Title: Hierarchical star formation across the grand design spiral NGC1566,
Abstract: We investigate how star formation is spatially organized in the grand-design
spiral NGC 1566 from deep HST photometry with the Legacy ExtraGalactic UV
Survey (LEGUS). Our contour-based clustering analysis reveals 890 distinct
stellar conglomerations at various levels of significance. These star-forming
complexes are organized in a hierarchical fashion with the larger congregations
consisting of smaller structures, which themselves fragment into even smaller
and more compact stellar groupings. Their size distribution, covering a wide
range in length-scales, shows a power-law as expected from scale-free
processes. We explain this shape with a simple "fragmentation and enrichment"
model. The hierarchical morphology of the complexes is confirmed by their
mass--size relation which can be represented by a power-law with a fractional
exponent, analogous to that determined for fractal molecular clouds. The
surface stellar density distribution of the complexes shows a log-normal shape
similar to that for supersonic non-gravitating turbulent gas. Between 50 and 65
per cent of the recently-formed stars, as well as about 90 per cent of the
young star clusters, are found inside the stellar complexes, located along the
spiral arms. We find an age-difference between young stars inside the complexes
and those in their direct vicinity in the arms of at least 10 Myr. This
timescale may relate to the minimum time for stellar evaporation, although we
cannot exclude the in situ formation of stars. As expected, star formation
preferentially occurs in spiral arms. Our findings reveal turbulent-driven
hierarchical star formation along the arms of a grand-design galaxy.