The potential of Shannon entropy to find the large separation of δ Scuti stars: The entropy spectrum - Suárez, J. C. (Frontiers in Astronomy and Space Sciences, 2022)
This papers explores the use of the Shannon entropy to find periodic patterns in the oscillation spectra of delta Scuti stars. We have developed a new diagnostic tool for detecting potential patterns that scans for minimal entropic states in the well-known echelle diagrams, the Entropy spectrum, HSpec. Here we describe the basic mathematical grounds of the Shannon entropy and how it can be applied to echelle diagrams. The method is first validated with the solar-like star HD49933, for which the large separation was found compatible with values published in the literature. Then we computed the entropy spectrum for two well-studied delta Scuti stars, HD 174936 and HD 174966, for which HSpec analysis was able to accurately determine their large separation or some of its or submultiples. 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 echelle diagram, and on the way it is calculated. We discuss possible solutions to this that rely on 2D probability distributions and conditional entropy.