Characteristic Scales in Stellar Clustering: A Transition Near the Disk Scale Height

The autocorrelation function provides an objective test for the existence of special scales in the hierarchical clustering of young stars. We apply this measure to single-star photometry for the brightest main sequence stars in the Small Magellanic Cloud (SMC), the Large Magellanic Cloud (LMC), M33, and M31, using data from the Magellanic Clouds Photometric Survey and the Massey Local Group Survey. Our primary result is the identification of a transition to a higher correlation dimension (weaker clustering) at one kpc in the LMC and M31, and at 300 pc in M33. We suggest that this transition marks the large-scale regime where disk geometry and dynamics set the scale for structure. On smaller scales, the correlation functions for each galaxy are scale-free over at least two orders of magnitude, with a projected correlation dimension varying from 1.0 for M31 to 1.8 for the SMC. This variation is probably caused by a combination of differences in stellar ages and masses, physical environment, and extinction. Subject headings: galaxies: structure — galaxies: star clusters — stars: formation — Magellanic Clouds — galaxies: individual (M31, M33)