Towards a direct measure of the Galactic acceleration
  High precision spectrographs can enable not only the discovery of exoplanets,
but can also provide a fundamental measurement in Galactic dynamics. Over about
ten year baselines, the expected change in the line-of-sight velocity due to
the Galaxy's gravitational field for stars at $\sim$ kpc scale distances above
the Galactic mid-plane is $\sim$ few - 10 cm/s, and may be detectable by the
current generation of high precision spectrographs. Here, we provide
theoretical expectations for this measurement based on both static models of
the Milky Way and isolated Milky Way simulations, as well from controlled
dynamical simulations of the Milky Way interacting with dwarf galaxies. We
simulate a population synthesis model to analyze the contribution of planets
and binaries to the Galactic acceleration signal. We find that while low-mass,
long-period planetary companions are a contaminant to the Galactic acceleration
signal, their contribution is very small. Our analysis of $\sim$ ten years of
data from the LCES HIRES/Keck precision radial velocity (RV) survey shows that
slopes of the RV curves of standard RV stars agree with expectations of the
local Galactic acceleration near the Sun within the errors, and that the error
in the slope scales inversely as the square root of the number of observations.
Thus, we demonstrate that a survey of stars with low intrinsic stellar jitter
at kpc distances above the Galactic mid-plane for realistic sample sizes can
enable a direct determination of the dark matter density.
