toy model based on linearized Euler equations. We conclude that an external perturbation of the disc might not be a requirement to explain all of the observed structures in the vertical velocity of stars across the Galactic disc. Non-axisymmetric internal perturbations can also be the source of the observed mean velocity patterns.