The potential of Shannon entropy to find the large separation of δ Scuti stars: The entropy spectrum

Abstract

This study explores the use of Shannon entropy to find periodic patterns in the oscillation spectra of δ Scuti stars. We have developed a new diagnostic tool for detecting potential patterns that scans for minimal entropic states in the well-known échelle diagrams. Here, we describe the basic mathematical grounds of the Shannon entropy and how it can be applied to échelle diagrams through a new diagnostic diagram: the entropy (H) spectrum (HSpec). The method is first validated with the solar-like pulsator HD 49933, for which the large separation was found compatible with values published in the literature. Then we computed the entropy spectrum for two well-studied δ Scuti stars: HD 174936 and HD 174966, for which HSpec analysis was able to accurately determine their large separation (or some multiple or submultiple of it). Although these results are promising, the HSpec tool presents several limitations: it has a strong dependence on the probability distribution of the frequencies in the échelle diagram, and on the way it is calculated. We discuss possible solutions to this that rely on 2D probability distributions and conditional entropy.