Toward a New Paradigm in the Analysis of Asteroseismic Lightcurves

This paper aims at being a provocative guide to the future of asteroseismology from the perspective of the analysis of time series, where the fundamentals of harmonic analysis are subjected to stress tests. In this context, we give an annotated summary of our research over the last decades on harmonic analysis of A-F stars. We discuss and explore the consequences of our findings, which may extend to any kind of pulsators. As well, we analyse the impact of this reconsideration on future asteroseismic studies, which would entail a paradigm shift. This includes a discussion on the presence of fractal behavior in δ Sct stars, and how this can be used to develop a stopping criterion of the pre-whitening process, as an alternative to SNR (or significance) criterion. Drilling a scientific paradigm has its natural resilience, hence the path described here is being arduous, although fruitful at the same time.