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Register a new userBayesian Analysis of Two Stellar Populations in Galactic Globular Clusters I: Statistical and Computational Methods
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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 (vanDyk et al. 2009, Stein et al. 2013). 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 mass---are 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 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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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.
We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of Galactic Globular Clusters to find and characterize two stellar populations in NGC 5024 (M53), NGC 5272 (M3), and NGC 6352. For these three clusters, both single and double-population analyses are used to determine a best fit isochrone(s). We employ a sophisticated Bayesian analysis technique to simultaneously fit the cluster parameters (age, distance, absorption, and metallicity) that characterize each cluster. For the two-population analysis, unique population level helium values are also fit to each distinct population of the cluster and the relative proportions of the populations are determined. We find differences in helium ranging from $sim$0.05 to 0.11 for these three clusters. Model grids with solar $alpha$-element abundances ([$alpha$/Fe] =0.0) and enhanced $alpha$-elements ([$alpha$/Fe]=0.4) are adopted.
We have calculated synthetic spectra for typical chemical element mixtures (i.e., a standard alpha-enhanced distribution, and distributions displaying CN and ONa anticorrelations) found in the various subpopulations harboured by Galactic globular clusters. From the spectra we have determined bolometric corrections to the standard Johnson-Cousins and Stroemgren filters, and finally predicted colours. These bolometric corrections and colour-transformations, coupled to our theoretical isochrones with the appropriate chemical composition, provide a complete and self-consistent set of theoretical predictions for the effect of abundance variations on the observed cluster CMD. CNO abundance variations affect mainly wavelengths shorter than 400 nm, due to the arise of molecular absorption bands in cooler atmospheres. As a consequence, colour and magnitude changes are largest in the blue filters, independently of using broad or intermediate bandpasses. Colour-magnitude diagrams involving uvy and UB filters (and their various possible colour combinations) are thus the ones best suited to infer photometrically the presence of multiple stellar generations in individual clusters. They are particularly sensitive to variations in the N abundance, with the largest variations affecting the Red Giant Branch (RGB) and lower Main Sequence (MS). BVI diagrams are expected to display multiple sequences only if the different populations are characterized by variations of the C+N+O sum and helium abundance, that lead to changes in luminosity and effective temperature, but leave the flux distribution above 400 nm practically unaffected. A variation of just the helium abundance, up to the level we investigate here, affects exclusively the interior structure of stars, and is largely irrelevant for the atmospheric structure and the resulting flux distribution in the whole wavelength range spanned by our analysis.
Multiple stellar populations (MPs) are a distinct characteristic of Globular Clusters (GCs). Their general properties have been widely studied among main sequence, red giant branch (RGB) and horizontal branch (HB) stars, but a common framework is still missing at later evolutionary stages. We studied the MP phenomenon along the AGB sequences in 58 GCs, observed with the Hubble Space Telescope in ultraviolet (UV) and optical filters. By using UV-optical color-magnitude diagrams, we selected the AGB members of each cluster and identified the AGB candidates of the metal-enhanced population in type II GCs. We studied the photometric properties of AGB stars and compared them to theoretical models derived from synthetic spectra analysis. We observe the following features: i) the spread of AGB stars in photometric indices sensitive to variations of light-elements and helium is typically larger than that expected from photometric errors; ii) the fraction of metal-enhanced stars in the AGB is lower than in the RGB in most of the type II GCs; iii) the fraction of 1G stars derived from the chromosome map of AGB stars in 15 GCs is larger than that of RGB stars; v) the AGB/HB frequency correlates with the average mass of the most helium-enriched population. These findings represent a clear evidence of the presence of MPs along the AGB of Galactic GCs and indicate that a significant fraction of helium-enriched stars, which have lower mass in the HB, does not evolve to the AGB phase, leaving the HB sequence towards higher effective temperatures, as predicted by the AGB-manque scenario.
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.
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