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.

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Fig. 1: Lightcurve of ZTF J1539 + 5027.
Fig. 2: Orbital decay and gravitational-wave strain of ZTF J1539 + 5027.
Fig. 3: Optical spectrum of ZTF J1539 + 5027.
Fig. 4: Constraints on component masses in ZTFJ1539 + 5027.

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).

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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

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.

Correspondence to Kevin B. Burdge.

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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.

Extended Data Table 1 Summary of observations

Source data

Source Data Fig. 2

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