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.

# General relativistic orbital decay in a seven-minute-orbital-period eclipsing binary system

## Abstract

General relativity1 predicts that short-orbital-period binaries emit considerable amounts of gravitational radiation. The upcoming Laser Interferometer Space Antenna2 (LISA) is expected to detect tens of thousands of such systems3 but few have been identified4, of which only one5 is eclipsing—the double-white-dwarf binary SDSS J065133.338+284423.37, which has an orbital period of 12.75 minutes. Here we report the discovery of an eclipsing double-white-dwarf binary system, ZTF J153932.16+502738.8, with an orbital period of 6.91 minutes. This system has an orbit so compact that the entire binary could fit within the diameter of the planet Saturn. The system exhibits a deep eclipse, and a double-lined spectroscopic nature. We see rapid orbital decay, consistent with that expected from general relativity. ZTF J153932.16+502738.8 is a strong source of gravitational radiation close to the peak of LISA’s sensitivity, and we expect it to be detected within the first week of LISA observations, once LISA launches in approximately 2034.

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

## Access options

\$32.00

All prices are NET prices.

## Data availability

Upon request, K.B.B. will provide reduced photometric and spectroscopic data, and available ZTF data for the object. We have included the eclipse time data used to construct the orbital decay diagram in Fig. 2a, and Extended Data Figs. 2 and 3. The X-ray observations are already in the public domain, and their observation IDs have been supplied in the text. The proprietary period for the spectroscopic data will expire at the start of 2020, at which point this data will also be public and readily accessible.

## Code availability

Upon request, K.B.B. will provide the code (primarily in Python) used to analyse the observations and data such as the posterior distributions used to produce the figures in the text (MATLAB was used to generate most of the figures).

## References

1. Einstein, A. Näherungsweise Integration der Feldgleichungen der Gravitation. Sitz. König. Preußisch. Akad. Wissenschaften 688–696 (1916).

2. Amaro-Seoane, P. et al. Laser interferometer space antenna. Preprint at https://arxiv.org/abs/1702.00786 (2017).

3. Nissanke, S., Vallisneri, M., Nelemans, G. & Prince, T. A. Gravitational-wave emission from compact galactic binaries. Astrophys. J. 758, 131 (2012).

4. Kupfer, T. et al. LISA verification binaries with updated distances from Gaia data release 2. Mon. Not. R. Astron. Soc. 480, 302–309 (2018).

5. Brown, W. R. et al. A 12-minute orbital period detached white dwarf eclipsing binary. Astrophys. J. Lett. 737, 23 (2011).

6. Bellm, E. C. et al. The Zwicky Transient Facility: system overview, performance, and first results. Publ. Astron. Soc. Pacif. 131, 018002 (2019).

7. Graham, M. J. et al. The Zwicky Transient Facility: science objectives. Publ. Astron. Soc. Pacif. 131, 078001 (2019).

8. Coughlin, M. W. et al. The Kitt Peak Electron Multiplying CCD demonstrator. Mon. Not. R. Astron. Soc. 485, 1412–1419 (2019).

9. Harding, L. K. et al. CHIMERA: a wide-field, multi-colour, high-speed photometer at the prime focus of the Hale telescope. Mon. Not. R. Astron. Soc. 457, 3036–3049 (2016).

10. Taylor, J. H., Fowler, L. & McCulloch, P. Measurements of general relativistic effects in the binary pulsar PSR1913 + 16. Nature 277, 437 (1979).

11. Masci, F. J. et al. The IPAC image subtraction and discovery pipeline for the Intermediate Palomar Transient Factory. Publ. Astron. Soc. Pacif. 129, 014002 (2017).

12. Law, N. M. et al. The Palomar Transient Factory: system overview, performance, and first results. Publ. Astron. Soc. Pacif. 121, 1395 (2009).

13. McCarthy, J. K. et al. Blue channel of the Keck low-resolution imaging spectrometer. In Optical Astronomical Instrumentation Vol. 3355, 81–93 (International Society for Optics and Photonics, 1998).

14. Hermes, J. et al. Rapid orbital decay in the 12.75-minute binary white dwarf J0651 + 2844. Astrophys. J. Lett. 757, 21 (2012).

15. Fuller, J. & Lai, D. Dynamical tides in compact white dwarf binaries: helium core white dwarfs, tidal heating and observational signatures. Mon. Not. R. Astron. Soc. 430, 274–287 (2013).

16. Shah, S., Nelemans, G. & van der Sluys, M. Using electromagnetic observations to aid gravitational-wave parameter estimation of compact binaries observed with LISA-II. The effect of knowing the sky position. Astron. Astrophys. 553, A82 (2013).

17. Holberg, J. & Bergeron, P. Calibration of synthetic photometry using DA white dwarfs. Astron. J. 132, 1221 (2006).

18. Istrate, A. G. et al. Models of low-mass helium white dwarfs including gravitational settling, thermal and chemical diffusion, and rotational mixing. Astron. Astrophys. 595, A35 (2016).

19. Ramsay, G., Cropper, M., Wu, K., Mason, K. & Hakala, P. Detection of the optical counterpart of the proposed double degenerate polar RX J1914 + 24. Mon. Not. R. Astron. Soc. 311, 75–84 (2000).

20. Roelofs, G. H. et al. Spectroscopic evidence for a 5.4 minute orbital period in HM Cancri. Astrophys. J. Lett. 711, 138 (2010).

21. Marsh, T. & Steeghs, D. V407 Vul: a direct impact accretor. Mon. Not. R. Astron. Soc. 331, L7–L11 (2002).

22. Gehrels, N. et al. The Swift gamma-ray burst mission. Astrophys. J. 611, 1005 (2004).

23. Jansen, F. et al. XMM-Newton observatory—I. The spacecraft and operations. Astron. Astrophys. 365, L1–L6 (2001).

24. Wolf, W. M., Bildsten, L., Brooks, J. & Paxton, B. Hydrogen burning on accreting white dwarfs: stability, recurrent novae, and the post-nova supersoft phase. Astrophys. J. 777, 136 (2013).

25. Kaplan, D. L., Bildsten, L. & Steinfadt, J. D. Orbital evolution of compact white dwarf binaries. Astrophys. J. 758, 64 (2012).

26. Marsh, T. R., Nelemans, G. & Steeghs, D. Mass transfer between double white dwarfs. Mon. Not. R. Astron. Soc. 350, 113–128 (2004).

27. Paczynski, B. Evolution of single stars. IV. Helium stars. Acta Astron. 21, 1 (1971).

28. Shen, K. J., Kasen, D., Miles, B. J. & Townsley, D. M. Sub-Chandrasekhar-mass white dwarf detonations revisited. Astrophys. J. 854, 52 (2018).

29. Bildsten, L., Townsley, D. M., Deloye, C. J. & Nelemans, G. The thermal state of the accreting white dwarf in AM Canum Venaticorum binaries. Astrophys. J. 640, 466 (2006).

30. Althaus, L. G., Camisassa, M. E., Bertolami, M. M. M., Córsico, A. H. & García-Berro, E. White dwarf evolutionary sequences for low-metallicity progenitors: the impact of third dredge-up. Astron. Astrophys. 576, A9 (2015).

31. Graham, M. J., Drake, A. J., Djorgovski, S., Mahabal, A. A. & Donalek, C. Using conditional entropy to identify periodicity. Mon. Not. R. Astron. Soc. 434, 2629–2635 (2013).

32. Bellm, E. C. et al. The Zwicky Transient Facility: surveys and scheduler. Publ. Astron. Soc. Pacif. 131, 068003 (2019).

33. Maxted, P. ellc: A fast, flexible lightcurve model for detached eclipsing binary stars and transiting exoplanets. Astron. Astrophys. 591, A111 (2016).

34. Gianninas, A., Strickland, B., Kilic, M. & Bergeron, P. Limb-darkening coefficients for eclipsing white dwarfs. Astrophys. J. 766, 3 (2013).

35. Claret, A. & Bloemen, S. Gravity and limb-darkening coefficients for the Kepler, CoRoT, Spitzer, uvby, UBVRIJHK, and Sloan photometric systems. Astron. Astrophys. 529, A75 (2011).

36. Shklovskii, I. Possible causes of the secular increase in pulsar periods. Sov. Astron. 13, 562 (1970).

37. Lorimer, D. R. & Kramer, M. Handbook of Pulsar Astronomy (Cambridge Univ. Press, 2012).

38. Brown, A. et al. Gaia data release 2—summary of the contents and survey properties. Astron. Astrophys. 616, A1 (2018).

39. Bovy, J. galpy: a Python library for galactic dynamics. Astrophys. J. Suppl. Ser. 216, 29 (2015).

40. Levenhagen, R. S., Diaz, M. P., Coelho, P. R. T. & Hubeny, I. A grid of synthetic spectra for hot DA white dwarfs and its application in stellar population synthesis. Astrophys. J. Suppl. Ser. 231, 1 (2017).

41. Horne, K. & Schneider, D. P. Evidence for a high-mass white dwarf in nova V1500 Cygni 1975. Astrophys. J. 343, 888–901 (1989).

42. Green, G. M. et al. Galactic reddening in 3d from stellar photometry—an improved map. Mon. Not. R. Astron. Soc. 478, 651–666 (2018).

43. Korol, V. et al. Prospects for detection of detached double white dwarf binaries with Gaia, LSST and LISA. Mon. Not. R. Astron. Soc. 470, 1894–1910 (2017).

44. Fuller, J. & Lai, D. Dynamical tides in compact white dwarf binaries: tidal synchronization and dissipation. Mon. Not. R. Astron. Soc. 421, 426–445 (2012).

45. Benacquista, M. J. Tidal perturbations to the gravitational inspiral of J0651 + 2844. Astrophys. J. Lett. 740, 54 (2011).

46. Paxton, B. et al. Modules for experiments in stellar astrophysics (MESA): binaries, pulsations, and explosions. Astrophys. J. Suppl. Ser. 220, 15 (2015).

47. Kalberla, P. M. et al. The Leiden/Argentine/Bonn (LAB) survey of galactic HI—final data release of the combined LDS and IAR surveys with improved stray-radiation corrections. Astron. Astrophys. 440, 775–782 (2005).

48. Fuller, J. & Lai, D. Tidal novae in compact binary white dwarfs. Astrophys. J. Lett. 756, L17 (2012).

49. Brown, W. R., Kilic, M., Kenyon, S. J. & Gianninas, A. Most double degenerate low-mass white dwarf binaries merge. Astrophys. J. 824, 46 (2016).

50. Bovy, J. & Rix, H.-W. A direct dynamical measurement of the Milky Way’s disk surface density profile, disk scale length, and dark matter profile at 4 kpc < R < 9 kpc. Astrophys. J. 779, 115 (2013).

## Acknowledgements

K.B.B. thanks the National Aeronautics and Space Administration and the Heising Simons Foundation for supporting his research. This work was based on observations obtained with the Samuel Oschin Telescope 48-inch and the 60-inch Telescope at the Palomar Observatory as part of the Zwicky Transient Facility project. ZTF is supported by the National Science Foundation under grant number AST-1440341 and a collaboration including Caltech, IPAC, the Weizmann Institute for Science, the Oskar Klein Center at Stockholm University, the University of Maryland, the University of Washington (UW), Deutsches Elektronen-Synchrotron and Humboldt University, Los Alamos National Laboratories, the TANGO Consortium of Taiwan, the University of Wisconsin at Milwaukee, and the Lawrence Berkeley National Laboratories. Operations are conducted by Caltech Optical Observatories, IPAC, and the University of Washington. The KPED team thanks the National Science Foundation and the National Optical Astronomical Observatory for making the Kitt Peak 2.1-m telescope available. The KPED team thanks the National Science Foundation, the National Optical Astronomical Observatory and the Murty family for support in the building and operation of KPED. In addition, they thank the CHIMERA project for use of the Electron Multiplying CCD (EMCCD). 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. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. We wish to recognize and acknowledge the very important 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. This research benefited from interactions at the ZTF Theory Network Meeting that were funded by the Gordon and Betty Moore Foundation through grant GBMF5076 and support from the National Science Foundation through PHY-1748958. We thank J. Hoffman, the creator of cuvarbase. We thank T. Marsh, S. Phinney and V. Korol for discussions. We thank G. Hallinan and C. Fremling for helping to observe the object.

## Author information

Authors

### Contributions

K.B.B. discovered the object, conducted the lightcurve analysis and eclipse time analysis, and was the primary author of the manuscript. K.B.B. and M.W.C. conducted the spectroscopic analysis. K.B.B., M.W.C. and T.A.P. conducted the combined mass–radius analysis. K.B.B. and M.W.C. reduced the optical data. K.B.B., M.W.C. and D.L.K. reduced and analysed the X-ray observations. J.F. conducted the theoretical analysis, including that on tides, and developed the MESA evolutionary models. K.B.B., M.W.C., T.K., S.R.K., J.v.R. and T.A.P. all contributed to collecting data on the object. K.B.B., M.W.C., J.F., T.K., E.C.B., L.B., M.J.G., D.L.K., J.v.R., S.R.K. and T.A.P. contributed to the physical interpretation of the object. T.K., E.C.B., R.G.D., M.F., M.G., S.K., R.R.L., A.A.M., F.J.M., R.R., D.L.S., M.T.S., R.M.S., P.S. and R.W. contributed to the implementation of ZTF; M.J.G. is the project scientist, T.A.P. and G.H. are co-PIs, and S.R.K. is the PI of ZTF. R.G.D., D.A.D., M.F. and R.R. contributed to the implementation of KPED; M.W.C. is project scientist, and S.R.K. is PI of KPED. T.A.P. is K.B.B.’s PhD advisor.

### Corresponding author

Correspondence to Kevin B. Burdge.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

Peer review information Nature thanks Warren Brown and J. J. Hermes for their contribution to the peer review of this work.

## Extended data figures and tables

### Extended Data Fig. 1 Corner plots of lightcurve modelling.

The corner plots of the lightcurve fit to 12,999 g′ epochs taken with CHIMERA on 5, 6 and 7 July 2018. We note that the two limb-darkening coefficients, as well as the gravity darkening of the secondary (bottom three panels), were allowed to vary to ensure that assumptions regarding these coefficients were not strongly covariant with the other physical quantities of interest.

### Extended Data Fig. 2 Fits to archival PTF/iPTF data.

PTF least-squares fits of single harmonic sinusoids (smooth blue lines) to archival PTF/iPTF data used to determine the orbital decay rate. This archival data was extracted by using forced photometry on difference images. Because this is a least-squares fit of a sinusoid to the data, this timing technique uses the reflection effect in the system as its primary clock, rather than the mid-eclipse time. All error bars are 1σ. To determine the time of the epoch, we take the mean of all epochs used, and then calculate the phase of eclipse nearest to this mean time.

### Extended Data Fig. 3 Orbital decay measured with CHIMERA and KPED.

A quadratic fit (smooth red curve) to timing epochs exclusively originating from CHIMERA and KPED data (with the 68% confidence interval shown by the red dashed lines). This solution yielded a $$\dot{P}$$ consistent with the much more precise solution derived by including PTF/iPTF data. All error bars on the timing epochs are 1σ. The time on the x axis is measured with respect to the T0 reported in Table 1.

### Extended Data Fig. 4 Radial-velocity measurements of ZTFJ1539 + 5027.

A plot of the measured Doppler shifts versus orbital phase for the primary and secondary. The primary eclipse occurs at orbital phase 0. In the top panel, we plot measured Doppler shifts of the more massive primary, extracted from 12 phase bins of coadded spectra. The dashed blue line illustrates the fit of a sinusoid to this data (adjusted R2 = 0.7118). The bottom panel shows the Doppler shift measurements of the secondary, and also the best-fit sinusoid to this data (adjusted R2 = 0.9757). Because of the low SNR of the spectra, these fits have large uncertainties (especially in the case of the primary, with its shallow and broad absorption lines). This is reflected in the broad distribution of possible masses associated with the spectroscopic constraint illustrated in Fig. 4. All error bars are 68% confidence intervals.

### Extended Data Fig. 5 Binary evolution models.

Binary stellar evolution models for systems similar to ZTF J1539 + 5027. The top panel shows the mass transfer rate as a function of orbital period. Systems begin at large orbital period and move towards smaller periods owing to gravitational radiation, and in some cases they move back out owing to stable mass transfer. Except for high-mass donors with thin hydrogen envelopes $$\left({M}_{{\rm{do}}}=0.25\;{M}_{\odot },\;{M}_{{\rm{H}}}=6\times 1{0}^{-4}\;{M}_{\odot }\right.$$, mass transfer is expected to begin at orbital periods longer than 7 min. The bottom panel shows the corresponding accretion temperature from equation (11).

### Extended Data Fig. 6 X-ray and optical constraints on accretion in ZTFJ1539 + 5027.

These constraints on mass transfer result from the non-detection of any signatures of accretion in both the optical and X-ray bands. The upper limits are expressed in terms of the mass accretion rate contributing to the accretion luminosity of a hypothetical hotspot. The solid red curve illustrates the constraint imposed by the XMM EPIC-pn X-ray non-detection, which rules out statistically significant mass transfer contributing to a hotspot with temperatures greater than about 150,000 K, while the green dotted line illustrates a weaker upper limit imposed by the non-detection in a SWIFT XRT observation. We constructed the dashed blue curve, which represents the optical constraint, by requiring that any accretion luminosity originating from a hotspot should contribute <10% to the luminosity in the band ranging from 320 nm to 540 nm, as we know from the optical spectrum (Fig. 3) that this light is dominated by the approximately 50,000-K photosphere of the hot primary, and also we see no signature of a hotspot in the CHIMERA lightcurve (Fig. 1). We chose the threshold of <10% because, given the SNR of the spectra, we expect we should be able to detect optically thin emission with an amplitude at the 10% level. Other white dwarfs with such a hotspot (such as HM Cancri) exhibit such emission, particularly in lines associated with ionized helium.

## Rights and permissions

Reprints and Permissions

Burdge, K.B., Coughlin, M.W., Fuller, J. et al. General relativistic orbital decay in a seven-minute-orbital-period eclipsing binary system. Nature 571, 528–531 (2019). https://doi.org/10.1038/s41586-019-1403-0

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41586-019-1403-0

• ### A 62-minute orbital period black widow binary in a wide hierarchical triple

• Kevin B. Burdge
• Thomas R. Marsh
• Thomas A. Prince

Nature (2022)

• ### A highly magnetized and rapidly rotating white dwarf as small as the Moon

• Ilaria Caiazzo
• Kevin B. Burdge
• Maayane T. Soumagnac

Nature (2021)

• ### Gravitational-wave physics and astronomy in the 2020s and 2030s

• M. Bailes
• B. K. Berger
• S. Vitale

Nature Reviews Physics (2021)

• ### Merged white dwarfs and nucleosynthesis

• C. Simon Jeffery
• X. Zhang

Journal of Astrophysics and Astronomy (2020)

• ### The plunging pirouette of two low-mass stars

• J. J. Hermes

Nature Astronomy (2019)

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.