Hierarchical star formation in M33: properties of the star-forming regions

Star formation within galaxies occurs on multiple scales, from spiral structure, to OB associations, to individual star clusters, and often as substructure within these clusters. This multitude of scales calls for objective methods to find and classify star-forming regions, regardless of spatial size. To this end, we present an analysis of star-forming groups in the Local Group spiral galaxy M33, based on a new implementation of the Minimum Spanning Tree (MST) method. Unlike previous studies, which limited themselves to a single spatial scale, we study star-forming structures from the effective resolution limit (～20 pc) to kpc scales. Once the groups have been identified, we study their properties, such as their size and luminosity distributions, and compare these with studies of young star clusters and giant molecular clouds (GMCs). We find evidence for a continuum of star-forming group sizes, which extends into the star cluster spatial-scale regime. We do not find a characteristic scale for OB associations, unlike that found in previous studies, and we suggest that the appearance of such a scale was caused by spatial resolution and selection effects. The luminosity function of the groups is found to be well represented by a power law with an index of ?2, as has also been found for the luminosity and mass functions of young star clusters, as well as for the mass function of GMCs. Additionally, the groups follow a similar mass-radius relation as GMCs. The size distribution of the groups is best described by a log-normal distribution, the peak of which is controlled by the spatial scale probed and the minimum number of sources used to define a group. We show that within a hierarchical distribution, if a scale is selected to find structure, the resulting size distribution will have a log-normal distribution. We find an abrupt drop of the number of groups outside a galactic radius of ～4 kpc (although individual high-mass stars are found beyond this limit), suggesting a change in the structure of the star-forming interstellar medium, possibly reflected in the lack of GMCs beyond this radius. Finally, we find that the spatial distribution of H?ii regions, GMCs, and star-forming groups are all highly correlated.