The Spatial Distribution of the Young Stellar Clusters in the Star
  Forming Galaxy NGC 628
  We present a study of the spatial distribution of the stellar cluster
populations in the star forming galaxy NGC 628. Using Hubble Space Telescope
broad band WFC3/UVIS UV and optical images from the Treasury Program LEGUS
(Legacy ExtraGalactic UV Survey), we have identified 1392 potential young (<100
Myr) stellar clusters within the galaxy, identified from a combination of
visual inspection and automatic selection. We investigate the clustering of
these young stellar clusters and quantify the strength and change of clustering
strength with scale using the two-point correlation function. We also
investigate how image boundary conditions and dust lanes affect the observed
clustering. The distribution of the clusters is well fit by a broken power law
with negative exponent $\alpha$. We recover a weighted mean index of $\alpha$ ~
-0.8 for all spatial scales below the break at 3".3 (158 pc at a distance of
9.9 Mpc) and an index of $\alpha$ ~ -0.18 above 158 pc for the accumulation of
all cluster types. The strength of the clustering increases with decreasing age
and clusters older than 40 Myr lose their clustered structure very rapidly and
tend to be randomly distributed in this galaxy whereas the mass of the star
cluster has little effect on the clustering strength. This is consistent with
results from other studies that the morphological hierarchy in stellar
clustering resembles the same hierarchy as the turbulent interstellar medium.
