The different methods to calculate cluster membership probabilities

arXiv:2607.13711 · astro-ph.GA, astro-ph.IM, astro-ph.SR · Submitted 2026-07-15 · Read on arXiv

Tahereh Ramezani, Prapti Mondal, Katerina Neumannova, Ernst Paunzen, Johana Supikova, Gabriel Szasz

astro-ph.GA, astro-ph.IM, astro-ph.SR

Submitted: 2026-07-15

Comments: 14 pages; 3 figures; 8 tables; submitted to A&A

License: http://creativecommons.org/licenses/by/4.0/

The gist: Reliable membership determination is a fundamental step in the study of star clusters.

Terminology

Clustering — 17× in this paper · explained in 2 episodes
Interpretability — 9× in this paper · explained in 15 episodes
Bayesian Inference — 4× in this paper · explained in 5 episodes
Metallicity — 4× in this paper · explained in 3 episodes
Consistency — 3× in this paper · explained in 3 episodes
Core — 3× in this paper · explained in 2 episodes
Gaussian Mixture Models — 3× in this paper
Accuracy — 2× in this paper · explained in 1 episode
Inverse Problem — 2× in this paper · explained in 2 episodes
Velocity Dispersion — 2× in this paper · explained in 2 episodes
Abundance — 1× in this paper · explained in 1 episode
Alignment — 1× in this paper · explained in 1 episode
Benchmark — 1× in this paper · explained in 2 episodes
Calibration — 1× in this paper · explained in 7 episodes
Degeneracy — 1× in this paper · explained in 3 episodes
Diffusion Model — 1× in this paper · explained in 8 episodes
Diffusion Models — 1× in this paper · explained in 6 episodes
Explainability — 1× in this paper · explained in 3 episodes
GNNs — 1× in this paper · explained in 2 episodes
Graph Neural Networks (GNNs) — 1× in this paper · explained in 7 episodes
Observational Selection Effects — 1× in this paper · explained in 2 episodes
Observatory Legacy Survey of Space and Time — 1× in this paper
Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 6 episodes
Robustness — 1× in this paper · explained in 5 episodes
Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Abstract

Reliable membership determination is a fundamental step in the study of star clusters. With the advent of Gaia astrometry, a wide range of statistical and machine-learning techniques has been developed to assign membership probabilities. However, the current situation of membership lists is very unsatisfactory. This review summarises the main methodologies, compares their strengths and limitations, and discusses future directions. The aim is to provide a comprehensive overview and to lead to a more efficient and reliable approach for the forthcoming Gaia DR4. Basically, we know of spatial, classical kinematic, and photometric methods, as well as maximum likelihood and Bayesian statistical methods, and machine learning and clustering algorithms. These different methods come with many modifications and flavours. We assessed all the advantages and disadvantages of the known methods to determine cluster membership probabilities. Although nowadays most methods are based on poor statistical numerics, the more robust algorithms should still be taken into account. It is important to apply and compare several methods. The next step must be to define a list of standard star clusters to test and verify all known methods. The list must cover the complete grid of cluster parameters (age, distance, reddening, and metallicity) and total masses.

Terminology

Abstract

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