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.

Polarimetric detection of non-radial oscillation modes in the β Cephei star β Crucis

Abstract

Here we report the detection of polarization variations due to non-radial modes in the β Cephei star β Crucis. In so doing we confirm 40-year-old predictions of pulsation-induced polarization variability and its utility in asteroseismology for mode identification. In an approach suited to other β Cephei stars, we combine polarimetry with space-based photometry and archival spectroscopy to identify the dominant non-radial mode in polarimetry, f2, as mode degree  = 3, azimuthal order m = −3 (in the m-convention of Dziembowski) and determine the stellar axis position angle as 25 (or 205) ± 8°. The rotation axis inclination to the line of sight was derived as ~46° from combined polarimetry and spectroscopy, facilitating identification of additional modes and allowing for asteroseismic modelling. This reveals a star of 14.5 ± 0.5 M and a convective core containing ~28% of its mass—making β Crucis the most massive star with an asteroseismic age.

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

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: β Cru time-series examples.
Fig. 2: Selected amplitude spectra for β Cru.
Fig. 3: Photometric and polarimetric data phase-folded to f2 for β Cru.
Fig. 4: Polarimetric mode determination diagrams for the f2 mode of β Cru.
Fig. 5: Line-profile analysis for β Cru.
Fig. 6: Distributions of β Cru’s rotation axis inclination angle.

Data availability

The new data that support the plots within this paper and other findings of this study will be available from the VizieR service upon print publication. All other data analysed in this work come from public repositories; where this is the case, the origin of the data is indicated in the text.

Code availability

Our polarimetric modelling code is based on the publicly available ATLAS9, SYNSPEC and VLIDORT codes. Our modified version of SYNSPEC is available on request. The spectroscopic mode identification was performed with the software package FAMIAS available from https://fys.kuleuven.be/ster/Software/famias/famias, applied to the time-series spectroscopy available from https://fys.kuleuven.be/ster/Software/helas/helas. The neural network is available from https://github.com/l-hendriks/asteroseismology-dnn. The joint frequency analysis was conducted using a custom MATLAB package that is available on request.

References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Aerts, C., Mathis, S. & Rogers, T. M. Angular momentum transport in stellar interiors. Annu. Rev. Astron. Astrophys. 57, 35–78 (2019).

    Article  ADS  Google Scholar 

  4. Pamyatnykh, A. A. Pulsational instability domains in the upper main sequence. Acta Astron. 49, 119–148 (1999).

    ADS  Google Scholar 

  5. Aerts, C. et al. Evidence for binarity and multiperiodicity in the β Cephei star β Crucis. Astron. Astrophys. 329, 137–146 (1998).

    ADS  Google Scholar 

  6. Briquet, M. & Aerts, C. A new version of the moment method, optimized for mode identification in multiperiodic stars. Astron. Astrophys. 398, 687–696 (2003).

    Article  ADS  Google Scholar 

  7. Aerts, C. Probing the interior physics of stars through asteroseismology. Rev. Mod. Phys. 93, 015001 (2021).

    Article  ADS  MathSciNet  Google Scholar 

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

  9. Aerts, C. et al. Asteroseismology of the β Cep star HD 129929. I. Observations, oscillation frequencies and stellar parameters. Astron. Astrophys. 415, 241–249 (2004).

    Article  ADS  Google Scholar 

  10. Handler, G. et al. Asteroseismology of the β Cephei star 12 (DD) Lacertae: photometric observations, pulsational frequency analysis and mode identification. Mon. Not. R. Astron. Soc. 365, 327–338 (2006).

    Article  ADS  Google Scholar 

  11. Briquet, M. et al. Multisite spectroscopic seismic study of the β Cep star V2052 Ophiuchi: inhibition of mixing by its magnetic field. Mon. Not. R. Astron. Soc. 427, 483–493 (2012).

    Article  ADS  Google Scholar 

  12. Handler, G. et al. Asteroseismology of hybrid pulsators made possible: simultaneous MOST space photometry and ground-based spectroscopy of γ Peg. Astrophys. J. Lett. 698, L56–L59 (2009).

    Article  ADS  Google Scholar 

  13. Stokes, G. G. On the composition and resolution of streams of polarized light from different sources. Trans. Camb. Philos. Soc. 9, 399–416 (1851).

    ADS  Google Scholar 

  14. Clarke, D. Stellar Polarimetry (Wiley, 2010).

    Google Scholar 

  15. Chandrasekhar, S. On the radiative equilibrium of a stellar atmosphere. X. Astrophys. J. 103, 351–370 (1946).

    Article  ADS  MathSciNet  Google Scholar 

  16. Odell, A. P. Possible polarization effects in the β Cephei stars. Publ. Astron. Soc. Pac. 91, 326–328 (1979).

    Article  ADS  Google Scholar 

  17. Stamford, P. A. & Watson, R. D. Polarization models for hot nonradial pulsators. Acta Astron. 30, 193–214 (1980).

    ADS  Google Scholar 

  18. Watson, R. D. Mode constraints on nonradial pulsations from polarization data. Astrophys. Space Sci. 92, 293–306 (1983).

    Article  ADS  Google Scholar 

  19. Schafgans, J. J. & Tinbergen, J. An attempt to detect non-radial pulsation in β Cephei. Astron. Astrophys. Suppl. 35, 279–280 (1979).

    ADS  Google Scholar 

  20. Clarke, D. Polarization measurements of β Cep stars. Astron. Astrophys. 161, 412–416 (1986).

    ADS  Google Scholar 

  21. Elias, N. M. II, Koch, R. H. & Pfeiffer, R. J. Polarimetric measures of selected variable stars. Astron. Astrophys. 489, 911–921 (2008).

    Article  ADS  Google Scholar 

  22. Odell, A. P. Nonradial pulsation detected through polarization variation in BW Vul. Astrophys. J. Lett. 246, L77–L80 (1981).

    Article  ADS  Google Scholar 

  23. Aerts, C. et al. Mode identification of the β Cephei star BW Vulpeculae. Astron. Astrophys. 301, 781–787 (1995).

    ADS  Google Scholar 

  24. Bailey, J. et al. A high-sensitivity polarimeter using a ferro-electric liquid crystal modulator. Mon. Not. R. Astron. Soc. 449, 3064–3073 (2015).

    Article  ADS  Google Scholar 

  25. Bailey, J., Cotton, D. V., Kedziora-Chudczer, L., De Horta, A. & Maybour, D. HIPPI-2: a versatile high-precision polarimeter. Publ. Astron. Soc. Aust. 37, e004 (2020).

    Article  ADS  Google Scholar 

  26. Cotton, D. V. et al. Polarization due to rotational distortion in the bright star Regulus. Nat. Astron. 1, 690–696 (2017).

    Article  ADS  Google Scholar 

  27. Bailey, J., Cotton, D. V., Howarth, I. D., Lewis, F. & Kedziora-Chudczer, L. The rotation of α Oph investigated using polarimetry. Mon. Not. R. Astron. Soc. 494, 2254–2267 (2020).

    Article  ADS  Google Scholar 

  28. Cotton, D. V. et al. The linear polarization of southern bright stars measured at the parts-per-million level. Mon. Not. R. Astron. Soc. 455, 1607–1628 (2016).

    Article  ADS  Google Scholar 

  29. Pedersen, M. G. et al. Diverse variability of O and B stars revealed from 2-minute cadence light curves in sectors 1 and 2 of the TESS mission: selection of an asteroseismic sample. Astrophys. J. Lett. 872, L9 (2019).

    Article  ADS  Google Scholar 

  30. Pigulski, A. & Pojmański, G. β Cephei stars in the ASAS-3 data. I. Long-term variations of periods and amplitudes. Astron. Astrophys. 477, 907–915 (2008).

    Article  ADS  Google Scholar 

  31. Buzasi, D. Asteroseismic Results from WIRE. In Astronomical Society of the Pacific Conference Series Vol. 259 (eds Aerts, C. et al.) 616–619 (ASP, 2002).

  32. Cuypers, J. et al. Multiperiodicity in the light variations of the β Cephei star β Crucis. Astron. Astrophys. 392, 599–603 (2002).

    Article  ADS  Google Scholar 

  33. Bailey, J. et al. Polarization of hot Jupiter systems: a likely detection of stellar activity and a possible detection of planetary polarization. Mon. Not. R. Astron. Soc. 502, 2331–2345 (2021).

    Article  ADS  Google Scholar 

  34. Dziembowski, W. Light and radial velocity variations in a nonradially oscillating star. Acta Astron. 27, 203–211 (1977).

    ADS  Google Scholar 

  35. Briquet, M. et al. Ground-based observations of the β Cephei CoRoT main target HD 180 642: abundance analysis and mode identification. Astron. Astrophys. 506, 269–280 (2009).

    Article  ADS  Google Scholar 

  36. Handler, G. Confirmation of simultaneous p and g mode excitation in HD 8801 and γ Peg from time-resolved multicolour photometry of six candidate ‘hybrid’ pulsators. Mon. Not. R. Astron. Soc. 398, 1339–1351 (2009).

    Article  ADS  Google Scholar 

  37. Zima, W. A new method for the spectroscopic identification of stellar non-radial pulsation modes. I. The method and numerical tests. Astron. Astrophys. 455, 227–234 (2006).

    Article  ADS  Google Scholar 

  38. Zima, W. FAMIAS User Manual. Commun. Asteroseismol. 155, 17–121 (2008).

    Article  ADS  Google Scholar 

  39. Hendriks, L. & Aerts, C. Deep learning applied to the asteroseismic modeling of stars with coherent oscillation modes. Publ. Astron. Soc. Pac. 131, 108001 (2019).

    Article  ADS  Google Scholar 

  40. Coffey, V. C. TESS: the little satellite with a big job. Opt. Photonics News 31, 22–29 (2020).

    Article  Google Scholar 

  41. Stankov, A. & Handler, G. Catalog of galactic β Cephei stars. Astrophys. J. Suppl. 158, 193–216 (2005).

    Article  ADS  Google Scholar 

  42. Bernardi, M. et al. Early-type galaxies in the Sloan Digital Sky Survey. IV. Colors and chemical evolution. Astrophys. J. 125, 1882–1896 (2003).

    Google Scholar 

  43. Bruntt, H., Kjeldsen, H., Buzasi, D. L. & Bedding, T. R. Evidence for granulation and oscillations in procyon from photometry with the WIRE satellite. Astrophys. J. 633, 440–446 (2005).

    Article  ADS  Google Scholar 

  44. Bailey, J., Cotton, D. V. & Kedziora-Chudczer, L. A high-precision polarimeter for small telescopes. Mon. Not. R. Astron. Soc. 465, 1601–1607 (2017).

    Article  ADS  Google Scholar 

  45. G. R, Ricker. et al. Transiting Exoplanet Survey Satellite (TESS). Proc. SPIE 9143, 914320 (2014).

    Article  Google Scholar 

  46. Jenkins, J. M. (ed.) Kepler Data Processing Handbook: KSCI-19081-002 (NASA Ames Research Center, 2017).

  47. Nielsen, M. B. et al. TESS asteroseismology of the known planet host star λ2 Fornacis. Astron. Astrophys. 641, A25 (2020).

    Article  Google Scholar 

  48. Fausnaugh, M. M. et al. TESS Data Release Notes: Sector 11, DR16 (STScI, 2019).

  49. Sturrock, P. A., Scargle, J. D., Walther, G. & Wheatland, M. S. Combined and comparative analysis of power spectra. Sol. Phys. 227, 137–153 (2005).

    Article  ADS  Google Scholar 

  50. Bailey, J., Cotton, D. V., Kedziora-Chudczer, L., De Horta, A. & Maybour, D. Polarized reflected light from the Spica binary system. Nat. Astron. 3, 636–641 (2019).

    Article  ADS  Google Scholar 

  51. Hubeny, I., Stefl, S. & Harmanec, P. How strong is the evidence of superionization and large mass outflows in B/Be stars? Bull. Astron. Inst. Czechoslov 36, 214–230 (1985).

    ADS  Google Scholar 

  52. Spurr, R. J. D. VLIDORT: a linearized pseudo-spherical vector discrete ordinate radiative transfer code for forward model and retrieval studies in multilayer multiple scattering media. J. Quant. Spectrosc. Radiat. Transf. 102, 316–342 (2006).

    Article  ADS  Google Scholar 

  53. Morel, T., Hubrig, S. & Briquet, M. Nitrogen enrichment, boron depletion and magnetic fields in slowly-rotating B-type dwarfs. Astron. Astrophys. 481, 453–463 (2008).

    Article  ADS  Google Scholar 

  54. Telting, J. H., Aerts, C. & Mathias, P. A period analysis of the optical line variability of β Cephei: evidence for multi-mode pulsation and rotational modulation. Astron. Astrophys. 322, 493–506 (1997).

    ADS  Google Scholar 

  55. Pedersen, M. G., Escorza, A., Pápics, P. I. & Aerts, C. Recipes for bolometric corrections and Gaia luminosities of B-type stars: application to an asteroseismic sample. Mon. Not. R. Astron. Soc. 495, 2738–2753 (2020).

    Article  ADS  Google Scholar 

  56. Moravveji, E., Aerts, C., Pápics, P. I., Triana, S. A. & Vandoren, B. Tight asteroseismic constraints on core overshooting and diffusive mixing in the slowly rotating pulsating B8.3V star KIC 10526294. Astron. Astrophys. 580, A27 (2015).

    Article  ADS  Google Scholar 

  57. Tkachenko, A. et al. The mass discrepancy in intermediate- and high-mass eclipsing binaries: the need for higher convective core masses. Astron. Astrophys. 637, A60 (2020).

    Article  Google Scholar 

  58. Hanbury Brown, R., Davis, J. & Allen, L. R. The angular diameters of 32 stars. Mon. Not. R. Astron. Soc. 167, 121–136 (1974).

    Article  ADS  Google Scholar 

  59. van Leeuwen, F. Validation of the new Hipparcos reduction. Astron. Astrophys. 474, 653–664 (2007).

    Article  ADS  Google Scholar 

  60. Perryman, M. A. C. et al. The Hipparcos Catalogue. Astron. Astrophys. 500, 501–504 (1997).

    ADS  Google Scholar 

  61. Hubrig, S. et al. Discovery of magnetic fields in the β Cephei star ξ1 CMa and in several slowly pulsating B stars. Mon. Not. R. Astron. Soc. 369, L61–L65 (2006).

    Article  ADS  Google Scholar 

  62. Hubrig, S. et al. New magnetic field measurements of β Cephei stars and slowly pulsating B stars. Astron. Nachr. 330, 317–329 (2009).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This research has made use of the SIMBAD database and VizieR catalogue access tool, operated at CDS (Strasbourg, France). This research has made use of NASA’s Astrophysics Data System. We thank the Director of Siding Spring Observatory, C. Lidman, for his support of the HIPPI-2 project on the AAT. We thank M. Filipovic for providing access to the Penrith Observatory. D.V.C. would also like to thank M. Filipovic and B. Carter for their support of his initially unfunded research on this project in the form of adjunct positions at WSU and USQ. We thank N. Cohen, G. Santucci and D. Maybour for assisting with the observations. We thank Wm. B. Weaver for useful comments on the manuscript. Funding for the construction of HIPPI-2 was provided by UNSW through the Science Faculty Research Grants Program (J.B.). Part of the research leading to these results has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme by means of a European Research Council AdG to C.A. (grant agreement No. 670519: MAMSIE). This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 (M.G.P.). D.L.B. acknowledges support from the TESS Guest Investigator Program through award NNH17ZDA001N-TESS.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the discussion and drafting of the final manuscript. D.V.C., D.L.B., C.A., J.B., D.S., M.G.P., P.D.C., L.K.-C. and A.D.H. contributed to observing proposals and/or scheduling. D.V.C., J.B., D.L.B., A.D.H., L.K.-C., F.L. and S.P.M. carried out polarimetric observations. In addition, the following authors made specific contributions to the work: D.V.C. initiated the work, contributed the polarimetric data processing and analysis, calculations of and comparisons with the analytical model, investigated binary effects, the interstellar polarization and co-ordinated the observations and analysis. D.L.B. carried out the frequency analysis and contributed analysis of asteroseismic data. C.A. analysed the spectroscopic data and carried out the associated mode identification, as well as the asteroseismic modelling. J.B. contributed the polarized radiative transfer modelling, investigated binary effects and aided with interpretation of the analytical model. S.B. computed theoretical stellar models and pulsation modes for the asteroseismic modelling and ran the neural network. M.G.P. computed bolometric corrections and the luminosity of β Cru, based on its spectroscopic properties. D.S. helped facilitate the initial collaboration and provided valuable context for the work.

Corresponding authors

Correspondence to Daniel V. Cotton or Derek L. Buzasi.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Astronomy thanks Dietrich Baade, Swetlana Hubrig and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary discussion, Figs. 1–5, Tables 1–7 and references.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cotton, D.V., Buzasi, D.L., Aerts, C. et al. Polarimetric detection of non-radial oscillation modes in the β Cephei star β Crucis. Nat Astron 6, 154–164 (2022). https://doi.org/10.1038/s41550-021-01531-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-021-01531-9

This article is cited by

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