Separating halo and disk stars in galaxies with Fuzzy Set Theory

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 ($ε$). 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.

Figures (2)

• Figure 1: Probability density distributions of stellar properties for all stars in a galaxy (Subhalo ID 400974) in the TNG50 MW/M31 catalogue. The gray histograms show the simulated data. The red and green curves represent the two Gaussian components obtained from the double-Gaussian fits, while the blue curve denotes their sum (the total model). Each panel corresponds to one property: metallicity [Fe/H], circularity parameter $\varepsilon$, and velocity components $v_\phi$, $v_r$, and $v_z$.
• Figure 2: Different panels show the disk membership functions (blue) and halo membership functions (green) constructed for the stellar properties: metallicity [Fe/H], circularity parameter $\varepsilon$, and azimuthal velocity component ($v_{\phi}$).