The Dependence of the Hierarchical Distribution of Star Clusters on
  Galactic Environment
  We use the angular Two Point Correlation Function (TPCF) to investigate the
hierarchical distribution of young star clusters in 12 local (3--18 Mpc)
star-forming galaxies using star cluster catalogues obtained with the
\textit{Hubble Space Telescope} (\textit{HST}) as part of the Treasury Program
LEGUS (Legacy ExtraGalactic UV Survey). The sample spans a range of different
morphological types, allowing us to infer how the physical properties of the
galaxy affect the spatial distribution of the clusters. We also prepare a range
of physically motivated toy models to compare with and interpret the observed
features in the TPCFs. We find that, conforming to earlier studies, young
clusters ($T \la 10\, \mathrm{Myr}$) have power-law TPCFs that are
characteristic of fractal distributions with a fractal dimension $D_2$, and
this scale-free nature extends out to a maximum scale $l_{\mathrm{corr}}$
beyond which the distribution becomes Poissonian. However, $l_{\mathrm{corr}}$,
and $D_2$ vary significantly across the sample, and are correlated with a
number of host galaxy physical properties, suggesting that there are physical
differences in the underlying star cluster distributions. We also find that
hierarchical structuring weakens with age, evidenced by flatter TPCFs for older
clusters ($T \ga 10\, \mathrm{Myr}$), that eventually converges to the residual
correlation expected from a completely random large-scale radial distribution
of clusters in the galaxy in $\sim 100 \, \mathrm{Myr}$. Our study demonstrates
that the hierarchical distribution of star clusters evolves with age, and is
strongly dependent on the properties of the host galaxy environment.
