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.