Hierarchical distribution of star clusters in external galaxies

Star formation is distributed in a hierarchical fashion, from kiloparsec scale aggregates down to the scales of star-forming cores. Quantifying the nature of the hierarchical distribution is a useful approach to infer the underlying physical mechanism(s) driving it, and as a result uncover what sets how star formation is distributed. The distribution of star clusters in galaxies trace the largest scales of this hierarchy. In Menon et al. 2021b, we used star cluster catalogues for 12 external galaxies observed with the LEGUS survey, and used the angular two-point correlation function (TPCF) to quantify the nature of the hierarchical distribution.

The spatial distribution of star clusters, colored by their age, for 3 of the 12 galaxies we studied..

Functional forms we explored with toy models.

We combined the TPCFs of our observed galaxies with toy model distributions to infer the nature of the underlying distribution. Our exploration with toy models uncovered predominantly three forms for the TPCF: i) a single power law that represents a fractal distribution over the entire range of scales observed, ii) a piecewise power law, which represents a fractal distribution that randomizes at a specific length scale, and iii) a relatively flat power law with an exponential fall-off at large scales, which represent the TPCF from the radially exponential distribution of star formation in galaxies. These toy-model TPCF profiles and parameters that define them are shown in the schematic on the right.

Plot showing a weakening of hierarchical structure with age of the stellar population in NGC 5194.

We found, consistent with previous work, that the hierarchical distribution weakens as the age of the stellar population increases; this weakening can be inferred from a flatter slope for the TPCF, especially at smaller length scales, and eventually converging to the form of TPCF expected from a purely exponential distribution of star clusters in a galaxy. Interestingly, however, we also found that there are differences in the nature of hierarchy of the young clusters between galaxies. We found that the fractal nature of young clusters for some galaxies vanish at relatively smaller scales (~ 100 - 400 pc), whereas for some other galaxies it persists for very large scales (> 1 kpc), sometimes even beyond the field-of-view scale. This implies that the hierarchical distribution in galaxies are not universal unlike suggested in some earlier studies, rather they differ from galaxy to galaxy. We also quantified the scales at which this hierarchy is lost, and checked for correlations with different galaxy-scale physical and morphological properties. We found some signs of correlation of increasing hierarchy scale with the star formation rate surface density and the galaxy-averaged Toomre length; however, larger sample sizes are required to make any conclusive inferences.

Plot showing the TPCF of young (blue) and old (red) clusters for 3 of our 12 galaxies. We can see the differences in the slope of the TPCF, and the scale to which a scale-free power law exists; these correspond to the strength of the fractal distribution, or fractal dimension, and the largest scale of correlation respectively. These quantities differ between galaxies, suggesting a physical origin for how large star complexes get in galaxies.