SIMBAD references

Context. The multiscale entropy assesses the complexity of a signal across different timescales. It originates from the biomedical domain and was recently successfully used to characterize light curves as part of a supervised machine learning framework to classify stellar variability.
Aims. We aim to explore the behavior of the multiscale entropy in detail by studying its algorithmic properties in a stellar variability context and by linking it with traditional astronomical time series analysis methods and metrics such as the Lomb-Scargle periodogram. We subsequently use the multiscale entropy as the basis for an interpretable clustering framework that can distinguish hybrid pulsators with both p- and g-modes from stars with only p-mode pulsations, such as δ Scuti (δ Sct) stars, or from stars with only g-mode pulsations, such as γ Doradus (γ Dor) stars.
Methods. We calculate the multiscale entropy for a set of Kepler light curves and simulated sine waves. We link the multiscale entropy to the type of stellar variability and to the frequency content of a signal through a correlation analysis and a set of simulations. The dimensionality of the multiscale entropy is reduced to two dimensions and is subsequently used as input to the HDBSCAN density-based clustering algorithm in order to find the hybrid pulsators within sets of δ Sct and γ Dor stars that were observed by Kepler.
Results. We find that the multiscale entropy is a powerful tool for capturing variability patterns in stellar light curves. The multiscale entropy provides insights into the pulsation structure of a star and reveals how short- and long-term variability interact with each other based on time-domain information only. We also show that the multiscale entropy is correlated to the frequency content of a stellar signal and in particular to the near-core rotation rates of g-mode pulsators. We find that our new clustering framework can successfully identify the hybrid pulsators with both p- and g-modes in sets of δ Sct and γ Dor stars, respectively. The benefit of our clustering framework is that it is unsupervised. It therefore does not require previously labeled data and hence is not biased by previous knowledge.