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

## Abstract

Over a dozen millisecond pulsars are ablating low-mass companions in close binary systems. In the original ‘black widow’, the eight-hour orbital period eclipsing pulsar PSR J1959+2048 (PSR B1957+20)1, high-energy emission originating from the pulsar2 is irradiating and may eventually destroy3 a low-mass companion. These systems are not only physical laboratories that reveal the interesting results of exposing a close companion star to the relativistic energy output of a pulsar, but are also believed to harbour some of the most massive neutron stars4, allowing for robust tests of the neutron star equation of state. Here we report observations of ZTF J1406+1222, a wide hierarchical triple hosting a 62-minute orbital period black widow candidate, the optical flux of which varies by a factor of more than ten. ZTF J1406+1222 pushes the boundaries of evolutionary models5, falling below the 80-minute minimum orbital period of hydrogen-rich systems. The wide tertiary companion is a rare low-metallicity cool subdwarf star, and the system has a Galactic halo orbit consistent with passing near the Galactic Centre, making it a probe of formation channels, neutron star kick physics6 and binary evolution.

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## Data availability

Reduced HiPERCAM photometric data and LRIS spectroscopic data are available at https://github.com/kburdge/ZTFJ1406-1222. The X-ray observations are in the public domain, and their observation IDs are supplied in the text. The ZTF data are also 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, and any data used to generate figures (MATLAB was used to generate most of the figures).

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## Acknowledgements

K.B.B. is a Pappalardo Postdoctoral Fellow in Physics at MIT and thanks the Pappalardo fellowship programme for supporting his research. T.R.M. was supported by a Leverhulme Research Fellowship and STFC grant ST/T000406/1. I.C. is a Sherman Fairchild Fellow at Caltech and thanks the Burke Institute at Caltech for supporting her research. M.W.C. acknowledges support from the National Science Foundation with grant number PHY-2010970. A.B.P. is a McGill Space Institute (MSI) Fellow and a Fonds de Recherche du Quebec – Nature et Technologies (FRQNT) postdoctoral fellow. 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 no. 340040 (HiPERCAM). V.S.D. and HiPERCAM operations are supported by STFC grant ST/V000853/1. E.C.K. acknowledges support from the G.R.E.A.T. research environment funded by Vetenskapsrådet, the Swedish Research Council, under project number 2016-06012, and support from The Wenner-Gren Foundations. J.F. and E.S.P. acknowledge support from the Gordon and Betty Moore Foundation through grant GBMF5076 to E.S.P. E.C.B. acknowledges support from the NSF AAG grant 1812779 and grant #2018-0908 from the Heising-Simons Foundation. K.-L.L. is supported by the Ministry of Science and Technology of the Republic of China (Taiwan) through grant 110-2636-M-006-013, and he is a Yushan (Young) Scholar of the Ministry of Education of the Republic of China (Taiwan). This work is 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 (ZTF) project. ZTF is supported by the National Science Foundation under grant no. 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 Caltech Optical Observatories, IPAC and University of Washington. 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 wish to 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

### Contributions

K.B.B. discovered the object, conducted the LCURVE and ICARUS light curve analysis, spectroscopic data reduction and analysis of Keck LRIS data, the reduction and analysis of the Swift UVOT and XRT data, reduction and analysis of the NuSTAR data, and was the primary author of the manuscript. T.R.M. conducted the HiPERCAM data reduction and assisted with the overall analysis and interpretation of the object. K.B.B. performed the analysis of the Fermi LAT data, with assistance from D.L.K., A.K.H.K. and K.L.L. W.A.M. and A.B.P. conducted the DSN observations of the system and A.B.P. performed the pulsation searches of these data and contributed the text describing the results and the implications. J.F. contributed text regarding the evolutionary history of the system. T.A.P., T.R.M., J.F., I.C. and E.S.P. all contributed to the interpretation of the object’s evolutionary history. All authors contributed comments and edits to the manuscript. A.D.J. submitted the NuSTAR proposal on the object and K.D. conducted the WASP observations of the object. V.S.D. conducted the HiPERCAM observations of the object and is principal investigator (PI) of HiPERCAM. P.R.-G. was PI of the HiPERCAM proposal that observed the object. S.R.K., T.A.P., M.J.G. and E.C.B. are, respectively, the PI, co-investigator, project scientist and survey scientist of ZTF.

### Corresponding author

Correspondence to Kevin B. Burdge.

## Ethics declarations

### Competing interests

The authors declare that they have no competing financial interests.

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## Extended data figures and tables

### Extended Data Fig. 1 CHIMERA and ZTF light curve of ZTF J1406+1222.

a, The CHIMERA light curve of ZTF J1406+1222. Similar to the HiPERCAM light curve illustrated in Fig. 1, the variability is much more pronounced at shorter wavelengths. This light curve was used to confirm the signal observed in the ZTF light curve, prompting further follow-up of the target. b, The ZTF light curve of ZTF J1406+1222. The object appears more variable in the shorter-wavelength passbands, but is brighter overall at longer wavelengths, primarily owing to the contribution of the sdK tertiary component, and thus the true fractional variability is underestimated in redder passbands. All the error bars illustrated represent 1σ flux uncertainties.

### Extended Data Fig. 2 Swift UVOT and corrected HiPERCAM light curve of ZTF J1406+1222.

The HiPERCAM and Swift UVOT light curves on a magnitude scale after correcting for the contribution of the sdK star. Only >1σ detections have been shown for the Swift data, as the object magnitude lies below the detection threshold for over half of the orbit. The prominent phase shifts in the peak flux indicate that the object transitions from a cooler to a hotter surface over the course of the flux maximum. Our LCURVE and ICARUS models were not able to account for this physical effect, so we arbitrarily shifted the other light curves to match the us-band maximum flux for the purpose of constructing simple models. To estimate the temperature of the dayside of the irradiated object, we fitted the spectral energy distribution from the apparent magnitudes at orbital phase 0.55, the peak of the Swift UVOT UVW2 light curve. One orbital cycle has been repeated for display purposes. All the error bars illustrated represent 1σ uncertainties in apparent magnitude.

### Extended Data Fig. 3 ICARUS model fit to light curve.

An example ICARUS toy model fitted to data between orbital phases 0.25 and 0.75 (ignoring data outside these phases), with the temperature of the dayside of the companion fixed to 10,462 K, the distance fixed to 1,140 pc, a fitted inclination of i ≈ 66° and an irradiated object with a radius of just 0.029R. The data from left to right illustrate the HiPERCAM us, gs, rs, is and zs filters, with the dashed black lines illustrating the best-fit model in that filter. The light curves have been artificially shifted to line up with the us-band maximum light, as the ICARUS model is unable to capture the strong colour-dependent phase shifts seen in the data. We did not perform an MCMC over these models, as we found that there were acceptable fits for a wide range of inclinations and other parameters given the limitations of using a simple direct-heating model. Because we chose to fit the flux at peak, but not at minimum (where the wind contributes considerably), most models fit the peak flux well, but the excess flux at minimum increases gradually to the redder passbands, suggesting that there may be a colour dependence associated with the flux contribution from the wind, although this is difficult to disentangle from the flux contribution of the sdK at minimum light.

### Extended Data Fig. 4 Model fit to peak of ZTF J1406+1222’s spectral energy distribution.

The spectral energy distribution at the orbital phase of the Swift UVOT maximum flux. The red squares illustrate the filter-averaged model, which convolves the model spectrum with the respective HiPERCAM and Swift filters. The solid line is the best-fit white dwarf model spectrum. We used a grid of white dwarf model atmospheres because they naturally cover the appropriate surface gravities and temperatures needed to model the irradiated face of the companion, which could be either a brown dwarf or a white dwarf. The Swift detection strongly constrains its dayside temperature, giving a best-fit value of Tday = 10,462 ± 150 K. All the error bars illustrated represent 1σ uncertainties in apparent magnitude.

### Extended Data Fig. 5 Red LRIS spectrum of ZTF J1406+1222.

The red LRIS spectrum of ZTF J1406+1222 illustrating the substantial contribution from the cool sdK component. The broad feature at 6,700–7,000 Å is a combination of titanium oxide (TiO) absorption bands commonly seen in late-type stars and strong calcium hydride (CaH) bands, which are more intense in low-metallicity sdM/sdK stars. We classify the object as a low-metallicity star by measuring the ratio of the TiO to CaH bands in a coadd of spectra at close to the minimum flux of the black widow component to avoid major contamination of the continuum. Additionally, we also estimated the metallicity by performing a fit of atmospheric models to the region of the spectrum around the TiO+CaH band, as illustrated in the inset.

### Extended Data Fig. 6 SDSS colour image of ZTF J1406+1222.

An SDSS Data Release 9 (DR9) colour image cut-out of the ZTF J1406+1222, revealing an asymmetric colour across the point spread function with the sdK on the left. The two red boxes indicate the J2016.0 positions of the two Gaia eDR3 sources. This image has been centred on the same coordinates as the Pan-STARRS1 cut-out shown in Extended Data Fig. 7.

### Extended Data Fig. 7 Pan-STARRS1 colour image of ZTF J1406+1222.

A Pan-STARRS1 colour image cut-out at the same centroid as the SDSS image in Extended Data Fig. 6. The Pan-STARRS1 point spread function exhibits the same colour asymmetry as seen in the SDSS image, and the centroid is closer to the Gaia source position than the SDSS image owing to the 74.5 mas yr−1 proper motion of the system.

### Extended Data Fig. 8 Astrometric characterization of ZTF J1406+1222.

a, The measured Gaia eDR3 J2016 position of the sdK is shown by the blue circles and the measured position of the variable black widow component is illustrated by the red diamonds. The magenta stars represent the projected J2021.5 position of the sdK, given the proper motion in its Gaia astrometric solution. The solid black line shows the position angle between the two Gaia source positions. The pink star indicates the position of the source in an SDSS u image obtained in J2003.4, and the black star indicates the source position in the SDSS z image at this epoch. Because the black widow component dominates in the u band, and the sdK in the z band, these positions should approximately reflect the positions of the two components in J2003.4, and the dashed arrows indicate that these sources are co-moving, having both translated their positions considerably since that epoch (by about an arcsecond). b, The black points indicate the measured centroid of the point spread function of the variable source with respect to a reference star on the HiPERCAM r-band images. This centroid moves back and forth between the two sources of luminosity as the black widow component brightens and fades, and gives a precise estimate of the position angle between the two sources when the data were obtained, at epoch J2021.5. The solid blue line is a linear fit to the data used to derive a slope to measure this position angle, the value of which is shown in the legend. The slope is consistent with the J2016 position angle and clearly inconsistent with only the sdK having moved since epoch J2016.0, demonstrating that the two sources must indeed be co-moving, and thus part of a hierarchical triple system.

### Extended Data Fig. 9 X-ray luminosity constraint of ZTF J1406+1222.

The 0.2–10 keV X-ray luminosity, LX, versus $$\dot{E}$$ for known black widow systems16,84 (detections shown as black circles and upper limits as red triangles). The red dashed line indicates the region to which we have constrained ZTF J1406+1222, on the basis of the X-ray luminosity upper limit derived from our Swift observation and the estimate of E&#x0307; based on the peak temperature of the irradiated face of the neutron star’s companion. Several known millisecond pulsars with a similar E&#x0307; are currently below our X-ray flux upper limit, and thus deeper observations may yield an X-ray detection of ZTF J1406+1222.

### Extended Data Fig. 10 Radial versus scale height orbital solution of ZTF J1406+1222 around the Galaxy.

A plot illustrating the Milky Way orbit of ZTF J1406+1222 over the course of 10 Gyr. The colours (green, orange and blue) indicate three different distances corresponding to our best distance estimate of 1,140 ± 200 pc and the 1σ upper and lower bounds of this distance estimate. In all cases, the object reaches a scale height (z) of more than 10 kpc above the Galactic disk and travels a great distance (R) away from the Galactic Centre in the radial direction, clearly indicating that it is a halo object. Notably, the green line, illustrating the orbital solution if ZTF J1406+1222 is at ~940 ± 200 pc, passes within 50 pc of the Galactic Centre.

### Extended Data Fig. 11 Cross-section of the orbital solution of ZTF J1406+1222 in the Galaxy.

Cross-section of the Milky Way orbit of ZTF J1406+1222 over the course of 10 Gyr. The colours (green, orange and blue) indicate three different distances corresponding to our best distance estimate of 1,140 ± 200 pc and the 1σ upper and lower bounds of this distance estimate.

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Burdge, K.B., Marsh, T.R., Fuller, J. et al. A 62-minute orbital period black widow binary in a wide hierarchical triple. Nature 605, 41–45 (2022). https://doi.org/10.1038/s41586-022-04551-1

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• DOI: https://doi.org/10.1038/s41586-022-04551-1