Toward 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 10 year baselines, the expected change in the line-of-sight velocity due to the Galaxy's gravitational field for stars at ∼kiloparsec scale distances above the Galactic midplane is ∼few tens of cm s⁻¹, 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 ∼10 years of data from the Lick–Carnegie Exoplanet Survey 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 kiloparsec distances above the Galactic midplane for realistic sample sizes can enable a direct determination of the dark matter density.