Multiple Regular Frequency Spacings in δ Scuti Stars from Automated Analysis of TESS Oscillation Spectra

Abstract The oscillation spectra of rapidly rotating δ Scuti stars are difficult to interpret because rotation modifies both the frequencies and spatial structure of the modes. Although theoretical studies predict that acoustic modes should organize into approximately equally spaced frequency sequences, systematic searches for such patterns have been limited by the absence of scalable, statistically robust detection methods. We present an automated statistical framework for identifying approximately equally spaced mode sequences in stellar oscillation spectra while quantifying the significance of each candidate detection. We apply this method to oscillation spectra of 4681 δ Scuti stars observed by the Transiting Exoplanet Survey Satellite (TESS). The analysis identifies regular mode sequences in a large number of stars and, in many cases, reveals multiple independent regular frequency spacings within the same oscillation spectrum. While the existence of regular sequences is broadly consistent with theoretical expectations for rapidly rotating acoustic modes, the occurrence of multiple dissimilar spacings is not readily explained by current models. Differences in acoustic travel times between known island-mode families appear insufficient to account for the observed diversity of spacings, suggesting that additional mode families or other physical effects contribute to the organization of oscillation spectra of δ Scuti stars. Our results provide a scalable framework for studying regular mode sequences in large stellar surveys and new observational constraints on oscillations in rapidly rotating stars.