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.