Spatial and Kinematic Clustering of Stars in the Galactic Disk

The Galactic disk is expected to be spatially, kinematically, and chemically clustered on many scales due to both star formation and non-axisymmetries in the Galactic potential. In this work we calculate the spatial and kinematic two-point correlation functions using a sample of $1.7 \times 10^6$ stars within 1 kpc of the Sun with 6D phase space information available from \textit{Gaia} DR2. Clustering is detected on spatial scales of 1-300 pc and velocity scales of at least 15 km s$^{-1}$. With bound structures included, the data have a power-law index ($\xi(\Delta r) \propto \Delta r^{\gamma}$) of $\gamma\approx-2$ at most spatial scales, which is in line with theoretical predictions. After removing bound structures, the data have a power-law index of $\gamma\approx-1$ for $<100$ pc and $\gamma \lesssim -1.5$ for $>100$ pc. We interpret these results with the aid of a novel star-by-star simulation of the Galaxy in which stars are born in clusters orbiting in a realistic potential that includes spiral arms, a bar, and GMCs. We find that the simulation largely agrees with the observations (within a factor of 2-3) at all spatial and kinematic scales. In detail, the correlation function in the simulation is shallower than the data at $< 20$ pc scales, and steeper than the data at $> 30$ pc scales. We also find a persistent clustering signal in the kinematic correlation function for the data at large $\Delta v$ ($>5$ km s$^{-1}$) not present in the simulations. We speculate that this mismatch between observations and simulations may be due to two processes not included in the simulation: hierarchical star formation and transient spiral arms. We also use the simulations to predict the clustering signal as a function of pair-wise metallicity and age separations. Ages and metallicities measured with a precision of $50\%$ and $0.05$ dex are required in order to enhance the clustering signal.