Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Very regular high-frequency pulsation modes in young intermediate-mass stars

Abstract

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.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Pulsation spectra of 15 high-frequency δ Scuti stars observed with TESS.
Fig. 2: Mode identification in δ Scuti stars.
Fig. 3: Properties of high-frequency δ Scuti stars.
Fig. 4: Examples of more complicated échelle diagrams of δ Scuti pulsations.

Similar content being viewed by others

Data availability

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.

Code availability

We have made use of standard data analysis tools in Python, as noted and referenced in Methods.

References

  1. Aerts, C., Christensen-Dalsgaard, J. & Kurtz, D. W. Asteroseismology (Springer, 2010).

  2. García, R. A. & Ballot, J. Asteroseismology of solar-type stars. Living Rev. Sol. Phys. 16, 4 (2019).

    ADS  Google Scholar 

  3. Hekker, S. & Christensen-Dalsgaard, J. Giant star seismology. Astron. Astrophys. Rev. 25, 1 (2017).

    ADS  Google Scholar 

  4. Aerts, C. in New Windows on Massive Stars: Asteroseismology, Interferometry, and Spectropolarimetry (eds Meynet, G., Georgy, C., Groh, J. & Stee, P.) 154–164 (IAU Symp. 307, Cambridge Univ. Press, 2015).

  5. Córsico, A. H., Althaus, L. G., Miller Bertolami, M. M. & Kepler, S. O. Pulsating white dwarfs: new insights. Astron. Astrophys. Rev. 27, 7 (2019).

    ADS  Google Scholar 

  6. Goupil, M. J. et al. Asteroseismology of δ Scuti stars: problems and prospects. J. Astron. Astrophys. 26, 249–259 (2005).

    ADS  Google Scholar 

  7. Handler, G. Delta Scuti variables. AIP Conf. Proc. 1170, 403–409 (2009).

    ADS  Google Scholar 

  8. Ouazzani, R. M., Roxburgh, I. W. & Dupret, M. A. Pulsations of rapidly rotating stars. II. Realistic modelling for intermediate-mass stars. Astron. Astrophys. 579, A116 (2015).

    Google Scholar 

  9. Reese, D. R. et al. Frequency regularities of acoustic modes and multi-colour mode identification in rapidly rotating stars. Astron. Astrophys. 601, A130 (2017).

    Google Scholar 

  10. Mirouh, G. M., Angelou, G. C., Reese, D. R. & Costa, G. Mode classification in fast-rotating stars using a convolutional neural network: model-based regular patterns in δ Scuti stars. Mon. Not. R. Astron. Soc. 483, L28–L32 (2019).

    ADS  Google Scholar 

  11. Reese, D., Lignières, F. & Rieutord, M. Regular patterns in the acoustic spectrum of rapidly rotating stars. Astron. Astrophys. 481, 449–452 (2008).

    ADS  Google Scholar 

  12. Murphy, S. J., Hey, D., Van Reeth, T. & Bedding, T. R. Gaia-derived luminosities of Kepler A/F stars and the pulsator fraction across the δ Scuti instability strip. Mon. Not. R. Astron. Soc. 485, 2380–2400 (2019).

    CAS  ADS  Google Scholar 

  13. Balona, L. A., Daszyńska-Daszkiewicz, J. & Pamyatnykh, A. A. Pulsation frequency distribution in δ Scuti stars. Mon. Not. R. Astron. Soc. 452, 3073–3084 (2015).

    CAS  ADS  Google Scholar 

  14. Bowman, D. M. & Kurtz, D. W. Characterizing the observational properties of δ Sct stars in the era of space photometry from the Kepler mission. Mon. Not. R. Astron. Soc. 476, 3169–3184 (2018).

    CAS  ADS  Google Scholar 

  15. Antoci, V. et al. The first view of δ Scuti and γ Doradus stars with the TESS mission. Mon. Not. R. Astron. Soc. 490, 4040–4059 (2019).

    ADS  Google Scholar 

  16. Ziaali, E., Bedding, T. R., Murphy, S. J., Van Reeth, T. & Hey, D. R. The period-luminosity relation for δ Scuti stars using Gaia DR2 parallaxes. Mon. Not. R. Astron. Soc. 486, 4348–4353 (2019).

    ADS  Google Scholar 

  17. Petersen, J. O. & Christensen-Dalsgaard, J. Pulsation models of δ Scuti variables. I. The high-amplitude double-mode stars. Astron. Astrophys. 312, 463–474 (1996).

    ADS  Google Scholar 

  18. Suárez, J. C. et al. Measuring mean densities of δ Scuti stars with asteroseismology. Theoretical properties of large separations using TOUCAN. Astron. Astrophys. 563, A7 (2014).

    Google Scholar 

  19. García Hernández, A. et al. Observational ∆ν–ρ relation for δ Sct stars using eclipsing binaries and space photometry. Astrophys. J. 811, L29 (2015).

    ADS  Google Scholar 

  20. Paparó, M., Benkő, J. M., Hareter, M. & Guzik, J. A. Unexpected series of regular frequency spacing of δ Scuti stars in the non-asymptotic regime. II. Sample-échelle diagrams and rotation. Astrophys. J. Suppl. Ser. 224, 41 (2016).

    ADS  Google Scholar 

  21. Suárez, J. C. et al. A study of correlation between the oscillation amplitude and stellar parameters of δ Scuti stars in open clusters. Toward selection rules for δ Scuti star oscillations. Astron. Astrophys. 390, 523–531 (2002).

    ADS  Google Scholar 

  22. White, T. R. et al. Calculating asteroseismic diagrams for solar-like oscillations. Astrophys. J. 743, 161 (2011).

    ADS  Google Scholar 

  23. Zorec, J. & Royer, F. Rotational velocities of A-type stars. IV. Evolution of rotational velocities. Astron. Astrophys. 537, A120 (2012).

    ADS  Google Scholar 

  24. Evano, B., Lignières, F. & Georgeot, B. Regularities in the spectrum of chaotic p-modes in rapidly rotating stars. Astron. Astrophys. 631, A140 (2019).

    ADS  Google Scholar 

  25. Mamajek, E. E. & Bell, C. P. M. On the age of the β Pictoris moving group. Mon. Not. R. Astron. Soc. 445, 2169–2180 (2014).

    ADS  Google Scholar 

  26. Curtis, J. L., Agüeros, M. A., Mamajek, E. E., Wright, J. T. & Cummings, J. D. TESS reveals that the nearby Pisces-Eridanus stellar stream is only 120 Myr old. Astron. J. 158, 77 (2019).

    CAS  ADS  Google Scholar 

  27. Meingast, S., Alves, J. & Fürnkranz, V. Extended stellar systems in the solar neighborhood. II. Discovery of a nearby 120° stellar stream in Gaia DR2. Astron. Astrophys. 622, L13 (2019).

    CAS  ADS  Google Scholar 

  28. van der Plas, G. et al. An 80 au cavity in the disk around HD 34282. Astron. Astrophys. 607, A55 (2017).

    Google Scholar 

  29. Lai, D. Star–disc–binary interactions in protoplanetary disc systems and primordial spin–orbit misalignments. Mon. Not. R. Astron. Soc. 440, 3532–3544 (2014).

    ADS  Google Scholar 

  30. Williams, J. P. & Cieza, L. A. Protoplanetary disks and their evolution. Annu. Rev. Astron. Astrophys. 49, 67–117 (2011).

    ADS  Google Scholar 

  31. Paunzen, E. A spectroscopic survey for λ Bootis stars. III. Final results. Astron. Astrophys. 373, 633–640 (2001).

    CAS  ADS  Google Scholar 

  32. Antoci, V. et al. The role of turbulent pressure as a coherent pulsational driving mechanism: the case of the δ Scuti star HD 187547. Astrophys. J. 796, 118 (2014).

    ADS  Google Scholar 

  33. Ricker, G. R. et al. Transiting Exoplanet Survey Satellite (TESS). J. Astron. Telesc. Instrum. Syst. 1, 014003 (2014).

    ADS  Google Scholar 

  34. Borucki, W. J. et al. Kepler planet-detection mission: introduction and first results. Science 327, 977 (2010)

    CAS  PubMed  ADS  Google Scholar 

  35. MAST: Barbara A. Mikulski Archive for Space Telescopes (Space Telescope Science Institute, 2019); https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html.

  36. Hey, D. & Ball, W. Echelle: Dynamic Echelle Diagrams for Asteroseismology v.1.4 (2020); https://doi.org/10.5281/zenodo.3629933.

  37. Høg, E. et al. The Tycho-2 catalogue of the 2.5 million brightest stars. Astron. Astrophys. 355, L27–L30 (2000).

    ADS  Google Scholar 

  38. Bessell, M. S. The Hipparcos and Tycho photometric system passbands. Publ. Astron. Soc. Pacif. 112, 961–965 (2000).

    ADS  Google Scholar 

  39. Flower, P. J. Transformations from theoretical Hertzsprung-Russell diagrams to color-magnitude diagrams: effective temperatures, B-V colors, and bolometric corrections. Astrophys. J. 469, 355–365 (1996).

    ADS  Google Scholar 

  40. Lindegren, L. et al. Gaia Data Release 2. The astrometric solution. Astron. Astrophys. 616, A2 (2018).

    Google Scholar 

  41. Bovy, J., Rix, H.-W., Green, G. M., Schlafly, E. F. & Finkbeiner, D. P. On Galactic density modeling in the presence of dust extinction. Astrophys. J. 818, 130 (2016).

    ADS  Google Scholar 

  42. Huber, D. et al. The K2 Ecliptic Plane Input Catalog (EPIC) and stellar classifications of 138,600 targets in campaigns 1–8. Astrophys. J. 224, 2 (2016).

    Google Scholar 

  43. Choi, J. et al. Mesa Isochrones and Stellar Tracks (MIST). I. Solar-scaled models. Astrophys. J. 823, 102 (2016).

    ADS  Google Scholar 

  44. Casagrande, L. et al. New constraints on the chemical evolution of the solar neighbourhood and Galactic disc(s). Improved astrophysical parameters for the Geneva-Copenhagen Survey. Astron. Astrophys. 530, A138 (2011).

    Google Scholar 

  45. Huber, D. et al. Revised stellar properties of Kepler targets for the quarter 1-16 transit detection run. Astrophys. J. Suppl. Ser. 211, 2 (2014).

    ADS  Google Scholar 

  46. Mathur, S. et al. Revised stellar properties of Kepler targets for the Q1-17 (DR25) transit detection run. Astrophys. J. Suppl. Ser. 229, 30 (2017); erratum 234, 43 (2018).

    ADS  Google Scholar 

  47. Brown, T. M., Latham, D. W., Everett, M. E. & Esquerdo, G. A. Kepler input catalog: photometric calibration and stellar classification. Astron. J. 142, 112 (2011).

    ADS  Google Scholar 

  48. Casey, M. P. et al. MOST observations of the Herbig Ae δ-Scuti star HD 34282. Mon. Not. R. Astron. Soc. 428, 2596–2604 (2013).

    ADS  Google Scholar 

  49. Vogt, S. S. et al. HIRES: the high-resolution echelle spectrometer on the Keck 10-m Telescope. Proc. SPIE 2198, 362 (1994).

    CAS  ADS  Google Scholar 

  50. Howard, A. W. et al. The California Planet Survey. I. Four new giant exoplanets. Astrophys. J. 721, 1467–1481 (2010).

    CAS  ADS  Google Scholar 

  51. Siverd, R. J. et al. NRES: the network of robotic echelle spectrographs. Proc. SPIE 10702, 107026C (2018).

    Google Scholar 

  52. Brown, T. M. et al. Las Cumbres Observatory global telescope network. Publ. Astron. Soc. Pacif. 125, 1031 (2013).

    ADS  Google Scholar 

  53. Gilbert, J. et al. Veloce Rosso: Australia’s new precision radial velocity spectrograph. Proc. SPIE 10702, 107020Y (2018).

    Google Scholar 

  54. Smith, K. C. & Dworetsky, M. M. in Elemental Abundance Analyses (eds Adelman, S. J. & Lanz, T.) 32–37 (Institut d'Astronomie de l'Université de Lausanne, 1988).

  55. Smith, K. C. The Chemical Compositions of Mercury-Manganese Stars from Ultraviolet Spectra. PhD. thesis, Univ. London (1992).

  56. Castelli, F., Gratton, R. G. & Kurucz, R. L. Notes on the convection in the ATLAS9 model atmospheres. Astron. Astrophys. 318, 841–869 (1997).

    ADS  Google Scholar 

  57. Kupka, F., Piskunov, N., Ryabchikova, T. A., Stempels, H. C. & Weiss, W. W. VALD-2: Progress of the Vienna atomic line data base. Astron. Astrophys. Suppl. Ser. 138, 119–133 (1999).

    CAS  ADS  Google Scholar 

  58. Niemczura, E. et al. Spectroscopic survey of Kepler stars. I. HERMES/Mercator observations of A- and F-type stars. Mon. Not. R. Astron. Soc. 450, 2764–2783 (2015).

    CAS  ADS  Google Scholar 

  59. Niemczura, E. et al. Spectroscopic survey of Kepler stars. II. FIES/NOT observations of A- and F-type stars. Mon. Not. R. Astron. Soc. 470, 2870–2889 (2017).

    CAS  ADS  Google Scholar 

  60. Tkachenko, A. Grid search in stellar parameters: a software for spectrum analysis of single stars and binary systems. Astron. Astrophys. 581, A129 (2015).

    ADS  Google Scholar 

  61. Tsymbal, V. STARSP: A software system for the analysis of the spectra of normal stars. In M.A.S.S., Model Atmospheres and Spectrum Synthesis (eds Adelman, S. J., Kupka, F. & Weiss, W. W.) 198–199 (Astron. Soc. Pacif. Conf. Ser. Vol. 108, Astronomical Society of the Pacific, 1996).

  62. Shulyak, D., Tsymbal, V., Ryabchikova, T., Stütz, C. & Weiss, W. W. Line-by-line opacity stellar model atmospheres. Astron. Astrophys. 428, 993–1000 (2004).

    ADS  Google Scholar 

  63. Burgh, E. B. et al. Prime focus imaging spectrograph for the Southern African Large Telescope: optical design. Proc. SPIE 4841, 1463–1471 (2003).

    ADS  Google Scholar 

  64. Kobulnicky, H. A. et al. Prime focus imaging spectrograph for the Southern African Large Telescope: operational modes. Proc. SPIE 4841, 1634–1644 (2003).

    ADS  Google Scholar 

  65. Buckley, D. A. H., Swart, G. P. & Meiring, J. G. Completion and commissioning of the Southern African Large Telescope. Proc. SPIE 6267, 62670Z (2006).

    ADS  Google Scholar 

  66. Kanodia, S. & Wright, J. Python leap second management and implementation of precise barycentric correction (barycorrpy). Res. Not. AAS 2, 4 (2018).

    ADS  Google Scholar 

  67. Wright, J. T. & Eastman, J. D. Barycentric corrections at 1 cm s1 for precise Doppler velocities. Publ. Astron. Soc. Pacif. 126, 838–852 (2014).

    ADS  Google Scholar 

  68. Gagné, J. et al. BANYAN. XI. The BANYAN Σ multivariate Bayesian algorithm to identify members of young associations with 150 pc. Astrophys. J. 856, 23 (2018).

    ADS  Google Scholar 

  69. Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA). Astrophys. J. Suppl. Ser. 192, 3 (2011).

    ADS  Google Scholar 

  70. Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA): planets, oscillations, rotation, and massive stars. Astrophys. J. Suppl. Ser. 208, 4 (2013).

    ADS  Google Scholar 

  71. Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA): binaries, pulsations, and explosions. Astrophys. J. Suppl. Ser. 220, 15 (2015); erratum 223, 18 (2016).

    ADS  Google Scholar 

  72. Ball, W. H. & Gizon, L. A new correction of stellar oscillation frequencies for near-surface effects. Astron. Astrophys. 568, A123 (2014).

    ADS  Google Scholar 

  73. Asplund, M., Grevesse, N., Sauval, A. J. & Scott, P. The chemical composition of the Sun. Annu. Rev. Astron. Astrophys. 47, 481–522 (2009).

    CAS  ADS  Google Scholar 

  74. Zwintz, K. et al. Echography of young stars reveals their evolution. Science 345, 550–553 (2014).

    CAS  PubMed  ADS  Google Scholar 

  75. Handler, G. et al. Delta Scuti Network observations of XX Pyx: detection of 22 pulsation modes and of short-term amplitude and frequency variations. Mon. Not. R. Astron. Soc. 318, 511–525 (2000).

    ADS  Google Scholar 

  76. García Hernández, A. et al. Asteroseismic analysis of the CoRoT δ Scuti star HD 174936. Astron. Astrophys. 506, 79–83 (2009).

    ADS  Google Scholar 

  77. Breger, M., Lenz, P. & Pamyatnykh, A. A. Towards mode selection in δ Scuti stars: regularities in observed and theoretical frequency spectra. Mon. Not. R. Astron. Soc. 396, 291–298 (2009).

    ADS  Google Scholar 

  78. Breger, M. et al. Regularities in frequency spacings of δ Scuti stars: the Kepler star KIC 9700322. Mon. Not. R. Astron. Soc. 414, 1721–1731 (2011).

    CAS  ADS  Google Scholar 

  79. Antoci, V. et al. The excitation of solar-like oscillations in a δ Sct star by efficient envelope convection. Nature 477, 570–573 (2011).

    CAS  PubMed  ADS  Google Scholar 

  80. Zwintz, K. et al. Regular frequency patterns in the classical δ Scuti star HD 144277 observed by the MOST satellite. Astron. Astrophys. 533, A133 (2011).

    Google Scholar 

  81. Zwintz, K. et al. Regular frequency patterns in the young δ Scuti star HD 261711 observed by the CoRoT and MOST satellites. Astron. Astrophys. 552, A68 (2013).

    Google Scholar 

  82. Paparó, M. et al. CoRoT 102749568: mode identification in a δ Scuti star based on regular spacings. Astron. Astrophys. 557, A27 (2013).

    Google Scholar 

  83. García Hernández, A. et al. An in-depth study of HD 174966 with CoRoT photometry and HARPS spectroscopy. Large separation as a new observable for δ Scuti stars. Astron. Astrophys. 559, A63 (2013).

    Google Scholar 

  84. Maceroni, C. et al. KIC 3858884: a hybrid δ Scuti pulsator in a highly eccentric eclipsing binary. Astron. Astrophys. 563, A59 (2014).

    Google Scholar 

  85. Paparó, M., Benkő, J. M., Hareter, M. & Guzik, J. A. Unexpected series of regular frequency spacing of δ Scuti stars in the non-asymptotic regime. I. The methodology. Astrophys. J. 822, 100 (2016).

    ADS  Google Scholar 

  86. Michel, E. et al. What CoRoT tells us about δ Scuti stars. Existence of a regular pattern and seismic indices to characterize stars. Eur. Phys. J. Web Conf. 160, 03001 (2017).

    Google Scholar 

  87. Mora, A. et al. EXPORT: Spectral classification and projected rotational velocities of Vega-type and pre-main sequence stars. Astron. Astrophys. 378, 116–131 (2001).

    CAS  ADS  Google Scholar 

  88. Mékarnia, D. et al. The δ Scuti pulsations of β Pictoris as observed by ASTEP from Antarctica. Astron. Astrophys. 608, L6 (2017).

    ADS  Google Scholar 

  89. Zwintz, K. et al. Revisiting the pulsational characteristics of the exoplanet host star β Pictoris. Astron. Astrophys. 627, A28 (2019).

    CAS  Google Scholar 

  90. Web TESS viewing tool (WTV) (TESS Science Support Center, 2020); https://heasarc.gsfc.nasa.gov/cgi-bin/tess/webtess/wtv.py.

  91. Mellon, S. N. et al. Bright southern variable stars in the bRing survey. Astrophys. J. Suppl. Ser. 244, 15 (2019).

    ADS  Google Scholar 

  92. Khalack, V. et al. Rotational and pulsational variability in the TESS light curve of HD 27463. Mon. Not. R. Astron. Soc. 490, 2102–2111 (2019).

    ADS  Google Scholar 

  93. Mason, B. D., Wycoff, G. L., Hartkopf, W. I., Douglass, G. G. & Worley, C. E. The 2001 US Naval Observatory double star CD-ROM. I. The Washington double star catalog. Astron. J. 122, 3466–3471 (2001).

    ADS  Google Scholar 

  94. Holdsworth, D. L. et al. High-frequency A-type pulsators discovered using SuperWASP. Mon. Not. R. Astron. Soc. 439, 2078–2095 (2014).

    ADS  Google Scholar 

  95. Rodríguez, E., López-González, M. J. & López de Coca, P. A revised catalogue of δ Sct stars. Astron. Astrophys. Suppl. Ser. 144, 469–474 (2000).

    ADS  Google Scholar 

  96. Amado, P. J. et al. The pre-main-sequence star HD34282: a very short-period δ Scuti-type pulsator. Mon. Not. R. Astron. Soc. 352, L11–L15 (2004).

    ADS  Google Scholar 

  97. Gray, R. O. et al. The discovery of λ Bootis stars: the southern survey I. Astron. J. 154, 31 (2017).

    ADS  Google Scholar 

  98. Murphy, S. J. et al. An evaluation of the membership probability of 212 λ Boo stars. I. A catalogue. Publ. Astron. Soc. Aust. 32, e036 (2015).

    ADS  Google Scholar 

  99. Zuckerman, B., Rhee, J. H., Song, I. & Bessell, M. S. The Tucana/Horologium, Columba, AB Doradus, and Argus associations: new members and dusty debris disks. Astrophys. J. 732, 61 (2011).

    ADS  Google Scholar 

  100. Torres, C. A. O. et al. Search for associations containing young stars (SACY). I. Sample and searching method. Astron. Astrophys. 460, 695–708 (2006).

    CAS  ADS  Google Scholar 

  101. Murphy, S. J. & Lawson, W. A. New low-mass members of the Octans stellar association and an updated 30–40 Myr lithium age. Mon. Not. R. Astron. Soc. 447, 1267–1281 (2015).

    CAS  ADS  Google Scholar 

  102. Paunzen, E. et al. λ Bootis stars in the SuperWASP survey. Mon. Not. R. Astron. Soc. 453, 1241–1248 (2015).

    CAS  ADS  Google Scholar 

  103. Royer, F., Zorec, J. & Gómez, A. E. Rotational velocities of A-type stars. III. Velocity distributions. Astron. Astrophys. 463, 671–682 (2007).

    ADS  Google Scholar 

  104. Royer, F., Grenier, S., Baylac, M. O., Gómez, A. E. & Zorec, J. Rotational velocities of A-type stars in the northern hemisphere. II. Measurement of vsini. Astron. Astrophys. 393, 897–911 (2002).

    CAS  ADS  Google Scholar 

  105. Schröder, C., Reiners, A. & Schmitt, J. H. M. M. Ca II HK emission in rapidly rotating stars. Evidence for an onset of the solar-type dynamo. Astron. Astrophys. 493, 1099–1107 (2009).

    ADS  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

Authors

Contributions

T.R.B., S.J.M., D. R. Hey, W.J.C., G.L., Y.L., I.L.C. and J.Y. analysed the photometric observations; T.L., D.S., W.H.B., T.R.W., D.R.R., J.F. and J.J.H. calculated and/or interpreted theoretical models; V.A. and H.K. coordinated the selection of the targets for the TESS observations; D.H., D. R. Harbeck, S.S., B.S., T.M.B., A.W.H., H.I., C.M., M.R., C.B., A.D.R., C.G.T, M.J.I. and D.L.H. obtained and/or analysed the spectroscopic observations; E.G. and A.W.M. identified objects that belong to moving groups; G.R.R., R.K.V. and J.M.J. were key architects of the TESS Mission. All authors reviewed the manuscript.

Corresponding author

Correspondence to Timothy R. Bedding.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 More examples of mode identifications in δ Scuti stars.

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.

Extended Data Fig. 2 Correlation between Δν and the frequency of the fundamental radial mode.

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.

Extended Data Table 1 Properties of high-frequency δ Scuti stars
Extended Data Table 2 Projected rotational velocities from high-resolution spectroscopy

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-020-2226-8

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing