We use Hubble Space Telescope (HST) imaging from the ACS Treasury Survey to determine fits for single population isochrones of 69 Galactic globular clusters. Using robust Bayesian analysis techniques, we simultaneously determine ages, distances, absorptions, and helium values for each cluster under the scenario of a "single" stellar population on model grids with solar ratio heavy element abundances. The set of cluster parameters is determined in a consistent and reproducible manner for all clusters using the Bayesian analysis suite BASE-9. Our results are used to re-visit the age-metallicity relation. We find correlations with helium and several other parameters such as metallicity, binary fraction, and proxies for cluster mass. The helium abundances of the clusters are also considered in the context of CNO abundances and the multiple population scenario.

We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations. Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical properties-age, metallicity, helium abundance, distance, absorption, and initial massare common to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to (iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model and computational tools are incorporated into an open-source software suite known as BASE-9. We use numerical studies to demonstrate that our method can recover parameters of two-population clusters, and also show how model misspecification can potentially be identified. As a proof of concept, we analyze the two stellar populations of globular cluster NGC 5272 using our model and methods. (BASE-9 is available from GitHub: https://github.com/argiopetech/base/releases).

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In this paper we apply a Bayesian technique to determine the best fit of stellar evolution models to find the main sequence turn off age and other cluster parameters of four intermediate-age open clusters: NGC 2360, NGC 2477, NGC 2660, and NGC 3960. Our algorithm utilizes a Markov chain Monte Carlo technique to fit these various parameters, objectively finding the best-fit isochrone for each cluster. The result is a high-precision isochrone fit. We compare these results with the those of traditional "by-eye" isochrone fitting methods. By applying this Bayesian technique to NGC 2360, NGC 2477, NGC 2660, and NGC 3960, we determine the ages of these clusters to be 1.35 ± 0.05, 1.02 ± 0.02, 1.64 ± 0.04, and 0.860 ± 0.04 Gyr, respectively. The results of this paper continue our effort to determine cluster ages to higher precision than that offered by these traditional methods of isochrone fitting.

We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of 30 Galactic Globular Clusters to characterize two distinct stellar populations. A sophisticated Bayesian technique is employed to simultaneously sample the joint posterior distribution of age, distance, and extinction for each cluster, as well as unique helium values for two populations within each cluster and the relative proportion of those populations. We find the helium differences among the two populations in the clusters fall in the range of ∼0.04 to 0.11. Because adequate models varying in CNO are not presently available, we view these spreads as upper limits and present them with statistical rather than observational uncertainties. Evidence supports previous studies suggesting an increase in helium content concurrent with increasing mass of the cluster and also find that the proportion of the first population of stars increases with mass as well. Our results are examined in the context of proposed globular cluster formation scenarios. Additionally, we leverage our Bayesian technique to shed light on inconsistencies between the theoretical models and the observed data.