The Spatial Relation between Young Star Clusters and Molecular Clouds in
  M 51 with LEGUS
  We present a study correlating the spatial locations of young star clusters
with those of molecular clouds in NGC~5194, in order to investigate the
timescale over which clusters separate from their birth clouds. The star
cluster catalogues are from the Legacy ExtraGalactic UV Survey (LEGUS) and the
molecular clouds from the Plateau de Bure Interefrometer Arcsecond Whirpool
Survey (PAWS). We find that younger star clusters are spatially closer to
molecular clouds than older star clusters. The median ages for clusters
associated with clouds is 4~Myr whereas it is 50~Myr for clusters that are
sufficiently separated from a molecular cloud to be considered unassociated.
After $\sim$6~Myr, the majority of the star clusters lose association with
their molecular gas. Younger star clusters are also preferentially located in
stellar spiral arms where they are hierarchically distributed in kpc-size
regions for 50-100~Myr before dispersing. The youngest star clusters are more
strongly clustered, yielding a two-point correlation function with
$\alpha=-0.28\pm0.04$, than the GMCs ($\alpha=-0.09\pm0.03$) within the same
PAWS field. However, the clustering strength of the most massive GMCs,
supposedly the progenitors of the young clusters for a star formation
efficiency of a few percent, is comparable ($\alpha=-0.35\pm0.05$) to that of
the clusters. We find a galactocentric-dependence for the coherence of star
formation, in which clusters located in the inner region of the galaxy reside
in smaller star-forming complexes and display more homogeneous distributions
than clusters further from the centre. This result suggests a correlation
between the survival of a cluster complex and its environment.
