A "complex network" perspective on δ Scuti stars

In order to conduct a more comprehensive study of pulsating stars as nonlinear systems accompanied by asteroseismology, we applied the “complex network” approach by considering δ Scuti stars as “complex systems”. δ Scuti stars are stars with spectral types A0-F5 and intermediate masses that pulsate in low-order pressure modes as well as gravity modes. They have dominant frequencies in the 5−80 c/d range, and they are relevant targets for our study, since they span a broad range of complexity behaviour from Low Amplitude to High Amplitude δ Scuti stars (LADS and HADS, respectively). Complex systems are composed of a large number of highly interconnected dynamical units that exhibit emergent collective properties. The “complex network” idea is applied widely in many different disciplines, ranging from nonlinear science to biology, as well as from statistical mechanics to medicine and engineering. By using the horizontal visibility algorithms, the light curves of 73 δ Scuti stars observed by TESS are mapped to Horizontal Visibility Graphs (HVGs), where the graph nodes represent the light curve points. In the HVG, connections between nodes happen when light curve points are able to see each other along the horizontal lines of sight. We studied the networks' local and global characteristics for HADS and LADS stars. Our analysis of degree distributions shows that these scale-free networks have multiplicative processes, pointing to the necessity of improving the modelling of these stars. The theoretical expression for degree distribution of HVGs can guide us to distinguish stellar pulsations from the background noise.