Miec: A Bayesian hierarchical model for the analysis of nearby young open clusters

TL;DR

This paper introduces a Bayesian hierarchical model that accurately identifies members and luminosity distributions of embedded young stellar clusters despite high extinction and missing data, improving analysis of star formation.

Contribution

It extends and validates a Bayesian methodology for analyzing embedded stellar clusters, effectively handling high extinction and missing data with minimal bias.

Findings

Accurately recovers cluster members with up to 6 mag extinction.

Achieves over 99% true positive rate and 80% accuracy.

Effectively reduces artifacts using informative priors.

Abstract

Context. The analysis of luminosity and mass distributions of young stellar clusters is essential to understanding the star-formation process. However, the gas and dust left over by this process extinct the light of the newborn stars and can severely bias both the census of cluster members and its luminosity distribution. Aims. We aim to develop a Bayesian methodology to infer, with minimal biases due to photometric extinction, the candidate members and magnitude distributions of embedded young stellar clusters. Methods. We improve a previously published methodology and extend its application to embedded stellar clusters. We validate the method using synthetically extincted data sets of the Pleiades cluster with varying degrees of extinction. Results. Our methodology can recover members from data sets extincted up to Av ~ 6 mag with accuracies, true positive, and contamination rates that are better than 99%, 80%, and 9%, respectively. Missing values hamper our methodology by introducing contaminants and artifacts into the magnitude distributions. Nonetheless, these artifacts vanish through the use of informative priors in the distribution of the proper motions. Conclusions. The methodology presented here recovers, with minimal biases, the members and distributions of embedded stellar clusters from data sets with a high percentage of sources with missing values (>96%).