Visual Orbits of Wolf-Rayet Stars II: The Orbit of the Nitrogen-Rich WR Binary WR 138 measured with the CHARA Array

Classical Wolf-Rayet (WR) stars are evolved massive stars that are core helium-burning and have lost their hydrogen-rich envelope. These stars were first observed at the Paris Observatory by Wolf & Rayet (1867). There are two evolutionary pathways to create these stars, through single-star or binary-star evolution. In the single star evolutionary pathway, the star lost its envelope through a strong stellar wind in what is now often called the “Conti scenario” (Conti, 1975). This scenario has strong stellar winds throughout the main-sequence lifetime followed by potential eruptions during a luminous blue variable stage leading to the observed WR star. This scenario may be dominant in some environments, as is evidenced in the recent study of WR stars in the SMC (Schootemeijer et al., 2024).

The second scenario involves the WR star being formed through interactions with a companion star. In this scenario, the WR star progenitor evolved to fill its Roche lobe and then was stripped of its outer envelope. Recent multiplicity surveys of massive stars have shown that a vast majority of O stars are formed in systems where Roche lobe overflow or mergers may occur for 75% of O stars (Sana et al., 2012, 2013, 2014). This formation mechanism is likely to dominate for WR stars in orbits with periods shorter than $\sim$1 year. However, the exact binary separation or period where the formation channel has to be either through stellar winds with larger separations or binary interactions with smaller orbits remains somewhat ambiguous. For example, Thomas et al. (2021a) studied the massive binary WR 140 to measure a precise orbit with long-baseline interferometry and optical spectroscopy and compared the results to models from the Binary Population and Spectral Synthesis model grid to show that the WR star in that system formed primarily through mass-loss in the stellar winds. Despite a long 7.93-yr period and a high eccentricity of 0.8993, there was still a moderate amount of mass lost or transferred through binary interactions to form the current system, where the eccentricity could have been the byproduct of imparted “kicks” near periastron like the models of Sepinsky et al. (2007b).

Short-period WR binaries are readily studied with photometric, spectroscopic, and polarimetric techniques. However, the amplitudes of variability for all of these techniques become increasingly smaller with longer-period systems. Long-baseline interferometry offers the capabilities of resolving the individual stars moving about each other in longer-period WR binaries that are within $\sim$2-3 kpc. Recently, Richardson et al. (2021) demonstrated that the technique of interferometry could resolve an orbit smaller than 1 mas in separation with the CHARA Array with the first visual orbit of the nitrogen-rich WR binary WR 133 (WN5o$+$O9I; the “o” suffix denotes no measurable hydrogen in the WR spectrum). Richardson et al. (2016a) resolved two other WR binaries with the CHARA Array, but those observations represent a single epoch and not full orbits. Further observations of WR 137 have resolved the orbit and helped describe the geometry of the dust formation in the binary (Richardson et al., submitted).

This paper revisits WR 138 (HD 193077; WN5o+O9V) which was resolved by Richardson et al. (2016a) with the CHARA Array. It is one of eight relatively bright WR stars ($V<8.5$) located in the constellation Cygnus. Although absorption lines in the spectrum of WR 138 have been recognized by (Hiltner, 1945), the system’s multiplicity remained a topic of debate until recently. Massey (1980) determined that there was no orbital motion for emission lines with an amplitude larger than 30 km s^-1 over a period of six months during his studies of WR stars with absorption lines present. This led him to suggest that the broad absorption lines, which have an estimated $v\sin i\approx 500$ km s^-1, were intrinsic to the WN star itself and not formed in the atmosphere of a companion O star.

Lamontagne et al. (1982) collected a more extensive set of photographic spectra and then performed a period search and adopted a period of 2.3238$\pm$0.0001 days as the period of the WN suggested that WR 138 is a triple system consisting of the WN6 star orbited by an unseen companion star, potentially a neutron star, every 2.32 days. Both of these objects are orbiting a fainter, rapidly rotating, late-O type main-sequence star every $\sim$1763 days. Following this analysis, Annuk (1990) collected additional spectra of the system. They found no evidence of the short period suggested by Lamontagne et al. (1982) and found that the star was a binary with the OB star in a wide orbit with a period of 1538 d (4.2 yr). These results were confirmed by Palate et al. (2013), who studied both optical and X-ray data on the system.

Richardson et al. (2016a) resolved WR 138 into a binary system using $H-$band CHARA interferometry, deriving a wide separation of 12.4mas, marking the first time a WN binary was resolved with interferometry. They suggested that the system might have gone through a previous mass-transfer episode, which created the WR star and presented a spectral model of the system using the non-LTE code PoWR, measuring the mass-loss rates and properties of the two stars in the system. Inspired by the stars being resolved with CHARA, Rauw et al. (2023) examined spectra taken of the system spanning nearly three orbits. They also confirmed that there is no signal in the radial velocity time series at frequencies around the 2.3238 day period found by Lamontagne et al. (1982). After analyzing the results provided by Richardson et al. (2016a), Rauw et al. (2023) identified discrepancies between the CHARA observations and their own spectroscopic radial velocity solution. They suggested that the secondary star resolved through interferometry was not responsible for the orbital motion of the WN6o star with a period of 1559 days, but rather the interferometric companion was a putative third component that does not undergo significant RV variations.

The aim of our study is to better characterize the WR 138 binary system, determining the orbital parameters and masses of both stars through a combination of spectroscopy and new interferometry from the CHARA Array. We present the observations in Section 2, along with our astrometric and spectroscopic measurements in Section 3. Then, in Section 3, we present the 3-dimensional orbit. We discuss our results in Section 4 and conclude this study in Section 5.

With our orbit, we can begin to explore the system and how it relates to other WR and O stars. We will begin the comparisons by examining how the system compares to other WN+O binaries as well as the masses from theoretical expectations. The Wolf-Rayet star in WR 138 has the same spectral type as the only other WN star with a visual orbit, WR 133 (Richardson et al., 2021), namely WN5o. In the WR 133 system, Richardson et al. (2021) found the mass of the WN star was 9.3$\pm$1.6 $M_{\odot}$, which is considerably smaller than the WR star in WR 138 measuring 13.9$\pm$1.5 $M_{\odot}$.

A better comparison to WN stars with measured masses could be made with short-period binaries with either geometric or wind eclipses. The largest sample of somewhat similar spectral types of WN stars is in the photometric analysis of Lamontagne et al. (1996), who modeled the wind eclipses in a sample of eleven short-period systems. The wind eclipses are caused by electon scattering as the WR star passes in front of the O star, with the ionized wind of the WR star having the free electrons to scatter the light of the O star. The resulting ‘v’-shaped eclipses are then dependent on orbital parameters measured from spectroscopy (e.g., $P$, $T_{0}$, $a\sin i$), along with the mass-loss rate of the WR star (free electrons), and the orbital inclination. In the cases of the WN4 and WN6 stars measured by Lamontagne et al. (1996), they had masses in the range of 15–19 $M_{\odot}$, which is quite similar to our measurement of 13.9 $M_{\odot}$.

We can also use the spectroscopic model for the system reported by Richardson et al. (2016a). With the modeled parameters, we can then use mass-luminosity relations such as those of Gräfener et al. (2011), which would place the WR star at 12.8 $\pm$0.5 $M_{\odot}$, close to that of our measurement. We do caution that this value is dependent on the luminosity of the star, which Richardson et al. (2016a) placed at a distance of 1.38 kpc, but our visual orbit and the Gaia measurements have both placed at a distance of 2.1 kpc. It is beyond the scope of this paper to recalculate the spectroscopic models of the system, but the general agreement of the WR mass with similar WR stars and the predictions of the mass-luminosity relations is promising.

For the O star, there are two plausible routes for comparing the measured mass of 26.3$\pm$1.7 $M_{\odot}$ to other O stars. First, we will use the spectroscopic models of the binary from Richardson et al. (2016a) again. In this case, the constraints come from the measured values of $\log g$ (cgs), which was 4.0$\pm$0.3 dex. Unfortunately, the large error on this parameter means that the O star mass from the spectroscopic models was 29$\pm$19 $M_{\odot}$, which obviously agrees with our value given the error in the spectroscopic models.

Another way to consider the mass of the secondary is to use its spectral type and the models for the O star masses, namely those of Martins et al. (2005). Richardson et al. (2016a) report the spectral type of the companion to be an O9V star. An O9V star should have a mass around 18 $M_{\odot}$, which is a bit lower than our value of 26 $M_{\odot}$. However, an O9III star would have a mass close to 23 $M_{\odot}$, very similar to our measured value. We note that the spectral luminosity classification of O9 stars is largely done with weak lines in the blue such as Si IV $\lambda\lambda$4089,4116 and N V $\lambda$4379. These lines are weak in all luminosity classes, and would likely be very hard to detect with the combined spectrum of a WN star and a projected rotational velocity of the O star of 350$\pm$30 km s^-1 (Richardson et al., 2016a).

Palate et al. (2013) examined both the radial velocity and X-ray variability of the WR 138 system. The X-ray observations of WR 138 are sparse and taken with multiple satellites. The models of the six epochs of observations show some variation, but the largest variation was seen with ROSAT which had a very small energy range for which it was sensitive. It is likely that the system should show a variation dependent on the separation $D$ in the system, resulting in either an adiabatic cooling ($D^{-1}$) or a radiative cooling dependency ($D^{-2}$) as described by Cantó et al. (1996) and Gayley (2009). The observations presented by Palate et al. (2013) are not dense enough in phase coverage nor all of high enough quality for an appropriate fit of the cooling of the gas. We suggest that a dedicated X-ray variability campaign across an entire orbit of WR 138 should be a high-priority in order to best constrain the variability of the system and place constraints on how the wind collisions cool in orbits with well-established orbits.

Other observations of WR 138 could allow for better constraints on the colliding wind geometry and a better understanding of the way in which polarization is impacted by the geometry of the colliding winds. Fullard et al. (2020) examined many WR+O binaries with spectropolarimetry, finding a fairly small polarization for WR 138. The SMEX satellite Polstar is currently being proposed to NASA as a small mission to explore the wavelength-dependent polarization of stars in the ultraviolet. Compared to the mission expectations, WR 138 is fainter than most of the main targets. However, with selected epochs to observe the system and long ($\sim$1 day) exposures, strong constraints on the polarization changes could provide insights into the wind collisions given the known orbital elements presented here (St-Louis et al., 2022) as well as the rapid rotation of the O star companion (Jones et al., 2022).

We compare the observational constraints for WR 138, including the current masses, the $UBVJHK$ magnitudes and current circularized separation of the binary to BPASS v2.2 binary stellar evolution models (Eldridge et al., 2017; Stanway & Eldridge, 2018) at over the range of metallicities allowed in BPASS. The comparison to BPASS models reveals two main evolutionary pathways sets of models that agree with the current observed parameters which we show in Fig. 3. The first pathway has initial masses for the binary system of 178$\pm$71 M_⊙ and 28.2$\pm$2.8 M_⊙ with initial periods of $\log(P/{\rm days})=1.76\pm 0.26$ with a super-Solar metallicity mass fraction of $Z=0.038\pm 0.005$. These systems do not interact and the primary star loses most of its mass by strong stellar winds on the main sequence, before any binary interaction can occur. This mass loss is what drives the system to such long observed periods. The current age predicted today is 2.88 Myrs.

The second pathway also shown in Fig. 3 has initial masses of the binary systems with of 37.4$\pm$7.5 M_⊙ and 24.0$\pm$1.4 M_⊙, initial periods of $\log(P/{\rm days})$ = 3.17$\pm$0.16 and a slightly lower metallicity of $Z=0.026\pm 0.009$. These systems interact when the primary reaches its red supergiant phase. The interactions begin with some slight mass transfer before a common envelope phase reducing the orbit slightly to values observed today. The current age predicted today is 5.0 Myrs. Both sets of models will have the current O star accreting some material and angular momentum, aiding the star to becoming the rapid rotator we observe today, even though rotation is not fully accounted for in BPASS.

When considering the full set of models the best fitting initial parameters have an initial primary mass of 35 M_⊙, a secondary mass of 24.5 M_⊙ and an initial period of $\log(P/{\rm days})=3.2$. While the higher mass model set are possible, we consider that the lower mass set is more representative of the binary system’s prior evolution, especially with the steep initial mass function for star formation. As discussed in the BPASS modeling of WR 140 (Thomas et al., 2021a), the caveats around these fits is that BPASS is currently unable to model eccentric orbits. However, as discussed by Hurley et al. (2002), orbits with the same semi-latus rectum evolve through similar pathways. Thus we have constrained our models to have the same circular orbital radius as the semi-latus rectum of the observed binary. Given the relatively low value of eccentricity, we expect this to be a good approximation in this case.

WR 138 is a member of a growing class of massive, eccentric binaries with observational and theoretical evidence of at least some binary interactions being necessary to form the system as observed today. Such systems have included the LBV candidates HD 326823 and MWC 314 (Richardson et al., 2011, 2016b) and even the prototype LBV binary $\eta$ Car (Hirai et al., 2021). With $\eta$ Car, the models indicate a merger that formed the modern day primary star after complex interactions with a third component. However, in the case of the short period systems HD 326823 and MWC 314, the eccentricity observed in these interacting binaries is hyopthesized to be driven through a transfer of angular momentum during a periastron passage that works to increase eccentricity with time. The process of increasing the eccentricity with time was modeled in a series of papers by Sepinsky et al. (2007a, b, 2009, 2010). Some evidence presented in the evolutionary analysis of WR 140 presented by Thomas et al. (2021a) also indicated that the high eccentricity (0.9) was driven by the angular momentum transfer at periastron increasing the eccentricity with time. If similar results are seen now with WR 138, it is an opportune time for theorists to model how these interactions can occur to build a growing number of eccentric binaries with both short and long periods.

We have presented the second visual orbit for a WN-type star in a binary system derived using a combination of long-baseline infrared interferometry and radial velocities from optical spectra. The resulting masses are in agreement with the masses expected from spectral modeling previously done for this system and the orbital parallax derived is in agreement with the Gaia parallax. The observations reported here show that the speculation of a third body in the system by Rauw et al. (2023) is not plausible although we adjusted different data sets’ $\gamma$-velocity to fit our orbit. We suspect that this adjustment only adjusts the various measuring techniques from different authors more than an intrinsic change in the $\gamma$-velocity with time, and furthermore we see no evidence of a third body in our interferometry. Furthermore, the system may have undergone some past interactions through a common envelope phase or mass transfer when the current WN star was in a red supergiant phase. Finding more systems like WR 138 that can be measured with both spectroscopy and interferometry will place strong constraints on the formation mechanisms for these stars and binaries in the future.

We thank Peredur Williams for comments that improved this manuscript. This work is based upon observations obtained with the Georgia State University Center for High Angular Resolution Astronomy Array at Mount Wilson Observatory. The CHARA Array is supported by the National Science Foundation under Grant No. AST-1636624 and AST-2034336. Institutional support has been provided from the GSU College of Arts and Sciences and the GSU Office of the Vice President for Research and Economic Development. Time at the CHARA Array was granted through the NOIRLab community access program (NOIRLab PropIDs: 2017B-0088, 2021B-0159, and 2023A-452855; PI: N. Richardson). This research has made use of the Jean-Marie Mariotti Center Aspro and SearchCal services.

Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

AMH is grateful for support through Embry-Riddle Aeronautical University’s Undergraduate Research Institute and the NASA Arizona Space Grant program. NDR is grateful for support from the Cottrell Scholar Award #CS-CSA-2023-143 sponsored by the Research Corporation for Science Advancement. SK acknowledges funding for MIRC-X received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Starting Grant No. 639889 and Consolidated Grant No. 101003096). JDM acknowledges funding for the development of MIRC-X (NASA-XRP NNX16AD43G, NSF-AST 1909165) and MYSTIC (NSF-ATI 1506540, NSF-AST 1909165). JM acknowledges funding from a Royal Society - Science Foundation Ireland University Research Fellowship.

The appendix includes Figure Set 4 showing the interferometric data and the binary fits for each epoch of MIRC-X and MYSTIC. Each figure in the set shows the ($u,v$) coverage, the $\chi^{2}$ map from the binary grid search, the visibilities, and the closure phases. The $\chi^{2}$ maps are centered at the predicted location based on the updated orbit fit. The nights with reliable detections show a clear minimum in the $\chi^{2}$ indicated by the colored circles. The large red, orange, yellow, green, blue, purple, and black symbols show solutions within a $\Delta chi^{2}$ interval of 1, 4, 9, 16, 25, 36, and 49 from the minimum $\chi^{2}$. The small black circles show solutions where the difference in the $\chi^{2}$ is greater than 49. Similar plots are shown in the appendix of Richardson et al. (2024) and show that the high-quality interferometric data from MIRC-X and MYSTIC frequently will only show the best fit, and hence only red points.

NOTE for arXiv readers: These figures make the pdf too large for arXiv and we only include one. A full copy can be requested from the corresponding author until the paper is published in ApJ.