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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.

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, , to probe the quality of the angular momentum Lz 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., 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. [ABSTRACT FROM AUTHOR]

We use the number density distributions of K and M dwarf stars with vertical height from the Galactic disk, determined using observations from the Sloan Digital Sky Survey, to probe the structure of the Milky Way disk across the survey’s footprint. Using photometric parallax as a distance estimator we analyze a sample of several million disk stars in matching footprints above and below the Galactic plane, and we determine the location and extent of vertical asymmetries in the number counts in a variety of thin- and thick-disk subsamples in regions of some 200 square degrees within 2 kpc in vertical distance from the Galactic disk. These disk asymmetries present wave-like features as previously observed on other scales and at other distances from the Sun. We additionally explore the scale height of the disk and the implied offset of the Sun from the Galactic plane at different locations, noting that the scale height of the disk can differ significantly when measured using stars only above or only below the plane. Moreover, we compare the shape of the number density distribution in the north for different latitude ranges with a fixed range in longitude and find the shape to be sensitive to the selected latitude window. We explain why this may be indicative of a change in stellar populations in the latitude regions compared, possibly allowing access to the systematic metallicity difference between thin- and thick-disk populations through photometry. [ABSTRACT FROM AUTHOR]