A complex network approach to TESS light curves of δ Sct stars

¹ Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía s/n, E-18008 Granada, Spain
² Department of Physics, University of Guilan, 41335–1914 Rasht, Iran
³ Department of Physics, Faculty of Science, University of Zanjan, 45371-38791 Zanjan, Iran

^⋆ Corresponding authors: ziaali@iaa.csic.es; javier@iaa.csic.es

Received: 25 February 2025
Accepted: 8 August 2025

Abstract

Context. Complex systems are characterised by many highly interconnected dynamical units that exhibit non-linear properties. The type of pulsating stars known as δ Sct stars have intrinsic brightness variations that require non-linear models to be described comprehensively. These stars span a broad range of properties, from low to high amplitudes, as well as a broad range of complex features. We applied the complex network approach to δ Sct stars as non-linear complex systems.

Aims. Differences among the constructed networks, which might appear in the network metrics of low-amplitude and high-amplitude δ Sct stars, can indicate intrinsic asteroseismic differences that are essential for classification of pulsating stars. Additionally, the relations between the asteroseismic parameters and network metrics (such as degree or clustering distributions) can lead us to a better understanding of pulsating stars dynamics.

Methods. By using the horizontal visibility algorithm, we mapped the TESS light curves of 69 δ Sct stars to undirected horizontal visibility graphs (HVGs), where the graph nodes represent the light curve points. This allowed us to measure the morphological characteristics of HVGs, such as the distribution of links between nodes (degree distribution) and the average fraction of triangles around each node (average clustering coefficient).

Results. The average clustering coefficients for HADS and LADS display two different linear correlations with the peak-to-peak amplitude of the TESS light curves that naturally separates them into two groups. This novel approach enabled us to obtain this result without having to use an ad hoc criterion, for the first time. Exponential fits on HVG degree distributions for both HADS and LADS stars offer indices that suggest correlated stochastic generating processes for δ Sct light curves. By applying the theoretical expression for the HVGs degree distribution of random time series, we have the ability to distinguish significant pulsations from the background noise, which could become a practical tool in frequency analyses of stars going forward.