Bayesian Analysis of Two Stellar Populations in Galactic Globular Clusters. I. Statistical and Computational Methods

Abstract

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).

The ACS survey of Galactic globular clusters – XIV. Bayesian single-population analysis of 69 globular clusters

“…The cluster level parameters are age (base-10 logarithm, θage), metallicity (θ [F e/H] ), distance modulus (θm−M V ), absorption (θA V ), and helium fraction (φY ). We represent the observed photometric data as Xij, for the ith star in the jth filter (for N stars and n filters), as described by De Gennaro et al (2009, Stein et al (2013), and Stenning et al (2016). The known Gaussian measurement errors are in the variance-covariance matrix Σi for each star i.…”

Bayesian Analysis of Two Stellar Populations in Galactic Globular Clusters. Ii. NGC 5024, NGC 5272, and NGC 6352

“…Hence, we aim for relative accuracy and precision rather than an absolute accuracy (see Stenning et al 2016), especially when comparing to previous studies and methods.…”

“…A Markov-chain Monte Carlo (MCMC) algorithm, specifically an adaptive Metropolis (AM) implementation, explores the posterior distribution; see Stenning et al (2016) for details. We run each MCMC chain for 11,000 iterations.…”

“…The Bayesian Analysis for Stellar Evolution software suite (BASE-9; see von Hippel et al 2006;De Gennaro et al 2009;van Dyk et al 2009;Stein et al 2013), fits a cluster consisting of a single population by deriving the joint posterior distribution of age, distance, absorption, metallicity, and the initial stellar masses, while allowing for field star contamination. We have adapted BASE-9 for use on a globular cluster assumed to host two distinct populations (Stenning et al 2016). With theoretical models, we are able to precisely characterize two helium values in clusters and determine the proportion of stars in each population.…”

“…By beginning to analyze helium abundances in a growing number of clusters using BASE-9 (as described in Stenning et al 2016), we hope to learn more about multiple populations in globular clusters. In doing so, we gain insight into the formation mechanism of these clusters and the implications for the history of the Milky Way.…”