Discriminating Gravitational Potential Models of the Milky Way Galaxy: A Three-Dimensional Test Based on Gaia DR2

We present a new three-dimensional test in terms of Jeans equations to the gravitational potential models of the Milky Way Galaxy (MW), based on the data with Gaia DR2 astrometry. Both the rotation curve and velocity dispersion data are used to discriminate the modified-gravity models such as quasi-linear MOND (QUMOND) and modified gravity (MOG), versus the cold dark matter (CDM) models of various prescribed parameters. We find that, given the current data -- precision within ~10km/s in rotation velocity and ~1km/s in velocity dispersion, and based on any set of the mass distribution parameters recently calibrated in the CDM context, both the two modified-gravity models and the fine-tuned CDM models are generally consistent with the data, except that MOG is beyond the 95 percent confidence level in a few cases of certain data or baryonic parameter sets. Our tests in terms of 3-integral Jeans equations, especially on the vertical direction (namely T_z), are sensitive to the density profile of the tracer; i.e., in turn, our methods can be used to place tight constraints on the mass profile of tracer stars in the future. But, no matter what a density profile of the tracers is used, QUMOND and CDM models work almost equivalently for most data and baryonic parameter sets. Because there is no free parameter in the QUMOND model and the baryonic parameters used by QUMOND are actually fine-tuned in the CDM context, this equivalence is intriguing and might be suggesting a deep causality between baryons and dark matter.