Spatial and Kinematic Clustering of Stars in the Galactic Disk

The Galactic disk is expected to be spatially and kinematically clustered on many scales due to both star formation and the Galactic potential. In this work we calculate the spatial and kinematic two-point correlation functions (TPCF) using a sample of 1.7 × 106 stars with radial velocities from Gaia DR2. Clustering is detected on spatial scales of 1-300 pc and a velocity scale of 15 km s-1. After removing bound structures, the data have a power-law index of γ ≈ -1 for 1 pc < Δr < 100 pc and γ ≲ -1.5 for Δr > 100 pc. We interpret these results with the aid of a 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 giant molecular clouds. We find that the simulation largely agrees with the observations at most spatial and kinematic scales. In detail, the TPCF in the simulation is shallower than the data at ≲20 pc scales, and steeper than the data at ≳30 pc. We also find a persistent clustering signal in the kinematic TPCF for the data at large Δv (>5 km s-1) that is not present in the simulations. We speculate that this mismatch between observations and simulations may be due to two processes: hierarchical star formation and transient spiral arms. We also predict that the addition of ages and metallicities measured with a precision of 50% and 0.05 dex, respectively, will enhance the clustering signal beyond current measurements.