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

Star formation within galaxies appears on multiple scales, from spiral structure, to OB associations, to individual star clusters, and often 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 method. Unlike previous studies which limited themselves to a single spatial scale, we study star-forming structures from the effective resolution limit (similar to 20 pc) to kpc scales. Once the groups are identified, we study their properties, for example, size and luminosity distributions, and compare them 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, -2, the same as has been found for the luminosity and mass functions (MFs) of young star clusters, as well as the MF of GMCs. Additionally, the groups follow a similar mass-radius relation as GMCs. The size distribution of the groups is best described by a lognormal 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 lognormal distribution. We find an abrupt drop of the number of groups outside a galactic radius of similar to 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.