Phase-dependent Study of Near-infrared Disk Emission Lines in LB-1

First, we determined the radial velocity amplitude of the secondary star, by fitting the position of the He I absorption lines. We obtain a projected velocity semiamplitude ${K}_{2}=52.62\,\pm 0.15$ km s⁻¹, confirming the results of L19 but with higher precision. The eccentricity is consistent with 0 ($e\lesssim 0.01$). The systemic velocity (center-of-mass velocity of the binary system) is ${V}_{\mathrm{sys}}=28.3\pm 0.1$ km s⁻¹.

The ephemeris of the system is

$$\begin{eqnarray}&&T(\phi =0)=58845.6(1){BJD}+78.9(3)\times N,\end{eqnarray} \tag{ 1 }$$

where $\phi =0$ corresponds to the secondary star in inferior conjunction with the primary object, and BJD is the Barycentric modified Julian Date.

An accurate measurement of the stellar motion enables us to subtract the stellar absorption component (properly shifted by the radial velocity offset corresponding to each phase) from the Paschen emission lines. For the absorption-line profile, we use the Kurucz atmosphere model (Kurucz 1979) with ${T}_{\mathrm{eff}}=13,500$ K and $\mathrm{log}[g/(\mathrm{cm}\ {{\rm{s}}}^{-2})]=3.5$. As we focus on analyzing the peaks of emission lines, our results are robust to different choices of absorption-line profiles corresponding to a plausible range of temperatures (13,000–18,000 K). In particular, we have performed tests using different absorption profiles, calculated in two ways: (i) with a Kurucz atmosphere model with ${T}_{\mathrm{eff}}=18,000$ K and $\mathrm{log}g=3.5;$ (ii) with the Potsdam Wolf-Rayet (PoWR) models (Sander et al. 2015; Gräfeneret al. 2002; Hamann & Gräfener 2003) with ${T}_{\mathrm{eff}}=13,500$ K, $\mathrm{log}g=2.8$, and extremely high mass-loss rate $\dot{M}={10}^{-7.5}{M}_{\odot }{\mathrm{yr}}^{-1}$. The peak positions of the emission components and thus our main results are found to be essentially unaffected.

The observed Paβ (12,821.6 Å) and Paγ (10,941.2 Å) profiles are double peaked at all orbital phases (Figure 1), and their stacks (Figure 2) are textbook examples of disk-like emission lines ("Smak profiles": Smak 1981; see also Horne & Marsh 1986). They are similar to the double-peaked Hα profiles observed from confirmed Galactic BHs in quiescence; for example, A0620−00 (Johnston et al. 1989; Orosz et al. 1994), GRS 1124−684 (Orosz et al. 1994), Swift J1357.2−0933 (Torres et al. 2015). The emission profiles of another Paschen line covered by our CARMENES spectra (Paδ at 10,052.6 Å) are also double peaked, but at a lower signal-to-noise ratio than for Paβ and Paγ, and we will not use them here.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The simple shape of the Paschen line profiles is in stark contrast with the complex structure and multiple peaks of the Hα line profiles in L19. We interpret this difference as an effect of optical depth: we argue that Hα is optically thick, and includes contributions from multiple scattered photons as observed in nearly pole-on disks (Hanuschik et al. 1996; Hummel & Hanuschik 1997). In contrast, Paβ and Paγ are optically thin, and their profiles are not modified by scattering. Thus, the peaks are formed mainly by the photons emitted in the outer disk, and their velocity is a proxy for the projected rotational velocity at the outer edge of the disk (Paczynski 1977; Smak 1981; Horne & Marsh 1986); the wings are instead emitted from disk annuli at smaller radii.

The extent of the wings provides a crucial test to determine whether the lines are emitted by a disk inside the Roche lobe of the primary object (hence, also tracing its orbital motion), or by a circumbinary disk (expected to be stationary). The wing velocity should not substantially exceed the projected rotational velocity of the inner edge of the disk (more exactly, the inner edge of the disk region in the right temperature range to emit a particular line). For a circumbinary disk, Artymowicz & Lubow (1994) computed an inner truncation radius ${R}_{{\rm{c}}}\approx 1.7a$, where a is the binary separation; slightly larger truncation radii, ${R}_{{\rm{c}}}\approx 2.0$–$2.3a$, were derived in subsequent works (Holman & Wiegert 1999; MacFadyen & Milosavljević 2008; Pichardo et al. 2008). In the LB-1 case, with a B-star radial velocity semiamplitude of 52.6 $\mathrm{km}\,{{\rm{s}}}^{-1}$, the predicted inner-edge velocity of a circumbinary disk ranges from $\approx 40$ km s⁻¹ for a mass ratio ${M}_{2}/{M}_{1}\approx 0.1$, to $\approx 70$ km s⁻¹ for a mass ratio ${M}_{2}/{M}_{1}\approx 1$ (Blundell et al. 2008).

Our new spectral results show that the wings of Paβ and Paγ extend to more than ± 200 km s⁻¹ in the stacked profiles (Figure 2); indeed, the FWHM is $\approx 200$ km s⁻¹ for both lines, already broader than possible for a circumbinary disk. Even in the individual spectra, it is clear that there is significant wing emission beyond ± 100 km s⁻¹ (Figure 1). Thus, we strongly confirm the argument presented by L19 (based on the width of the Hα line) in favor of a Roche-lobe disk.

The phase sequence of the Paβ and Paγ profiles (Figure 1) shows that the relative flux of the two peaks varies with orbital phase (a phenomenon usually referred to as "Violet/Red variations" or "V/R variations"). The red peak is higher than the blue peak during the half orbital phase in which the companion star is receding; the blue peak dominates when the star is approaching (Figure 3). Averaged over an orbital cycle, the emission from the two sides of the disks is consistent with being equal (Figure 2); the small residual asymmetry in the peak heights of our stacked profiles is simply due to nonuniform phase coverage.

Zoom In Zoom Out Reset image size

A direct emission contribution to the asymmetry from the surface of the secondary star is ruled out because the radial velocity amplitude of the star (52.6 $\mathrm{km}\,{{\rm{s}}}^{-1}$) is significantly smaller than the velocity of the line peaks (with half-separation ∼70 $\mathrm{km}\,{{\rm{s}}}^{-1}$). In addition, such a contribution would lead to line peaks always higher than those at phase $\phi \sim 0$ or 0.5, inconsistent with what is seen in the profiles (e.g., Figure 4). There is also no evidence of an "S-wave" (Honeycutt et al. 1987) moving across the two peaks, which is often seen in cataclysmic variables and is interpreted as the emission from the hot spot at the interface of an accretion stream and disk. We suggest that the simplest explanation for the peak asymmetry and its variation with phase is that the gas in the disk is illuminated or heated by the B star, which increases the line emissivity on the disk side close to the star. We leave a detailed modeling of the effect of irradiation on the line profiles to future work. Here, we focus instead on the positions of the line peaks and their behavior with orbital phase, regardless of the physical reasons for the alternate enhancement of the red and blue peaks.

Zoom In Zoom Out Reset image size

To measure the positions of the Paschen line peaks in a model-independent way, we used two methods. First, we fit each peak with a Gaussian. For this, we used a data interval of ±35 $\mathrm{km}\,{{\rm{s}}}^{-1}$ around the apparent position of each peak, at each orbital phase (Figure 3). We take the center of each Gaussian fit as the peak position. The second method we used to determine the peak position is a fit to the analytic Smak profile (Smak 1981; Horne & Marsh 1986; Johnston et al. 1989) extended with two additional free parameters (amplitude and radial dependence) to describe emissivity asymmetry and thus the peak asymmetry. For this method, we considered the full velocity range from −250 km s⁻¹ to +250 km s⁻¹ in the observed velocity.

Following Paczynski (1977), we then construct two quantities from the measured phase-dependent peak velocities. The first quantity, ${V}_{1{\rm{d}}}$, is the mean of the red and blue peak velocities (${V}_{\mathrm{red}}$ and ${V}_{\mathrm{blue}}$): ${V}_{1{\rm{d}}}\equiv ({V}_{\mathrm{red}}+{V}_{\mathrm{blue}})/2$. The second one, ${V}_{\mathrm{rot}}$, is the half-separation between the two peaks: ${V}_{\mathrm{rot}}\equiv ({V}_{\mathrm{red}}-{V}_{\mathrm{blue}})/2$. The quantity ${V}_{1{\rm{d}}}$ is a measure of the orbital motions of the disk around the center of mass of the system (a proxy for the primary orbital velocity), while ${V}_{\mathrm{rot}}$ characterizes the rotation of the outer edge of the disk around the primary. We calculated ${V}_{1{\rm{d}}}$ and ${V}_{\mathrm{rot}}$ for Paβ and Paγ, with two sets of values for each line (corresponding to the two fitting methods described above).

We find (Figure 5) that for both Paβ and Paγ, regardless of fitting method, ${V}_{1{\rm{d}}}$ has a low-amplitude (∼10 km s⁻¹) but clear sinusoidal behavior, in antiphase with the B star, consistent with our interpretation as the orbital motion of the primary object (which must then be substantially more massive than the secondary star). The quantity ${V}_{\mathrm{rot}}$ shows periodic modulations with half of the orbital period; this is consistent with the slightly noncircular shape of the gas streamlines (which determine the outer disk boundary) in the Roche lobe potential (Paczynski 1977), as discussed in Section 4.

Zoom In Zoom Out Reset image size

In the model of Paczynski (1977), the outer edge of the BH accretion disk is determined by the outermost closed streamline, under the influence of the binary potential in the rotating frame. The shape of the outer edge of the disk slightly deviates from a circle, and the amount of ellipticity depends on the binary mass ratio. This effect leads to a small difference between the amplitude of the fitted orbital motion ${V}_{1{\rm{d}}}$ and the true orbital motion of the primary; it also introduces phase-dependent variations in the peak separation ${V}_{\mathrm{rot}}$. To derive the mass ratio in the framework of this model, we fit ${V}_{1{\rm{d}}}$ with a sinusoidal curve, $\propto \ \sin (2\pi \phi$), and ${V}_{\mathrm{rot}}$ with linear combinations of $\sin (4\pi \phi$) and $\cos (4\pi \phi$), where $\phi \in [0,1]$ is the binary phase. We applied this model first to Paβ and then to Paγ, for both sets of peak values (from Gaussian and extended Smak fits).

For Paβ, using the extended Smak fitting function, the mean peak position ${V}_{1{\rm{d}}}$ has a semiamplitude ${K}_{1{\rm{d}}}=12.7\,\pm 0.3$ $\mathrm{km}\,{{\rm{s}}}^{-1}$, with the baseline fixed to the systemic velocity of 28.3 $\mathrm{km}\,{{\rm{s}}}^{-1}$ determined from the B-star radial velocity. In the initial run of our model, the phase of the sinusoidal curve for the disk motion was left free: we obtained a best-fitting phase value of 0.006 ± 0.004, that is almost perfectly in antiphase with the motion of the companion star. Based on this close match, we then fixed the phase angle to 0 for our subsequent modeling, to reduce the number of free parameters. The mean peak half-separation is $\langle {V}_{\mathrm{rot}}\rangle =74.4\pm 0.2$ $\mathrm{km}\,{{\rm{s}}}^{-1}$. The value of ${K}_{1{\rm{d}}}/\langle {V}_{\mathrm{rot}}\rangle \approx 0.171$ corresponds to a mass ratio ${M}_{1}/{M}_{2}\,=4.0\pm 0.1$ (Paczynski 1977, Table 2). The same model also provides a correction factor to convert ${K}_{1{\rm{d}}}$ to the semiamplitude ${K}_{1}$ of the primary radial velocity: we infer ${K}_{1}=11.2\,\pm 0.3$ $\mathrm{km}\,{{\rm{s}}}^{-1}$. If we compare this value with the radial velocity semiamplitude ${K}_{2}=52.6\pm 0.2$ $\mathrm{km}\,{{\rm{s}}}^{-1}$ of the star, we obtain an alternative estimate of the mass ratio ${M}_{1}/{M}_{2}=4.7\pm 0.2$.

Also from the extended Smak profile fitting of Paβ, we find a semiamplitude ${\rm{\Delta }}{V}_{\mathrm{rot}}\approx 3.6$ $\mathrm{km}\,{{\rm{s}}}^{-1}$, corresponding to ${\rm{\Delta }}{V}_{\mathrm{rot}}/\langle {V}_{\mathrm{rot}}\rangle \approx 0.048$. According to Table 2 in Paczynski (1977) with the correction factor 2 mentioned in the note added in proof, this would imply a high-mass ratio of about 12.4. We suggest that this discrepancy is explained if viscosity shapes the outer edge of the disk to be more circular than in the pure streamline model of Paczynski (1977), leading to a smaller amplitude in the orbital variation of ${V}_{\mathrm{rot}}$. We also find a phase shift of ∼41° in the variation, compared to the model in Paczynski (1977). Therefore, we do not use the orbital variations of ${V}_{\mathrm{rot}}$ to infer the mass ratio. A more circular outer disk would reduce the correction factor between the observed ${K}_{1{\rm{d}}}\approx 12.7$ $\mathrm{km}\,{{\rm{s}}}^{-1}$ and the true orbital semiamplitude of the primary; in the limiting case that ${K}_{1{\rm{d}}}={K}_{1}$, the mass ratio ${M}_{1}/{M}_{2}={K}_{2}/{K}_{1}\approx 4.1$, still in the same ballpark as the values inferred above.

We repeated the same analysis for the ${V}_{1{\rm{d}}}$ and ${V}_{\mathrm{rot}}$ from Gaussian fitting of the Paβ peaks, and for Paγ with both fitting methods. In total, we obtain eight alternative values of mass ratio ${M}_{1}/{M}_{2}$ (Table 2). Our full range of estimates spans ≈3.9–8.4 (including their 68% error ranges), with a mean value of $\approx 5.3$ and a 1σ dispersion of ≈1.4. If we remove the largest and the smallest values, we obtain a range of ≈4.2–6.5 with a mean value of $\approx 5.1$ and a 1σ dispersion of ≈0.8.

For the observed mass ratio ${M}_{1}/{M}_{2}\approx 5$, the tidal truncation radius of the disk (Paczynski 1977; Warner 1995) is ${r}_{{\rm{d}}}\approx 0.60\,{{aM}}_{1}/({M}_{1}+{M}_{2})\approx 0.50\,a$, where a is the binary separation. An alternative definition for the outer edge of the disk is the 3:2 resonance radius (Whitehurst & King 1991), which is ≈0.45 a for a mass ratio of ≈5.

To determine whether the observed disk parameters are consistent with those predictions, first we used the simplifying approximation of a circular outer disk (radius ${r}_{{\rm{d}}}$) in Keplerian rotation around the primary (i.e., rotating with a speed $v=\sqrt{{{GM}}_{1}/{r}_{{\rm{d}}}}$). The inferred $\langle {V}_{\mathrm{rot}}\rangle$ and mass ratio, in combination with the observed radial velocity semiamplitude of the secondary star (${K}_{2}$), enable us to determine ${r}_{d}/a$. Somewhat surprisingly, we obtain a large value ${r}_{{\rm{d}}}\approx 0.6\,a$, even larger than the expected volume-averaged radius of the Roche lobe (${r}_{{\rm{L}}}\approx 0.52\,a$: Eggleton 1983). However, the circular Keplerian approximation is too simplistic for an accurate estimate of the outer disk radius in the Roche lobe geometry. When the proper gravitational potential of the binary is taken into account (Huang 1967), the rotational speed in the outer rings of a large disk is lower than the Keplerian speed of rotation around an isolated body of mass M₁; in other words, the Keplerian approximation overestimates the outer disk radius. We used a fitting formula to the values in Table 2 of Huang (1967) to derive a more accurate disk size. With this method, we find an outer radius ${r}_{{\rm{d}}}\approx 0.36\,a$ (Table 2). This is smaller than the tidal truncation radius calculated by Paczynski (1977). As the orbits in the disk are expected to be more circular at smaller radii, this result suggests that we may have overcorrected ${K}_{1{\rm{d}}}$ to obtain ${K}_{1}$ and thus we may have overestimated the mass ratio ${M}_{1}/{M}_{2}$. However, this effect is small (only a few percent), and even in the implausibly extreme case of ${K}_{1}={K}_{1{\rm{d}}}$, the estimated mass ratio is still well within the range of ≈4–7 we derived before (Section 4.1).

Table 2.  Kinematics and Mass Ratios Inferred from the Disk Emission Lines

Model	Line	${K}_{1{\rm{d}}}$	$\langle {V}_{\mathrm{rot}}\rangle$	${K}_{1}$	${M}_{1}/{M}_{2}{| }_{P}$	${M}_{1}/{M}_{2}{| }_{V}$	${r}_{d}/a{| }_{P}$	${r}_{d}/a{| }_{V}$
		($\mathrm{km}\,{{\rm{s}}}^{-1}$)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)
Extended Smak Fit	Paβ	12.7 ± 0.3	74.4 ± 0.2	11.2 ± 0.3	4.04 ± 0.11	4.70 ± 0.13	0.347 ± 0.001	0.345 ± 0.001
	Paγ	11.6 ± 0.3	70.9 ± 0.2	10.1 ± 0.4	4.27 ± 0.17	5.20 ± 0.19	0.362 ± 0.001	0.360 ± 0.001
Local Gaussian Fit	Paβ	7.9 ± 0.2	67.4 ± 0.2	6.5 ± 0.2	6.51 ± 0.23	8.11 ± 0.27	0.375 ± 0.001	0.374 ± 0.001
	Paγ	11.0 ± 0.3	70.7 ± 0.2	9.6 ± 0.3	4.53 ± 0.14	5.50 ± 0.15	0.363 ± 0.001	0.361 ± 0.001

Note. The projected radial velocity amplitude of the primary, ${K}_{1}$, in column (5), is defined as the observed disk line velocity amplitude ${K}_{1{\rm{d}}}$ in column (3), corrected by a factor given in the model of Paczynski (1977). The mass ratio in column (6) is obtained from the observed values of ${K}_{1{\rm{d}}}/\langle {V}_{\mathrm{rot}}\rangle$, compared with the values tabulated by Paczynski (1977). The mass ratio in column (7) is inferred from the ratio of the secondary to primary velocity amplitudes, ${K}_{2}/{K}_{1}$. Columns (8) and (9) are the outer disk size in units of binary separation, estimated based on the ratio of the disk outer edge velocity $\langle {V}_{\mathrm{rot}}\rangle$ and the secondary velocity ${K}_{2}$, where the radial dependent disk velocity is assumed to follow the subKeplerian solution in Huang (1967), with mass ratios from column (6) and (7), respectively.

Download table as:  ASCIITypeset image

In this work, we have traced the orbital motion and calculated the mass ratio from the sinusoidal shift of the Paschen emission-line peaks, with two alternative methods for the identification of the peaks and two alternative conversions between peak position and mass ratio. Systematic uncertainties include the amount of smearing of the peaks (which tends to reduce the apparent peak separation: Marsh et al. 1994), the tidal distortion and possible eccentricity of the outer disk (Smak & Plavec 1997), and perhaps most importantly, the mean radius of the outer disk edge. The last factor could be either the largest nonintersecting streamline, or the 3:2 resonance radius, or perhaps, as we suggested here (Section 4.2), the 2:1 resonance radius. In principle, emission-line profiles could also be affected by S-wave contributions of accretion stream and hot spot (Wade & Ward 1985; Kaitchuck et al. 1994), or emission enhancements from spiral density waves in the disk (Steeghs & Stehle 1999); however, we do not see any evidence of such terms in our observed Paschen line profiles. What we do see, instead, is a periodic enhancement of the flux from the red or blue side of the line profile, in phase with the position of the secondary star. We suggested that this effect is caused by the asymmetric irradiation of the gas in the outer disk by the secondary star.

Instead of tracing the orbital motion of the disk from its emission-line peaks, we can do it by fitting the wing position. The wing fitting was the method used by L19, on the Hα line profile, which does not show clear double peaks as in Paschen lines. In principal, the wings are emitted from smaller disk radii, thus more sensitive to the orbital motion of the primary and less affected by the tidal distortion of the outer disk or by hypothetical S-wave emission. However, wing fitting has its own downsides compared with peak fitting. First, the emission wing position is more sensitive to the accurate subtraction of the pressure-broadened absorption wings of the stellar line (which moves in antiphase with the disk line). The exact profile of the stellar absorption line depends on the temperature and surface gravity adopted for the stellar template. The second problem is that wing profiles are more easily affected by stellar and disk winds. Third, for LB-1, the alternate enhancement of blue and red peaks in phase with the stellar motion, from the stellar irradiation effect, causes a corresponding displacement of the wing positions measured at a fixed fraction of peak flux; if not properly accounted for, this effect leads to cancellation or severe underestimation of the true orbital motion of the primary. Both Abdul-Masih et al. (2020) and El-Badry & Quataert (2020) showed that the stellar absorption term may cause an apparent motion of ∼6 km/s mimicking that measured by L19, then the contributions of stellar winds and irradiation effects, not considered in neither Abdul-Masih et al. (2020) nor El-Badry & Quataert (2020), may cause an opposite apparent motion of ∼6–10 km s⁻¹ in the line wings based on the primary motion from the Paschen line peaks.

In contrast, flux asymmetry does not substantially affect the peak position, which is tied to the location of the outer disk edge. Variations in relatively broad spectral features, such as the stellar absorption profile and possible wind emission features, should also have little effect on the velocity amplitude ${V}_{1{\rm{d}}}$ of the mean peak position.¹⁶ This is why in this work we focused on peak fitting, considering its results a more reliable indicator of the binary mass ratio. We leave a wing-fitting study of the same set of Paschen lines in combination with the Hα line to a follow-up work currently in preparation.

Two types of solutions, corresponding to two classes of evolutionary tracks, appear to be consistent with the observed B3-type colors and spectra. The first class of solutions represents stars that have already moved off the main sequence, but not yet reached the giant stage. Such stars are moving from higher to lower temperatures in the Hertzsprung-Russell diagram. The second class of solutions represents stars that have been partially stripped of their hydrogen envelopes during close binary evolution.

For the first class, L19 proposed a subgiant mass ${M}_{2}\,=8.2\pm 0.9\,{M}_{\odot }$ based on the tlusty model (Hubeny & Lanz 1995) fitting to Keck/HIRES spectra (resulting in ${T}_{\mathrm{eff}}=18,100\pm 820$ K, $\mathrm{log}g=3.43\pm 0.15$) and the PARSEC evolutionary tracks. Several works re-estimated the atmospheric parameters using new high-resolution spectral observations or archive data. For example, Simón-Díazet al. (2020) derived ${T}_{\mathrm{eff}}=14,000\pm 500$ K and $\mathrm{log}g\,=3.5\pm 0.15$, using the nonlocal thermodynamic equilibrium stellar atmosphere code fastwind. These spectroscopic parameters correspond to ${M}_{2}={5.2}_{-0.6}^{+0.3}{M}_{\odot }$ by comparison with the evolutionary tracks of Ekströmet al. (2012) and Brott et al. (2011). Using the Grid Search in Stellar Parameters fitting suite (Tkachenko 2015), Abdul-Masih et al. (2020) modeled the spectrum with an effective temperature ${T}_{\mathrm{eff}}=13,500\pm 700$ K and a surface gravity $\mathrm{log}g=3.3\pm 0.3;$ this corresponds to a mass ${M}_{2}\,={4.2}_{-0.7}^{+0.8}{M}_{\odot }$, according to the evolutionary tracks from Brott et al. (2011).

To summarize, several groups have obtained a mass range of 3–6 ${M}_{\odot }$ based on spectroscopy, lower than the L19 results. Note that the mass estimate depends on the models adopted. For example, if PARSEC evolutionary tracks are adopted instead, the (${T}_{\mathrm{eff}}$, $\mathrm{log}g$) values in Abdul-Masih et al. (2020) would correspond to ${5.6}_{-1.2}^{+1.3}{M}_{\odot }$ instead of ${4.2}_{-0.7}^{+0.8}{M}_{\odot }$, as similarly shown in Figure 2 of Simón-Díazet al. (2020). Nevertheless, if the secondary star is indeed a B star with a conservative mass estimate of 3–6${M}_{\odot }$, then the mass of the primary is about 13–36${M}_{\odot }$ (12–50${M}_{\odot }$) for our new mass ratio of 5.1 ± 0.8 (3.9–8.4).

The second class of solutions moves from the redder to the bluer part of the Hertzsprung-Russell diagram on their way to the subdwarf stage (Götberget al. 2018); thus, they cross the main sequence to subgiant tracks. The mass of such stars is much lower than the mass of a main sequence or subgiant with similar temperature and surface gravity. Spectral modeling of LB-1 by Irrgang et al. (2020), Simón-Díazet al. (2020), and Shenar et al. (2020) highlighted the supersolar He abundance and the presence of CNO-processed material (enhanced in N and depleted in C and O), normally not present near the surface of main sequence or subgiant stars. This suggests that the star has been partially stripped of its hydrogen envelopes during close binary evolution.

Using a modified version of the Binary-Star Evolution code (Hurley et al. 2002), Yungelson et al. (2020) proposed that the secondary star (with current mass $0.5\lesssim {M}_{2}\lesssim 1.7{M}_{\odot }$) had an initial mass ∼4–9M_⊙ but is now in its He-shell burning phase, after a phase of case-B Roche lobe overflow in which it lost most of its envelope to the primary. Yungelson et al. (2020) estimated an age of the system of $\approx 80\,\mathrm{Myr}$, and a duration of the He-shell burning phase of $\approx 7\,\mathrm{Myr}$. Similarly, using the Binary Population and Spectral Synthesis (BPASS) V2.2 models (Eldridge et al. 2017; Stanway & Eldridge 2018), Eldridge et al. (2020) found acceptable solutions for the secondary star at two different stages (separated by $\approx 25$ Myr) of its evolution toward the subdwarf (and eventually white dwarf) stage. An analogous suggestion about the evolutionary track of the He-burning star was put forward by Irrgang et al. (2020), based on the binary models of Götberget al. (2018). Using the PoWR model, we derived an effective temperature ${T}_{\mathrm{eff}}=13,500$ K, a surface gravity $\mathrm{log}g=2.8$, and a luminosity $L={10}^{3.1}{L}_{\odot }$, with $d=2.14\,\mathrm{kpc}$ and $E(B-V)=0.6$ mag. This corresponds to a companion mass ${M}_{2}\approx 1{M}_{\odot }$.

In summary, although the secondary star may have started its life on the main sequence as a ∼4–9M_⊙ B-type star, abundance ratios support the view that its mass is now only ∼1–2 M_⊙. If the secondary is indeed such a stripped helium star, the mass of the primary would be 4–12${M}_{\odot }$ (4–17${M}_{\odot }$) for our new mass ratio of 5.1 ± 0.8 (3.9–8.4).

Shenar et al. (2020) proposed that the optical continuum in LB-1 is the superposition of an almost non-rotating stripped star and a fast-rotating B3e main-sequence star. Note that the definitions of primary and secondary in Shenar et al. (2020) are opposite to ours. To be consistent within this paper, we adopt our definitions here to discuss their results, with the fast-rotating B3e star as the primary and the almost non-rotating stripped star as the secondary. Their subsequent decomposition finds a B3Ve star with strong Hα emission line that moves at ${K}_{1}=11\pm 1$ $\mathrm{km}\,{{\rm{s}}}^{-1}$ (interestingly close to our estimate in this paper), and a stripped helium star with narrow absorption lines that move at 53 $\mathrm{km}\,{{\rm{s}}}^{-1}$as reported by L19. By calibrating the mass of the B3Ve primary to ${M}_{1}=7\pm 2{M}_{\odot }$, Shenar et al. (2020) derived an orbital mass for the stripped secondary of ${M}_{2}=1.5\pm 0.4{M}_{\odot }$.

In this scenario, the primary is a fast rotator (which explains its decretion disk) because it has been spun up by mass and angular momentum transfer from the stripped secondary. The archetype of this class of systems is φ Per (Gies et al. 1993; Gies et al. 1998; Hummel & Štefl 2001; Schootemeijer et al. 2018). Other systems in this class (five confirmed plus a dozen strong candidates) are discussed in Schootemeijer et al. (2018) and Wang et al. (2018). When reliable measurements for the stripped secondary are available, such systems typically show temperatures ≳25,000 K (hence the alternative name Be + sdO systems, the stripped star having an O-type spectrum). However, it was suggested (Schootemeijer et al. 2018; Wang et al. 2018) that the known Be + sdO systems are only the high-luminosity end of the distribution, and a much larger (so far undetected) population with fainter, cooler secondary stars should also exist. LB-1 could be an example of this population, in which the secondary is only partially stripped and has an effective temperature of ≈13,000 K.

Such a scenario, however, relies on the decomposition of the optical spectra, which is a reverse problem that can hardly have a unique solution. For example, their decomposition led to double-peaked Balmer emission lines (as seen in their Figure 1) from the cold stripped helium star, which is hard to explain for a cold secondary that is far from filling its Roche lobe. On the other hand, these could be residuals given the low S/N of their spectra data and the neglect of the irradiation effect in the spectral disentangling. We will combine PoWR modeling and our high S/N CARMENES spectra data to verify such a decomposition in a future work. Solid evidence for this intriguing scenario has to wait for Gaia astrometric data, as discussed later. In this scenario, the hydrogen emission lines come from the decretion disk of the Be primary star. In the majority of cases, such stars have X-ray luminosities ≲10³¹ erg/s (Rauwet al. 2015; Nazé & Motch 2018), consistent with the non-detection of X-ray emission in our Chandra observation of LB-1 (L19).

Rivinius et al. (2020) studied in depth HR6819 that appears as a bright early Be star but can be decomposed with an additional B3III component. Their spectroscopic time series taken in 2004 revealed the narrow absorption lines in its B3III component, which exhibit a period of 40 days in a circular orbit, and also broad Hα emission lines without apparent motion, stunningly similar to the observations of LB-1. Rivinius et al. (2020) interpreted HR6819 as a triple system, where the line emission comes from the disk around a distant third body in the system: a Be star (Rivinius et al. 2013 for a review) with a decretion disk, while the B3III motion comes from an inner binary with a BH above $4{M}_{\odot }$.

Rivinius et al. (2020) suggested that LB-1 is also such a triple star system, and the mass of the primary in LB-1 can then be reduced from $\sim 70{M}_{\odot }$ to a level more typical of Galatic stellar remnant BHs. In this scenario, the orbital motion of the third body would be too slow and its period too long (>1 year) to show up in the spectroscopic observations to date. However, as our CARMENES spectra clearly show, the emission lines in LB-1 are actually moving in antiphase with the absorption lines, thus they cannot come from a distant third Be star as proposed for HR6819. In any case, short-cadence, high-precision radial velocity monitoring of such systems helps constrain their nature (e.g., Hayashi et al. 2020).