We study a set of solar neighborhood (d < 3 kpc) stars from Gaia Data Release 2 to determine azimuthal star count differences, i.e., left and right of the line from the Galactic center through the sun -and compare these differences north and south. In this companion paper to Gardner et al. (2020), we delineate our procedures to remove false asymmetries from sampling effects, incompleteness, and/or interloper populations, as this is crucial to tests of axisymmetry. Particularly, we have taken care to make appropriate selections of magnitude, color, in-plane Galactocentric radius and Galactic |b| and |z|. We find that requiring parallax determinations of high precision induces sampling biases, so that we eschew such requirements and exclude, e.g., regions around the lines of sight to the Magellanic clouds, along with their mirror-image lines of sight, to ensure well-matched data sets. After making conservative cuts, we demonstrate the existence of azimuthal asymmetries, and find differences in those, north and south. These asymmetries give key insights into the nature and origins of the perturbations on Galactic matter, allowing us to assess the relative influence of the Magellanic Clouds (LMC & SMC), the Galactic bar, and other masses on the Galactic mass distribution, as described in Gardner et al. (2020). The asymmetry's radial dependence reveals variations that we attribute to the Galactic bar, and it changes sign at a radius of (0.95 ± 0.03)R 0 , with R 0 the Sun-Galactic-Center (GC) distance, to give us the first direct assessment of the outer Lindblad resonant radius.

We apply Noether's theorem to observations of main-sequence stars from the Gaia Data Release 2 archive to probe the matter distribution function of the Galaxy. That is, we examine the axial symmetry of stars at vertical heights z, 0.2 ≤ |z| ≤ 3 kpc, to probe the quality of the angular momentum L z as an integral of motion. The failure of this symmetry test would speak to a Milky Way, in both its visible and dark matter, that is not isolated and/or not in steady state. The left-right symmetry-breaking pattern we have observed, north and south, reveals both effects, with a measured deviation from symmetry of typically 0.5%. We show that a prolate form of the gravitational distortion of the Milky Way by the Large Magellanic Cloud, determined from fits to the Orphan stream by Erkal et al. (2019), is compatible with the size and sign of the axial-symmetry-breaking effects we have discovered in our sample of up to 14.4 million main-sequence stars, speaking to a distortion of an emergent, rather than static, nature.

Our recent studies of axial-symmetry breaking in the nearby (d < 3 kpc) star counts are sensitive to the distortions of stellar orbits perpendicular and parallel to the orientation of the bar just within and beyond the outer Lindblad resonance (OLR) radius. Using the location of the sign flip in the left–right asymmetry in stars counts about the anticenter line to determine the OLR radius R OLR, and treating the bar as if it were a weakly nonaxisymmetric effect, we use R OLR and recent measurements of the Galactic rotation curve and the Sun–Galactic-center distance R 0 to determine the pattern speed Ωp of the Galactic bar, as well as the Galactic corotation radius R CR. After removing the effect of the Large and Small Magellanic Clouds from our asymmetry measurement, we find that R OLR = (0.96 ± 0.03)R 0 = 7.85 ± 0.25 kpc, Ωp = 49.3 ± 2.2 km s−1 kpc−1, R CR = (0.58 ± 0.04)R 0 = 4.76 ± 0.27 kpc, revealing, as we shall show, that the Milky Way’s bar is likely both weak and fast, though we also note possible evidence for non-steady-state effects in the bar region.

We introduce a two-particle correlation function (2PCF) for the Milky Way, constructed to probe spatial correlations in the orthogonal directions of the stellar disk in the Galactic cylindrical coordinates of R, ϕ, and z. We use this new tool to probe the structure and dynamics of the Galaxy using the carefully selected set of solar neighborhood stars (d ≲ 3 kpc) from Gaia Data Release 2 that we previously employed for studies of axial symmetry breaking in stellar number counts. We make additional, extensive tests, comparing to reference numerical simulations, to ensure our control over possibly confounding systematic effects. Supposing either axial or north–south symmetry, we divide this data set into two nominally symmetric sectors and construct the 2PCF, in the manner of the Landy–Szalay estimator, from the Gaia data. In so doing, working well away from the midplane region in which the spiral arms appear, we have discovered distinct symmetry-breaking patterns in the 2PCF in its orthogonal directions, thus establishing the existence of correlations in stellar number counts alone at subkiloparsec length scales for the very first time. In particular, we observe extensive wavelike structures of amplitude greatly in excess of what we would estimate if the system were in a steady state. We study the variations in these patterns across the Galactic disk, and with increasing ∣z∣, and we show how our results complement other observations of non-steady-state effects near the Sun, such as vertical asymmetries in stellar number counts and the Gaia snail.

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