11institutetext: 1Université Libre de Bruxelles, Av. Franklin Roosevelt 50,
1050 Brussels
Celestijnenlaan 200D, 3001 Leuven, Belgium
2Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
3Anton Pannekoek Institute for Astronomy, University of Amsterdam, Postbus
94249, 1090 GE Amsterdam, The Netherlands
11email<EMAIL_ADDRESS>
# A spectroscopic multiplicity survey of Galactic Wolf-Rayet stars

III. The northern late-type nitrogen-rich sample

K. Dsilva 11 T. Shenar 2233 H. Sana 22 P. Marchant 22

(Received xx; accepted xx)

###### Abstract

Context. Massive stars are powerful cosmic engines that have a huge impact on
their surroundings and host galaxies. The majority of massive stars will
interact with a companion star during their evolution. The effects of this
interaction on their end-of-life products are currently poorly constrained. In
the phases immediately preceding core-collapse, massive stars in the Galaxy
with $M_{i}\gtrsim 20\,$$M_{\odot}$ may appear as classical Wolf-Rayet (WR)
stars. The multiplicity properties of the WR population are thus required to
further our understanding of stellar evolution at the upper-mass end.

Aims. As the final contribution of a homogeneous radial velocity (RV) survey,
this work aims to constrain the multiplicity properties of northern Galactic
late-type nitrogen-rich Wolf-Rayet (WNL) stars. We compare their intrinsic
binary fraction and orbital period distribution to the carbon-rich (WC) and
early-type nitrogen-rich (WNE) populations from previous works.

Methods. We obtained high-resolution spectra of the complete magnitude-limited
sample of 11 Galactic WNL stars with the Mercator telescope on the island of
La Palma. We used cross-correlation with a log-likelihood framework to measure
relative RVs and flagged binary candidates based on the peak-to-peak RV
dispersion. By using Monte Carlo sampling and a Bayesian framework, we
computed the three-dimensional likelihood and one-dimensional posteriors for
the upper period cut-off ($\log P_{\mathrm{max}}^{\textrm{WNL}}$), power-law
index ($\pi^{\textrm{WNL}}$), and intrinsic binary fraction
($f_{\textrm{int}}^{\textrm{WNL}}$).

Results. Adopting a threshold $C$ of 50 km s-1, we derived
$f_{\textrm{obs}}^{\textrm{WNL}}$$\,=\,0.36\,\pm\,0.15$. Our Bayesian analysis
produces
$f_{\textrm{int}}^{\textrm{WNL}}$$\,=\,0.42\begin{subarray}{c}+0.15\\\
-0.17\end{subarray}$,
$\pi^{\textrm{WNL}}$$\,=\,-0.70\begin{subarray}{c}+0.73\\\
-1.02\end{subarray}$ and $\log
P_{\mathrm{max}}^{\textrm{WNL}}$$\,=\,4.90\begin{subarray}{c}+0.09\\\
-3.40\end{subarray}$ for the parent WNL population. The combined analysis of
the Galactic WN population results in
$f_{\textrm{int}}^{\textrm{WN}}$$\,=\,0.52\begin{subarray}{c}+0.14\\\
-0.12\end{subarray}$,
$\pi^{\textrm{WN}}$$\,=\,-0.99\begin{subarray}{c}+0.57\\\ -0.50\end{subarray}$
and $\log P_{\mathrm{max}}^{\textrm{WN}}$$\,=\,4.99\begin{subarray}{c}+0.00\\\
-1.11\end{subarray}$. The observed period distribution of Galactic WN and WC
binaries from the literature is in agreement with what is found.

Conclusions. The period distribution of Galactic WN binaries peaks at
$P{\sim}1$-$10\,$d and that of the WC population at $P{\sim}5000\,$d. This
shift cannot be reconciled by orbital evolution due to mass loss or mass
transfer. At long periods, the evolutionary sequence O ($\xrightarrow{}$LBV)
$\xrightarrow{}$ WN$\xrightarrow{}$WC seems feasible. The high frequency of
short-period WN binaries compared to WC binaries suggests that they either
tend to merge, or that the WN components in these binaries rarely evolve into
WC stars in the Galaxy.

###### Key Words.:

stars: binaries – stars: Wolf-Rayet – techniques: cross-correlation

##  1 Introduction

Wolf-Rayet (WR) stars are a spectroscopic class of objects with strong, broad
emission lines of helium and H$\beta$. They are thought to be the descendants
of main-sequence O stars with initial masses greater than about 20-30
$M_{\odot}$, as well as immediate progenitors of black holes. Wolf-Rayet
binary systems are therefore natural progenitors of black-hole binaries, which
could coalesce to produce observable gravitational waves. Based on the
chemical composition of their spectra, WR stars are divided into nitrogen-
(WN), carbon- (WC), and oxygen-rich (WO) WR stars. These elements are thought
to be the exposed products of hydrogen, helium, and carbon burning,
respectively. Conti (1976) hypothesised that main-sequence O stars could strip
themselves through their stellar winds and appear as WR stars before ending
their lives as compact objects (called the Conti scenario). However, most
massive stars live in binary systems that will interact over the course of
their lifetime (e.g. Sana et al., 2012), and in this way, envelope stripping
via a companion can also form WR stars. The dominant formation channel, and
hence subsequent evolution, of WR stars is still an open question (Paczyński,
1967; Neugent & Massey, 2014; Shenar et al., 2019, 2020). Constraining the
intrinsic multiplicity properties of the WN and WC populations allows us to
understand the consequences of binary interaction on the final stages of
stellar evolution. Moreover, orbital analysis of WR binaries directly allows
us to measure masses of black-hole progenitors prior to core-collapse in a
model-independent fashion.

The observed binary fraction of Galactic WR stars has been reported to be
${\sim}0.4$ in the literature, with a total of 227 objects (van der Hucht,
2001, henceforth VDH01). This well-studied sample consisted of 127 WN stars,
87 WC stars, 10 WN/WC stars, and 3 WO stars. The reported binary fraction of
${\sim}0.4$ includes photometric, spectroscopic, and visual binaries,
alongside candidates flagged as binaries due to the dilution of the emission
lines in their spectra. As VDH01 is a compilation of studies with different
data sets collected with different instruments and analysed using various
techniques, it is non-trivial to correct for the observational biases. As a
result, determining the intrinsic multiplicity properties of the Galactic WR
population using these observational statistics is problematic.

The Galactic Catalogue of WR stars111http://pacrowther.staff.shef.ac.uk/WRcat/
(henceforth GCWR; originally Appendix 1 in Rosslowe & Crowther, 2015) has a
total of 667 Galactic WR stars (v1.25). Most of the recent additions to this
catalogue were discovered through near- and mid-infrared surveys (Mauerhan et
al., 2009; Shara et al., 2009, 2012; Faherty et al., 2014; Rosslowe &
Crowther, 2018). Unfortunately, not all of these WR stars have been
investigated for possible companions. In order to obtain a reasonable
observational-bias correction using spectroscopy, for example, it is of
paramount importance to accurately quantify the uncertainties on the radial
velocity (RV) measurements. With this in mind, we undertook a magnitude-
limited ($V\leq 12$ mag) spectroscopic survey of northern Galactic WR stars
with the Mercator telescope on La Palma in 2017. Using the High-Efficiency and
high-Resolution Mercator Echelle Spectrograph (HERMES; Raskin et al., 2011),
we obtained at least six epochs of data for 39 northern Galactic WR stars.

The 12 WC stars in our sample were analysed in Dsilva et al. (2020, henceforth
Paper 1). We determined the observed binary fraction
($f_{\textrm{obs}}^{\textrm{WC}}$) to be 0.58 $\pm$ 0.14. Using Monte Carlo
(MC) simulations with the measured RV uncertainties, we derived the intrinsic
binary fraction ($f_{\textrm{int}}^{\textrm{WC}}$) of the Galactic WC
population to be at least 0.72 at the 10% significance limit with orbital
periods up to $10^{5}\,$d. The 16 early-type WN (WNE) stars were analysed in
Dsilva et al. (2022, henceforth Paper 2), where the observed binary fraction
($f_{\textrm{obs}}^{\textrm{WNE}}$) was found to be 0.44 $\pm$ 0.12. After
adopting a Bayesian framework, our MC simulations revealed the intrinsic
binary fraction of WNE stars ($f_{\textrm{int}}^{\textrm{WNE}}$) to be
$0.56\begin{subarray}{c}+0.20\\\ -0.15\end{subarray}$ with orbital periods
explored up to $10^{5}\,$d. The orbital period distribution of the parent WNE
population revealed that the majority of binaries have periods shorter than 10
d, similar to what is found for main-sequence O stars (Sana et al., 2012).

Using the same Bayesian framework, Paper 2 also re-derived the multiplicity
properties for the WC population. We found that the underlying orbital period
distribution was significantly different from that derived for the WNE
population ($f_{\textrm{int}}^{\textrm{WC}}$ $=0.96\begin{subarray}{c}+0.04\\\
-0.22\end{subarray}$ and $\pi^{\textrm{WC}}$ $=1.90\begin{subarray}{c}+1.26\\\
-1.25\end{subarray}$), with a majority of WC binaries having orbital periods
greater than 1000 d. By comparing the distributions for the orbital period of
the WNE and WC populations, we found a lack of short-period WC binaries
($P<10\,$d), questioning the evolutionary link between WNE and WC binaries.
This deficit is backed by the literature, where the number of short-period WC
binaries is much smaller than that of the corresponding WNE binaries, even
though they should be easiest to detect given the large Doppler motion
exhibited by their spectral lines.

As the third paper in this series, the focus of this work is to analyse the 11
WNL stars in our sample and to investigate the multiplicity properties of the
underlying late-type nitrogen-rich (WNL) WR population. WNL stars can either
be classical (post-main-sequence, hydrogen-rich) or very massive main-sequence
(hydrogen-burning) WR stars (e.g. 1997deKoter). It is challenging to
differentiate between the two, although the main-sequence WNL stars are
generally more luminous (and more massive) than classical WNL stars (Hamann et
al., 2019). While attempting to link the WNL population with the WNE and WC
populations through binary evolution, it is important to differentiate between
main-sequence and classical WNL stars. When the known binaries are excluded,
the luminosities of the stars in our sample are lower than or around
$10^{6}\,L_{\odot}$ (Hamann et al., 2019). We aim to increase the analysed
sample size and explore the connection between the multiplicity properties of
main-sequence O stars, WN, and WC stars. The sample and data are presented in
Sect. 2. The method of measuring RVs is explained in Sect. 3. Section 4
presents our results. The discussion is presented in Sect. 5, and our
conclusions are presented in Sect. 6.

##  2 Sample and data reduction

From the GCWR, we selected WN stars that have spectral types later than WN5.
Entries listed as ‘WN5-6’ were considered to be WN5 for simplicity. For
objects to be visible with the Mercator telescope, we applied a magnitude cut
of $V\leq 12$ and $\delta\geq-30\degree$. For stars with missing $V$-band
magnitudes, we used their narrow-band $\varv$ magnitudes (Smith, 1968; Massey,
1984) and applied the criterion $\varv\,\leq\,13$. This resulted in a sample
of 11 WNL stars. We discuss the selection biases in Sect. 5.2.

Over the course of the RV monitoring campaign, we obtained at least six epochs
with the 1.2 m Mercator telescope on La Palma using the HERMES spectrograph.
HERMES covers the optical regime with a wavelength range from 3800 Å to 9000 Å
with a resolving power of $R=\lambda/\Delta\lambda\sim 85\,000$. We also used
archival HERMES data in our analysis when available, resulting in a time
baseline of two to eight years. The number of spectra and time coverage for
the 11 WNL stars in our sample is shown in Table 1.

Table 1: Eleven WNL stars in our RV monitoring campaign with the number of spectra, time baseline of coverage ,and average S/N per resolution element at 5100 Å. WR# | Spectra | Time coverage (d) | S/N
---|---|---|---
108 | 11 | 1140 | 125
120 | 7 | 385 | 30
123 | 8 | 387 | 60
124 | 10 | 577 | 50
134 | 15 | 2901 | 170
136 | 39 | 2907 | 280
148 | 20 | 1161 | 110
153 | 49 | 2858 | 200
155 | 85 | 3075 | 140
156 | 18 | 797 | 70
158 | 13 | 1031 | 70

The data reduction and normalisation is described in Paper 1. In short, the
data were first reduced using the standard HERMES pipeline (Raskin et al.,
2011) and then corrected for the instrumental response ( Paper 1, Royer et al.
in prep). In addition to the bias and flat-field correction, the HERMES
pipeline also corrects for barycentric motion. Following this, the spectra
were corrected for telluric contamination using Molecfit (Smette et al., 2015;
Kausch et al., 2015). After correcting for these effects, the spectra are only
affected by interstellar (and maybe circumstellar) reddening. In order to
normalise them in a homogeneous fashion and to minimise the human systematics,
we used a normalised WNL model spectrum from the Potsdam Wolf-Rayet code
(Gräfener et al., 2002; Todt et al., 2015) to identify pseudo-continuum
regions around 8100 Å in the red and 5100 Å in the blue. We then anchored a
continuum WNL model to the red and applied a reddening to fit the spectrum in
the blue. After exploring various reddening laws, we concluded that they did
not affect the homogeneity of the normalisation process. We therefore decided
to use the reddening law from Fitzpatrick (2004).

##  3 Radial velocity measurements

As the spectra of WR stars are dominated by strong and broad emission lines,
measuring RVs is a challenging task. We decided to use cross-correlation to
measure RVs for the stars in our sample. An implicit assumption of cross-
correlation is that the template is an accurate representation of the data.
Therefore, the choice of template is important. Because stellar atmospheric
models usually do not accurately reproduce the complex line profiles of WR
spectra and and the line profiles cannot be reproduced by Gaussian or
Lorentzian functions, we decided to construct and use a spectrum with a high
signal-to-noise ratio (S/N) as a template. We briefly describe the method and
assumptions below.

###  3.1 Cross-correlation for measuring radial velocities

The cross-correlation function (CCF) is a convolution of the template with the
data, and it is described using a log-likelihood function (Zucker, 2003, see
Paper 1 for more details). The RV of an epoch is measured by maximising this
function, and the uncertainty can be derived from maximum log-likelihood
theory. The measured RVs are then used to create a co-added spectrum, which is
in the rest frame of the initial template. The co-added spectrum is then used
to re-measure the RVs. This iterative process is continued until the measured
RVs do not change within their measurement errors. One caveat of this method
is that the measured RVs are relative to an epoch, and not absolute. This is
not a problem when probing RV variations to identify binary candidates (as in
this work), but an absolute shift must be applied when combining them with RVs
from the literature.

###  3.2 Wind variability and its effect on radial velocity measurements

Comparing the WNL stars in our sample to the WCs (Paper 1) and WNEs (Paper 2),
we observe significantly more variability in the WNL line profiles. This is
expected because strong line-profile variability has been observed in WNL
stars before (St-Louis et al., 2009; Chené & St-Louis, 2011; Michaux et al.,
2014; Chené et al., 2020). This directly increases the measurement
uncertainties on the RVs, as the assumption of the template reproducing the
data partially breaks down. In addition to correcting for observational
biases, it is also important to understand the effect of this variability on
the RV measurements.

In order to reduce the effect of wind variability on RV measurements, we
selected spectral lines that were least affected by spectral variability for
each star. Since the line-forming regions in WR stars are spatially extended,
spectral lines of different elements probe different physical regions in the
outflowing wind. Therefore, the behaviour of these lines is sensitive to local
wind physics and can exhibit disparate RVs. To address this, we used lines of
He ii, N iii, N iv, and in some cases, N v, to measure RVs. Additionally, for
each star, we used the combination of all the above-mentioned masks and called
it ‘full spec’. The final masks for each object are indicated in Appendix. B.
In Paper 1 and Paper 2, we obtained high-cadence data of the long-period
binaries WR 137 and WR 138 away from their periastron passages. This allowed
us to quantify the amplitude of this variability on the RV measurements in WC
and WNE stars, which were found to be ${\sim}5$ and ${\sim}15$ km s-1
respectively.

In this work, we focus on WR 136, which has a spectral type of WN6b(h).
Although it is classified as an SB1? system in the GCWR with a period of 4.5 d
(Koenigsberger et al., 1980; Aslanov & Cherepashchuk, 1981), there is no
derived orbit for this system. Further studies with photometry (Moffat &
Shara, 1986) and polarimetry (Robert & Moffat, 1989) failed to confirm this
period. We chose WR 136 for this purpose due to a lack of a long-period binary
in our sample. Assuming it is a single star, we obtained high-cadence data
with HERMES over two periods. We first procured 18 spectra over 16 days in
August 2019. Second, we obtained between 1 and 6 epochs within a night on
seven occasions between August and September of 2019. Finally, we obtained
between 6 and 15 epochs per night over ten nights in October 2019. This
resulted in a total of 87 high-cadence spectra.

Figure 1: High-cadence RV measurements for WR 136 over a variety of masks. In
brackets at the bottom are values of ($\sigma_{w}$, $\sigma_{\textrm{RV}}$)
(km s-1). As there are 87 data points for each mask, the legend has been
omitted for clarity.  Figure 2: Non-parametric threshold plot showing the
observed binary fraction as a function of the threshold $C$. The adopted
threshold of 50 km s-1 is shown by the dot-dashed vertical line. The entries
in bold are confirmed spectroscopic binaries in the literature. Table 2:
Radial velocity measurements for our sample of WNL stars together with an
overview of their known multiplicity properties. $\Delta$ RV and
$\sigma_{\textrm{RV}}$ are calculated in this work and are used to identify
tentative spectroscopic binaries. The spectral types are taken from the GCWR
unless indicated otherwise, with ‘d.e.l.’ implying the dilution of emission
lines, and ‘a’ indicating the presence of absorption lines. The binary status
of this work is reported based on the spectroscopic observations.

WR# | Spectral Type | Binary Status | Period | e |  $\Delta$ RV | $\sigma_{\textrm{RV}}$ |  $\Delta$RV $>$ C
---|---|---|---|---|---|---|---
| (GCWR) | (GCWR) | This work | (d) |  | (km s-1) | (km s-1) |
108 | WN9ha | a, d.e.l. | - | - | - | 15.7 | 5.0 | no
120 | WN7o | - | - | - | - | 40.5 | 15.7 | no
123 | WN8o | SB1?, no d.e.l. | SB | - | - | 57.1 | 18.2 | yes
124 | WN8h | SB1?, no d.e.l. | - | - | - | 19.3 | 5.9 | no
134 | WN6b | SB1?, no d.e.l. | - | - | - | 29.6 | 9.3 | no
136 | WN6b(h) | SB1?, no d.e.l. | - | - | - | 15.4 | 3.0 | no
148 | WN8h+ | SB1, d.e.l. | SB | 4.3(a) | 0 (fixed)(a) | 171.8 | 54.5 | yes
153 |  | WN6o/CE+O3-6
---
\+ B0:I+B1:V-III
SB2 + SB2 | SB |  | 6.6887(b)
---
\+ 3.4663 $\pm$ 0.0011
| 0.0(b)
---
\+ 0.16 $\pm$ 0.03
576.6 | 150.3 | yes
155 | WN6o+O9II-Ib | SB2 | SB | 1.6412436(c) | 0.034 $\pm$ 0.008(c) | 609.5 | 212.0 | yes
156 | WN8h | d.e.l. | - | - | - | 16.1 | 4.4 | no
158 | WN7h | d.e.l. | - | - | - | 15.0 | 4.1 | no

  * (a)

$P=4.317336\,\pm\,0.000026\,$d (Munoz et al., 2017),

  * (b)

Demers et al. (2002),

  * (c)

Marchenko et al. (1995) fixed period

We used lines of He ii, N iii, N iv, and N v and the Balmer lines to measure
RVs for WR 136. The RV dispersion is shown in Fig. 1. The observed RV
dispersion comprises a statistical part (i.e. the measurement errors,
$\sigma_{p}$) and contribution from wind variability ($\sigma_{w}$). Assuming
they are uncorrelated, the weighted standard deviation of the RVs for each
mask can be represented by

$\sigma_{\textrm{RV}}=\sqrt{\sigma_{p}^{2}+\sigma_{w}^{2}}\textrm{.}$ (1)

By measuring $\sigma_{\textrm{RV}}$ and $\sigma_{p}$, we obtain an upper limit
on the wind variability. For each mask, values of ($\sigma_{\textrm{RV}}$,
$\sigma_{w}$) are indicated in Fig. 1. We find that lines of He ii are less
affected by wind variability than N v $\lambda 4945$. One possible reason is
that the N v $\lambda 4945$ line is a very weak line in the spectrum of WR
136, limiting its RV accuracy. In any case, the trend of He ii lines showing
greater stability than lines of nitrogen is unusual (see e.g. Paper 2, ). A
plethora of reasons might explain this, such as different wind structures or
simply different wind physics across the various line-forming regions. This
good example demonstrates that each WR star is unique. The RV amplitudes for
the masks are similar to what was found in Koenigsberger et al. (1980),
although we did not find the same period as they reported after analysing the
data with a Lomb-Scargle periodogram (Lomb, 1976; Scargle, 1982). We used
diagnostic plots such as Fig. 1 for each object to select an appropriate mask
for measuring RVs. These are indicated in Appendices A and B.

Figure 3: Marginalised posteriors of $\log P_{\mathrm{max}}^{\textrm{WNL}}$,
$f_{\textrm{int}}^{\textrm{WNL}}$, and $\pi^{\textrm{WNL}}$ for the Galactic
WNL population. The one-dimensional posteriors are calculated assuming flat
priors. For each posterior, the solid red lines show HDI68, and the dashed red
line shows the mode.

##  4 Results

###  4.1 Observed binary fraction and detection probability

After measuring the RVs, we computed the peak-to-peak amplitude ($\Delta$RV)
for each object. We chose a threshold $C$ above which we attributed the
observed $\Delta$RV to Doppler motion in a binary system. Figure 2 is a non-
parametric threshold plot that shows the observed binary fraction as a
function of the chosen threshold. By moving right to left, we attribute the RV
amplitude of these stars to Doppler motion, and classify them as candidate
spectroscopic binaries.

In principle, the chosen threshold should be high enough to avoid false
positives due to intrinsic variability. The high-cadence study on WR 136
demonstrated that with the appropriate mask, the measured peak-to-peak RV
amplitude due to intrinsic variability is ${\sim}15$ km s-1. This is similar
to what was found for the N v lines in WR 138 ( Paper 1, ). Therefore, we
adopted a similar strategy and chose a threshold that is at least three times
higher than the peak-to-peak intrinsic variability, at $C=50$ km s-1. This
resulted in the classification of 4 out of 11 stars as RV variable objects for
which binarity is likely the cause. This corresponds to an observed binary
fraction ($f_{\textrm{obs}}^{\textrm{WNL}}$) of 0.36 $\pm$ 0.15.

Figure 4: Same as Fig. 2, but for the 27 WN stars (16 WNE + 11 WNL) in our
sample. The threshold $C=50\,$km s-1 is shown by the vertical dot-dashed line.
Entries in bold represent confirmed spectroscopic binaries in the literature.
Figure 5: Same as Fig. 3, but for the combined (WNE + WNL) Galactic WN
population. Figure 6: Visualisation of the $10^{7}$ period distributions
created by sampling the posteriors from Fig. 5. The light and dark red regions
depict 95% and 68% of all distributions. The solid red line is the
distribution created with the best-fit values from the posteriors. The blue
regions and lines are the same for the WC population from Paper 2. The dashed
black line is the period distribution for O stars from Sana et al. (2012).

###  4.2 Multiplicity properties: WNL population

We performed a Bayesian analysis with MC simulations with a method developed
in Paper 2 to formally account for the observational biases. The ideal
solution is to calculate the likelihood of the observed RV time series for
each object based on the sampling and possible binary properties of the
system. However, this is too computationally intensive, and instead, we
divided the objects into multiple $\Delta$RV bins and tried to reproduce them
with our simulations. The $\Delta$RV bins were $\Delta$RV $<$ 50 km s-1 (seven
objects), $50\,\leq\,$$\Delta$RV$\,<\,250\,$km s-1 (two objects),
$250\,\leq\,$$\Delta$RV$\,<\,650\,$km s-1 (two objects), $\Delta$RV
$\geq\,650\,$km s-1 (no object).

The parameters included in the model for the population with binaries are the
period distribution, intrinsic binary fraction, inclination, eccentricity,
mass ratio, time of periastron passage, and the orientation of the binary
system in three-dimensional space. The period distribution is characterised by
the minimum period ($\log P_{\mathrm{min}}^{\textrm{WNL}}$), maximum period
($\log P_{\mathrm{max}}^{\textrm{WNL}}$), and the power-law index
($\pi^{\textrm{WNL}}$). The power-law index $\pi$ determines the shape of the
distribution of binaries with orbital periods $P$ as follows:

$p(\log P)\sim(\log P)^{\pi}.$ (2)

Along with the period distribution, we included the intrinsic binary fraction,
$f_{\textrm{int}}^{\textrm{WNL}}$, as a model parameter. The eccentricities
were drawn from a flat distribution between 0.0 and 0.9, with random
inclinations, times of periastron passage, and three-dimensional orientations
of the orbital planes. We also assumed a flat mass-ratio distribution from 0.1
- 2, with the mass of the WNL star to be 20 $M_{\odot}$. We refrained from
using the observed distributions of eccentricity and mass-ratio since they
show observational biases, which we aim to correct for. Moreover, we explored
various mass-ratio distributions in Paper 2 and noted that they did not affect
the posteriors significantly. Given the presence of very short-period binaries
in the WNL sample, we fixed the value of $\log
P_{\mathrm{min}}^{\textrm{WNL}}$ at 0.15 [d] (approximately 1 d). We explored
values of $\log P_{\mathrm{max}}^{\textrm{WNL}}$ from 1.5 to 5.0 [d] in steps
of 0.1 dex, $\pi^{\textrm{WNL}}$ from $-2.0$ to $1.0$ in steps of 0.1, and
$f_{\textrm{int}}^{\textrm{WNL}}$ from 0.30 to 1.00 in steps of 0.02. We also
used prior information on the known orbital periods for those classified as
binaries (Table 2), and required at least three objects with $1<P<10\,$d.

With the framework set up, we simulated 10 000 sets of 11 WNL stars for each
$P-M_{2}$ grid point, resulting in almost $4\times 10^{8}$ populations. We
calculated the three-dimensional likelihood of reproducing the observed
distribution of objects in $\Delta$RV bins. Assuming flat priors on $\log
P_{\mathrm{max}}^{\textrm{WNL}}$, $\pi^{\textrm{WNL}}$ and
$f_{\textrm{int}}^{\textrm{WNL}}$, we computed their marginalised posterior
likelihoods (Fig. 3). We computed the 68% credible intervals for each
posterior (the highest-density interval, HDI68). For the three model
parameters, our posteriors yield values of
$f_{\textrm{int}}^{\textrm{WNL}}$$\,=\,0.42\begin{subarray}{c}+0.15\\\
-0.12\end{subarray}$,
$\pi^{\textrm{WNL}}$$\,=\,-0.70\begin{subarray}{c}+0.73\\\
-1.02\end{subarray}$ and $\log
P_{\mathrm{max}}^{\textrm{WNL}}$$\,=\,4.90\begin{subarray}{c}+0.09\\\
-3.40\end{subarray}\,$ [d] for the parent WNL population. The value of $\log
P_{\mathrm{max}}^{\textrm{WNL}}$ is set by the upper limit of the grid due to
the lack of long-period constraints introduced by the orbital bins because no
WNL binaries are confirmed at $P>10\,$d.

The derived multiplicity properties agree with those of the Galactic WNE
population (Paper 2). An interesting difference is that of the upper-period
cutoff, which is better constrained for the WNE population ($\log
P_{\mathrm{max}}^{\textrm{WNE}}$ $=4.60\begin{subarray}{c}0.40\\\
-0.77\end{subarray}$) given the prior information on the presence of long-
period binaries. We lack these constraints for the WNL population, where the
only orbital periods that are constrained in the literature are shorter than
10 days (Table 2). This results in a large HDI68 for $\log
P_{\mathrm{max}}^{\textrm{WNL}}$, which is reconcilable with $\log
P_{\mathrm{max}}^{\textrm{WNE}}$ within the credible intervals.

The negative power-law index for the WNL sample indicates a preference for
binary systems with shorter orbital periods. This is similar to what was found
for the WNE (Paper 2) and O-type populations (Sana et al., 2012). The lower
cutoff for the orbital period distribution ($\log
P_{\mathrm{min}}^{\textrm{WNL}}$) was fixed at 0.15 [d] in order to account
for binaries with periods as short as 1.6 d in our sample. The similarities
with respect to the WNE population indicate that the overall multiplicity
properties of the Galactic WN population are consistent. We therefore combined
the WNE and WNL populations and performed a similar Bayesian analysis.

###  4.3 Multiplicity properties: Combined WN population

After merging the data sets of the 16 WNE stars in Paper 2 and the 11 WNL
stars in this paper, we ended up with 27 Galactic WN stars. Based on their
$\Delta$RV values, we created Fig. 4, similar to Fig. 2, depicting
$f_{\textrm{obs}}^{\textrm{WN}}$ as a function of the threshold $C$. The
characteristic kink in the curve can be seen around 50 km s-1, differentiating
RV variation due to Doppler motion and intrinsic variability, thereby
reaffirming our choice of threshold. We therefore constrained the observed
binary fraction for the WN sample to be $f_{\textrm{obs}}^{\textrm{WN}}$
$=\,0.41$ $\pm$ $0.09$.

We performed a Bayesian analysis on the combined WN sample with the same
underlying assumptions for the distributions stated in Sect. 4.2. We divided
the sample into various $\Delta$RV bins as follows: $\Delta$RV $<50\,$km s-1
(16 objects), 50 $\leq$ $\Delta$RV $<250\,$km s-1 (6 objects), 250 $\leq$
$\Delta$RV $<650$ (6 objects), $\Delta$RV $\geq\,650$ km s-1 (no object).
Similarly, we also defined minimum orbital period bins based on what is known
for the sample: $P\,>\,1\,$d (10 objects), $P\,>\,10\,$d (3 objects),
$P\,>\,100\,$d (2 objects) and $P\,>\,1000\,$d (1 object). The one- and two-
dimensional marginalised posteriors (computed by assuming flat priors) are
shown in Fig. 5. As compared to Fig. 3, the power-law index
($\pi^{\textrm{WN}}$) becomes more negative, and
$f_{\textrm{int}}^{\textrm{WN}}$ on the WN population increases due to the
contribution from the WNE sample.

The derived multiplicity properties for the WN sample were used to construct a
visualisation of the period distribution. Similar to Paper 2, we sampled
$10^{7}$ sets of parameters from the posteriors in Fig. 5 and used them to
create orbital period distributions. The density cloud representing these
distributions is shown in red in Fig. 6. The period distribution constructed
using the best-fit parameters is shown with a solid red line. We also plot the
density cloud of distributions for the Galactic WC population in blue (Paper
2). The period distribution for main-sequence O stars is shown with a dashed
black line (Sana et al., 2012).

Figure 7: Cumulative distribution of the reported orbital periods from the
literature for the Galactic WN (solid red) and WC (dash-dotted blue)
populations. The observed distributions based on spectroscopic periods from
our sample are also plotted, with the WN (dashed red) and WC (dotted blue)
binaries.

##  5 Discussion

###  5.1 Comparison with the literature

In order to verify if what is observed agrees with our results, we
investigated the literature to consider WR stars beyond those included our
sample. Since the objects from VDH01 have been thoroughly analysed for
binarity, we focused on this subset of WR stars. The catalogue contains 87 WC
stars and 127 WN stars, of which 78 are WNL stars. Of these 78 objects, 21 are
classified as spectroscopic binaries and 14 currently have orbital solutions.
Of these, only one has a period longer than 100 days.

The total number of Galactic WN binaries with known orbital periods is 28.
Combining this with the 18 known orbital periods for Galactic WC binaries, we
constructed the cumulative observed orbital period distribution along with the
observed distributions from our sample (Fig. 7). While a few WC binaries have
periods shorter than 10 d, this fraction is still much smaller than that of
short-period WN binaries. This shows that the analysed samples are
representative of the Galactic WR population.

###  5.2 Observational biases due to the limiting magnitude

Another potential observational bias introduced by the conditions of the RV
campaign is that of the limiting magnitude. Because WR stars are generally
faint in the optical, the selection criteria of $V\leq 12$ inherently favour
binaries. Vanbeveren & Conti (1980) demonstrated this clearly for the Large
Magellanic Cloud, although this effect is not dominant in the Galaxy due to
the large spread in the distances.

Similar to what was done in Paper 2, we assumed that the companion contributes
to around 50% of the flux in a WR $+$ OB system (e.g. Shenar et al., 2019).
Therefore, WR binaries would be twice as bright as single WR stars on average.
To account for this bias, we need to account for single WR stars between 12.0
and 12.7 mag. When the $V$-band magnitude was missing, we searched for
$\varv$-band magnitudes between 13.0 and 13.7.

We found four single WNL entries in that range: WR 58 (WN4b/CE), WR 82
(WN7(h)), WR 130 (WN8(h)), and WR 131 (WN7h+absorption). Although WR 131 could
be considered a candidate binary, no evidence of a companion has been found in
the literature, and hence we conservatively considered it to be a single star.
Including these stars in our sample would change the intrinsic binary
statistics from 5 binaries out of 11 WNL stars to 5 binaries out of 15 WNL
stars. This would result in a binary fraction of 0.33, which is within our
credible interval.

###  5.3 Consequences on binary evolution

Depending on their mass, main-sequence O stars are thought to evolve into
either red supergiants or luminous blue variables (LBVs) before becoming WR
stars, after which they are expected to collapse to form compact objects
(Conti, 1976; Meynet & Maeder, 2003; Crowther, 2007; Langer, 2012). In this
section, we use our derived multiplicity properties for the Galactic WN and WC
populations to infer possible connections between the evolutionary stages
before collapse. As the multiplicity properties of the WNL and WNE populations
are compatible, we discuss the WN population as a whole.

####  5.3.1 Linking the O and WN populations

As indicated in Fig. 6, the orbital period distributions of O stars and WN
stars is in excellent agreement. This is not surprising because WN stars can
be formed by the envelope stripping of the primary by the secondary in an OB
binary. Using the analytical expressions from Soberman et al. (1997), we can
calculate the change in the orbital period due to mass transfer. Depending on
the mass ratio of the OB binary, mass transfer does not increase the orbital
period by more than a factor of three, regardless of the conditions for mass
transfer. For example, conservative mass transfer in a 40 $+$ 30 $M_{\odot}$
binary where the primary transfers 20 $M_{\odot}$ would have an increase in
the period ($P_{f}/P_{i}$) of a factor of 1.7. Therefore, the increase in the
orbital period would not shift the distribution drastically, which is in
accordance with what we find.

A different process that can significantly harden a binary is common-envelope
evolution, triggered by mass transfer in systems with extreme mass ratios or
after the donor has developed a deep convective envelope (see e.g. the review
by Ivanova et al. 2013). However, envelope ejection is energetically
disfavoured unless interaction occurs after the star becomes a red supergiant
(e.g. Klencki et al., 2021), but this phase is potentially not reached by the
most massive stars as it would require evolution beyond the Humphreys-Davidson
limit (Humphreys & Davidson, 1979; Davies et al., 2018; Gilkis et al., 2021).

Depending on their initial mass, some massive stars are also thought to go
through the LBV phase during their transition from main-sequence O stars to
the WN phase (see e.g. Lamers & Nugis, 2002; Crowther, 2007; Langer, 2012).
Multiplicity studies of the LBV population indicate a binary fraction of 0.70
$\pm$ 0.09, with the majority of them at periods of a year or longer (Mahy et
al., 2022). The multiplicity properties of the LBVs seem inconsistent with the
large number of short-period WN binaries that are found both in our sample and
in the GCWR (Fig. 7). However, this could just be a consequence of shorter-
period systems being too compact to fit an LBV star, leading an O star to fill
its Roche lobe before reaching that evolutionary phase. This would imply that
the progeny of the LBV binary population are the WN binaries with $P>1$ yr.

####  5.3.2 Evolution from the WN to WC populations

The largest discrepancy between the orbital period distributions for both the
observed (Fig. 7) and intrinsic (Fig. 6) populations is the glaring lack of WC
binaries at short periods. Because WN stars are expected to evolve into WC
stars by further stripping their envelope, the change in their orbital
parameters is governed by wind or binary mass loss. This results in an
increase of the orbital period by a factor of ${\sim}1.5$-2. Therefore, this
implies that only WN binaries with $P>100\,$d would preferentially evolve into
WC binaries. In the short-period regime of $P<10\,$d, only a small fraction of
WN binaries might become WC binaries.

One possible factor preventing WNE stars in short-period binaries from
evolving into WC binaries is that they are unable to strip their envelopes
further before they reach core collapse, for example, due to reduced mass-loss
rates (possible implications from Neijssel et al., 2021). Why this would only
affect WN binaries with short periods and not the entire population is
unclear. Another possibility is that short-period WN binary systems undergo
interaction before they can reach the WC phase. The cause of this interaction
might be the expansion of the WN star due to inflation (Gräfener et al., 2012;
Sanyal et al., 2015; Grassitelli et al., 2018; Ro, 2019). While it is unclear
whether inflation occurs in nature and how an inflated donor star would
respond to mass transfer, an unstable mass-transfer phase resulting in a
merger could prevent short-period WN stars from evolving into WC binaries.
Conversely, if these mass transfer episodes are stable, they would result in
further stripping, leading to more short-period WC stars and worsening the
discrepancy in the period distributions.

Additionally, in systems undergoing wind-wind collisions, slowed outflows may
potentially interact with the binary and be ejected with additional angular
momentum, leading to a contraction of the orbit and possibly a merger. For
example, MacLeod & Loeb (2020) showed how the interaction of colliding winds
with the stars in equal-mass main-sequence binaries could lead to a shrinkage
of the orbit. Depending on the ratio of the orbital velocity to the wind
velocity, this effect could also occur in WN binaries. Whether this scenario
provides a valid explanation remains to be shown.

A final possible scenario could be that the O star companion fills its Roche
lobe before the WN evolves into a WC. The likelihood of this occurring during
the short-lived WNE phase is too small for this to be the predominant
explanation for the lack of short-period WC systems, however.

Due to the duration and sampling of the RV campaign, it is also possible that
there is a population of long-period binaries ($P>1000\,$d) that we do not
detect. This is because the intrinsic variability of WN stars is higher than
that of the WC, making it challenging to detect low RV amplitudes. To
elaborate, the progenitor binary population would be composed of WNL plus mid-
to late-type O star pairs. The observed RV variations for these systems across
our observing campaign would be about 15 to 20 km s-1. Therefore, the
progenitor population of long-period WC binaries might simply be undetected.
However, this would imply that for the Galactic WN population, the value of
$f_{\textrm{int}}^{\textrm{WN}}$ is close to 1.00, as most (all?) of the
apparently single WN stars would then reside in long-period binary systems.

A large fraction of the main-sequence O population are in hierarchical triple
systems (e.g. Sana et al., 2014; Moe & Di Stefano, 2017). Mass loss due to
stellar winds or binary stripping, among other things, will change the ratio
of the inner and outer separation. If the stripping of the primary by the
secondary resulted in a WN $+$ OB binary, then the nature of mass transfer and
evolution of the inner orbit determines the stability of the triple. When this
ratio changes beyond a critical point, the system becomes dynamically
unstable. This could result in the disruption of the triple, or in a merger of
the inner binary (Toonen et al., 2020).

In the case of mass loss through stellar winds, the dynamically unstable phase
can last from thousands to millions of years (Toonen et al., 2022). Although
the most common predicted outcome is the preservation of the triple hierarchy,
it is also common for the system to be disrupted, with one of the stars
ejected. In case of an ejection, the resulting orbit has a period of the order
of $10^{3}$-$10^{5}\,$d (Toonen et al., 2022). As an example in a hierarchical
triple, if the inner WN $+$ OB binary was formed through a combination of
stripping via stellar winds and mass transfer, it could be dynamically
unstable. An ejection could result in the formation of a WN $+$ OB binary in a
wide orbit, where the WN star would proceed to evolve and become a wide WC $+$
OB binary. Detailed simulations involving the formation of the WR star, mass
transfer, and stellar winds are required to investigate the frequency and
feasibility of this channel.

##  6 Conclusions

With a homogeneous, magnitude-limited spectroscopic monitoring of 11 northern
Galactic WNL stars, we measured relative RVs using cross-correlation and found
$f_{\textrm{obs}}^{\textrm{WNL}}$ $=0.36\,\pm\,0.15$. Using a Bayesian
framework around MC simulations, we derived a fraction corrected for
observational biases
($f_{\textrm{int}}^{\textrm{WNL}}$$\,=\,0.62\begin{subarray}{c}+0.16\\\
-0.17\end{subarray}$). We observed that the computed intrinsic multiplicity
properties for the Galactic WNL population are congruous with those derived
for the WNE population in Paper 2.

We combined the WNE and WNL samples and simulated ${\sim}4\,\times\,10^{8}$
populations of 27 WN stars. We found the intrinsic multiplicity properties for
the Galactic WN population to be similar to those derived for main-sequence O
stars in Sana et al. (2012). We constructed the orbital period distribution
for Galactic WNs and noted the peak at $P<5\,$d. The abundance of short-period
WN binaries can be explained through case A or case B mass transfer in O
binaries. Short-period WN binaries can also form via common envelope evolution
through late case B or case C mass transfer, regardless of the mass ratio.
However, it is observationally non-trivial to distinguish between the
multitude of channels.

From the intrinsic multiplicity properties of the Galactic WC population (
Paper 1, ), we see a clear lack of short-period WC binaries, with the orbital
period distribution peaking at $P\,{\sim}\,5000\,$d. The lack of short-period
WC binaries is also supported by the literature. While a few are known, their
number is smaller than for their WN counterparts, even though the number of
WNs and WCs in the Galaxy is similar. The discrepancy in distributions is not
only found in our simulations (Fig. 6), but can also be seen in the observed
period distribution of Galactic WR binaries (Fig. 7). Orbital evolution via
mass loss from the WN to WC phase cannot explain the shift towards longer
periods.

The multiplicity properties of Galactic LBVs (Mahy et al., 2022) appear to
agree with that of the long-period O, WN, and WC binary populations. This
might imply that at long periods, an evolutionary channel of
O$\,(\xrightarrow{}$ LBV) $\xrightarrow{}$ WN $\xrightarrow{}$ WC might exist.
However, the evolution of the short-period WN binaries is still an enigma.
Invoking exotic channels such as common-envelope evolution and dynamical
interactions in triples could explain their evolution, but these channels are
highly uncertain. Further observational and theoretical studies are required
to understand their importance in the grand scheme of binary evolution.

As the immediate progenitors of black holes, the multiplicity properties of WR
stars directly affect those for black-hole binaries (e.g. through black-hole
kicks in a core-collapse scenario), and hence the predictions for
gravitational-wave progenitors. Expanding the sample size of magnitude-limited
studies is critical for understanding the binary evolution of massive stars.

###### Acknowledgements.

This work was published with funds from the European Research Council under
European Union’s Horizon 2020 research programme (grant agreement No. 772225).
TS also acknowledges funding received from the European Union’s Horizon 2020
under the Marie Skłodowska-Curie grant agreement No. 101024605. PM
acknowledges support from the FWO junior postdoctoral fellowship No. 12ZY520N.

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##  Appendix A Comments on individual objects

WR 108: According to the GCWR, the spectra of WR 108 have diluted emission
lines and show absorption. While it is quite common for WNL stars to show
absorption, diluted emission lines are often attributed to a companion star.
We measured a $\Delta$RV of ${\sim}16\,$km s-1 over 1140 days, and classified
WR 108 as a single star.

WR 120: The GCWR classifies WR 120 as a single WN7 star. The few absorption
lines in the spectra exhibit moderate line-profile variability. However, the
S/N of the data in the extreme blue regions makes it challenging to identify
whether this is simply due to intrinsic variability or due to Doppler motion.
With seven epochs spanning 385 days, we find a $\Delta$RV of 40.5 km s-1 using
N iii, and classified it as a single star.

WR 123: WR 123 is notorious for its strong photometric and spectral line-
profile variability (Marchenko & Moffat 1998). It was found to have a
periodicity of ${\sim}10\,$hours using photometric and spectroscopic
monitoring (Lefèvre et al. 2005; Dorfi et al. 2006; Chené et al. 2011).
Similar to WR 120, we find the absorption lines in the spectra to vary quite
significantly. By monitoring N v $\lambda\lambda 4604,4620$ for eight epochs
over 387 days, we measured a $\Delta$RV of 57.1 km s-1 and classified it as a
binary system. The sampling and number of spectra are too sparse to find any
significant periodicity, and so further monitoring is required to verify its
binary status.

WR 124: The GCWR classifies WR 124 as a SB1? with no dilution of emission
lines. It is surrounded by a spectacular nebula M1-67 and is the fastest
runaway in the Galaxy (Moffat et al. 1982). Given its 2.4 d and 2.7 d
periodicity (Moffat et al. 1982; Moffat & Shara 1986), it was considered to be
a binary with a neutron star. Toalá et al. (2018) were unable to rule out the
presence of an embedded neutron star when studying the system with X-rays. If
this were the case, the RV amplitude of the WR star would be below our
threshold. In any case, we measured $\Delta$RV to be 19.3 km s-1 with ten
epochs over 577 days, and classified WR 124 as a single star.

WR 134: Similar to WR 123 and WR 124, WR 134 is classified as a SB1? with no
dilution of emission lines. Its binary status has been widely debated in the
literature, and the observed periodicity has been attributed to a low-mass
companion (Marchenko & Moffat 1998; Rustamov & Cherepashchuk 2012). However,
Aldoretta et al. (2016) demonstrated that large-scale structures in the wind,
particularly in He ii $\lambda 5412$, exist with a period of 2.255 $\pm$ 0.008
d. We obtained 15 epochs over 2901 days and measured $\Delta$RV to be 29.6 km
s-1 using N v $\lambda 4945$ and classified it as a single star.

WR 136: WR 136 is surrounded by a ring nebula (NGC 6888), and is classified as
a SB1? with no dilution of emission lines in the GCWR. A period of 4.554 d was
found using line-profile variations (Koenigsberger et al. 1980) and RV
measurements (Aslanov & Cherepashchuk 1981). However, this period was not
verified later with polarisation (Robert & Moffat 1989) and photometry (Moffat
& Shara 1986). A neutron star companion was suggested as a companion, which
would again result in small RV variations of the WR star. With 39 epochs over
a time baseline of 2907 days, we measured a $\Delta$RV of 15.4 km s-1 using He
ii lines and classified it as a single star.

WR 148: WR 148 is one of the few WN8 stars in the Galaxy that is confirmed to
be in a binary system. The GCWR classifies it as a SB1 system, as it has a
short period of 4.3 d and was thought to have a compact companion (Drissen et
al. 1986a; Bracher 1979; Marchenko et al. 1996). However, Munoz et al. (2017)
found a period of 4.317336 $\pm$ 0.000026 and were able to disentangle the
spectra to find a O4-6 companion. Hamann et al. (2019) found a luminosity
($\log L$ $(L_{\odot})$) of 6.2, indicating that it might be a main-sequence
star. However, they also reported that 15% of the flux is contributed by its
companion, so that further analysis taking this into account is required. We
obtained 20 epochs over 1161 days and measured RVs using N iv
$\lambda\lambda\lambda 7103,7109,7123$. We found WR 148 to have a $\Delta$RV
of 171.8 km s-1 and classified it as a binary system.

WR 153: The GCWR classifies WR 153 to be a quadruple system (WN6o/CE+O3-6 +
B0:I+B1:V-III) where the WR binary has a period of 6.6887 days and a circular
orbit (Massey 1981; Demers et al. 2002). With 49 epochs over 2858 days, we
measured a $\Delta$RV of 576.6 km s-1 using N v $\lambda\lambda 4604,4620$ and
classified it as a binary system.

WR 155: The GCWR classifies WR 155 as a SB2 (WN6o + O9II-Ib) system. This
binary has the shortest known period (1.6412436 d; Moffat & Shara 1986;
Marchenko et al. 1995). Drissen et al. (1986b) studied the system with
polarimetry and found masses of 42 and 30 $M_{\odot}$ for the WN and O stars,
respectively. We obtained 85 epochs over 3075 days, measured $\Delta$RV to be
609.5 km s-1 using N v $\lambda 4945$ and $\lambda 4058$ and classified it as
a binary system.

WR 156: WR 156 is another WN8 star with large photometric and spectral line-
profile variability, with diluted emission lines. Photometric studies did not
find any conclusive periodicity (Moffat & Shara 1986; Marchenko et al. 1998).
It is reported to have a luminosity of 6.01 (Hamann et al. 2019), which
questions its status as a massive WNL versus a classical WNL star. We observed
WR 156 over 797 days and obtained 18 epochs. Using N iv $\lambda\lambda\lambda
7103,7109,7123$ and $\lambda 5737$ lines, we measured a $\Delta$RV of 16.1 km
s-1 and classified it as a single star.

WR 158: The GCWR classifies WR 158 as a WN7h star with diluted emission lines.
Andrillat & Vreux (1992) discovered O i $\lambda 8446$ in its spectrum,
hypothesising that it is produced in the slowly expanding cool shocked region
located outside the ionisation front of the bubble created by the WR wind, or
in a binary with a Be companion. Hamann et al. (2019) reported a luminosity
($\log L$ $(L_{\odot})$) of 6.06, which might indicate its status as a main-
sequence WNL star. We obtained 13 spectra over 1031 days, measured a
$\Delta$RV of 15.0 km s-1 using N iv $\lambda\lambda\lambda 7103,7109,7123$
and classified it as a single star.

##  Appendix B Relative radial velocity measurements

Relative RVs for the 11 WNLs in our sample. The reference epoch has a RV of
0.0 km s-1. We refrain from providing absolute RV measurements as this is
highly method dependent, especially for WR stars. The barycentric Julian date
(BJD) is given as the middle of the exposure. The average S/N is given in
Table 1. Along with the measured RVs, we indicate the measurement error, that
is, the statistical uncertainty $\sigma_{p}$ (Eq. 9 in Paper 1).

Table 3: Journal of HERMES observations for WR 108. Mask used: N iii $\lambda\lambda 4634,4641$ and $\lambda\lambda 5321,5327$ BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
7880.6447 | 6.7 | 0.4
7908.5761 |  $-$8.6 | 0.4
7910.5874 |  $-$8.8 | 0.9
8226.7346 | 0.0 | 0.3
8249.6662 |  $-$1.9 | 0.3
8255.6139 |  $-$3.8 | 0.3
8647.6343 |  $-$8.0 | 0.4
8651.5446 |  $-$4.2 | 0.5
8671.5345 |  $-$9.0 | 0.4
9002.5960 | 2.1 | 0.6
9020.6068 |  $-$3.3 | 0.4
Table 4: Journal of HERMES observations for WR 120. Mask used: N iii $\lambda\lambda 4634,4641$ BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
9000.5647 | 8.2 | 1.4
9000.5754 | 9.7 | 1.8
9029.5217 | 0.0 | 1.3
9343.5826 |  $-$9.1 | 2.1
9352.6879 |  $-$30.8 | 3.3
9364.6366 | 2.2 | 1.6
9385.6108 |  $-$21.1 | 1.3
Table 5: Journal of HERMES observations for WR 123. Mask used: N v $\lambda\lambda 4604,4620$. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
9009.6572 |  $-$41.2 | 4.7
9041.4644 |  $-$5.2 | 6.3
9078.5129 | 0.0 | 4.9
9150.3408 | 15.9 | 9.0
9341.6353 |  $-$27.3 | 7.1
9370.6808 |  $-$20.5 | 7.7
9382.6264 |  $-$13.3 | 5.4
9396.5899 |  $-$34.3 | 4.8
Table 6: Journal of HERMES observations for WR 124. Mask used: N iv $\lambda\lambda\lambda 7103,7109,7123$. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
8779.3312 | 2.9 | 4.3
8909.7390 |  $-$6.1 | 2.5
9007.5659 | 0.0 | 1.5
9024.4541 | 7.3 | 1.3
9341.7066 | 1.4 | 2.0
9342.6831 | 12.2 | 1.5
9345.5820 | 11.4 | 1.7
9346.6531 | 4.1 | 1.6
9355.6618 | 13.2 | 1.9
9356.6234 | 1.0 | 1.5
Table 7: Journal of HERMES observations for WR 134. Mask used: N v $\lambda 4945$. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
6119.7082 |  $-$17.4 | 1.6
6889.4453 | 8.5 | 1.0
7902.7067 |  $-$16.2 | 1.8
7919.7115 |  $-$6.3 | 2.6
7938.7064 |  $-$16.6 | 1.8
8195.7332 | 11.5 | 2.4
8206.6993 |  $-$18.1 | 2.1
8262.7226 |  $-$9.9 | 2.0
8276.6976 | 0.0 | 1.5
8625.7223 |  $-$3.2 | 1.9
8652.6205 |  $-$15.6 | 2.0
8663.7183 |  $-$7.0 | 2.1
8779.4245 | 3.8 | 2.8
9008.7157 | 3.2 | 2.3
9020.7094 |  $-$8.6 | 2.0
Table 8: Journal of HERMES observations for WR 136. Mask used: He ii $\lambda 4201$, $\lambda 4542$, $\lambda 4687$, $\lambda 5412$, $\lambda 6312$ and $\lambda 6685$. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
6113.4883 |  $-$2.9 | 0.6
7899.7208 |  $-$3.2 | 0.6
7915.7252 |  $-$4.7 | 0.8
7919.6966 |  $-$2.4 | 1.2
7988.5162 |  $-$2.3 | 0.5
8195.7629 | 1.2 | 0.8
8206.7539 | 2.4 | 0.8
8262.6675 |  $-$2.7 | 0.5
8276.7222 | 0.1 | 0.6
8308.5859 |  $-$6.8 | 0.6
8608.7275 | 5.6 | 0.6
8652.6254 | 2.1 | 0.5
8680.5815 | 0.8 | 0.5
8700.6889 | 3.2 | 0.4
8705.5711 |  $-$0.4 | 0.4
8706.5963 | 1.0 | 0.4
8707.5559 | 4.7 | 0.5
8708.4991 | 4.7 | 0.4
8709.4306 |  $-$2.9 | 0.4
8710.5613 |  $-$2.2 | 0.4
8712.5417 |  $-$3.3 | 0.4
8713.5110 |  $-$1.9 | 0.5
8714.4924 |  $-$1.1 | 0.4
8715.5051 | 0.2 | 0.5
8716.5422 |  $-$9.9 | 0.3
8717.5973 |  $-$0.5 | 1.1
8718.4901 |  $-$2.0 | 0.4
8719.4433 |  $-$0.2 | 0.4
8720.4152 | 0.9 | 0.5
8721.5437 |  $-$3.9 | 0.5
8729.5184 | 2.0 | 0.3
8766.4506 | 1.3 | 0.2
8767.4729 | 1.0 | 0.3
8771.3722 | 1.4 | 0.2
8772.4400 | 2.7 | 0.2
8773.3992 | 0.0 | 0.3
8779.4334 |  $-$0.7 | 0.5
9009.5365 | 1.2 | 0.5
9020.6861 |  $-$2.0 | 0.6
Table 9: Journal of HERMES observations for WR 148. Mask used: N iv $\lambda\lambda\lambda 7103,7109,7123$ and $\lambda 4058$. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
7912.6900 | 51.0 | 1.2
7934.7125 |  $-$22.9 | 1.3
7952.6962 |  $-$74.7 | 1.0
8203.7536 |  $-$60.6 | 0.7
8262.6954 | 0.0 | 0.6
8332.6787 |  $-$80.9 | 0.6
8684.5886 | 90.9 | 0.8
8757.4993 | 65.7 | 0.8
8775.4903 | 87.1 | 1.0
8776.4943 | 12.7 | 1.2
8778.4304 | 4.2 | 3.7
8779.3554 | 89.3 | 4.8
8780.4683 | 52.8 | 1.5
8781.3212 |  $-$51.7 | 1.4
8791.3731 | 5.0 | 1.6
8792.3957 | 82.5 | 1.7
8796.4216 | 73.3 | 1.2
8798.3922 |  $-$46.3 | 1.9
9029.6207 | 63.2 | 1.3
9073.5716 | 59.8 | 1.1
Table 10: Journal of HERMES observations for WR 153. Mask used: N v $\lambda\lambda 4604,4620$. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
6305.3277 |  $-$11.8 | 3.0
6889.5378 | 41.7 | 3.2
6889.5592 | 27.0 | 3.7
6889.7109 |  $-$19.2 | 3.8
6889.7324 | 0.0 | 5.0
6890.4169 |  $-$151.0 | 4.1
6890.4383 |  $-$152.5 | 4.5
6890.6822 |  $-$223.8 | 3.3
6890.7036 |  $-$211.2 | 4.1
6892.4550 |  $-$336.0 | 2.9
6892.4764 |  $-$372.0 | 2.9
6892.7059 |  $-$293.0 | 2.2
6892.7273 |  $-$291.0 | 3.0
6894.3935 | 49.1 | 3.1
6894.4149 | 58.0 | 3.4
6894.5856 | 79.3 | 2.6
6894.6070 | 93.3 | 4.0
6896.4275 | 3.6 | 2.6
6896.4489 | 0.0 | 2.6
6896.6675 |  $-$71.7 | 5.7
6896.6855 |  $-$49.4 | 3.5
6903.4817 |  $-$64.8 | 3.0
6903.5031 |  $-$82.6 | 2.9
6903.6291 |  $-$123.0 | 3.1
6903.6505 |  $-$123.6 | 2.7
6946.3828 |  $-$278.5 | 2.3
6946.4121 |  $-$279.7 | 1.9
6946.5195 |  $-$233.3 | 3.4
6946.5435 |  $-$229.1 | 4.1
7952.7273 | 113.9 | 3.9
7958.7316 | 179.4 | 8.9
7963.6529 |  $-$101.2 | 5.5
8102.3196 |  $-$318.9 | 3.8
8198.7456 | 78.9 | 5.2
8267.7027 | 16.0 | 5.2
8310.6395 |  $-$287.8 | 3.7
8319.6697 | 151.2 | 4.4
8660.7183 | 130.3 | 4.1
8754.4247 | 130.2 | 3.2
8760.5219 | 27.5 | 3.6
8775.5577 | 72.1 | 2.6
8779.4643 |  $-$220.4 | 3.1
8796.4808 |  $-$122.2 | 3.9
8798.4221 |  $-$397.2 | 0.0
8799.4985 |  $-$238.5 | 2.7
8800.4418 | 11.9 | 6.5
8819.3970 |  $-$255.4 | 3.8
8820.3165 |  $-$40.2 | 5.7
8858.3385 |  $-$104.5 | 0.0
9010.6960 |  $-$153.8 | 2.4
9044.6388 |  $-$262.1 | 2.4
9073.6140 |  $-$223.5 | 2.5
9074.5856 |  $-$47.6 | 3.7
9075.6012 | 94.5 | 3.2
9076.5776 | 50.8 | 2.3
9077.5882 |  $-$145.7 | 2.7
9078.6008 |  $-$325.5 | 1.3
9079.5884 |  $-$351.2 | 2.1
Table 11: Continued for WR 153. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
9080.5761 |  $-$185.6 | 1.9
9146.3619 |  $-$321.9 | 3.3
9147.4905 |  $-$160.5 | 4.9
9148.3736 | 28.2 | 3.5
9151.4101 |  $-$202.9 | 2.3
9152.3290 |  $-$320.1 | 1.6
9153.4017 |  $-$312.2 | 3.1
9154.4319 |  $-$97.8 | 3.4
9155.5509 | 79.1 | 5.4
9156.5313 | 114.1 | 2.9
9157.3331 |  $-$10.4 | 3.7
9163.4296 | 74.1 | 21.3
Table 12: Journal of HERMES observations for WR 155. Mask used: N v $\lambda 4945$ and $\lambda 4058$. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
6132.6769 | 316.0 | 0.9
6134.5244 | 324.1 | 0.9
6135.6394 |  $-$14.1 | 0.9
6209.4378 |  $-$89.5 | 0.9
6210.3816 | 60.3 | 1.0
6210.4044 | 24.5 | 1.1
6210.5143 |  $-$118.3 | 1.0
6210.5288 |  $-$133.4 | 0.9
6211.4146 | 290.0 | 0.7
6212.4061 |  $-$247.2 | 0.9
6213.5000 | 253.7 | 1.1
6214.4316 | 0.0 | 1.0
6215.5349 |  $-$203.8 | 0.6
7948.6674 |  $-$197.8 | 0.8
7956.6991 |  $-$23.8 | 1.2
7962.7296 | 354.7 | 1.2
8091.4423 |  $-$194.7 | 1.5
8102.3489 | 342.7 | 1.2
8132.3478 |  $-$85.3 | 1.3
8335.5487 | 278.6 | 1.8
8336.6230 | 98.9 | 1.7
8668.7252 | 267.6 | 1.3
8721.6561 |  $-$171.8 | 1.2
8733.5426 |  $-$160.8 | 1.6
8775.3155 | 298.6 | 1.1
8775.6162 | 48.7 | 1.6
8776.5293 | 159.5 | 0.8
8776.5871 | 217.1 | 0.8
8778.4172 | 335.2 | 1.6
8778.5538 | 314.4 | 1.3
8779.3193 |  $-$235.6 | 3.7
8779.4735 |  $-$188.6 | 2.9
8794.3532 |  $-$102.8 | 5.0
8794.3736 |  $-$77.8 | 2.7
8796.3591 | 287.6 | 1.0
8796.4956 | 333.0 | 1.3
8800.3673 |  $-$105.3 | 1.2
8819.3904 | 331.3 | 1.2
8819.4572 | 350.2 | 1.4
8820.3269 |  $-$239.6 | 1.4
8858.3542 |  $-$100.5 | 1.6
8859.3150 | 82.0 | 1.8
9009.7119 | 288.0 | 1.1
9041.5810 |  $-$61.4 | 2.2
9042.5025 | 259.4 | 1.5
9042.6246 | 334.2 | 1.2
9044.6499 | 206.8 | 1.1
9076.4782 |  $-$201.3 | 2.6
9077.5154 | 161.5 | 1.8
9077.6831 |  $-$64.1 | 1.2
9078.4845 | 134.0 | 1.3
9080.5906 | 312.5 | 1.1
9082.5059 | 76.7 | 1.2
9082.7455 |  $-$183.4 | 3.0
9083.3961 | 118.0 | 1.6
9083.5871 | 297.5 | 1.2
9088.5333 | 312.8 | 1.7
9088.6721 | 332.2 | 1.6
Table 13: Continued for WR 155. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
9089.6076 |  $-$211.0 | 4.3
9089.6304 |  $-$200.2 | 1.2
9098.5925 | 323.5 | 1.3
9098.7359 | 263.4 | 1.3
9099.5498 |  $-$154.5 | 2.8
9146.3472 | 246.8 | 1.7
9146.5890 |  $-$30.0 | 2.2
9147.4761 | 187.5 | 1.3
9147.5661 | 277.5 | 1.6
9148.3213 |  $-$139.8 | 3.2
9148.5401 |  $-$254.9 | 4.1
9152.3438 | 136.5 | 1.3
9152.5696 | 338.3 | 1.8
9153.4166 |  $-$244.0 | 3.3
9153.5375 | 270.5 | 12.1
9154.4476 | 306.5 | 1.9
9155.3228 |  $-$186.9 | 2.4
9155.5357 | 11.6 | 1.4
9157.3185 | 195.3 | 1.2
9157.3482 | 221.8 | 1.1
9160.4016 |  $-$34.4 | 1.0
9162.3752 | 311.7 | 1.1
9196.4044 |  $-$148.5 | 2.4
9206.3166 |  $-$56.8 | 2.1
9206.4406 | 61.1 | 1.7
9207.3304 |  $-$42.3 | 2.1
9207.4586 |  $-$172.5 | 11.4
Table 14: Journal of HERMES observations for WR 156. Mask used: N iv $\lambda\lambda\lambda 7103,7109,7123$ and $\lambda 5737$. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
8336.6487 | 5.4 | 1.2
8754.4051 |  $-$2.9 | 1.1
8761.5931 | 0.0 | 1.1
8775.4585 |  $-$3.5 | 1.0
8786.4646 |  $-$9.7 | 1.2
8798.5261 |  $-$6.0 | 1.7
8798.5368 |  $-$4.7 | 2.1
8821.3559 |  $-$6.3 | 1.2
8826.4376 |  $-$8.9 | 1.2
9073.6574 | 0.3 | 1.0
9079.6211 |  $-$6.5 | 1.0
9081.5919 |  $-$0.2 | 1.0
9106.6019 |  $-$3.9 | 1.2
9120.5904 |  $-$2.5 | 1.3
9124.4972 |  $-$8.8 | 1.2
9127.5059 |  $-$8.6 | 1.3
9132.5919 | 6.4 | 1.1
9133.5744 |  $-$2.8 | 1.1
Table 15: Journal of HERMES observations for WR 158. Mask used: N iv $\lambda\lambda\lambda 7103,7109,7123$. BJD $-$ 2450000 (d) | Relative RV (km s-1) |  $\sigma_{p}$ (km s-1)
---|---|---
8091.4727 |  $-$2.7 | 0.4
8336.7140 | 3.1 | 0.4
8736.6307 |  $-$1.9 | 0.4
8737.5247 | 0.0 | 0.3
8775.3857 |  $-$1.0 | 0.4
8798.4824 |  $-$3.5 | 0.5
8821.4275 |  $-$2.2 | 0.3
8875.3741 | 6.5 | 0.4
9075.6776 |  $-$4.5 | 0.4
9089.6552 |  $-$8.5 | 0.5
9097.6090 | 3.6 | 0.6
9106.6458 | 0.6 | 0.5
9122.4711 | 4.6 | 0.4