The Age of the Universe with Globular Clusters IV: Multiple Stellar Populations

Abstract

We revisit the determination of the age of the Universe from galactic globular clusters, extending previous analyses by explicitly accounting for the presence of multiple stellar populations within each cluster. Using high--quality \textit{Hubble Space Telescope} color--magnitude diagrams for 69 globular clusters, we relax the standard single--population assumption, and model two stellar populations with independent ages, metallicities, helium abundances, and population fractions. The inference is performed using the full color--magnitude diagram morphology, an explicit treatment of field contamination, and a hierarchical framework that propagates non--Gaussian age posteriors. Allowing for multiple stellar populations has a negligible impact on globular cluster age estimates. The ages of the oldest populations remain fully consistent with those obtained under the single--population assumption, with differences at the $0.6σ$ level. Restricting to the metal--poor subsample ([Fe/H] $< -1.5$), we infer a dominant old component with mean age $t_{\rm GC}=13.61\pm0.25\,\mathrm{(stat)}\,\pm0.23 \mathrm{(sys)}\,\mathrm{Gyr}$. Adopting a conservative delay between the Big Bang and the formation of the first globular clusters, we obtain an age of the Universe of $t_{\rm U}=13.81\pm0.25\,\mathrm{(stat)}\,\pm0.23 \mathrm{(sys)}\,\mathrm{Gyr}$. In addition to age constraints, our analysis yields simultaneous measurements of metallicity and helium content for the different populations, including constraints on helium enrichment and population fractions which are consistent with independent determinations from the literature. These results demonstrate that globular--cluster--based cosmic chronometry is robust to stellar population complexity, reinforcing its role as a precise and largely cosmological model--independent probe of the age of the Universe.

Figures (12)

• Figure 1: Cleaning diagnostics and final Color--Magnitude Diagram (CMD) selection.Top: Quality-control projections used to define the cleaning masks, including magnitude--error cuts, qfit thresholds, detector edge masking, and CMD color outlier rejection. Gray points are retained stars and orange points are rejected sources. Bottom: Final cleaned color--magnitude diagram after all selections, showing that removed stars preferentially occupy field and outlier regions for an representative GC (Arp2). The annotated fraction indicates the small percentage of stars discarded.
• Figure 2: Visualization of the multi-pass ridgeline extraction. Gray points show all cleaned CMD stars. Blue and red markers correspond to the ridgeline estimates obtained from the first and second (half-bin–shifted) passes, respectively. Black points indicate the final merged sequence after duplicate consolidation. The staggered binning improves sampling near bin boundaries and produces a smoother, more robust fiducial line.
• Figure 3: Age posterior distributions for the 36 metal-poor globular clusters ($\mathrm{[Fe/H]} < -1.5$) analyzed in this work. Thin red curves show the individual PoCoMC age posteriors for each cluster. The filled distribution indicates the total posterior obtained by stacking all individual samples, while the black curve represents a kernel density estimate of this combined distribution. The blue curve shows a Gaussian mixture model fit to the aggregated PoCoMC samples. The wide range of posterior shapes, including skewness and extended low-age tails, illustrates the departure from Gaussianity induced by degeneracies between age and helium abundance in the multi-population framework.
• Figure 4: Hierarchical reconstruction of the age distribution of metal-poor globular clusters. Grey: stacked cluster-level posteriors; blue: posterior predictive distribution; red: inferred intrinsic mixture model (dashed lines indicate individual components). The three components have posterior mean ages which are Normal distributions characterised by a mean $\mu$ and variance $\sigma$ as: $(\mu,\,\sigma) \simeq (11.25,\,1.40)$, $(12.99,\,0.38)$, and $(13.61,\,0.25)$ Gyr. The black dashed line marks the posterior predictive 95th percentile, $t_{95}$ (see text for interpretation).
• Figure 5: Posterior distribution of the 95th percentile $t_{95}$ of the globular cluster age distribution, derived from the hierarchical posterior predictive model. The dashed line indicates the median, and the shaded region the central 68% credible interval.