Axial Symmetry Tests of Milky Way Disk Stars Probe the Galaxy\u27s Matter Distribution

In Galactic dynamics, various assumptions have been employed for mathematical ease. These assumptions are approximately valid, but departures reveal perturbations on our Galaxy. In this dissertation, we select a complete, Gaia DR2 data set, and using this data, we find evidence for axial symmetry breaking in the Galaxy, away from the spiral arms and the Galactic bar. This asymmetry is compatible with a prolate dark matter halo tilted with respect to the disk, with a long axis pointing in the direction of the Magellanic Clouds, and this matches an inventory of nearby torques. These asymmetries vary North and South of the mid-plane, which we interpret as evidence of non-steady-state effects, and we note that it varies radially. Indeed, the axial asymmetry changes sign towards the Galactic center, and this matches expectations of an orbit ``flip near the Outer Lindblad Resonance. Using this, we infer the pattern speed of the Galactic bar, though other interpretations are possible. Finally, we test the symmetry of pair counts via correlation function analyses, probing structural differences throughout the nearby Galaxy. Accounting for survey geometry, we show that two-particle correlations abound which cannot be explained by steady-state effects