Analysis of age-concentration parameter correlations in globular clusters based on Gaia DR3

This study investigates the empirical relationship between the ages and structural concentration parameters (λ) of globular clusters (GCs). It underscores the cosmological role of GC ages as a lower limit for the Universe's age and a probe of early galactic assembly. The analysis critiques traditional age-dating challenges and leverages the superior astrometry of Gaia DR3 to compute λ for 106 Galactic GCs, expanding previous methodological work. We calculate concentration parameters of GCs using the Nuker profile fitting and analyze relationships with age determinations from major age catalogs (2008{2020). Using four modern age catalogs (Valcin et al. 2020, Dotter et al. 2010, Forbes & Bridges 2010, and VandenBerg et al. 2013), we find statistically significant inverse correlations (p < 0:05) between λ and age, with Pearson coefficients r = -0.52 to -0.78 and Spearman coefficients \mathrm{r_s} = -0.36 to -0.59. The core finding is a moderate to strong inverse correlation (r ≈ -0.52 to -0.73) between λ and age in most modern catalogs, suggesting that older clusters are more centrally concentrated. The correlation with dynamical age is weaker and not statistically significant ( \mathrm{r_s} = -0.15, p = 0.233). No significant correlation (0.30) is detected with the Koleva et al. (2008) data, potentially due to smaller sample size and larger standard deviation (2.27 Gyr). Our findings could provide robust constraints on galactic evolution scenarios and highlight the importance of homogeneous parameter analysis in the GC research. The correlation strength is method-dependent, reflecting systematic differences between catalogs. Furthermore, the synthesis indicates that the GC age likely serves as the dominant parameter governing horizontal branch morphology. The established link between cluster age and present-day structure could provide critical empirical constraints for models of stellar dynamics, galactic archaeology, and cosmological timelines.

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