Separating halo and disk stars in galaxies with Fuzzy Set Theory

TL;DR

This paper introduces a fuzzy set theory-based method for classifying disk and halo stars in galaxies, providing a more flexible and accurate alternative to traditional hard-cut classification techniques.

Contribution

It develops a novel fuzzy set approach that overcomes limitations of conventional methods, improving the classification of galactic stellar populations.

Findings

Reduces contamination in star classification

Recovers genuine galactic members often excluded by traditional methods

Provides a more realistic and robust star classification framework

Abstract

Disk and halo stars are generally classified using several conventional methods, such as the Toomre diagram, sharp cuts in metallicity ([Fe/H]), vertical distance ($\left|Z\right|$) from the Galactic plane, or thresholds on the orbital circularity parameter ($\epsilon$). However, all these methods rely on hard selection cuts, which either contaminate samples when relaxed or exclude genuine members when applied too strictly, leading to uncertain and biased classifications. We develop a flexible and reliable approach to classify disk and halo stars in galaxies by applying fuzzy set theory, which can overcome the limitations of traditional hard-cut selection methods. As a case study, we analyze one of the Milky Way/M31-like galaxies in the TNG50 catalogue. We consider multiple stellar properties as fuzzy variables and characterize their variations between disk and halo stars to construct the respective membership functions. These functions are then combined to assign each star a membership degree corresponding to its galactic component. Our fuzzy set approach provides a more realistic distinction between the disk and the halo stars. This method effectively reduces contamination and recovers genuine members that are often excluded by rigid selection criteria. The fuzzy set theory framework offers a robust alternative to conventional hard-cut methods, enabling more accurate and physically meaningful separation of stellar populations in galaxies.