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.
