Machine learning for understanding pulsating stars I: the non-linear phenomenon in δ Scuti stars

TL;DR

The paper tackles the limitations of the traditional amplitude-based classification of δ Scuti stars by pursuing intrinsic subgroups through data-driven clustering that leverages frequency-domain and non-linear pulsation features. It uses the Best Parent Method to extract parent and nonlinear frequencies from 142 stars observed by CoRoT, Kepler, and TESS, producing a nine-feature set that includes harmonics and combination frequencies. Hierarchical clustering with Ward's linkage reveals only partial alignment with the HADS/LADS dichotomy and uncovers additional subgroups characterized by nonlinear subtraction/harmonic content, suggesting resonance- or mode-coupling–driven regimes. The work demonstrates that non-linear features carry substantial discriminative power, motivating a move toward a physically grounded classification that can improve models of stellar interiors and pulsation mechanisms in δ Scuti stars.

Abstract

$δ$ Scuti stars are pulsating variable stars that exhibit both radial and non-radial pulsations, making them key objects for understanding stellar evolution and internal structures. The current classification of $δ$ Scuti stars into High-Amplitude $δ$ Scuti (HADS) and Low-Amplitude $δ$ Scuti (LADS) stars is based on the peak-to-peak amplitude of their light curves (>0.3 mag). Nevertheless, this classification may not fully capture the complexity of their pulsation mechanisms and non-linear effects, leading to possible misclassifications. This investigation aims to challenge the existing classification of $δ$ Scuti stars according to amplitude, employing the exploration of frequency domain features and non-linear mechanisms in order to identify intrinsic subgroups. The objective is to get a deeper understanding of the properties of $δ$ Scuti stars. We use machine learning clustering techniques, specifically hierarchical clustering (HC) with Ward's linkage, to analyze a sample of 142 $δ$ Scuti stars observed by space telescopes such as CoRoT, Kepler, and TESS. We focus on frequency-domain features, including fundamental and overtone modes, as well as non-linear features such as harmonic, sums, and subtraction frequencies, to uncover intrinsic subgroups within $δ$ Scuti stars. The results of the clustering process indicate that the present amplitude-based classification (HADS/LADS) exhibits partial alignment with the clusters identified by using features from the frequency-domain. However, the study identified additional sub-groups, suggesting a greater variety of nonlinear effects that are not captured by the amplitude alone. It highlights the importance of non-linear features, such as the number of subtraction combinations, which may be indicative of resonance effects or other internal physical mechanisms.

Figures (5)

• Figure 1: Performance comparison against different types of distributions (columns) of the considered clustering techniques (rows). Image modified from scikit-learn.
• Figure 2: Fundamental amplitude histogram. On the left, depicted with thicker bins to show the tendency. On the right, with unitary bins and statistical measures for distribution analysis.
• Figure 3: Dendrogram and t-SNE visualisation of the 3 clusters obtained by applying HC with Ward's method to the 142 $\delta$ Sct sample using 9-frequency-domain features.
• Figure 4: Dendrogram and t-SNE visualisation of the 6 clusters obtained by applying HC with Ward's method to the 142 $\delta Sct$ sample using 9-frequency-domain features.
• Figure 6: Dendrogram and t-SNE visualisation of the 11 clusters obtained by applying HC with Ward's method to the 142 $\delta$ Sct sample using 3-non-linear frequency-domain features.