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 $\sim15\,\text{pc}$ for a thin disk-like orbit or $\sim
120\,\text{pc}$ for a thick disk-like orbit induces a $25\%$ systematic error
in the vertical action $J_z$. In FIRE simulations of Milky Way-mass galaxies,
these variations are on the order of $\sim100\,\text{pc}$ at the solar circle.
From observations of the mean vertical velocity variation of
$\sim5\text{--}10\,\text{km}\,\text{s}^{-1}$ with radius, we estimate that the
Milky Way midplane variations are $\sim60\text{--}170\,\text{pc}$, 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.
