The Implications of Local Fluctuations in the Galactic Midplane for Dynamical Analysis in the Gaia Era

Orbital properties of stars, computed from their six-dimensional phase-space measurements and an assumed Galactic potential, are used to understand the structure and evolution of the Galaxy. Stellar actions, computed from orbits, have the attractive quality of being invariant under certain assumptions and are therefore used as quantitative labels of a star's orbit. We report a subtle but important systematic error that is induced in the actions as a consequence of local midplane variations expected for the Milky Way. This error is difficult to model because it is non-Gaussian and bimodal, with neither mode peaking on the null value. An offset in the vertical position of the Galactic midplane of similar to 15 pc for a thin disk-like orbit or similar to 120 pc for a thick disk-like orbit induces a 25% systematic error in the vertical action J(z). In Feedback in Realistic Environments simulations of Milky Way-mass galaxies, these variations are on the order of similar to 100 pc at the solar circle. From observations of the mean vertical velocity variation of similar to 5-10 km s(-1) with radius, we estimate that the Milky Way midplane variations are similar to 60-170 pc, consistent with three-dimensional dust maps. Action calculations and orbit integrations, which assume the global and local midplanes are identical, are likely to include this induced error, depending on the volume considered. Variation in the local standard of rest or distance to the Galactic center causes similar issues. The variation of the midplane must be taken into account when performing dynamical analysis across the large regions of the disk accessible to Gaia and future missions.