Influence of star cluster mass, age, and galaxy star formation rate on star cluster radii

TL;DR

This study analyzed how star cluster radius relates primarily to mass rather than age or galaxy star formation rate, challenging some theoretical expectations and highlighting the complexity of cluster size determinants.

Contribution

It demonstrates that cluster mass is the dominant predictor of radius, with age and sSFR adding negligible predictive power, thus refining understanding of cluster formation models.

Findings

Mass strongly correlates with cluster radius.

Age and sSFR do not significantly improve radius prediction.

Most variance in cluster radius remains unexplained by these variables.

Abstract

Star clusters are key components of galaxies, and the relationship between cluster radius and mass encodes information about cluster formation and evolution. Theoretical models predict that age and specific star formation rate (sSFR) should influence cluster size through stellar mass loss and gas dynamics during formation. We hypothesized that if these theoretical predictions hold, multivariate models including age and sSFR should predict cluster radius better than models using mass alone. To test this, we used regression analysis on 5,105 star clusters from the LEGUS survey, comparing a full multivariate model against a mass-only baseline. We found that mass dominated the radius-mass relation: log(Mass) showed a strong correlation with radius (coefficient = 0.131 +/- 0.008, p < 0.001), while log(sSFR) and log(Age) contributed negligibly (0.0002 +/- 0.015 and 0.038 +/- 0.006, respectively). Cross-validation revealed that the mass-only model generalized better (CV R^2 = 0.028 vs -0.017), with the negative value for the multivariate model indicating overfitting. Contrary to our hypothesis, adding age and sSFR did not improve predictive performance. The low R^2 (0.115) indicated that most variance in cluster radius remained unexplained by these variables, suggesting other factors may play important roles. Among the variables tested, our findings were consistent with virial equilibrium predictions, with mass serving as a more fundamental parameter than evolutionary age or galaxy star formation rate.