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Article A wide –black-hole from radial-velocity measurements

https://doi.org/10.1038/s41586-019-1766-2 Jifeng Liu1,2,3*, Haotong Zhang1*, Andrew W. Howard4, Zhongrui Bai1, Youjun Lu1,2, Roberto Soria2,5, Stephen Justham1,2,6, Xiangdong Li7,8, Zheng Zheng9, Tinggui Wang10, Received: 1 March 2019 Krzysztof Belczynski11, Jorge Casares12,13, Wei Zhang1, Hailong Yuan1, Yiqiao Dong1, Yajuan Lei1, Accepted: 28 August 2019 Howard Isaacson14, Song Wang1, Yu Bai1, Yong Shao7,8, Qing Gao1, Yilun Wang1,2, Zexi Niu1,2, Kaiming Cui1,2, Chuanjie Zheng1,2, Xiaoyong Mu2, Lan Zhang1, Wei Wang3,15, Alexander Heger16, Published online: 27 November 2019 Zhaoxiang Qi1,17, Shilong Liao17, Mario Lattanzi18, Wei-Min Gu19, Junfeng Wang19, Jianfeng Wu19, Lijing Shao20, Rongfeng Shen21, Xiaofeng Wang22, Joel Bregman23, Rosanne Di Stefano24, Qingzhong Liu25, Zhanwen Han26, Tianmeng Zhang1, Huijuan Wang1, Juanjuan Ren1, Junbo Zhang1, Jujia Zhang26, Xiaoli Wang26, Antonio Cabrera-Lavers12,27, Romano Corradi12,27, Rafael Rebolo13,27, Yongheng Zhao1,2, Gang Zhao1,2, Yaoquan Chu10 & Xiangqun Cui28

All stellar-mass black holes have hitherto been identifed by X-rays emitted from gas that is accreting onto the from a companion star. These systems are all binaries with a black-hole mass that is less than 30 times that of the Sun1–4. Theory predicts, however, that X-ray-emitting systems form a minority of the total population of star–black-hole binaries5,6. When the black hole is not accreting gas, it can be found through radial-velocity measurements of the motion of the companion star. Here we report radial-velocity measurements taken over two years of the Galactic B-type star, LB-1. We fnd that the motion of the B star and an accompanying Hα emission line +11 require the presence of a dark companion with a mass of 68−13 solar masses, which can only be a black hole. The long of 78.9 days shows that this is a wide binary system. Gravitational-wave experiments have detected black holes of similar mass, but the formation of such massive ones in a high- environment would be extremely challenging within current theories.

A radial-velocity monitoring campaign using the Large Aperture lines: stellar absorption lines with apparent periodic motion, a broad Multi-Object Spectroscopic Telescope7 (LAMOST) to discover and Hα emission line moving in anti-phase with much smaller amplitude, study spectroscopic binaries has been running since 2016, and has and interstellar absorption lines that are time-independent (see Fig. 1). obtained 26 measurements each for about 3,000 targets brighter The overall spectral shape of LB-1 suggests a B-type star character- than 14 mag in the Kepler K2-0 field of the sky8. One of the B-type ized by prominent Balmer absorption lines without a significant Balmer towards the Galactic Anti-Centre, hereafter LB-1, located at coordinates jump. The metallicity, as measured from the Si ii/Mg ii lines, is about

(l, b) = (188.23526°, +02.05089°), where l is Galactic longitude and b is (1.2 ± 0.2)Z☉ (where the solar metallicity Z☉ = 0.017), consistent with Galactic latitude, with a V-band of about 11.5 mag, exhib- that expected for a young B-type star in the . TLUSTY11 ited periodic radial-velocity variation, along with a strong, broad Hα model fitting to the high-resolution Keck spectra leads to effective 9 emission line that is almost stationary. Subsequent GTC/OSIRIS and temperature Teff = 18,100 ± 820 K and logg = 3.43 ± 0.15, where g is the Keck/HIRES10 observations between 2017 December and 2018 April surface . (The Hα and Hβ lines were excluded from the fit because have confirmed the periodic variations and the prominent Hα emission of contamination from emission.) Such values of Teff and logg fit stellar line with higher spectral resolution. The spectra reveal three types of models12 around the main-sequence turn-off points with mass

1Key Laboratory of Optical , National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China. 2School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing, China. 3WHU-NAOC Joint Center for Astronomy, Wuhan University, Wuhan, China. 4Department of Astronomy, Caltech, Pasadena, CA, USA. 5Sydney Institute for Astronomy, The University of Sydney, Sydney, New South Wales, Australia. 6The Anton Pannekoek Institute for Astronomy, University of Amsterdam, Amsterdam, The Netherlands. 7School of Astronomy and Space Science, Nanjing University, Nanjing, China. 8Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing, China. 9Department of Physics and Astronomy, University of Utah, Salt Lake City, UT, USA. 10CAS Key Laboratory for Research in and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei, China. 11Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, Warsaw, Poland. 12Instituto de Astrofísica de Canarias, La Laguna, Spain. 13Departamento de Astrofísica, Universidad de La Laguna, Santa Cruz de Tenerife, Spain. 14Astronomy Department, University of California, Berkeley, CA, USA. 15School of Physics and Technology, Wuhan University, Wuhan, China. 16Monash Centre for Astrophysics, School of Physics and Astronomy, Monash University, Victoria, Australia. 17Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, China. 18INAF–Osservatorio Astrofisico di Torino, Pino Torinese, Italy. 19Department of Astronomy, Xiamen University, Xiamen, China. 20Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing, China. 21School of Physics and Astronomy, Yat-Sen University, Zhuhai, China. 22Physics Department and Tsinghua Center for Astrophysics, Tsinghua University, Beijing, China. 23Department of Astronomy, University of Michigan, Ann Arbor, MI, USA. 24Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA. 25Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China. 26Key Laboratory for the Structure and Evolution of Celestial Objects, Yunnan Observatories, Chinese Academy of Sciences, Kunming, China. 27GRANTECAN, Breña Baja, Spain. 28Nanjing Institute of Astronomical Optics and Technology, Chinese Academy of Sciences, Nanjing, China. *e-mail: [email protected]; [email protected]

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Fig. 1 | Optical spectra of LB-1. a, LAMOST spectrum (thin black trace; highest logg of the model grid but still lower than the typical value (logg > 5) for R ≈ 1,800) with stellar templates (A1, red; B3, green; offset for clarity) a B . The Balmer absorption lines from this model are much wider than overplotted. b, Keck/HIRES spectrum of the wavelength range boxed in the observed profiles. c, Phased line profiles from LAMOST (blue), GTC (red) a (black trace; R ≈ 60,000) with the best TLUSTY model (green trace; and Keck (green) observations of the Hα emission line (left), the He i −1 Teff = 18,100 K, logg = 3.43, Z = Z☉, vsini = 10 km s ) overplotted. The 90% absorption line at λ = 4,471 Å (‘He i λ4,471’) of the visible star (middle), and confidence level (CL) errors for the model are ΔTeff = 820 K and Δlogg = 0.15. interstellar Na i absorption lines (right). The dashed lines are plotted to guide Also overplotted is a comparison model with logg = 4.75 (blue), which is the the eye. The binary phase φ is for the period of P = 78.9 d.

+0.9 MB−=8.2 1.2 M⊙ (where M☉ is the ), radius RB = (9 ± 2)R☉ (where from a gaseous Keplerian disk, which can be around the B star, the black +13 R☉ is the solar radius) and age t =35M−7 yr. The best-fit model is a sub- hole, or the binary. However, the inferred gaseous disk cannot be giant B-type star about 0.2 Myr after the main-sequence turn-off point. around the B star, because the Hα emission line is not tracing the motion Its distance D and E(B − V), where B and V are respectively of the B star, as clearly shown in Fig. 1b. The line profile is distinctly B-band and V-band magnitude, can be derived simultaneously from different from a simple double-horned profile for a Keplerian disk fitting its wide-band spectral energy distribution (SED), resulting in viewed at high inclinations. It shows a ‘wine-bottle’ shape with multiple D = 4.23 ± 0.24 kpc and E(B − V) = 0.55 ± 0.03 mag (see Methods). These peaks in the line centre, which correspond to substantial non-coherent values are consistent with the 3D extinction map13 along LB-1’s direc- scattering components from a disk viewed at low inclination14,15. A cir- tion, so supporting this model. A subdwarf star with a similar tem- cumbinary disk would have an inner radius truncated at 1.7 times the perature is strongly ruled out by the narrow Balmer lines, as shown in binary separation16, and its corresponding projected velocity is 1 Fig. 1a, and also by the SED fitting. ≈0.75 times that of the visible star, that is, about 40 km s−1. The 1.7 The radial motion of the star, as measured from the stellar absorption emission line from such a circumbinary disk will be confined to within lines in 26 LAMOST, 21 GTC and 7 Keck observations obtained over two ±40 km s−1, yet the observed line is three times wider with wings extended years, can be best fitted with a period of P = 78.9 ± 0.3 d (see Methods). beyond ±300 km s−1. This supports the Hα emission line not coming Fitting a binary to the folded radial-velocity curve (see Fig. 2) from a circumbinary disk, but from a disk around the black hole. −1 yields a semi-amplitude KB = 52.8 ± 0.7 km s , an eccentricity The black-hole mass can be obtained directly, using the Hα emission −1 e = 0.03 ± 0.01, and a centre-of-mass velocity V0B = 28.7 ± 0.5 km s . For line to trace the motion of the black hole, and comparing it to the this binary with a nearly circular orbit, the mass function is motion of the visible star. The radial velocities of the Hα line, after 3 PKB/2π=GM(1.20±0.05) ⊙ (where G is the gravitational constant), folding with the period of 78.9 d, can be fitted with a sinusoid in anti- which is the absolute lower limit for the mass of the dark companion phase with the visible star. However, the line centre may contain con- to the B star. Given that MB is already known, the minimum mass of the tributions from circumbinary materials and spots that are +0.4 dark primary can be calculated to be 6.3−1.0 M⊙ for the edge-on geom- not symmetrically centred on the black hole, which would decrease etry with i = 90°. It must be a black hole, because a 6M☉ main-sequence the inferred black-hole motion and should be masked out. We experi- star is only about 4–6 times fainter than the B star, and the line features mented with different masking schemes, and found that unmasked would be easily detected from the Keck spectra. The black-hole mass line wings below 1/3 height can effectively avoid contamination from −1 (in M☉) will be 7.8/20/84/245 for lower inclinations at i = 60°/30°/15°/10°, the line centre, yielding a semi-amplitude Kα = 6.4 ± 0.8 km s and a −1 respectively. The binary separation is about 0.9–2.3 au for a black-hole centre-of-mass velocity V0α = 28.9 ± 0.6 km s (see Fig. 2a and Methods). mass of (6–250)M☉, making it a black-hole binary wider than any previ- Note that V0α is always consistent with V0B in different schemes, con- ously known Galactic black-hole binaries1,2. firming that the Hα emission is indeed associated with the B-star–black-

The prominent Hα emission line is too broad, with a full-width at hole binary. The black-hole mass MBH can then be estimated as −1 +11 half-maximum of 240 km s , to arise from an interloper M dwarf or MBH/MB = KB/Kα, resulting in MBH =68−13M⊙ (with 90% errors derived surrounding nebulae, nor can it be associated with a background AGN/ from the measurement uncertainties on KB, Kα and MB). Such a black- QSO, because this would have other prominent lines at non-zero red- hole mass corresponds to an inclination of i ≈ 15°–18°, fully consistent shift. Its complicated multi-peak profile (see Fig. 2) suggests an origin with the wine-bottle shape of the Hα emission line.

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−1 −1 2 Fig. 2 | Radial motions of the visible star and the dark primary. a, Folded Kα = 6.4 ± 0.8 km s and V0α = 28.9 ± 0.6 km s with a reduced χ of 0.8. The −1 radial-velocity (RV) curves and binary orbital fits for the star and the dark errors quoted here are for 90% CL. The grey line with V0 = 28.8 km s is plotted primary as probed by the Hα emission line. The observed data (filled circles) to guide the eye. b, Residuals for the binary orbital fits to the star (top) and are from LAMOST (blue), GTC (red) and Keck (green). The error bars are the to the Hα emission line (bottom). The error bars are calculated as above. quadratic sum of the wavelength calibration uncertainty and the measurement c, Representative Hα emission line profile from one Keck spectrum with high error. The best-fit binary orbit model for the star (purple) has parameters spectral resolution (R ≈ 60,000). The wine-bottle shape is caused by non- −1 −1 2 KB = 52.8 ± 0.7 km s , e = 0.03 ± 0.01, and V0B = 28.7 ± 0.5 km s with a reduced χ coherent scattering broadening for a disk viewed nearly pole-on. The red line of 2.0. The best-fit model for the Hα emission line (orange) has parameters represents an FWHM of about 240 km s−1.

The LIGO/Virgo experiments have revealed black holes with masses formed by dynamical capture of the B-type star by a black hole evolved of several tens of solar masses17,18, much higher than previously known from a low-metallicity star or by a , as such a capture 1,2 Galactic black holes . The discovery of a 70M☉ black hole in LB-1 would would result in an eccentric orbit that could not have been circular- confirm their existence in our . However, while massive stel- ized by now. In the case of a co-evolving binary, this indicates a very lar black holes are expected to predominantly form in low-metallicity small natal kick along with negligible mass loss when the black hole 19,20 (that is, <0.2Z☉) environments , LB-1 has a B-star companion with formed. Assuming an initial e = 0 and a symmetric mass ejection of ΔM solar metallicity. This would strongly challenge current stellar evolu- from the black-hole progenitor, the resultant orbit will have e = ΔM/ tion models, which only allow for the formation of black holes up to (MB + MBH). Given that e = 0.03 ± 0.01, ΔM must be less than 4% of the 21–23 25M☉ at solar metallicity . Formation of more-massive black holes remaining mass, thus helping to form a massive black hole. Stellar would require reducing mass loss rates substantially at solar metal- evolution theories predict fallback and direct black-hole licity, and even require overcoming the well-accepted pair-instability formation under certain conditions, and some observations might be pulsations that severely limit black-hole masses (see Methods). These in favour of their existence, but direct evidence is still lacking despite strongly expected limits may suggest that the black hole in LB-1 was observational efforts made in the past decade24,25. LB-1 may be direct not formed from the collapse of only one star. One alternative is that evidence for this process.

LB-1 was initially a triple system, in which the observed B star was the Our interpretation of an extraordinary 70M☉ dark mass in LB-1 will outermost, least-massive component, and the present black hole was be undermined if the companion mass is substantially lower than the formed by the initial inner binary. Potentially, a 70M☉ black hole could 8M☉ for the adopted B sub-giant model. To accommodate its high lumi- be formed after a ‘normal’ stellar-mass black hole merges into the core nosity, we need to place the B sub-giant at a distance about twice as +0.51 26 of a ≳ 60M☉ star during common-envelope evolution, followed by the large as the 2.14k−0.35 pc inferred from the Gaia DR2 astrometry . On accretion of the massive star onto its black-hole core (see Methods). one hand, this discrepancy could naturally be explained, because the An exciting possibility is that the dark mass still contains two black binary wobble of the optical component of LB-1 is not accounted for holes, orbiting each other in an inner binary to which the observed by the Gaia DR2 single-star astrometric solution. In particular, the Gaia star is a tertiary companion. This requires individual black-hole masses DR2 solution shows exceptionally large covariances, suggesting that approaching 35M☉, posing less of a challenge for their formation. In this it is unwise to simply interpret the astrometry as an accurate parallax case, this system would provide a laboratory to test the formation of measurement (see Methods). On the other hand, if LB-1 were indeed binary black holes in triple systems. at that close distance, with E(B − V) = 0.41 mag for the appropriate line This wide black-hole binary shows a surprisingly circular orbit that of sight at that distance13, its derived L would be as low as may shed light on its formation process. Circularization of such a wide about 1/6 of the luminosity for the B sub-giant (see Methods). Taking 4 binary with tidal torque would take at least a Hubble time, much longer LM∝/Tgeff , and retaining the same Teff and logg, this implies a stellar than its age (see Methods). This rules out the possibility that LB-1 was mass M about 1/6 of our adopted value, and consequently a black-hole

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Nature | Vol 575 | 28 November 2019 | 621 Article Methods used in this step, which is available from the home-page of the IACOB project (http://research.iac.es/proyecto/iacob/). The vsini is estimated Discovery and follow-up observations of LB-1 as ~10 km s−1, twice that of the spectral resolution (R ≈ 60,000) of Keck. LB-1 was among the targets in the LAMOST K2-C0 time-domain survey We performed a rotational and instrumental convolution of the (H.Z. et al., manuscript in preparation), which is designed to obtain original theoretical libraries to vsini = 10 km s−1 and full-width at half- time-domain spectra with the LAMOST low-resolution spectrograph maximum FWHM = 0.1 Å. Both the theoretical and observed spectra (R ≈ 1,800 over the wavelength range 3,690–9,100 Å) in a 20 square from the Keck telescope were normalized to a continuum level of unity. degree plate chosen from Kepler K2 Campaign 0. The plate was We used a Bayesian approach to estimate the param- 2 observed in 26 different nights from 2016 November 7 to 2018 March eters, in which each theoretical parameters is weighed by e−/χ 2, where 23. The spectra were then reduced with the LAMOST 2D pipeline31. χ2 is the goodness of fit of the model. We obtained a metallicity of One aim of the survey is to evaluate the binary mass function (1.18 ± 0.18)Z with Si ii λ4,131 and (1.17 ± 0.11)Z with Mg ii λ4,481. Finally, 3 ☉ ☉ 3 M BH 3 PK /2π=Gi2 sin once the complete radial-velocity curve can using the theoretical grids with solar abundances and the observed (+MMBBH) be derived from the time-domain spectral data. Here P is orbital period, hydrogen lines in the range of 3,750–4,150 Å, we obtained Teff as K is radial-velocity semi-amplitude, and i is viewing angle. Since the 18,104 ± 825 K and logg as 3.43 ± 0.15 dex. The errors were estimated mass of the brighter star in the binary can be estimated from its spec- using the standard deviations of the fitting results from the seven trum, the e and radial-velocity semi-amplitude K Keck spectra. These parameters prove that the optical counterpart is can be calculated directly from the radial-velocity curve, then the mass a B star. of the dimmer companion can be obtained immediately from the mass Assuming solar metallicity (Z = 0.017), we determined the mass, function given the viewing angle. About 200 out of 3,000 target stars radius and age of the B star. The evolutionary grid of Teff and logg for turn out to be spectroscopic binaries with periodic radial-velocity vari- stars with different initial masses were constructed on the basis of the ation. Among these, LB-1 exhibits periodic radial-velocity variations PARSEC isochrones12,35 (downloaded from http://stev.oapd.inaf.it/ with K = 52.8 km s−1, P = 78.9 d and e ≈ 0. cgi-bin/cmd_3.1). In Extended Data Fig. 1, stars located in the ellipse From the relative strength of the He i λ4,471 versus Mg ii λ4,481 lines, are considered as acceptable for the B star. We downloaded the we classify the star in LB-1 as a B3V star. Hot subdwarf B stars (sdBs) show sequences of isochrones at small steps of Δ(logt) = 0.0025, and col- spectra like B dwarfs but with much lower mass. sdBs have a shorter lected the points inside the ellipse as acceptable models. Finally, we Balmer series (n ≈ 12), and the He i λ4,387 line is much weaker than the find that at Z = 0.017, the physical solutions (with 90% uncertainty) 32 +0.9 He i λ4,471 line (ref. ). In LB-1, the Balmer series extends to more than consistent with our constraints are: MB−=8.2 1.2 M⊙ ; RB = (9 ± 2)R☉; +13 n ≈ 15, which is at the blue end of the LAMOST spectral range, and the tage−=35M7 yr. He i λ4,387 line is clearly stronger than the He i λ4,471 line. In addition, the LAMOST spectra show negligible N ii λ3,995 and very weak Si iii Distance and interstellar extinction λ4,552 lines, which means LB-1 can not be a supergiant (for example, a The SED of LB-1 was extracted from the UCAC4 catalogue, 2MASS and low-mass post-AGB star). The information from the LAMOST observa- the AllWISE data release. We used the acceptable PARSEC models to tions is listed in Extended Data Table 1. construct a grid of SEDs. By comparing the observed SEDs with the We carried out follow-up optical spectroscopic observations of LB-1 PARSEC ones, we fitted the distance and E(B − V) simultaneously. Con- with GTC/OSIRIS from 2017 December 2 to 2018 April 26, using the 0.4″ sidering that the and circumbinary materials can result slit with three gratings—R2500V, R2500R and R2500I. The spectral cov- in radiation in the near- and mid-infrared bands36, only the U, B and V erage for the OSIRIS data is 450–1,000 nm, with a resolution of ~3,750. magnitudes were used in the fitting. We present the fitting results in

The spectra were reduced in a standard way with IRAF. After the bias Extended Data Fig. 2. The excesses can be found from KS to W4 bands. subtraction and flat correction, the dispersion correction was carried The best fit yields the reddening value E(B − V) = 0.55 ± 0.03 mag and out based on the line lists given in the OSIRIS manual (http://www.gtc. the distance 4.23 ± 0.24 kpc (with 90% uncertainty). For such a distance, iac.es/instruments/osiris/). Raw spectra were then extracted with an the Pan-STARRS 3D dust map returns an extinction of E(B − V) ≈ 0.6, aperture size of ~6″, and a standard star taken at each night was used consistent with our fitting result (Extended Data Fig. 3). +0.51 to make the flux calibration. The wavelength calibration uncertainty is The distance derived above is larger than the 2.14−0.35 kpc value from about 0.02 Å (~1.2 km s−1). Information from the observations is listed the Gaia data release 2 astrometry24. This is possibly because the Gaia in Extended Data Table 1. DR2 solution has assumed a single star for LB-1, and has mistaken the In the period from 2017 December 9 to 2018 January 6, we observed binary motion itself as part of the parallax, making the parallax and LB-1 on seven individual nights using the Keck I telescope and the distance unreliable. In Gaia DR2, the covariances between position HIRES spectrometer. Exposure times range from 300 s to 600 s, and parameters (ra, dec) and parallax of LB-1 are much higher than other the signal-to-noise ratio (S/N) per pixel near 550 nm ranges from 80 to sources. The covariance dec_parallax_corr from the Gaia DR2 is −0.62, 120. Observations were collected using the standard California higher than the absolute value of dec_parallax_corr of 98% of sources Search (CPS) setup33, resulting in a spectral resolution of ~60,000. The between 10 mag and 13 mag (G band). The covariance of ra_parallax_corr C2 decker (0.87″ × 14.0″) was used to allow for removal of night sky line is 0.54, which is also higher than that of 96% of sources in the magnitude emission features and scattered moonlight. We list the information range. from the observations in Extended Data Table 1. Given the mode of operation of the Gaia astrometric instrument and the actual along scan single-CCD measurement error of 0.3 mas (ref. 37), Stellar properties from high-resolution spectra an astrometric error as small as 0.1 mas per visit can be anticipated

To derive the (Teff) and surface gravity (logg) of for the 11.5 magnitude of LB-1 (in each visit a star is measured on up to LB-1, we used the spectral libraries BSTAR200634, which are based on 9 different astrometric CCDs). Given its location, a total of about 80 the computer program TLUSTY11. The full set of BSTAR2006 models of such visits are predicted throughout the Gaia 5-yr nominal mission cover Teff from 15,000 K to 30,000 K with a step of 1,000 K, and logg lifetime (ending in September 2019). With these numbers in mind, from 1.75 to 4.75 with a step of 0.25 dex. These models include six initial there is actual hope that the 0.4 mas astrometric orbital motion can ; a micro-turbulence velocity of 2 km s−1 is adopted. be uncovered once the single visit data are properly reduced and/or The Keck spectra are used to estimate the stellar atmosphere param- made available in the future. eters. Using the lines Si ii λ3,856 and Si ii λ5,041, we measured the line The hot sdB scenario can also be rejected from the distance. The Gaia width broadened by the . The program iacob_broad was DR2 catalogue shows that38 hot subluminous stars have an around 5 mag. With the G-band magnitude of 11.918 mag While it is clear that the Hα emission line is associated with the black for LB-1, the distance estimation for an sdB would be less than 240 pc. hole, it is tricky to track the black-hole motion through the Hα line, This is seriously inconsistent with the Gaia DR2 distance and our fit- because the complex structures in the line centre may be contami- ting result, and is also inconsistent with the clear diffuse interstellar nated by components such as circumbinary materials, gravitationally bands (DiBs)39 in the spectra, which should be much shallower for an focused accretion streams, and hot spots in the accretion disk. These sdB at this distance. components are not symmetrically centred on the black hole, hence As a test, we calculated the radius and mass of the B star using their motion will not be in exact phase with that of the black-hole disk, the observational parameters, including the V-band magnitude and will act to decrease the black-hole motion if we include them in the (~11.51 mag), the reddening value, the distance, the effective tempera- calculation. Note that the line profiles can not be fitted with simple ture, and the surface gravity. With the bolometric correction40 analytic forms such as Gaussian or Lorentzian profiles, so we decided being about −1.6, the bolometric magnitude of the B star is instead to infer radial velocities using the barycentre of the line.

MB,bol = −4.93 mag, and the bolometric luminosity is calculated as First we calculate the barycentre of the whole Hα profile. The derived 0.4(MM⊙,bol−)B,bol LLB,bol =×⊙⊙,bol 10 ≈7, 000L ,bol . The solar bolometric radial velocities over two years can be folded with the orbital period, magnitude and luminosity are 4.74 mag and 3.828 × 1033 erg s−1, respec- resulting in a sinusoid with an amplitude of 1.7 ± 0.9 km s−1 in anti- L tively. The radius is calculated as B,bol , and the mass is phase with the B-star velocity. Such a line velocity, if it should repre- 2 RRB =≈4 8.7 ⊙ gRB 4πσT calculated as MB =≈7.5M . Both of them are consistent with the sent the black-hole motion, would suggest a mass ratio of 20–67 given G ⊙ GM 2 PARSEC model fitting results. The Kelvin–Helmholtz timescale tKH = RL MBH/MB = KB/Kα, hence a black-hole mass of (140–600)M☉. Second we is defined as the time required to radiate current gravitational binding mask out the core of the line profile and calculate the barycentre from energy at its current luminosity, and represents the timescale for a star the unmasked line wings. We start by measuring the barycentre from −1 in disequilibrium to adjust back to equilibrium. In our case, tKH is around velocity bands constrained between 1/2 FWHM up to 500 km s , on each 4 −1 2.7 × 10 yr. side of the line profile. This results in Kα = 4.4 ± 0.7 km s , as shown in However, if we use the Gaia distance (~2.14 kpc), which corresponds Extended Data Table 2. This demonstrates that the line centre is indeed to an extinction of E(B − V) = 0.41 from the Pan-STARRS 3D dust map, contaminated by components not centred on the black hole that will the bolometric luminosity can be estimated as LB,bol ≈ 1,300L☉,bol. The act to decrease the measured black-hole motion. radius and the mass would be RB ≈ 3.6R☉ and MB ≈ 1.3M☉, respectively. To explore the systematics of the derived black-hole motion, we Using these parameters, the Kelvin–Helmholtz timescale would be experiment with different mask limits with inner edges in the range 4 tKH ≈ 1.1 × 10 yr. corresponding to 2/3 to 1/5 heights of the Hα emission line, and inner Furthermore, if we use the Gaia distance (~2.14 kpc) and assume edges at 120/140/170/200 km s−1 from the barycentre. The result- an extinction of E(B − V) = 0.55 as derived from fitting the B ing amplitudes vary between 3.9 ± 0.8 km s−1 and 6.7 ± 1.0 km s−1, model to the SED, the bolometric luminosity can be estimated as as summarized in Extended Data Table 2. It is clear from the table

LB,bol ≈ 1,900L☉,bol. The radius and the mass would be RB ≈ 4.4R☉ and that the anti-phased Hα motion has larger amplitude as we move

MB ≈ 1.9M☉, respectively. The Kelvin–Helmholtz timescale is then esti- away from the central part of the line, but begins to saturate after 4 mated as tKH ≈ 1.4 × 10 yr. 1/3 height. This suggests that the unmasked line wings outside 1/3 We conclude that if we place the companion at the Gaia DR2 distance, height can largely avoid contamination from the line centre, and with E(B − V) ranging from 0.41 mag to 0.55 mag, we will get a star in dis- we decide to use the 1/3 height masking scheme to represent the −1 equilibrium, with the Kelvin–Helmholtz timescale of 11,000–14,000 yr. black-hole motion, that is, Kα = 6.4 ± 0.8 km s as shown in Extended Data Tables 2 and 3. Radial-velocity measurements If we had many more high-resolution Keck/HIRES spectra covering For the B star, we measured the by matching the model all binary phases, we would be able to reconstruct the morphology of templates using the cross-correlation method. For LAMOST data, we the accretion disk and other components, giving a detailed descrip- removed the Balmer lines and DiBs, and fitted the spectrum ranging tion of its asymmetric shape and size. This of course will give us a more from 4,000 to 5,200 Å. For GTC and Keck data, we removed DiBs and accurate determination of the black-hole mass, and we will pursue used the spectrum ranging from 4,000 to 6,000 Å. such a (costly) follow-up campaign in the coming years. Our current First, we Doppler-shifted the best theoretical spectra to a set of radial LAMOST/GTC/Keck observations, however, are already enough for a velocities. Second, we calculated the χ2 by comparing these model rough estimate of the black-hole mass. spectra with the observed ones, and used the radial velocity with mini- For LAMOST and GTC observations, there are multiple exposures mum χ2 as the best estimation. Also, we calculated the systematic shifts during a single night. We used the averaged value as the radial velocity between these exposures by comparing the absorption band of water at that day. The measurement error was estimated using the standard vapour in the range 6,850–6,940 Å. We first used the first exposure as deviation of multi-exposures during one night. For Keck observa- the reference spectra, and calculated the radial-velocity shift by cross- tions, we use the measurement error, which is about 1 km s−1. The correlating it with the other exposures. Then we used the exposure with system difference between days is calibrated by both the telluric the median value of shift as the new reference spectra, performed the emission (for LAMOST) or absorption (for GTC and Keck) lines, and calculation again, and obtained the final systematic shifts. also the diffuse interstellar absorption lines/bands at the Na i D lines, One key step before radial-velocity measurements is to determine 5,782 Å and 6,284 Å. The uncertainty for the radial velocity is the whether the Hα emission is from around the black hole or from a cir- quadratic sum of the wavelength calibration uncertainty and the cumbinary disk. For a circumbinary disk, the Keplerian velocity is measurement error.

GM(+BH MaB)/1.7 , where a is the binary separation and 1.7a is the 16 typical inner radius . The velocity of the visible star is GM(+BH MaBB)/ , Period and orbital parameters 41,42 where aB is the distance from the visible star to the barycentre Using the Lomb–Scargle method, we measured the period of LB-1 MBH αaB = . The projected velocity at the inner radius of the cir- with the radial-velocity curve from LAMOST, GTC and Keck obser- ( MMBB+ H ) 1 cumbinary disk would be ~≈0.75 times that of the visible star vations. The period is 78.9 ± 0.3 d (Extended Data Fig. 4). We fitted 1.7 (52.8 km s−1), that is, about 40 km s−1. However, the observed line is three the radial-velocity data of the B star (54 points) and the Hα line wing times wider with an FWHM of 240 km s−1. This means that the Hα emis- (54 points) simultaneously, using the equation sion line comes from a disk around the black hole rather than a circum- binary disk. VK=[cos(θω+)+ceωos()]+V0 (1) Article where K is the semi-amplitude of the radial-velocity curve, θ is the phase black-hole mass is now ~60M☉, from a star with an initial mass of 120M☉, angle, ω is the longitude of periastron, and V0 is the system velocity. which loses half of its mass in stellar winds before direct collapse. Stars

The best fit parameters (that is, eccentricity e, semi-amplitude KB and more massive than 120M☉ grow massive helium cores (MHe > 45M☉) and

Kα, velocity V0B and V0α) are listed in Extended Data Table 3. The best-fit are thus subject to pair-instability pulsation supernova mass losses. for the B-star motion has a reduced χ2 of 2.0, while the best-fit for the Precise estimates of this type of mass loss are model-dependent, but Hα motion (for the 1/3 height scheme) has a reduced χ2 of 0.8. To obtain most models agree50,51 that the black-hole remnants are less massive the uncertainty of one parameter, we fixed the other parameters at than ~50M☉. In our model, black holes formed after pair-instability 52 the best-fit values and re-did the fitting. Then, the uncertainty of that pulsations are assumed to be always less massive than ~40M☉ (ref. ). parameter was estimated with Δχ2 = 2.706 (at 90% confidence) and In our fourth model (black line), we not only reduce stellar winds by a Δχ2 = 6.635 (at 99% confidence). factor of 3, but also turn off pair-instability pulsation supernova mass

We compared the fittings of the Hα velocity using one sinusoid and losses. The maximum black-hole mass reaches ~80M☉, for a maximum one horizontal line. For the sinusoid fitting, there are two free param- initial of 200M☉: enough to explain the dark mass in LB-1 eters (that is, Kα and V0α); for the line fitting, there is one free parameter as a single stellar black hole.

(that is, V0α). Therefore, the degrees of freedom for the two fittings are 52 and 53, respectively. The χ2 for the two fittings are 109.49 and 219.24, Binary progenitor scenario. Second, let us suppose that the progeni- respectively. Using the F-test, we find the sinusoid fitting is statistically tor of LB-1 consisted of a massive (but not extraordinary) binary, with significantly better than the line fitting (P < 0.01%). two stars of initial mass ≳ 60M☉ each, and a much less massive third star The separation1 a can be calculated from Kepler’s third law (the B3 star we see today) orbiting around the O-star pair. The more 2 3  G(+MMPBBH)  a = for each pair of MBH and MB. The ranges of the sepa- massive of the two O stars evolves first, forming a black hole with a  4π2  ration a and the semi-major axis aB are shown in Extended Data Figs. 5 mass of ~(10–20)M☉ at solar metallicity. If the other O star has a mass ≳ and 6 respectively under the limitations of MB and MBH, which clearly 3.5 times the black-hole mass, the system is thought to evolve through show LB-1 is a wide binary. a phase19,53,54. Let us then assume that the black hole sinks towards the core of the O star before the common envelope is Black-hole formation ejected. What happens at this stage is an open question; one scenario is Individual stellar progenitor scenario. First, let us assume that the that the core is tidally disrupted and accreted by the in-spiralling black dark object in LB-1 is a single black hole formed from an individual hole, in a regime of radiatively inefficient (advective), hyper-critical star. Its mass depends on three major factors: (i) initial stellar mass; (ii) accretion55–57. If the radiative and mechanical feedback from the ac- wind mass loss during the star’s life; (iii) black-hole formation process creting black hole is not sufficient to destroy the star, or is collimated during the final core-collapse/supernova. The initial stellar mass sets along the direction, most of the O-star envelope may end up also an upper limit to the black-hole mass, while winds and collapse/explo- being accreted into the black-hole core58, in a kind of triggered direct sion processes are responsible for removing stellar mass and reducing collapse. The final result may be a single black hole with a mass >60M☉ the black-hole mass. All these aspects of stellar evolution are highly with the B3 star still orbiting around it. uncertain, which allows for a wide range of possibilities when it comes An alternative scenario is that the O-star plus black-hole binary sys- to black-hole mass calculations. tem is too wide to undergo a common envelope phase, or the mass ratio Guided by observations (or the lack thereof), we constructed a set is not high enough, and the system evolves instead in a slower spiral-in54. of models based on stellar evolution calculations43 to estimate the At the end of this phase, the O star will also collapse into a black hole, maximum black-hole mass at solar metallicity (Z = 0.017). We allow without a merger. The dark mass measured in LB-1 may be a binary stars to form with initial masses as high as 200M☉; at least one such black hole, with masses of ~35M☉ for each component. The advantage 44 star has already been discovered . Recent observations indicate that of this scenario is that the formation of two 35M☉ black holes from two stellar winds may be overestimated by as much as a factor of 10 for massive stars is less problematic than the formation of a 70M☉ black some massive stars45, compared with standard values46; hence, in our hole from a single star. In this scenario, too, the B3 optical counterpart calculation we reduce the theoretically predicted wind mass-loss rates is the small third component of the triple stellar system. by a factor of 2 to 3. At the end of a massive star’s life, we allow for direct black-hole formation with no supernova or associated mass Circularization timescale loss25. Such a mode of black-hole formation is supported by the low Tidal interactions in a binary tend to circularize its initially eccentric peculiar velocities observed in the most massive Galactic black holes orbit. To estimate the circularization timescale of a B-star–black-hole known to date47, and by the claimed observation of a luminous star binary, we use the MESA code59 to simulate the orbital evolution. The 26 disappearing without a supernova . Finally, we also eliminate mass B-star mass and the orbital period are initially set to be 8M☉ and 79 d, loss from pair-instability pulsations during the supernova explosion; respectively. During the evolution, we follow the evolution of the we note that, despite the large amount of theoretical work on pair- B star from the zero-age main-sequence phase to the age of 50 Myr instability mass loss and supernovae, so far there is no observational when the star slightly evolves off the main-sequence stage. Since such evidence to support this mechanism. a B star has a radiative envelope, we adopt the mechanism involv- We have incorporated all these options into the population synthe- ing dynamical tides with radiative damping60 to deal with the binary sis code StarTrack48,49 to estimate the maximum black-hole mass in orbital evolution. the . In Extended Data Fig. 7, we present our models that chal- We vary the initial orbital eccentricity in the range of 0.1–0.5 and the lenge the currently accepted paradigms, but that can possibly explain initial black-hole mass in the range (40–1,000)M☉ to test their influ- the black-hole mass in LB-1. Our first model (magenta line) shows the ence on orbital circularization. Our calculations show that the orbital standard prediction of black-hole mass as a function of initial stellar eccentricity of the binary is nearly unchanged and the corresponding 14 mass. Black holes form only with relatively low masses of ~(5–15)M☉, circularization timescale is always larger than 10 yr over the whole as a result of strong stellar winds that remove most of the stellar mass 50 Myr. It is argued that a significant enhancement of radiative damping before core-collapse. In our second model (blue line), we reduce stellar is required to match the observed eccentricity–period distribution in winds by a factor of 2. This reduction factor is applied to all types of late-type binaries61, so our calculated circularization timescale may be winds: from O stars, B supergiants, luminous blue variables, and Wolf– overestimated to some extent. Since the B star (with a radius less than 21 Rayet stars . As a result, the black-hole mass can reach ~30M☉. In our its current value of (9 ± 2)R☉) is well within its Roche lobe (with a size third model (red line), we reduce winds by a factor of 3. 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74. Narayan, R., Mahadevan, R., Grindlay, J. E., Popham, R. G. & Gammie, C. Advection- of Sciences. This work is partly based on observations made with the Gran Telescopio dominated accretion model of Sagittarius A*: evidence for a black hole at the Galactic Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the center. Astrophys. J. 492, 554–568 (1998). Instituto de Astrofísica de Canarias, in the island of La Palma. Part of the data was 75. Yuan, F. & Narayan, R. Hot accretion flows around black holes. Annu. Rev. Astron. obtained at the W.M. Keck Observatory, which is operated as a scientific partnership Astrophys. 52, 529–588 (2014). among the California Institute of Technology, the University of California and the National 76. Mahadevan, R. Scaling laws for advection-dominated flows: applications to low- Aeronautics and Space Administration. The Observatory was made possible by the luminosity galactic nuclei. Astrophys. J. 477, 585–601 (1997). generous financial support of the W.M. Keck Foundation. The scientific results reported in 77. Merloni, A., Heinz, S. & di Matteo, T. A fundamental plane of black hole activity. Mon. Not. this article are based in part on observations made by the Chandra X-ray Observatory R. Astron. Soc. 345, 1057–1076 (2003). (ObsID 20928). This research has made use of software provided by the Chandra X-ray 78. Russell, H. R. et al. Radiative efficiency, variability and on to massive Center (CXC) in the application packages CIAO. black holes: the transition from radio AGN to in brightest cluster galaxies. Mon. Not. R. Astron. Soc. 432, 530–553 (2013). Author contributions J.L. and H.Z. are equally responsible for supervising the discovery and follow-up observations. H.Z. and Z.H. proposed the LAMOST monitoring campaign, and H.Z.’s group reduced the LAMOST data with meticulous efforts. J.L. proposed the GTC/Keck/ Acknowledgements We thank D. Wang, J. Miller, E. Cackett, R. Narayan, H. Chen, Chandra observations, and his and H.Z.’s groups carried out subsequent data reduction and B. Zhang, C. Motch, M. Bessel, G. Da Costa, A. Bogomazov, S. Wang and many others for analysis. J.L. wrote the manuscript with help mainly from H.Z., Y. Lu, R.S., S.W., X.L., Y.S., T.W., helpful discussions. This work was supported by the National Science Foundation of Y.B., Z.B., W.Z., Q.G., Y.W., Z.Z., K.B. and J.C. W.W., A.H., W.M.G., J. Wang, J. Wu, L.S., R.S., X.W., China (NSFC) under grant numbers 11988101/11425313 (J.L.), 11773015/11333004/ J.B., R.D.S. and Q.L. also contributed to the physical interpretation and discussion. H.Y., Y.D., U1838201 (X.L.), 11603010 (Y.S.), 11690024 (Y. Lei), U1531118 (W.Z.), 11603035 (S.W.), Y. Lei, Z.N., K.C., C.Z., X.M., L.Z., T.Z., H.W., J.R., Junbo Zhang, Jujia Zhang and X.W. also 11733009 (Q.L.) and 11325313/11633002 (X.W.). It was also supported by the National Key contributed to data collection and reduction. A.W.H. and H.I. contributed to collecting and Research and Development Program of China (NKRDPC) under grant numbers reducing Keck data. A.C.L., R.C. and R.R. contributed to collecting and reducing GTC data. 2019YFA0405504 and 2016YFA0400804 (J.L.), 2016YFA0400803 (X.L.) and Z.Q., S.L. and M.L. contributed to utilization of Gaia data. Y.Z., G.Z., Y.C. and X.C. contributed to 2016YFA0400704 (Y. Lu). J.C. acknowledges support by the Spanish Ministry of Economy, the implementation of LAMOST. All contributed to the paper in various forms. Industry and Competitiveness (MINECO) under grant AYA2017-83216-P. K.B. acknowledges support from the Polish National Science Center (NCN) grants OPUS (2015/19/B/ST9/01099) and Maestro (2018/30/A/ST9/00050). This work was only made Competing interests The authors declare no competing interests. possible with LAMOST (Large Sky Area Multi-Object Fiber Spectroscopic Telescope), a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for Additional information the project was provided by the National Development and Reform Commission. LAMOST Correspondence and requests for materials should be addressed to J.L. or H.Z. is operated and managed by the National Astronomical Observatories, Chinese Academy Reprints and permissions information is available at http://www.nature.com/reprints. Extended Data Fig. 1 | Using isochrones from PARSEC models. The grid of of the Teff and logg of the B star; all points inside it are considered as acceptable logg and Teff was constructed using the PARSEC isochrones. The colour bar models for the B star. represents initial stellar mass. The black ellipse indicates the 90% uncertainty Article

Extended Data Fig. 2 | SED fitting results for the B star. a, E(B − V) versus indicates χ2 in a. d, Several examples of the SED fitting. The black squares are distance, both of which are determined from the SED fitting. The colour bar the data from the UCAC4, 2MASS and AllWISE catalogues. The diamonds with indicates χ2. b, Distance versus stellar mass, the latter being determined from different colours indicate magnitudes from different models. See Methods for the acceptable PARSEC models of the B star. The colour bar indicates χ2. details. c, E(B − V) versus distance. The colour bar indicates logg, while the colour bar Extended Data Fig. 3 | Variation of E(B − V) with distance in the direction of and distances from SED fitting for each acceptable model of the B star. The red LB-1. The black circles represent the extinction values corresponding to cross marks the extinction value from the 3D dust map at 4.23 kpc, while the red different distances from the 3D dust map. The green points are the extinction dashed line shows the Gaia distance of 2.14 kpc. Article

Extended Data Fig. 4 | Search for periodicities for LB-1 with the Lomb–Scargle method. The radial-velocity curve from LAMOST, GTC and Keck observations is being used here. The highest peak corresponds to the orbital period of ~78.9 d. Extended Data Fig. 5 | Separation a as a function of MB and MBH. Here a is white dashed lines in the contour plot outline a valid region of the separation of calculated from Kepler’s third law for each pair of MB (B-star mass) and MBH the binary system. It comes from the limitations on MB, (7–9.1)M☉, and on MBH,

(black-hole mass). The contours and colours both represent the values of a. The (55–79)M☉. See Methods for details. Article

Extended Data Fig. 6 | Semi-major axis of the orbit of the B-star aB as a both represent the values of aB. The white dashed lines in the contour plot function of MB and MBH. Here aB is calculated from Kepler’s third law for each outline a valid region for the semi-major axis of the B star. It comes from the pair of MB (B-star mass) and MBH (black-hole mass). The contours and colours limitations on MB, (7–9.1)M☉, and on MBH, (55–79)M☉. See Methods for details. Extended Data Fig. 7 | Black-hole mass versus initial mass in the zero age reduced to 30% (red curve) of the standard values. Note that to reach (ZAMS) for single stars. For standard wind mass-loss MBH = 80M☉ (black curve) it is necessary to switch off pair-instability pulsation prescriptions, only low-mass black holes are predicted: MBH < 15M☉ (pink curve). supernovae (PPSN) or pair-instability supernovae (PSN), which severely limit However, for reduced wind mass loss, much heavier black holes are formed: black-hole masses.

MBH = 30M☉ for winds reduced to 50% (blue curve) and MBH = 60M☉ for winds Article Extended Data Table 1 | Spectral observations of LB-1

See Methods section ‘Discovery and follow up observations of LB-1’, ‘Radial-velocity measurements’ for details. a The RVα corresponds to the 1/3 height method. Extended Data Table 2 | Hα measurement with different methods

See Methods section ‘Radial-velocity measurements’ for details. Article Extended Data Table 3 | Orbital parameters of LB-1

See Methods section ‘Period and orbital parameters’ for details. a The K0α and V0α correspond to the 1/3 height method.