For more than a century now, our inference of the mass distributions (including dark matter) in galaxies have been based on modeling the positions and velocities of stars, i.e., using kinematic analyses, which assume equilibrium. These kinematic estimates can be inaccurate for a time-dependent potential, and there are now many lines of observational evidence that show that our Galaxy has had a highly dynamic history. Recent technological advances now make it possible for us to carry out extreme-precision time-series measurements of the acceleration of stars that live within the gravitational potential of our Galaxy. I will talk about several different methods of direct acceleration measurements that we have developed, including our recent analysis of compiled pulsar timing data from which we were able to measure the Galactic acceleration for the first time, as well as our ongoing extreme-precision radial velocity survey. Given the measured acceleration, we can straightforwardly use the Poisson equation to determine the total density, and the local dark matter density.
There are testable differences between popular models of dark matter on small scales, i.e., in their sub-structure. We have recently shown that dark matter sub-structure can now be directly measured using eclipse timing, given the very precise baseline established by the Kepler mission about a decade ago. A contemporary measurement of some eclipsing binary stars in the Kepler field with HST/JWST can yield the small (~ 0.1 second), but measurable shift in the eclipse mid-point time induced by the Galactic potential over the past decade. This acceleration signal grows quadratically with time - in the future, such a measurement with the Roman telescope will extend the baseline even further.