We present an investigation of the relationship between giant molecular cloud ( GMC ) properties and the associated stellar clusters in the nearby flocculent galaxy NGC 7793 .
We combine the star cluster catalog from the HST LEGUS ( Legacy ExtraGalactic UV Survey ) program with the 15 parsec resolution ALMA CO ( 2–1 ) observations .
We find a strong spatial correlation between young star clusters and GMCs such that all clusters still associated with a GMC are younger than 11 Myr and display a median age of 2 Myr .
The age distribution increases gradually as the cluster–GMC distance increases , with star clusters that are spatially unassociated with molecular gas exhibiting a median age of 7 Myr .
Thus , star clusters are able to emerge from their natal clouds long before the timescale required for clouds to disperse .
To investigate if the hierarchy observed in the stellar components is inherited from the GMCs , we quantify the amount of clustering in the spatial distributions of the components and find that the star clusters have a fractal dimension slope of -0.35 \pm 0.03 , significantly more clustered than the molecular cloud hierarchy with slope of -0.18 \pm 0.04 over the range 40–800 pc .
We find , however , that the spatial clustering becomes comparable in strength for GMCs and star clusters with slopes of -0.44 \pm 0.03 and -0.45 \pm 0.06 respectively , when we compare massive ( > 10 ^ { 5 } M _ { \odot } ) GMCs to massive and young star clusters .
This shows that massive star clusters trace the same hierarchy as their parent GMCs , under the assumption that the star formation efficiency is a few percent .