replying to: M. Abdul-Masih et al. Nature (2020)


We reported1 a wide black-hole binary LB-1, discovered through a designated radial-velocity-monitoring campaign of a large sample of stars. Our estimate of the mass of the black hole of approximately 70M rests on the following arguments, some of which have been questioned in the accompanying Comment by Abdul-Masih et al.2 and by others3,4,5,6: (1) the Hα emission line comes from a disk around the black hole, seen moderately face-on as evidenced by its wine-bottle shape; (2) the barycentre motion of the Hα emission line wings traces the motion of the black hole and the absorption lines trace the motion of the donor star; and (3) the donor star has an effective temperature of Teff = 18,100 ± 820 K, the surface gravity is logg = 3.43 ± 0.15, and it has an evolutionary mass of \({8.2}_{-1.2}^{+0.9}\)M. Here we re-examine those arguments, in light of more recent spectroscopic observations and further analysis. We show that the data still favour a very high mass of 23M–65M (with a most probable donor mass range of 5M–8M); other lower-mass solutions are possible but less likely. Distinguishing definitively between solutions will require further Gaia astrometry data.

The key to the inference of an extraordinarily high black-hole mass in LB-1 is whether Hα and the other emission lines trace the motion of the unseen primary. Both Abdul-Masih et al.2 and El-Badry et al.3 demonstrate, correctly, that the Hα absorption line of the B-type star can induce an apparent barycentre motion of the Hα emission line wings that is similar to what we measured1. Their further inference of a static Hα emission line and its circumbinary origin, however, is unconvincing for several reasons.

First, it is too soon to claim a static Hα emission line on the basis of only one emission component and one absorption component, given the complexity of the profile. Hα may include contributions from: (1) emission, from the black-hole accretion disk, including the multi-scattering component that shapes the wine-bottle profile, as seen in nearly face-on disks; (2) emission, from the circumbinary disk; (3) absorption, from the atmosphere of the B-type star; (4) emission, from the stellar wind of the B-type star; and (5) emission, from hotspots or parts of the disk more strongly illuminated by the B-type star. In particular, irradiation from the B-type star causes alternating enhancement of the blue and red sides of the emission line, in phase with the orbital motion of the star. This leads to an apparent decrease of the observed barycentre motion of the emission line wings; that is, an effect opposite to that induced by the moving stellar absorption component. The likely presence of additional Hα emission from a moderate stellar wind7 should also partly offset the absorption wings from the stellar atmosphere.

Second, neither the width nor the shape of the Hα emission line supports a circumbinary origin. Emission lines that are primarily from a circumbinary disk usually exhibit double-horn shapes with sharp edges and little extended wings (as observed in cataclysmic variable stars and B[e] stars)8. The edge velocity corresponds to roughly the projected Keplerian velocity at the inner radius of the disk, and would range from around 40 km s−1 for a 70M black hole to around 80 km s−1 for a black hole of the same mass as the B-type star. The observed Hα emission line shows a full-width at half-maximum of 220 km s−1 with substantial wings extended to ±500 km s−1, clear evidence that its primary origin is not a circumbinary disk. Furthermore, the wine-bottle line profile is distinctly different from the double-horn shape of a circumbinary disk line, and can be attributed to multiple scatterings in the outer layers of the disk, as also pointed out by El-Badry et al.3, provided that the disk is seen at a low inclination.

Nonetheless, we accept that the interpretation of the Hα profile is more complex than originally envisaged. A Doppler tomography investigation in progress may resolve the individual components and determine their kinematics. We found that we can more easily measure the orbital motion of the black hole by monitoring the optically thin Paschen emission lines, which have a cleaner and simpler double-peaked profile than the optically thick Hα line. We will present the results of our phase-resolved spectroscopic study of the near-infrared double-peaked Paschen emission lines in Liu et al. (manuscript in preparation). The main preliminary result of that study is that the peak position in the Pa β line clearly shows orbital motion in anti-phase with the B-type star, re-confirming the black-hole-disk origin of the Pa β line. The velocity amplitude is small, unsurprisingly, and suggests a black-hole-to-B-star mass ratio of 4.6–8.1 (preliminary), consistent with the previous estimate using Hα emission line wings.

The second issue of contention is the mass of the donor star, which, combined with the kinematic mass ratio, gives us the mass of the primary. Abdul-Masih et al.2 obtained Teff = 13,500 ± 700 K, logg = 3.3 ± 0.3, and an evolutionary mass of \({4.7}_{-0.7}^{+0.8}\)M. Simón-Díaz et al.6 obtained Teff = 14,000 ± 700 K, logg = 3.5 ± 0.15, a spectroscopic mass of \({3.2}_{-1.9}^{+2.1}\)M (if the system is at the Gaia DR29 distance), and an evolutionary mass of \({5.2}_{-0.6}^{+0.3}\)M. The mismatch between the spectroscopic mass and the evolutionary mass arises from different distance values and suggests that the single-star solution in Gaia DR2 may underestimate the true distance of LB-1 from Earth. The difference between these and our results can be attributed to the different datasets used for spectral modelling, and the different stellar atmosphere and evolution models adopted by the various groups. For example, if the PARSEC stellar models are adopted, the Teff and logg parameters in Abdul-Masih et al.2 would instead correspond to \({5.6}_{-1.2}^{+1.3}\)M, as shown in figure 2 of Simón-Díaz et al.6. Even if the mass of the donor star is indeed approximately 5M instead of approximately 8M, the black-hole mass would be about 23–41M, for a black-hole-to-B-star mass ratio of 4.6–8.1.

There is another possible class for the donor—a stripped helium star in a short-lived evolutionary phase4. Irrgang et al.5 pointed out possible abundance patterns in the spectra for such a stripped star. From their best-fit values of Teff = 12,720 ± 260 K and logg =  3.00 ± 0.08, they derived a spectroscopic mass of 1.1 ± 0.5M. However, Abdul-Masih et al.2 argued that there is no observational evidence for such a stripped star. Another challenge to this scenario is the short lifetime of these stars, and thus the low probability of discovering one among the 3,000 stars in the LAMOST survey3.

Although it is difficult to determine the donor mass unambiguously from spectroscopy alone, Gaia astrometry can ultimately solve the problem. As we pointed out1, Gaia transit data can reach an astrometric error as small as 0.1 mas per visit, enough to resolve the binary wobble of LB-1. The full orbit and the parallax can be solved simultaneously by combining radial-velocity measurements and Gaia transit data. This will give the total mass of the binary by Kepler’s third law, and hence the donor mass and the black-hole mass from their mass ratio.