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A seven-Earth-radius helium-burning star inside a 20.5-min detached binary

Nature Astronomy volume 8, pages 491–503 (2024)Cite this article

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Abstract

Binary evolution theory predicts that the second common envelope ejection can produce low-mass (0.32–0.36 M⊙) subdwarf B (sdB) stars inside ultrashort-orbital-period binary systems, as their helium cores are ignited under nondegenerate conditions. With the orbital decay driven by gravitational-wave (GW) radiation, the minimum orbital periods of detached sdB binaries could be as short as ∼20 min. However, only four sdB binaries with orbital periods below an hour have been reported so far, and none of them has an orbital period approaching the above theoretical limit. Here we report the discovery of a 20.5-min-orbital-period ellipsoidal binary, TMTS J052610.43+593445.1, in which the visible star is being tidally deformed by an invisible carbon–oxygen white dwarf companion. The visible component is inferred to be an sdB star with a mass ∼0.33 M⊙ approaching the helium-ignition limit, although a He-core white dwarf cannot be completely ruled out. In particular, the radius of this low-mass sdB star is only 0.066 R⊙, about seven Earth radii. Such a system provides a key clue in mapping the binary evolution scheme from the second common envelope ejection to the formation of AM CVn stars having a helium-star donor. It may also serve as a crucial verification binary of space-borne GW observatories such as LISA and TianQin in the future.

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Fig. 1: Phase-folded RV curve and double-band light curves for J0526.
Fig. 2: Dynamical spectra of J0526 from GTC/OSIRIS and Keck/LRIS observations.
Fig. 3: Broadband SED of J0526.
Fig. 4: Kiel diagram for hot subdwarfs, low-mass WDs and J0526B.
Fig. 5: MRD for MS stars, WDs, hot subdwarfs and J0526B.

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Data availability

The ZTF g- and r-band photometry can be obtained from the NASA/IPAC Infrared Science Archive (https://irsa.ipac.caltech.edu). The optical and infrared photometric fluxes in the SED can be obtained from the VOSA online tool (http://svo2.cab.inta-csic.es/theory/vosa). The bolometric correction tables can be downloaded from MIST (http://waps.cfa.harvard.edu/MIST/model_grids.html). All light curves, observed and synthetic spectra, RV curve, photometric and synthetic fluxes in the SED, and the stellar/binary evolutionary models used for this work are available from our Zenodo page (https://www.zenodo.org/record/8074854 or https://doi.org/10.5281/zenodo.8074854). Source data are provided with this paper.

Code availability

The codes TLUSTY (v.207) and SYNSPEC (v.53) that were used for generating (non-LTE) model atmospheres and producing synthetic spectra are available at https://www.as.arizona.edu/∼hubeny, and the services for online spectral analyses (XTGRID) are provided by Astroserver (www.Astroserver.org). The Python package ellc (v.1.8.7), which was used for modelling light curves, can be obtained from https://pypi.org/project/ellc. The sensitivity curve of LISA can be computed using the codes from https://github.com/eXtremeGravityInstitute/LISA_Sensitivity. The software MESA (v.12778) used for stellar evolutionary calculations is available at http://mesastar.org, and the full inlists for evolutionary models used for this work are available from our Zenodo page (https://www.zenodo.org/record/8074854 or https://doi.org/10.5281/zenodo.8074854).

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Acknowledgements

We acknowledge the support of the staff of the 10.4 m GTC, Keck I 10 m telescope, LJT and Swift/UVOT. The work of X.W. is supported by the National Natural Science Foundation of China (NSFC; Grant Numbers 12033003, 12288102 and 11633002), the Ma Huateng Foundation, the New Cornerstone Science Foundation through the XPLORER PRIZE, China Manned-Spaced Project (CMS-CSST-2021-A12) and the Scholar Program of the Beijing Academy of Science and Technology (DZ:BS202002). J. Lin is supported by the Cyrus Chun Ying Tang Foundations. C.W. is supported by the NSFC (Grant Number 12003013) and the Yunnan Fundamental Research Projects (Grant Number 202301AU070039). C.W., Z.H., X.C., Jujia Zhang and Y.C. are supported by International Centre of Supernovae, Yunnan Key Laboratory (Grant Number 202302AN360001). P.N. acknowledges support from the Grant Agency of the Czech Republic (GAČR 22-34467S). The Astronomical Institute in Ondřejov is supported by project RVO:67985815. N.E.-R. acknowledges partial support from the Research Projects of National Relevance (PRIN) for 2017 as funded by the Italian Ministry of Education, University and Research (MIUR; Grant Number 20179ZF5KS, The new frontier of the Multi-Messenger Astrophysics: follow-up of electromagnetic transient counterparts of gravitational wave sources), from the Italian National Institute for Astrophysics (INAF) through PRIN-INAF 2022 (Shedding light on the nature of gap transients: from the observations to the models), from the Spanish Ministry of Science, Innovation and Universities (Grant Number PID2019-108709GB-I00) and from the European Regional Development Fund. I.S. is supported by funding from MIUR through PRIN 2017 (Grant Number 20179ZF5KS) and PRIN-INAF 2022 (Shedding light on the nature of gap transients: from the observations to the models) and acknowledges the support of the doctoral grant funded by Istituto Nazionale di Astrofisica through the University of Padova and MIUR. A.V.F.’s group at the University of California, Berkeley, has received financial assistance from the Christopher R. Redlich Fund, Alan Eustace (W.Z. is a Eustace Specialist in Astronomy), Frank and Kathleen Wood (T.G.B. is a Wood Specialist in Astronomy), Gary and Cynthia Bengier, Clark and Sharon Winslow, and Sanford Robertson (Y.Y. is a Bengier-Winslow-Robertson Postdoctoral Fellow), and many other donors. This research is based on observations made with the GTC, installed at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias on the island of La Palma. This research is based on data obtained with the instrument OSIRIS, which was built by a consortium led by the Instituto de Astrofísica de Canarias in collaboration with the Instituto de Astronomía of the Universidad Nacional Autónoma de Mexico. OSIRIS was funded by GRANTECAN and the National Plan of Astronomy and Astrophysics of the Spanish Government. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration (NASA). The observatory was made possible by the generous financial support of the W. M. Keck Foundation. We acknowledge the target-of-opportunity observations supported by the Swift Mission Operations Center. This research has used the services of www.Astroserver.org under references T4JRRH and Y75AKG and was based in part on observations obtained with the Samuel Oschin 48 inch Telescope at the Palomar Observatory as part of the ZTF project. ZTF is supported by the US National Science Foundation (NSF) under grant AST-1440341 and a collaboration including Caltech, Infrared Processing and Analysis Center (IPAC), the Weizmann Institute for Science, the Oskar Klein Center at Stockholm University, the University of Maryland, the University of Washington, Deutsches Elektronen-Synchrotron and Humboldt University, Los Alamos National Laboratory, the TANGO Consortium of Taiwan, the University of Wisconsin at Milwaukee and Lawrence Berkeley National Laboratory. Operations were conducted by COO, IPAC and the University of Wisconsin. This work has made use of data from the European Space Agency’s Gaia mission (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). Funding for DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes (the Max Planck Institute for Astronomy, Heidelberg, and the Max Planck Institute for Extraterrestrial Physics, Garching), Johns Hopkins University, Durham University, the University of Edinburgh, Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, NASA (under Grant Number NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate), NSF (Grant Number AST-1238877), the University of Maryland, Eotvos Lorand University, Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation. This publication makes use of data products from the WISE, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology as funded by NASA. This publication makes use of VOSA, developed under the Spanish Virtual Observatory (https://svo.cab.inta-csic.es) project funded by MCIN/AEI/10.13039/501100011033/ through Grant Number PID2020-112949GB-I00. VOSA was partially updated using funding from the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement Number 776403, EXOPLANETS-A).

Author information

Author notes

  1. These authors contributed equally: Jie Lin, Chengyuan Wu, Heran Xiong.

Authors and Affiliations

  1. Physics Department and Tsinghua Center for Astrophysics, Tsinghua University, Beijing, People’s Republic of China

    Jie Lin, Xiaofeng Wang, Shengyu Yan, Jun Mo, Gaobo Xi, Jialian Liu, Qiqi Xia, Danfeng Xiang, Gaici Li, Qichun Liu, Fangzhou Guo & Liyang Chen

  2. CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei, People’s Republic of China

    Jie Lin

  3. School of Astronomy and Space Sciences, University of Science and Technology of China, Hefei, People’s Republic of China

    Jie Lin

  4. Yunnan Observatories, Chinese Academy of Sciences, Kunming, People’s Republic of China

    Chengyuan Wu, Zhanwen Han, Jiangdan Li, Xuefei Chen, Jujia Zhang, Yongzhi Cai & Zhenwei Li

  5. Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming, People’s Republic of China

    Chengyuan Wu, Zhanwen Han, Jiangdan Li, Xuefei Chen, Jujia Zhang, Yongzhi Cai & Zhenwei Li

  6. International Centre of Supernovae, Yunnan Key Laboratory, Kunming, People’s Republic of China

    Chengyuan Wu, Zhanwen Han, Xuefei Chen, Jujia Zhang & Yongzhi Cai

  7. Research School of Astronomy & Astrophysics, Australian National University, Canberra, Australian Capital Territory, Australia

    Heran Xiong

  8. Beijing Planetarium, Beijing Academy of Sciences and Technology, Beijing, People’s Republic of China

    Xiaofeng Wang & Jincheng Guo

  9. Astronomical Institute of the Czech Academy of Sciences, Ondřejov, Czech Republic

    Péter Németh

  10. Astroserver.org, Malomsok, Hungary

    Péter Németh

  11. INAF-Osservatorio Astronomico di Padova, Padua, Italy

    Nancy Elias-Rosa & Irene Salmaso

  12. Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, Barcelona, Spain

    Nancy Elias-Rosa

  13. Dipartimento di Fisica e Astronomia ‘G. Galilei’, Università degli Studi di Padova, Padua, Italy

    Irene Salmaso

  14. Department of Astronomy, University of California, Berkeley, Berkeley, CA, USA

    Alexei V. Filippenko, Thomas G. Brink, Yi Yang & WeiKang Zheng

  15. School of Physical Science and Technology, Xinjiang University, Urumqi, People’s Republic of China

    Sufen Guo

  16. Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing, People’s Republic of China

    Jicheng Zhang

  17. Department of Astronomy, Beijing Normal University, Beijing, People’s Republic of China

    Jicheng Zhang

  18. National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China

    Wenxiong Li

  19. The School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel

    Wenxiong Li

Authors
  1. Jie Lin
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  2. Chengyuan Wu
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Contributions

J. Lin, C.W., H.X. and X.W. drafted the paper. Z.H. and A.V.F. edited the paper in detail. P.N., N.E.-R., X.C., Y.C. and S.G. also helped with the paper. X.W. is the principal investigator of TMTS and led the discussions. J. Lin discovered this source by analysing a large volume of data from TMTS observations and performed a detailed analysis of the spectroscopy, SED, orbital dynamic and light curves. C.W. computed the stellar and binary evolution models for low-mass sdB stars. H.X. provided some key ideas for these models. P.N. determined the atmospheric parameters from the GTC/OSIRIS spectra and computed RVs from both the GTC/OSIRIS and Keck I/LRIS spectra. J. Li and Q.X. helped with the analysis of SED and light curves. The GTC/OSIRIS spectra were provided and reduced by N.E.-R. and I.S. A.V.F., T.G.B., Y.Y. and W.Z. obtained and reduced the Keck I data. Jujia Zhang obtained and reduced the high-cadence observations of the LJT. S.G. computed the Galactic orbit. J. Liu reduced and analysed the observations made by Swift/UVOT. S.Y., Y.C., J.G., D.X. and G.L. assisted in the spectral observations and analysis. J. Lin, C.W., H.X., X.W., P.N., Z.H., J. Li, X.C., J.G., Q.X. and Z.L. contributed to beneficial discussions. X.W., Jicheng Zhang, J.M., G.X. and J. Lin contributed to the building of the TMTS and developing of its pipeline and database. G.X., J.M., J.G., Q.X., Q.L., F.G., L.C. and W.L. contributed to the operations and data products of TMTS.

Corresponding author

Correspondence to Xiaofeng Wang.

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Nature Astronomy thanks Kevin Burdge and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 TMTS light curve and Lomb-Scargle periodogram for J0526.

Upper panel: the TMTS L-band light curve over a 12 hr night on 18 December 2020. The magnitudes are presented as mean values ± 1σ. Middle panel: a 3000 s subset of the TMTS L-band light curve. The solid red line represents the best-fit sinusoidal model with a period of 10.3 min. Lower panel: the Lomb-Scargle periodogram (LSP) computed from the TMTS light curve. The vertical dashed line indicates the frequency corresponding to maximum power (\({{{{\rm{f}}}}}_{\max }\)). The purple dot-dashed line represents the confidence level of 0.1%, and the red arrow shows the frequency corresponding to the orbital period (that is, \({{{{\rm{f}}}}}_{\max }\)/2).

Extended Data Fig. 2 Relation between He abundance and effective temperature for hot subdwarfs.

All atmospheric parameters of hot subdwarfs are taken from reference25. The purple dashed line and green dotted-dash line represent the correlation for the He-rich sequence28 and the He-weak sequence29, respectively.

Extended Data Fig. 3 The characteristic strains of J0526 accompanied with dozens of verification/detectable binaries of GWs.

The characteristic strains were calculated from the component masses and distances provided from reference113. The blue dashed line and red dotted-dash line represent the detection sensitivity curves from LISA91 and TianQin92, respectively. The LISA sensitivity curve here includes the instrumental noise the foreground confusion noise, while the TianQin sensitivity curve includes only the instrumental noise. The error bars represent 68% credible intervals.

Extended Data Fig. 4 Binary evolution models for extremely-short-orbital-period sdB binaries.

Two models are differentiated owing to the different core masses of sdB stars. Mass transfers are expected to begin at around 14 and 17 min for Msd = 0.33 M⊙ and Msd = 0.36 M⊙, respectively. The red arrows denote the direction of evolution.

Supplementary information

Supplementary Information

Supplementary Figs. 1 and 2.

Source data

Source Data Fig. 4

Statistical source data.

Source Data Fig. 5

Statistical source data.

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Lin, J., Wu, C., Xiong, H. et al. A seven-Earth-radius helium-burning star inside a 20.5-min detached binary. Nat Astron 8, 491–503 (2024). https://doi.org/10.1038/s41550-023-02188-2

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