During most of their life, stars fuse hydrogen into helium in their cores. The mixing of chemical elements in the radiative envelope of stars with a convective core is able to replenish the core with extra fuel. If effective, such deep mixing allows stars to live longer and change their evolutionary path. Yet localized observations to constrain internal mixing are absent so far. Gravity modes probe the deep stellar interior near the convective core and allow us to calibrate internal mixing processes. Here we provide core-to-surface mixing profiles inferred from observed dipole gravity modes in 26 rotating stars with masses between 3 and 10 solar masses. We find a wide range of internal mixing levels across the sample. Stellar models with stratified mixing profiles in the envelope reveal the best asteroseismic performance. Our results provide observational guidance for three-dimensional hydrodynamical simulations of transport processes in the deep interiors of stars.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
The iterative prewhitening code is freely available and documented at https://github.com/IvS-KULeuven/IvSPythonRepository. The stellar evolution code, MESA, is freely available and documented at http://mesa.sourceforge.net/. The stellar pulsation code, GYRE, is freely available and documented at https://bitbucket.org/rhdtownsend/gyre/wiki/Home.
Nomoto, K., Kobayashi, C. & Tominaga, N. Nucleosynthesis in stars and the chemical enrichment of galaxies. Annu. Rev. Astron. Astrophys. 51, 457–509 (2013).
Maeder, A. & Meynet, G. The evolution of rotating stars. Annu. Rev. Astron. Astrophys. 38, 143–190 (2000).
Salaris, M. & Cassisi, S. Chemical element transport in stellar evolution models. R. Soc. Open Sci. 4, 170192 (2017).
Georgy, C. et al. Populations of rotating stars. I. Models from 1.7 to 15 M⊙ at Z = 0.014, 0.006, and 0.002 with Ω/Ωcrit between 0 and 1. Astron. Astrophys. 553, A24 (2013).
Zahn, J. P. Circulation and turbulence in rotating stars. Astron. Astrophys. 265, 115–132 (1992).
Chaboyer, B., Demarque, P. & Pinsonneault, M. H. Stellar models with microscopic diffusion and rotational mixing. I. Application to the Sun. Astrophys. J. 441, 865 (1995).
Mathis, S. & Zahn, J. P. Transport and mixing in the radiation zones of rotating stars. II. Axisymmetric magnetic field. Astron. Astrophys. 440, 653–666 (2005).
Rogers, T. M., Lin, D. N. C., McElwaine, J. N. & Lau, H. H. B. Internal gravity waves in massive stars: angular momentum transport. Astrophys. J. 772, 21 (2013).
Brott, I. et al. Rotating massive main-sequence stars. I. Grids of evolutionary models and isochrones. Astron. Astrophys. 530, A115 (2011).
Deupree, R. G. Stellar evolution with arbitrary rotation laws. III. Convective core overshoot and angular momentum distribution. Astrophys. J. 499, 340–347 (1998).
Chaboyer, B. & Zahn, J. P. Effect of horizontal turbulent diffusion on transport by meridional circulation. Astron. Astrophys. 253, 173–177 (1992).
Zahn, J. P. Convective penetration in stellar interiors. Astron. Astrophys. 252, 179–188 (1991).
Freytag, B., Ludwig, H.-G. & Steffen, M. Hydrodynamical models of stellar convection. The role of overshoot in DA white dwarfs, A-type stars, and the Sun. Astron. Astrophys. 313, 497–516 (1996).
Pinsonneault, M. Mixing in stars. Annu. Rev. Astron. Astrophys. 35, 557–605 (1997).
Charbonnel, C. & Lagarde, N. Thermohaline instability and rotation-induced mixing. I. Low- and intermediate-mass solar metallicity stars up to the end of the AGB. Astron. Astrophys. 522, A10 (2010).
Dotter, A. et al. The Dartmouth stellar evolution database. Astrophys. J. Suppl. Ser. 178, 89–101 (2008).
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).
Martins, F. et al. Observational effects of magnetism in O stars: surface nitrogen abundances. Astron. Astrophys. 538, A29 (2012).
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).
Aerts, C., Christensen-Dalsgaard, J. & Kurtz, D. W. Asteroseismology (Springer, 2010).
Miglio, A., Montalbán, J., Noels, A. & Eggenberger, P. Probing the properties of convective cores through g modes: high-order g modes in SPB and γ Doradus stars. Mon. Not. R. Astron. Soc. 386, 1487–1502 (2008).
Bossini, D. et al. Uncertainties on near-core mixing in red-clump stars: effects on the period spacing and on the luminosity of the AGB bump. Mon. Not. R. Astron. Soc. 453, 2290–2301 (2015).
Koch, D. G. et al. Kepler mission design, realized photometric performance, and early science. Astrophys. J. Lett. 713, L79–L86 (2010).
Van Reeth, T., Tkachenko, A. & Aerts, C. Interior rotation of a sample of γ Doradus stars from ensemble modelling of their gravity-mode period spacings. Astron. Astrophys. 593, A120 (2016).
Bouabid, M. P. et al. Effects of the Coriolis force on high-order g modes in γ Doradus stars. Mon. Not. R. Astron. Soc 429, 2500–2514 (2013).
Aerts, C. et al. Forward asteroseismic modeling of stars with a convective core from gravity-mode oscillations: parameter estimation and stellar model selection. Astrophys. J. Suppl. Ser. 237, 15 (2018).
Herwig, F. The evolution of AGB stars with convective overshoot. Astron. Astrophys. 360, 952–968 (2000).
Rogers, T. M. & McElwaine, J. N. On the chemical mixing induced by internal gravity waves. Astrophys. J. Lett. 848, L1 (2017).
Mathis, S., Palacios, A. & Zahn, J. P. On shear-induced turbulence in rotating stars. Astron. Astrophys. 425, 243–247 (2004).
Moravveji, E., Townsend, R. H. D., Aerts, C. & Mathis, S. Sub-inertial gravity modes in the B8V star KIC 7760680 reveal moderate core overshooting and low vertical diffusive mixing. Astrophys. J. 823, 130 (2016).
Szewczuk, W. & Daszyńska-Daszkiewicz, J. K. I. C. 3240411-thehottestknownS. P. Bstarwiththeasymptoticg-modeperiodspacing Mon. Not. R. Astron. Soc. 478, 2243–2256 (2018).
De Cat, P. & Aerts, C. A study of bright southern slowly pulsating B stars. II. The intrinsic frequencies. Astron. Astrophys. 393, 965–981 (2002).
Szewczuk, W. & Daszyńska-Daszkiewicz, J. Domains of pulsational instability of low-frequency modes in rotating upper main sequence stars. Mon. Not. R. Astron. Soc. 469, 13–46 (2017).
Anders, F. et al. Photo-astrometric distances, extinctions, and astrophysical parameters for Gaia DR2 stars brighter than G = 18. Astron. Astrophys. 628, A94 (2019).
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).
Kippenhahn, R., Weigert, A. & Weiss, A. Stellar Structure and Evolution (Springer, 2012).
Li, C. et al. Extended main-sequence turnoffs in the double cluster h and χ Persei: the complex role of stellar rotation. Astrophys. J. 876, 65 (2019).
Johnston, C., Aerts, C., Pedersen, M. G. & Bastian, N. Isochrone-cloud fitting of the extended main-sequence turn-off of young clusters. Astron. Astrophys. 632, A74 (2019).
Wu, T. et al. Asteroseismic analyses of slowly pulsating B star KIC 8324482: ultraweak element mixing beyond the central convective core. Astrophys. J. 899, 38 (2020).
Wu, T. & Li, Y. High-precision asteroseismology in a slowly pulsating B star: HD 50230. Astrophys. J. 881, 86 (2019).
Balona, L. A., Baran, A. S., Daszyńska-Daszkiewicz, J. & De Cat, P. Analysis of Kepler B stars: rotational modulation and Maia variables. Mon. Not. R. Astron. Soc. 451, 1445–1459 (2015).
Pápics, P. I. et al. Signatures of internal rotation discovered in the Kepler data of five slowly pulsating B stars. Astron. Astrophys. 598, A74 (2017).
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).
Triana, S. A. et al. The internal rotation profile of the B-type star KIC 10526294 from frequency inversion of its dipole gravity modes. Astrophys. J. 810, 16 (2015).
Aerts, C. Probing the interior physics of stars through asteroseismology. Rev. Mod. Phys. 93, 015001 (2021).
Raskin, G. et al. HERMES: a high-resolution fibre-fed spectrograph for the Mercator telescope. Astron. Astrophys. 526, A69 (2011).
Pápics, P. I. et al. Two new SB2 binaries with main sequence B-type pulsators in the Kepler field. Astron. Astrophys. 553, A127 (2013).
Tkachenko, A. Grid search in stellar parameters: a software for spectrum analysis of single stars and binary systems. Astron. Astrophys. 581, A129 (2015).
Aerts, C., Molenberghs, G., Kenward, M. G. & Neiner, C. The surface nitrogen abundance of a massive star in relation to its oscillations, rotation, and magnetic field. Astrophys. J. 781, 88 (2014).
Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA): pulsating variable stars, rotation, convective boundaries, and energy conservation. Astrophys. J. Suppl. Ser. 243, 10 (2019).
Aerts, C., Mathis, S. & Rogers, T. M. Angular momentum transport in stellar interiors. Annu. Rev. Astron. Astrophys. 57, 35–78 (2019).
Seaton, M. J. Opacity Project data on CD for mean opacities and radiative accelerations. Mon. Not. R. Astron. Soc. 362, L1–L3 (2005).
Przybilla, N., Nieva, M. F., Irrgang, A. & Butler, K. in New Advances in Stellar Physics: From Microscopic to Macroscopic Processes EAS Publications Series 63 (eds Alecian, G. et al.) 13–23 (EDP Sciences, 2013).
Vink, J. S., de Koter, A. & Lamers, H. J. G. L. M. Mass-loss predictions for O and B stars as a function of metallicity. Astron. Astrophys. 369, 574–588 (2001).
Björklund, R., Sundqvist, J. O., Puls, J. & Najarro, F. New predictions for radiation-driven, steady-state mass-loss and wind-momentum from hot, massive stars II. A grid of O-type stars in the Galaxy and the Magellanic Clouds. Astron. Astrophys. 648, A36 (2021).
Böhm-Vitense, E. Über die wasserstoffkonvektionszone in sternen verschiedener effektivtemperaturen und leuchtkräfte. Mit 5 textabbildungen. Z. Astrophys 46, 108–143 (1958).
Ouazzani, R.-M. et al. A new asteroseismic diagnostic for internal rotation in γ Doradus stars. Mon. Not. R. Astron. Soc 465, 2294–2309 (2017).
Townsend, R. H. D., Goldstein, J. & Zweibel, E. G. Angular momentum transport by heat-driven g-modes in slowly pulsating B stars. Mon. Not. R. Astron. Soc. 475, 879–893 (2018).
Bellinger, E. P. et al. Fundamental parameters of main-sequence stars in an instant with machine learning. Astrophys. J. 830, 31 (2016).
Claeskens, G. & Hjort, N. L. Model Selection and Model Averaging Cambridge Series in Statistical and Probabilistic Mathematics Vol. 27 (Cambridge Univ. Press, 2008).
We thank the MESA and GYRE code developers for their efforts, public dissemination and training initiatives to make their software so accessible to the worldwide astrophysics community. We thank S. Ekström of the Geneva Observatory for providing mixing profiles from Georgy et al.4 in electronic format. We acknowledge the work of the teams behind the NASA Kepler and ESA Gaia space missions. This work is based on observations with the HERMES spectrograph at the Mercator Telescope, which is operated at La Palma, Spain, by the Flemish Community. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and NASA’s Astrophysics Data System. The research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 670519: MAMSIE), from the National Science Foundation (grant number NSF PHY-1748958), from the KU Leuven Research Council (grant number C16/18/005: PARADISE) and from the Research Foundation Flanders (FWO) by means of PhD Fellowships to M.M. and S. Gebruers under contract numbers 11F7120N and 11E5620N and a senior post-doctoral fellowship to D.M.B. under grant agreement number 1286521N. Funding for the Kepler Mission was provided by NASA’s Science Mission Directorate. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC); funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA).
The authors declare no competing interests.
Peer review information Nature Astronomy thanks Joyce Guzik, Ernst Paunzen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Pedersen, M.G., Aerts, C., Pápics, P.I. et al. Internal mixing of rotating stars inferred from dipole gravity modes. Nat Astron 5, 715–722 (2021). https://doi.org/10.1038/s41550-021-01351-x
The Astronomy and Astrophysics Review (2021)