The VELOCE modulation zoo

III. Detecting additional pulsation modes in optical spectra of classical Cepheids using semi-partial distance correlation periodograms

¹ Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
² Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warsaw, Poland
³ Porter School of the Environment and Earth Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel
⁴ Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel
⁵ Astronomy Department of the University of Geneva, 51 Ch. des Maillettes, 1290 Versoix, Switzerland
⁶ School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel

^⋆ Corresponding authors: kentbarbey2598@gmail.com; richard.anderson@epfl.ch

Received: 11 December 2024
Accepted: 14 April 2025

Abstract

Known for their large amplitude radial pulsations, classical Cepheids are critical standard candles in astrophysics. However, they also exhibit various pulsational irregularities and additional signals that provide deeper insights into their structure and evolution. These signals appear in spectroscopic observations as shape deformations of the spectral lines. Using semi-partial distance correlation periodograms, we analysed high-precision spectroscopic data from the VELOCE project for four stars: δ Cephei (δ Cep), BG Crucis (BG Cru), X Sagittarii (X Sgr), and Polaris. For δ Cephei, our control star, only the main radial mode was detected, confirming its stability and suitability as a benchmark for the method. In BG Crucis, a strong additional signal at ∼3.01 days was identified, likely linked to line splitting. X Sagittarii exhibited dominant additional signals, notably one at ∼12.31 days, also associated with significant line splitting. Polaris revealed multiple low-frequency signals, with the most prominent candidate at ∼59.86 days, which might be linked to the star’s rotation period. We explored the semi-partial distance correlation periodograms by incorporating cross-correlation functions (CCFs) and their variants, such as the median-subtracted CCFs, which improved the sensitivity to variations in line shape. In particular, the latter enabled the faithful detection of primary and additional signals present in the 1D spectra of fainter stars and low-amplitude pulsators. The semi-partial distance correlation periodograms demonstrated their utility for isolating signals associated with line shape variations; although, the analyses were complicated by the presence of artefact subharmonics and a visible low-frequency power increase for Polaris and BG Crucis. This study underscores the method’s potential for finding new and unexpected signals as well as detailed analyses of Cepheid pulsations and opens new pathways for asteroseismic investigations.