Bayesian Hierarchical Modelling of Initial-Final Mass Relations Across Star Clusters

TL;DR

This paper introduces a Bayesian hierarchical model to estimate the initial-final mass relation of white dwarfs across multiple star clusters, improving accuracy and consistency over traditional methods.

Contribution

The paper develops and applies a Bayesian hierarchical approach to jointly analyze data from multiple star clusters, enhancing the estimation of the initial-final mass relation.

Findings

Hierarchical model provides more reliable IFMR estimates.

Pooling data improves estimation accuracy.

Cluster-specific analysis can be unreliable without hierarchical modeling.

Abstract

The initial-final mass relation (IFMR) of white dwarfs (WDs) plays an important role in stellar evolution. To derive precise estimates of IFMRs and explore how they may vary among star clusters, we propose a Bayesian hierarchical model that pools photo- metric data from multiple star clusters. After performing a simulation study to show the benefits of the Bayesian hierarchical model, we apply this model to five star clus- ters: the Hyades, M67, NGC 188, NGC 2168, and NGC 2477, leading to reasonable and consistent estimates of IFMRs for these clusters. We illustrate how a cluster-specific analysis of NGC 188 using its own photometric data can produce an unreasonable IFMR since its WDs have a narrow range of zero-age main sequence (ZAMS) masses. However, the Bayesian hierarchical model corrects the cluster-specific analysis by bor- rowing strength from other clusters, thus generating more reliable estimates of IFMR parameters. The data analysis presents the benefits of Bayesian hierarchical modelling over conventional cluster-specific methods, which motivates us to elaborate the pow- erful statistical techniques in this article.