Two-point correlation function studies for the Milky Way: discovery of spatial clustering from disk excitations and substructure

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 $R$, $\phi$, 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 ($d \lesssim 3\, \rm kpc$) from Gaia Data Release 2 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 mid-plane 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 at sub-kiloparsec length scales for the very first time. Particularly, we observe extensive wave-like 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.