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

TL;DR

This paper introduces a Bayesian hierarchical model and an adaptive MCMC algorithm for analyzing globular clusters with two stellar populations differing in helium abundance, implemented in the open-source BASE-9 software.

Contribution

It extends previous models to handle multiple stellar populations with hierarchical parameters and improves computational convergence with an adaptive MCMC approach.

Findings

Successfully recovers parameters of two-population clusters

Demonstrates potential to identify model misspecification

Analyzes real cluster NGC 5272 using the new method

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 (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).