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

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.