Asteroseismology probes the internal structures of stars by using their natural pulsation frequencies1. It relies on identifying sequences of pulsation modes that can be compared with theoretical models, which has been done successfully for many classes of pulsators, including low-mass solar-type stars2, red giants3, high-mass stars4 and white dwarfs5. However, a large group of pulsating stars of intermediate mass—the so-called δ Scuti stars—have rich pulsation spectra for which systematic mode identification has not hitherto been possible6,7. This arises because only a seemingly random subset of possible modes are excited and because rapid rotation tends to spoil regular patterns8,9,10. Here we report the detection of remarkably regular sequences of high-frequency pulsation modes in 60 intermediate-mass main-sequence stars, which enables definitive mode identification. The space motions of some of these stars indicate that they are members of known associations of young stars, as confirmed by modelling of their pulsation spectra.
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TESS and Kepler data are available from the MAST portal (https://archive.stsci.edu/access-mast-data). All other data are available from the corresponding author upon reasonable request.
We have made use of standard data analysis tools in Python, as noted and referenced in Methods.
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We gratefully acknowledge the TESS and Kepler teams, whose efforts made these results possible. This research was partially conducted during the Exostar19 programme at the Kavli Institute for Theoretical Physics at UC Santa Barbara, which was supported in part by the National Science Foundation under grant no. NSF PHY-1748958. We thank colleagues in that programme, especially R. Townsend, for many stimulating discussions. We also thank A. Moya, A. G. Hernández, J. C. Suárez and Z. Guo for comments on the manuscript. We gratefully acknowledge support from the Australian Research Council (grant DE 180101104), and from the Danish National Research Foundation (grant DNRF106) through its funding for the Stellar Astrophysics Center (SAC). D.H. acknowledges support from the Alfred P. Sloan Foundation, the National Aeronautics and Space Administration (80NSSC18K1585, 80NSSC19K0379), and the National Science Foundation (AST-1717000). H.K. acknowledges support from the European Social Fund via the Lithuanian Science Council (LMTLT) grant 09.3.3-LMT-K-712-01-0103. Y.L. acknowledges support from the Joint Research Fund in Astronomy (U1631236) under cooperative agreement between the National Natural Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS). D.L.H. acknowledges support by the Science and Technology Facilities Council under grant ST/M000877/1. The research leading to these results has (partially) received funding from the Research Foundation Flanders (FWO) under grant agreement G0H5416N (ERC Runner Up Project). This work makes use of observations from the LCOGT network. This work has also made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Some of the observations reported in this paper were obtained with the Southern African Large Telescope (SALT) under programmes 2015-2-SCI-007, 2016-2-SCI-015 and 2017-2-SCI-010. The ISIS instrument is mounted on the WHT, which is operated on the island of La Palma by the Isaac Newton Group of Telescopes in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofsica de Canarias. The Veloce Rosso facility was funded by Australian Research Council (ARC) Linkage Infrastructure, Equipment and Facility (LIEF) grants LE150100087 and LE160100014, and UNSW Research Infrastructure Scheme grant RG163088. C.G.T. and C.B. acknowledge the support of ARC Discovery grant DP170103491. V.A. was supported by a research grant (00028173) from VILLUM FONDEN. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community; we are most fortunate to have the opportunity to conduct observations from this mountain. We also acknowledge the traditional owners of the land on which the Anglo-Australian Telescope stands, the Gamilaraay people, and pay our respects to elders past, present and emerging.
The authors declare no competing interests.
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Extended data figures and tables
The amplitude spectra are shown in échelle format, segments of equal length being stacked vertically. a, V435 Car; b, HD 55863; c, HD 42608; d, HD 24975; e, HD 46722; f, HD 220811. The vertical dashed line shows the value of ∆ν used in each case, with a repeated overlap region added on the right for clarity. The greyscale shows the observed amplitude spectrum of data from the TESS spacecraft, where the number of 27-day sectors was four for V435 Car, three for HD 55863, two for HD 24975 and HD 46722, and one for HD 42608 and HD 220811. Smoothing was applied to the observed amplitude spectra before plotting, and the red stripes mark overtone sequences of l = 0 and l = 1 modes.
Symbols show 18 δ Scuti stars in which the fundamental radial mode, f1, is clearly identified. A correlation is expected because both quantities depend on the mean stellar density. We do not expect a perfect correlation owing to departures from the asymptotic relation1,2,3 (see Methods) and variations in ε from star to star (see Fig. 3c).
Extended Data Fig. 3 Fourier amplitude spectra and high-resolution spectra of high-frequency δ Scuti stars.
Left panel, Fourier amplitude spectra of 15 stars; each star has two catalogue names, as shown. Right panel, high-resolution spectra of the stars; measured vsini values are given. The stars are sorted by increasing vsini from top to bottom. See Methods section ‘High-resolution spectroscopy’ for details.
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Bedding, T.R., Murphy, S.J., Hey, D.R. et al. Very regular high-frequency pulsation modes in young intermediate-mass stars. Nature 581, 147–151 (2020). https://doi.org/10.1038/s41586-020-2226-8
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