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A dense 0.1-solar-mass star in a 51-minute-orbital-period eclipsing binary


Of more than a thousand known cataclysmic variables (CVs), where a white dwarf is accreting from a hydrogen-rich star, only a dozen have orbital periods below 75 minutes1,2,3,4,5,6,7,8,9. One way to achieve these short periods requires the donor star to have undergone substantial nuclear evolution before interacting with the white dwarf10,11,12,13,14, and it is expected that these objects will transition to helium accretion. These transitional CVs have been proposed as progenitors of helium CVs13,14,15,16,17,18. However, no known transitional CV is expected to reach an orbital period short enough to account for most of the helium CV population, leaving the role of this evolutionary pathway unclear. Here we report observations of ZTF J1813+4251, a 51-minute-orbital-period, fully eclipsing binary system consisting of a star with a temperature comparable to that of the Sun but a density 100 times greater owing to its helium-rich composition, accreting onto a white dwarf. Phase-resolved spectra, multi-band light curves and the broadband spectral energy distribution allow us to obtain precise and robust constraints on the masses, radii and temperatures of both components. Evolutionary modelling shows that ZTF J1813+4251 is destined to become a helium CV binary, reaching an orbital period under 20 minutes, rendering ZTF J1813+4251 a previously missing link between helium CV binaries and hydrogen-rich CVs.

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Fig. 1: Light curve of ZTF J1813+4251.
Fig. 2: Optical spectroscopy of ZTF J1813+4251.
Fig. 3: Signatures of accretion in ZTF J1813+4251.
Fig. 4: Evolutionary tracks of ZTF J1813+4251 generated using MESA.

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Data availability

Reduced HiPERCAM photometric data, LRIS spectroscopic data and MESA tracks resulting from the models are available at The ZTF data used are all in the public domain. The proprietary period for the spectroscopic data will expire at the start of 2022, at which point the raw spectroscopic images will also be accessible via the Keck observatory archive.

Code availability

Upon request, the corresponding author will provide the code (primarily in Python) used to analyse the observations, create the MESA models and any data used to generate the figures (MATLAB was used to generate most of the figures). The LCURVE modelling code can be found at


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K.B.B. is a Pappalardo Postdoctoral Fellow in Physics at MIT and thanks the Pappalardo fellowship programme for supporting his research. The design and construction of HiPERCAM was funded by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) under ERC-2013-ADG grant agreement number 340040 (HiPERCAM). V.S.D. and HiPERCAM operations are supported by STFC grant ST/V000853/1. T.R.M. and B.T.G. acknowledge support from the UK’s Science and Technology Facilities Council (STFC), grant ST/T000406/1. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 101020057). For the purpose of open access, the authors have applied a creative commons attribution (CC BY) licence to any author accepted manuscript version arising. Based on observations made with the Gran Telescopio Canarias, installed at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, on the island of La Palma. Based on observations obtained with the Samuel Oschin Telescope 48-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, Deutsches Elektronen-Synchrotron and Humboldt University, Los Alamos National Laboratories, the TANGO Consortium of Taiwan, the University of Wisconsin at Milwaukee and Lawrence Berkeley National Laboratories. Operations are conducted by COO, IPAC and UW. 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 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.

Author information

Authors and Affiliations



K.B.B. discovered the object, conducted the LCURVE light-curve analysis, spectroscopic data reduction and analysis of Keck LRIS and ESI data, the reduction and analysis of the Swift UVOT and X-ray telescope data, and was the primary author of the manuscript. K.E.-B., T.R.M. and S.R. contributed to the interpretation of the object and the implications of its evolutionary history, and helped in responding to the referees reports. K.E.-B. performed the MESA modelling used to construct Fig. 4, and supplied the section and figure on this in the extended data. T.R.M. conducted the HiPERCAM data reduction. S.R. constructed independent models of the system as a sanity check of those used in this paper. W.R.B. performed the cross-correlation radial velocity measurement as a sanity check of that obtained by fitting Voigt profiles to the absorption lines. K.B.B., K.E.-B., T.R.M., S.R., W.R.B., I.C., D.C., V.S.D., J.F., B.T.G., M.J.G., E.K., S.R.K., S.P.L., P.M., P.R.-G., J.V.R. and R.A.S. contributed comments and edits to the paper. V.S.D. is the principal investigator of HiPERCAM. P.R.-G. was the principal investigator of the HiPERCAM proposal that observed the object. A.J.D., R.G.D., S.L.G., R.R.L., F.J.M., R.R. and R.M.S. are ZTF builders. S.R.K., T.A.P., M.J.G. and E.C.B. are the principal investigator, the co-investigator, the project scientist and the survey scientist of ZTF, respectively.

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Correspondence to Kevin B. Burdge.

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Nature thanks Taichi Kato, Youngdae Lee, Lorne Nelson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Fit of ZTF J1813+4251’s SED.

a) A fit to the donor star’s SED. The blue vertical lines represent the measured donor star SED as inferred from the apparent magnitude during the primary eclipse. Because of the high SNR of the HiPERCAM data, these uncertainties are very small, and we have added in a systematic five percent uncertainty associated with contribution from the accretion disk. The red diamonds represent the filtered averaged apparent magnitudes of the best-fit synthetic spectrum, and this synthetic spectrum is plotted in black. b) A fit to the accreting white dwarf SED. The vertical blue lines represent the SED of the white dwarf, as measured by modelling the amount of flux lost during the primary eclipse, when it is occulted by the donor. We added a five percent model error to this SED in the optical to account for contribution from accretion features which might cause the white dwarf to deviate from a standard hydrogen-rich DA model spectrum39,40. The surface gravity of the white dwarf in the model spectrum was fixed using the values derived from the light-curve analysis. The red diamonds illustrate the filter averaged apparent magnitudes from the synthetic spectrum, which is plotted in black. In both panels, we have omitted the HiPERCAM zs-band measurement, which exhibits an excess likely associated with the accretion disk. The model deviates from the observed spectrum around the hydrogen absorption lines due to emission lines from the accretion disk around the white dwarf.

Extended Data Fig. 2 Fit of ZTF J1813+4251’s optical spectrum.

a, A best-fit spectral model consisting of a low-mass main-sequence model and a hydrogen-rich white dwarf model to the observed spectrum of ZTF J1813+4251. The model, shown in red, has been convolved with the resolution of the spectrograph and rotationally broadened, and fit to the spectrum co-added in the rest frame of the donor, shown in black. b, A model spectrum fixed to the parameters derived from the SED analysis. We consider this model more reliable because it takes into account the Swift ultraviolet flux measurement, which strongly constrains the temperature of the white dwarf. The model, shown in blue, slightly underfits the blue part of the spectrum, plotted in black, which may be due to the presence of an accretion disk, or simply a systematic error introduced in the data reduction.

Extended Data Fig. 3 Fit of rotational broadening in ZTF J1813+4251’s ESI spectrum.

Rotationally broadened atmospheric model fits to the moderate resolution ESI spectra of ZTF J1813+4251. Owing to the low SNR of the spectra, we were unable to constrain the rotational broadening of the lines with a precision better than approximately 50 km s−1, but the measured values are consistent with the predicted value of 145 km s−1.

Extended Data Fig. 4 Idealized constraints of light-curve modelling in ZTF J1813+5251.

A panel illustrating an idealized version of the basic constraints we obtain by modelling the primary and secondary eclipses of ZTF J1813+5251, which depend only on Roche geometry and Kepler’s laws. Using the light curve, we are able to measure the orbital period, Pb, the in-eclipse flux levels as a fraction of the out-of-eclipse flux, F1 and F2, and the third and fourth contact phases of the eclipse, ϕ3 and ϕ4. By combining these five quantities we can determine from the light curve, with the donor radial velocity semi-amplitude measured from the spectra, K2, and our knowledge that the donor is Roche-lobe-filling, we are able to obtain a robust solution for the two component masses, M1 and M2, the radii of the two components, R1 and R2, the surface brightness ratio, J, the semi-major axis of the binary, a, and the orbital inclination, i. The idealized expressions tying these constraints to the observable quantities are listed in the right half of the figure. We would like to emphasize that these are idealized expressions, and caution readers that there are further important subtleties not discussed here (for example, in a Roche-filling system, the relevant radii in the above equations R1 and R2 are complicated to define because of the ellipsoidal deformation of the components, however, light-curve modelling codes such as LCURVE take these effects into account–this means for example that the R2 in expressions 3 and 4 is not exactly the same as the \({R}_{2}^{* }\) in expression 5, as in the former case, R2 is measured perpendicular to the line between the two stars, whereas in the latter case, \({R}_{2}^{* }\) is a volume-averaged radius).

Extended Data Fig. 5 Corner plots of posterior distribution from LCURVE model.

A corner plot of some of the quantities derived from our final model, illustrating clean convergence in the distributions for all quantities. We would like to note that the radii are volume-averaged radii, and that R2 was not directly sampled (instead, the two masses+inclination are sampled, and because the system is fully eclipsing R2 is determined uniquely by the mass ratio and inclination). We also sampled over the surface brightness ratio J, but did not include it in these corner plots because we have five different Js (one for each filter-we avoided using a common J because doing this correctly requires atmospheric corrections in each passband, and the solutions for the other free params are largely independent of J). To ensure that using a different J for each filter was not influencing the other free params, we modelled all 5 filters independently, and found that they all converged to parameters in agreement with the combined fit.

Extended Data Fig. 6 Detailed fits and residuals of eclipses and overall HiPERCAM light curve.

a, Our best-fit model of the primary eclipse, with the model shown as a solid black line, the binned data as red points, and the model without an eclipse as the dashed black line. In this figure, a linear polynomial component (of the functional form y = a × t, where t is the time from mid-eclipse (we applied separate corrections for the primary and secondary), has been subtracted out of both the model and the data for better visualization. We constructed the model by simultaneously fitting data around the primarily eclipse as well as data from the secondary eclipse (panel c). b, A best-fit of the eclipse-derived model constructed from the eclipse data shown in panels a and c to the full HiPERCAM light curve. While the model roughly reproduces the correct amplitude of ellipsoidal variations, it does not to fully capture the structure seen in the full light curve. c, Our best-fit model to the secondary eclipse, with a linear correction subtracted out of both the data and models. d, The residuals of the best fit of the eclipse-derived model to the full dataset shown in panel b. As is readily apparent, the strongest residuals occur out-of-eclipse, and are likely to arise because of a combination of effects from the accretion disk, and an O’Connell effect associated with the donor.

Extended Data Fig. 7 Kinematic orbit of ZTF J1813+4251 in the Milky Way.

A set of panels illustrating the orbit of ZTF J1813+4251 around the Milky Way. The system is consistent with residing in the Galactic thick disk, orbiting between 5 and 8 kpc from the Galactic Centre, within half a kpc of the Galactic disk in height.

Extended Data Fig. 8 MESA evolutionary models of ZTF J1813+4251.

MESA binary evolution models (Extended Data Table 1). Red, black and blue lines show models that overflow their Roche lobes after 94, 95 and 97 percent of the donor’s main-sequence lifetime. The dashed vertical line shows 51 minutes.

Extended Data Table 1 Model parameters of MESA models

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Burdge, K.B., El-Badry, K., Marsh, T.R. et al. A dense 0.1-solar-mass star in a 51-minute-orbital-period eclipsing binary. Nature 610, 467–471 (2022).

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