Multiscale entropy analysis of astronomical time series Discovering subclusters of hybrid pulsators

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 delta Scuti (delta Sct) stars, or from stars with only g-mode pulsations, such as gamma Doradus (gamma 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 delta Sct and gamma 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 delta Sct and gamma 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.