11institutetext: Institut für Physik und Astronomie, Universität Potsdam,
Karl-Liebknecht-Str. 24/25, D-14476 Potsdam, Germany
11email<EMAIL_ADDRESS>22institutetext: Department of Physics
and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

# A low-metallicity massive contact binary undergoing slow Case A mass
transfer: A detailed spectroscopic and orbital analysis of SSN 7 in NGC 346 in
the SMC ††thanks: Based on observations with the NASA/ESA Hubble Space
Telescope, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5-2655. Also based on observations
collected at the European Organisation for Astronomical Research in the
Southern Hemisphere.

M. J. Rickard 1122 D. Pauli 11

(Received 1 February 2023 / Accepted 26 March 2023)

###### Abstract

Context. Most massive stars are believed to be born in close binary systems
where they can exchange mass, which impacts the evolution of both binary
components. Their evolution is of great interest in the search for the
progenitors of gravitational waves. However, there are unknowns in the physics
of mass transfer as observational examples are rare, especially at low
metallicity. Nearby low-metallicity environments are particularly interesting
hunting grounds for interacting systems as they act as the closest proxy for
the early universe where we can resolve individual stars.

Aims. Using multi-epoch spectroscopic data, we complete a consistent spectral
and orbital analysis of the early-type massive binary SSN 7 hosting a ON3
If∗+O5.5 V((f)) star. Using these detailed results, we constrain an
evolutionary scenario that can help us to understand binary evolution in low
metallicity.

Methods. We were able to derive reliable radial velocities of the two
components from the multi-epoch data, which were used to constrain the orbital
parameters. The spectroscopic data covers the UV, optical, and near-IR,
allowing a consistent analysis with the stellar atmosphere code, PoWR. Given
the stellar and orbital parameters, we interpreted the results using binary
evolutionary models.

Results. The two stars in the system have comparable luminosities of
${\log(L_{1}/L_{\odot})=5.75}$ and ${\log(L_{2}/L_{\odot})=5.78}$ for the
primary and secondary, respectively, but have different temperatures
(${T_{1}=$43.6\text{\,}\mathrm{k}\mathrm{K}$}$ and
${T_{2}=$38.7\text{\,}\mathrm{k}\mathrm{K}$}$). The primary ($32M_{\odot}$) is
less massive than the secondary ($55\,M_{\odot}$), suggesting mass exchange.
The mass estimates are confirmed by the orbital analysis. The revisited
orbital period is $3\text{\,}\mathrm{d}$. Our evolutionary models also predict
mass exchange. Currently, the system is a contact binary undergoing a slow
Case A phase, making it the most massive Algol-like system yet discovered.

Conclusions.  Following the initial mass function, massive stars are rare, and
to find them in an Algol-like configuration is even more unlikely. To date, no
comparable system to SSN 7 has been found, making it a unique object to study
the efficiency of mass transfer in massive star binaries. This example
increases our understanding of massive star binary evolution and the formation
of gravitational wave progenitors.

###### Key Words.:

Stars: winds, outflows, evolution, individual: NGC 346 SSN 7, – Binaries:
spectroscopic, Galaxies: Magellanic Clouds

##  1 Introduction

NE

NE

Figure 1: Optical (left) and infrared (right) image of NGC346 in the SMC. Each
image shows an area on the sky of approximately $3.5^{\prime}\times
3.5^{\prime}$ ($\approx 62$ pc$\,\times$ 62 pc at d=61 kpc). The positions of
the main ionising sources of NGC 346 (see Sect. 6.4), namely SSN 7 (ON3
If∗+O5.5 V((f))) and SSN 9 (O2 III(f*)), are highlighted by red and green
squares, respectively. The false-colour optical image was taken with the HST
ACS. Credit: A. Nota (ESA/STScI). The false-colour infrared image was taken
with the James Webb Space Telescopes (JWST) Near Infrared Camera (NIRCam).
Credits: NASA, ESA, CSA, O. Jones (UK ATC), G. De Marchi (ESTEC), and M.
Meixner (USRA). Image processing: A. Pagan (STScI), N. Habel (USRA), L. Lenkic
(USRA), and L. Chu (NASA/Ames).

Massive stars ($\mathrm{M}\gtrsim 8\mathrm{M}_{\odot}$) have a pivotal role in
the evolution of Galaxies. They influence their environments throughout their
entire evolution via multiple feedback mechanisms. Core hydrogen-burning
massive stars are hot, leading to ionisation feedback (Hollenbach & Tielens,
1999; Matzner, 2002) and forming spectacular H II regions. Their high
ultraviolet (UV) luminosity drives powerful stellar winds, depositing
mechanical feedback and heavy elements into the interstellar medium (Rogers &
Pittard, 2013). When a massive star evolves, it expands and becomes a red
supergiant (RSG) and cools down. These stars still have strong winds, powered
by radiation pressure on dust grains. Most massive stars are believed to end
their lives with a supernova explosion that rapidly deposits substantial
amounts of energy in the surrounding medium (Rogers & Pittard, 2013). During
these events, neutron stars (NSs, Baym et al., 2018; Vidaña, 2018) or black
holes (BHs, Orosz et al., 2011; Miller-Jones et al., 2021) are formed. All
these feedback mechanisms make massive stars, which are the drivers of the
chemical evolution of the interstellar medium (Burbidge et al., 1957;
Pignatari et al., 2010; Thielemann et al., 2011; Kasen et al., 2017; Kajino et
al., 2019) and the arbitrators of stellar formation; massive stars can
initiate or abort star formation (Mac Low et al., 2005).

Massive stars preferentially form in multiple systems (Sana et al., 2012,
2013, 2014; Moe & Di Stefano, 2017). The evolution of stars in binary systems
differs from single star evolution as the two components can interact and
exchange mass, for instance when one star in the binary (i.e. the more massive
one) expands and fills its Roche lobe (Pols, 1994; Vanbeveren et al., 1998;
Nelson & Eggleton, 2001; Smith, 2014). This mass can then, depending on other
factors such as rotation, accrete onto the companion star. Due to the fate of
massive stars as either NSs or BHs, close massive star binaries are the
progenitors of gravitational wave observations (Abbott et al., 2016, 2019).
However, the final mass of a star dictates its fate (Heger et al., 2003), and
in a binary system the final mass depends on the previous evolution and
interaction (Shenar et al., 2020a; Massey et al., 2021; Pauli et al., 2022a).

The duration of mass transfer strongly depends on the evolutionary stage of
the star (Paczyński, 1967; Vanbeveren & Conti, 1980; Wellstein & Langer,
1999). If the expanding star is still core H-burning, it first drops out of
nuclear equilibrium, making the first phase of mass transfer rapid as it takes
place on the thermal timescale (fast Case A). As soon as the star regains
nuclear equilibrium, it continues to expand on the nuclear timescale,
overflowing its Roche lobe and transferring mass to the companion star (slow
Case A). If the mass donor during the slow Case A mass transfer is less
massive than the mass gainer, the systems are called Algol-like system (named
for $\beta\,\mathrm{Per}$, Paczyński, 1971; Batten, 1989; Li et al., 2022).
Alternatively, stars that have finished core H-burning expand on the thermal
timescale, filling their Roche lobe quickly, and lose a large fraction of
their envelope (Case B). As most of the mass transfer events are on short
timescales, it is practically impossible to catch a system during the fast
Case A or Case B mass transfer phase. As slow Case A mass transfer occurs on
the nuclear timescale, it is possible to find observational counterparts.

Metallicity ($Z$) has many effects on stellar evolution. For instance, stars
are more compact and hotter, and line-driven winds get weaker for lower
metallicity stars (Mokiem et al., 2007). Low-$Z$ environments are of
particular interest when looking to understand the origin of gravitational
waves as the observed mergers take place in high-redshift galaxies. However,
it is only possible to study low-Z stars in nearby irregular dwarf galaxies,
such as the Small Magellanic Cloud (SMC, ${Z_{\mathrm{SMC}}=1/7\,Z_{\odot}}$)
as these stars can be resolved. To date, there are few detailed studies on
massive stars in pre- and post-interaction binaries in the SMC (de Mink et
al., 2007; Pauli et al., 2022b).

In this paper we remedy this by studying in detail one of the most massive
binaries in the low-$Z$ SMC galaxy, namely SSN 7 (Sabbi et al. 2007, also
known as MPG 435; Massey et al. 1989, or NMC 26; Niemela et al. 1986). Our
target is located within the core of the young cluster NGC 346 (Dufton et al.,
2019), which contains a large population of O stars (Niemela et al., 1986;
Massey et al., 1989; Rickard et al., 2022). The cluster is nearby ($d=61$ kpc,
Hilditch et al., 2005) and has been studied several times with different
instruments. Previous studies have categorised SSN 7 as a spectroscopic binary
with two moving components (SB2 Dufton et al., 2019), but it has never been
analysed consistently with a stellar atmosphere code.

The archival data, including spectra that cover the full range of the
electromagnetic spectrum as well as photometric observations, are detailed in
Section 2. In Section 3 we explain how the spectroscopic data is used to
obtain radial velocity (RV) shifts, used to conduct an orbital analysis.
Furthermore, this data is used in Section 4 to make a consistent spectroscopic
analysis, yielding stellar and wind parameters. The empirically derived
stellar and orbital parameters are put into an evolutionary context in Section
5 and its implications are discussed in Section 6.

Table 1: List of spectroscopic observations of NGC 346 SSN 7.

ID | Instrument | Wavelength | Res. power | Exp. time |  MJD(a) | Program ID | PI
---|---|---|---|---|---|---|---
|  | [Å] |  [$\lambda\ /\ \delta\lambda$] | [s] | [d] |  |
1 | FUSE | 920-1180 | $\sim 20,000$ | 4464 | 52146.44 | P203 | K. Sembach
2 | FUSE | 920-1180 | $\sim 20\,000$ | 6386 | 51828.57 | P117 | J. B. Hutchings
3 | HST FOS G130H | 1140-1605 | $\sim 1150$ | 2803 | 48948.09 | GO4110 | F.-P. Kudritzki
4 | HST FOS G130H | 1140-1605 | $\sim 1150$ | 2803 | 49287.81 | GO4110 | F.-P. Kudritzki
5 | HST STIS G140L | 1160-1705 | $\sim 1000$ | 225 | 58482.89 | GO15112 | L. Oskinova
6 | HST FOS G190H | 1560-2340 | $\sim 1150$ | 1215 | 48948.15 | GO4110 | F.-P. Kudritzki
7 | HST FOS G190H | 1560-2340 | $\sim 1150$ | 1215 | 49287.85 | GO4110 | F.-P. Kudritzki
8 | HST STIS G230LB | 1640-3100 | $\sim 700$ | 41 | 59363.76 | GO16230 | D. L. Massa
9 | X-Shooter | 2989-5560 | 6655 | 440 | 59216.11 | 1106.D-0775(A) | J. S. Vink
10 | HST STIS G430L | 3000-5550 | $\sim 500$ | 118 | 59363.76 | GO16230 | D. L. Massa
11 | UVES | 3281-4562 | 40 970 | 180 | 52249.01 | 68.D-0328(A) | D. Minniti
12 | GIRAFFE | 3960-4570 | 6300 | 1725 | 53277.28 | 074.D-0011(A) | C. J. Evans
13 | GIRAFFE | 3960-4570 | 6300 | 1725 | 53277.26 | 074.D-0011(A) | C. J. Evans
14 | GIRAFFE | 3960-4570 | 6300 | 22 | 53277.26 | 074.D-0011(A) | C. J. Evans
15 | GIRAFFE | 3960-4570 | 6300 | 50 | 53277.26 | 074.D-0011(A) | C. J. Evans
16 | GIRAFFE | 3960-4570 | 6300 | 1725 | 53276.24 | 074.D-0011(A) | C. J. Evans
17 | GIRAFFE | 4450-5080 | 7500 | 1725 | 53292.06 | 074.D-0011(A) | C. J. Evans
18 | GIRAFFE | 4450-5080 | 7500 | 1725 | 53280.2 | 074.D-0011(A) | C. J. Evans
19 | UVES | 4584-6687 | 42 310 | 180 | 52249.01 | 68.D-0328(A) | D. Minniti
20 | MUSE | 4620-9265 | 2989 | 315 | 57611.33 | 098.D-0211(A) | W.-R. Hamann
21 | MUSE | 4620-9265 | 2989 | 315 | 57613.25 | 098.D-0211(A) | W.-R. Hamann
22 | MUSE | 4620-9265 | 2989 | 315 | 57613.29 | 098.D-0211(A) | W.-R. Hamann
23 | MUSE | 4620-9265 | 2989 | 315 | 57617.23 | 098.D-0211(A) | W.-R. Hamann
24 | MUSE | 4620-9265 | 2989 | 315 | 57618.1 | 098.D-0211(A) | W.-R. Hamann
25 | MUSE | 4620-9265 | 2989 | 315 | 57620.15 | 098.D-0211(A) | W.-R. Hamann
26 | MUSE | 4620-9265 | 2989 | 315 | 57620.19 | 098.D-0211(A) | W.-R. Hamann
27 | MUSE | 4620-9265 | 2989 | 315 | 57620.23 | 098.D-0211(A) | W.-R. Hamann
28 | MUSE | 4620-9265 | 2989 | 315 | 57621.21 | 098.D-0211(A) | W.-R. Hamann
29 | MUSE | 4620-9265 | 2989 | 315 | 57621.25 | 098.D-0211(A) | W.-R. Hamann
30 | MUSE | 4620-9265 | 2989 | 315 | 57622.15 | 098.D-0211(A) | W.-R. Hamann
31 | X-Shooter | 5337-10200 | 11 333 | 510 | 59216.11 | 1106.D-0775(A) | J. S. Vink
32 | X-Shooter | 9940-24780 | 8031 | 300 | 59216.11 | 1106.D-0775(A) | J. S. Vink
33 | X-Shooter | 9940-24790 | 8031 | 300 | 59216.11 | 1106.D-0775(A) | J. S. Vink

111 (a) Mid-exposure time in $\mathrm{HJD}-2400000.5$. For brevity, the
spectra referred to in this paper use the ID numbers listed here.

##  2 Observations

NGC 346 SSN 7 has been observed numerous times across almost the entirety of
the electromagnetic spectrum, ranging from the far-ultraviolet (FUV) to the
infrared (IR). In this work we complement UV observations from the Hubble
Space Telescopes (HST) UV Space Telescopes Imaging Spectrograph (STIS) and
multi-epoch datacube observations obtained by the Multi Unit Spectroscopic
Explorer (MUSE), which is mounted on the Very Large Telescope (VLT), with
archival spectra from X-Shooter, GIRAFFE, the UV-visual Echelle Spectrograph
(UVES), and far-ultraviolet (FUV) spectra from the Far Ultraviolet
Spectroscopic Explorer (FUSE). A summary of all spectra employed in this work
is given in Table 1, where each spectrum is assigned an ID number.

The UV (including the FUV) spectra are rectified by division through the
synthetic model continuum, while the optical and near-IR spectra are rectified
by hand. The photometric data used for the fitting of the spectral energy
distribution (SED) is given in Table 2.

Table 2: Photometry of SSN 7, sorted by central wavelength. Filter | Magnitude | Reference
---|---|---
HST F255W | 11.98 | Rickard et al. (2022)
B | 12.56 | Nascimbeni et al. (2016)
$\mathrm{G}_{\mathrm{BP}}$ | 12.39 | Gaia Collaboration et al. (2022)
V | 12.56 | Nascimbeni et al. (2016)
HST F555W | 12.61 | Sabbi et al. (2007)
$\mathrm{G}_{\mathrm{RP}}$ | 12.69 | Gaia Collaboration et al. (2022)
J | 12.96 | Bonanos et al. (2010)
H | 13.00 | Bonanos et al. (2010)
K | 13.07 | Bonanos et al. (2010)

The core of NGC 346, including our target and other bright O stars (namely MPG
396 (O7V), MPG 417 (O7.5V), MPG 470 (O8.5III), and MPC 476 (O6V)), was
observed with the Chandra X-ray telescope (Weisskopf et al., 2000). The core
region has a combined X-ray flux, already corrected for reddening, of
${F_{\mathrm{X,\,obs}}=$1.5\text{\times}{10}^{34}\text{\,}\mathrm{e}\mathrm{r}\mathrm{g}\,\mathrm{s}^{-1}\,\mathrm{c}\mathrm{m}^{-2}$}$
in the
$0.3\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}10.0\text{\,}\mathrm{k}\mathrm{e}\mathrm{V}$
(Nazé et al., 2002). We use this as an upper constraint on the X-ray flux that
we can include in our atmospheric models. However, we are cautious in our use
of this value, as close O-type binaries in the Milky Way suggest that the
majority of the X-rays might originate from colliding wind zones of close
binaries (Rauw & Nazé, 2016).

##  3 Orbital analysis

NGC 346 SSN 7 is a known SB2 binary; both components show contributions in the
He I and He II lines. The ephemeris of this system was obtained by Niemela &
Gamen (2004) who obtained RVs by fitting helium lines, yielding an orbital
period of $24.2\text{\,}\mathrm{d}$ and an eccentricity of $0.42$. The high
eccentricity is surprising for an O-star system with an orbital period below
$50\text{\,}\mathrm{d}$, as theory predicts that the orbit in such systems is
quickly circularised. Unfortunately, we do not have access to their data.
Still, we have 17 optical spectra, of which 11 (the MUSE spectra) cover half
of the reported period, allowing us to make further restrictions to the
estimate of the orbital period and the eccentricity, and to constrain a mass
ratio.

Figure 2: Multi-epoch spectral observations of SSN 7. The X-Shooter spectrum
(ID 09) is shown as a solid line, the GIRAFFE spectrum (ID 17) as a dashed
line, the GIRAFFE spectrum (ID 18) as a dot-dashed line, and the UVES spectrum
(ID 19) as a dotted line. The shifting emission and absorption features are
associated with the primary and secondary, respectively.

###  3.1 Line associations to individual binary components

To prepare for the extraction of the RVs of each component, we identified
which lines originate from which star. The most prominent line, which is
detected in almost all of the used optical spectra of SSN 7, is the He ii
$\lambda$ 4686 line. In Fig. 2 we illustrate how the morphology of the line
changes within the individual observations. For clarity, only a handful of
observations are shown. The emission feature of He ii $\lambda$ 4686 line
shifts opposite to the absorption feature across multiple epochs. All lines
that shift with the emission feature of the He ii $\lambda$ 4686 line are
associated with the spectroscopic primary, and all lines that shift with the
He ii $\lambda$ 4686 absorption line are associated with the spectroscopic
secondary.

A full table of the considered lines is presented in Table 12, including which
line can be assigned to the primary, secondary, or to both. Spectral lines
that only show a contribution of either the primary or the secondary are
scarce.

###  3.2 Radial velocities

Measuring RVs in a binary, where both stars contribute to most of the
diagnostic lines, is a non-trivial task. We employed a Markov chain Monte
Carlo (MCMC) method combined with a least-squares fitting method to derive the
RVs of each component. In each MCMC step, the individual synthetic spectra,
which were obtained from the spectroscopic analysis (see Sect. 4), are shifted
by a different RV value until the combined synthetic spectrum matches the
observations. Thus, we can obtain RVs from complex absorption profiles. For a
more detailed explanation we refer to Pauli et al. (2022b, Section 3.1.2 and
Appendix A).

The MCMC method returns a final probability distribution around the true
solution. The errors quoted are the larger error margin of the 68% confidence
interval of the final distribution: commonly used codes for inferring binary
parameters from observables are not able to include asymmetric uncertainties.
To minimise uncertainties introduced by the intrinsic variability of the
lines, we fitted several lines that show distinguishable contributions of the
primary and secondary components and calculated their mean RV.

The mean RVs obtained for each spectrum, and binary component are listed in
Table 3. The fitted RVs of all lines used in this process are listed in Tables
10 and 11. The change in sign of the RV of the primary (from
$\sim\\!$100\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$$ to
$\sim\\!$-80\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$$) within
$\sim\\!$2\text{\,}\mathrm{d}$$ calls in to question the reported period of
$24.2\text{\,}\mathrm{d}$ and limits the orbital period to a few days.

Table 3: Mean RVs of the primary and secondary, sorted by MJD. The listed RVs
are corrected for the velocity of NGC 346 complex and for the barycentric
motion.

ID(a) | MJD |  RVprim |  RVsec
---|---|---|---
|  | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$
11 | 52249.01198 | $11\pm 10$ | $10\pm 21$
15 | 53277.25739 | $56\pm\,\,\,7$ | $-34\pm\,\,\,7$
14 | 53277.25939 | $51\pm\,\,\,7$ | $-32\pm\,\,\,9$
13 | 53277.26022 | $42\pm\,\,\,6$ | $-39\pm\,\,\,7$
12 | 53277.28112 | $48\pm\,\,\,6$ | $-39\pm\,\,\,7$
18 | 53280.19821 | $18\pm 15$ | $-12\pm 29$
17 | 53292.06195 | $-57\pm 15$ | $41\pm 27$
20 | 57611.32930 | $98\pm 14$ | $-57\pm 19$
21 | 57613.24630 | $-78\pm 15$ | $67\pm 23$
22 | 57613.28829 | $-77\pm 14$ | $73\pm 21$
23 | 57617.23463 | $55\pm 13$ | $-22\pm 19$
24 | 57618.10327 | $72\pm 13$ | $-34\pm 22$
25 | 57620.14865 | $36\pm 13$ | $-34\pm 22$
26 | 57620.19042 | $39\pm 13$ | $-34\pm 22$
27 | 57620.23262 | $43\pm 11$ | $-32\pm 22$
28 | 57621.20640 | $64\pm 13$ | $-24\pm 22$
29 | 57621.24834 | $49\pm 11$ | $-30\pm 20$
30 | 57622.14718 | $-85\pm 13$ | $72\pm 21$
31 | 59216.11133 | $92\pm 15$ | $-55\pm 19$

222 (a) Spectral ID taken from Table 1.

###  3.3 Radial velocity curve modelling

When fitting RVs obtained from spectroscopic data with observations separated
by several years, it is possible to find multiple orbital solutions consistent
with the observations. To obtain a constraint on alternative ephemeris, a
Monte Carlo sampler suitable for two-body systems with sparse and/or noisy
radial velocity measurements, namely The Joker (Price-Whelan et al., 2017), is
applied to the measured RVs. As The Joker is only able to model the RV curve
of one component at a time, its output is used in a second step as input
parameters for the Physics of Eclipsing Binaries (PHEOBE) code (Prša &
Zwitter, 2005; Prša et al., 2016; Horvat et al., 2018; Jones et al., 2020;
Conroy et al., 2020), which can model the orbits of both binary components
simultaneously.

####  3.3.1 Obtaining ephemerides with The Joker

The Joker uses a rejection sampling analysis on a densely sampled prior
probability density function (pdf) and produces a sample of multimodal pdfs
which contain the most important information about the ephemerides. The
default pdfs of The Joker code (Price-Whelan et al., 2017, their section 2)
are used here as the priors. As outlined in Section 3.2, the RVs obtained from
the MUSE spectra suggest that the orbital period should be of the order of a
few days (see Table 3). Hence, a log-uniform prior for the orbital period in
the range of $0.1\text{\,}\mathrm{d}40\text{\,}\mathrm{d}$ is adopted for the
fitting procedure. The upper limit was chosen as roughly two times the orbital
period obtained by Niemela & Gamen (2004) to enable their solution to be
considered, while the lower limit was set to a reasonably small value. For the
eccentricity we used the Beta distribution from Kipping (2013) with $a=0.867$
and $b=3.03$. For the argument of the pericentre and the orbital phase a
uniform prior without any restrictions is used. The RVs of the primary, which
are more reliable since they have lower error margins, are employed as input
data.

From the $1\text{\times}{10}^{7}$ samples created, $\leavevmode\nobreak\ 340$
pass the rejection step, equivalent to an acceptance rate of $0.0034\%$.
Afterwards, a standard MCMC method is used to sample around the most likely
solution found from the rejection step in order to fully explore the posterior
pdf. We find that the ephemerides are described best with a circular orbit
($e=0$) and an orbital period of $P_{\mathrm{Joker}}=$3.074\,38\pm
0.000\,02\text{\,}\mathrm{d}$$. The complete set of emphemerides obtained with
The Joker are listed in Table 4.

Table 4: Ephemerides obtained using the primary’s RVs and The Joker. parameter | value | unit
---|---|---
$P$ | $3.07438^{+0.00002}_{-0.00002}$ | $[\mathrm{d}]$
$e$ | $0.00^{+0.09}_{-0.00}$ |
$\omega$ | $-122.6^{+244.1}_{-38.4}$ | $[\mathrm{{}^{\circ}}]$
$M_{0}$ | $-0.80^{+1.05}_{-0.81}$ | $[\mathrm{d}]$
$K$ | $81.25^{+6.15}_{-6.05}$ | $[\mathrm{km\,s^{-1}}]$
$\varv_{0}$ | $13.40^{+3.26}_{-3.27}$ | $[\mathrm{km\,s^{-1}}]$

####  3.3.2 Obtaining orbital parameters with PHOEBE

The ephermerides obtained in Section 3.3.1 were determined by only using the
RVs of the primary. This was done to get a first constraint on the orbital
parameters; however, valuable information such as the mass ratio ($q$), the
projected orbital separation ($a\,\sin\,i$), and the projected Keplerian
masses ($M\,\sin\,i$) can only be obtained when fitting the RVs of the two
components simultaneously. Therefore, the PHOEBE light and RV curve modelling
software (version 2.3) was employed to model the observed RVs, with the built-
in option of the MCMC sampler `emcee` (Foreman-Mackey et al., 2013).

The initial probability distributions of the period $P$, the argument and
phase of the pericentre $\omega$ and $M_{0}$, and the barycentre velocity
$\varv_{0}$ are assumed to be of Gaussian shape. The Gaussians are centred at
the best-fitting value as obtained by The Joker (see Table 4) and have a
standard deviation similar to their respective largest error margin. The
ephemerides obtained with The Joker favour a circular orbit, and hence the
eccentricity is fixed at $e=0$. To constrain the current mass ratio we
employed the method of Wilson (1941) yielding $q_{\mathrm{wilson}}=1.34\pm
0.07$. Because of a lack of information about other parameters, we used a
uniform distribution in the range of
$q_{\mathrm{orb,\,i}}=$0.33\text{\,}3.0\text{\,}$$, where a starting value
$q_{\mathrm{orb,\,i}}=q_{\mathrm{wilson}}$ is assumed. The initial projected
orbital separation is approximated to be of the order of
$a\,\sin\,i_{\mathrm{i}}=$10\text{\,}\mathrm{R}_{\odot}$$ and that it is
uniformly distributed over the range of
$a\,\sin\,i_{\mathrm{i}}=$0.1\text{\,}\mathrm{R}_{\odot}100\text{\,}\mathrm{R}_{\odot}$$.

The best fit of the RV curve obtained with the PHOEBE code is shown in Fig. 3.
The final orbital parameters are listed in Tables 5 and 6. The RV fit yields
masses without information about the inclination. By using the results from
the spectroscopic analysis (see Sect. 4) we estimate the inclination to be
$i_{\mathrm{orb}}=$16\pm 1\text{\,}{}^{\circ}$$.

Table 5: Ephemerides obtained using the RVs of both binary components and the
PHOEBE code.

parameter | value | unit
---|---|---
$P$ | $3.07359^{+0.02481}_{-0.00001}$ | $[\mathrm{d}]$
$\omega_{0}$ | $242^{+9}_{-30}$ | $[\mathrm{{}^{\circ}}]$
$M_{0}$ | $1.5^{+7.8}_{-1.4}$ | $[\mathrm{d}]$
$\varv_{0}$ | $9.1^{+0.2}_{-0.5}$ | $[\mathrm{km\,s^{-1}}]$
$q_{\mathrm{orb}}$ | $1.47^{+0.13}_{-0.09}$ |
$a\,\sin\,i$ | $11.0^{+0.7}_{-0.3}$ | $[R_{\odot}]$
$i_{\mathrm{orb}}\,^{(a)}$ | $16^{+1}_{-1}$ | $[\mathrm{{}^{\circ}}]$
$a\,^{(b)}$ | $39.9^{+1.2}_{-2.5}$ | $[{R_{\odot}}]$

333 (a) Calibrated such that the orbital and spectroscopic masses agree within
their uncertainties. (b) Calculated using $i_{\mathrm{orb}}$.

Table 6: Orbital parameters of the individual binary components obtained using
the PHOEBE code.

parameter | primary | secondary | unit
---|---|---|---
$K$ | $107.9^{+3.9}_{-3.9}$ | $73.3^{+2.7}_{-2.7}$ | $[\mathrm{km\,s^{-1}}]$
$M_{\mathrm{orb}}\,\sin\,i\,^{3}$ | $0.77^{+0.15}_{-0.07}$ | $1.13^{+0.21}_{-0.10}$ | $[{M_{\odot}}]$
$M_{\mathrm{orb}}\,^{(a)}$ | $36.5^{+7.04}_{-3.5}$ | $53.8^{+10.1}_{-4.9}$ | $[{M_{\odot}}]$
$R_{\mathrm{RL}}^{\,\,\,\,\,\,\,\,\,(a)}$ | $13.8^{+0.8}_{-0.4}$ | $16.5^{+0.9}_{-0.4}$ | $[{R_{\odot}}]$

444 (a) Calculated using $i_{\mathrm{orb}}$ (see Table 5).

Figure 3: Observed (triangles) and synthetic (solid lines) RV curves of the
primary (green) and secondary (red) component, as obtained by the PHOEBE code.
The dashed black line indicates the barycentric velocity offset $\varv_{0}$.

To date, there is no observed light curve of NGC 346 SSN 7 reported in the
literature. Since the PHOEBE code is capable of modelling a light curve, it
can be used to make a prediction on the shape of a possible light curve (see
Appendix B for more details). From the predicted synthetic light curve, we
conclude that a detector with a precision below
$<$18\text{\,}\mathrm{m}\mathrm{m}\mathrm{a}\mathrm{g}$$ in the V band is
needed to see any kind of variability. This precision is hardly achievable for
stars in the SMC with current ground-based telescopes. Hence, it is not
surprising that no light curve has been detected so far.

##  4 Spectral analysis

Figure 4: Observed (blue) and combined synthetic (red) SED. The individual
synthetic SEDs of the primary and secondary are shown as the dotted black and
green line, respectively. The photometry, listed in Table 2, is shown as open
squares.

###  4.1 Stellar atmosphere modelling

Expanding stellar atmospheres of hot stars
(${T>$15\text{\,}\mathrm{k}\mathrm{K}$}$) are in non-local thermal equilibrium
(non-LTE) and can only be calculated using state of the art stellar atmosphere
codes such as the Potsdam Wolf-Rayet (PoWR, Gräfener et al., 2002; Oskinova et
al., 2011; Hainich et al., 2014, 2015; Shenar et al., 2015; Hamann & Gräfener,
2004; Sander et al., 2015; Hainich et al., 2015) code. Within PoWR, the
radiative transfer equations and the rate equations are solved iteratively in
the co-moving frame. The code is able to produce a synthetic spectrum that
accounts for mass-loss, line blanketing, and wind clumping.

For our stellar atmosphere models, we used tailored surface abundances that
are representative of the chemical composition of the SMC. For the modelling
of SSN 7 within NGC 346, the initial H abundance is adopted from Asplund et
al. (2005), while the initial abundances of C, N, O, Mg, and Si are based on
the works of Hunter et al. (2007) and Trundle et al. (2007). The abundances of
P and S are taken from Scott et al. (2015) and are scaled down to the
metallicity of the SMC (${Z_{\mathrm{SMC}}=1/7\,Z_{\odot}}$). The iron group
elements (Fe, Sc, Ti, V, Cr, Mn, Co, and Ni) are either taken from Trundle et
al. (2007) or, when not available, taken from solar values (Scott et al.,
2015) and multiplied by a factor $1/7$ to account for the lower metallicity of
the SMC (Table 7). The numerous complex iron lines are handled with a
‘superlevel’ approach (Gräfener et al., 2002).

Microturbulence within a stellar atmosphere leads to a Doppler-broadening of
spectral lines. The PoWR models used assume a depth-dependent microturbulence
starting in the photosphere at ${\xi_{\mathrm{ph}}=10\,\mathrm{km\,s}^{-1}}$
and increases outwards linearly with the wind velocity
$\xi(r)=0.1\cdot\varv(r)$.

Our PoWR models account for wind inhomogeneities and introduced optically thin
clumps (microclumping) within the stellar atmosphere. The density contrast of
the clumps within the wind is described by the clumping factor $D$. For NGC
346 SSN 7, a depth-dependent clumping factor is used, starting at the sonic
radius and reaching $D=10$ at ten times the stellar radius.

For the velocity stratification within the wind, a double $\beta$-law (Hillier
& Miller, 1999) of the form

$\varv(r)=\varv_{\infty}\left[f\left(1-\frac{r_{0}}{r}\right)^{\beta_{1}}+(1-f)\left(1-\frac{r_{1}}{r}\right)^{\beta_{2}}\right]$
(1)

is adopted. The inner part of the velocity stratification is described by an
exponent $\beta_{1}=0.8$, which is typical for O stars (Pauldrach et al.,
1986). The outer part is described with an exponent $\beta_{2}=4$ and only
contributes with a fraction of $f=0.4$. The parameters $r_{0}$ and $r_{1}$ are
set within the code, such that the wind is smoothly connected.

The effective temperatures quoted in this work are related via the Stefan-
Boltzmann law to the radius at which the Rosseland mean continuum optical
depth is $\tau=2/3$. Stellar and wind parameters can be obtained by adjusting
the synthetic spectrum until it matches the observed spectra simultaneously.
This also means that the abundance of a specific element (e.g. H, C, N, O) can
be adjusted if needed to match the strength of observed lines.

###  4.2 Resulting spectroscopic parameters

Deriving stellar and wind parameters from stellar spectra in which lines are
blended by two stars of a binary is a difficult task. The following
subsections describe the strategy employed and the final parameters that are
listed in Table 5.

####  4.2.1 Rotation rates

Before starting the spectral fitting process, accurate values for the
projected rotational velocities ($\varv\sin i$) of each component are needed.
These impact the depth and shape of all synthetic lines and hence conclusions
drawn from the spectroscopic fit. We employ the iacob-broad tool (Simón-Díaz &
Herrero, 2014) which uses a combination of a Fourier transform (FT) and a
goodness of fit (GOF) method to obtain accurate measurements of $\varv\sin i$.

When obtaining projected rotation rates, the preference is to use metal lines
over helium lines as the latter are, in addition to the rotational broadening,
also pressure broadened. For the primary, we use the N iv $\lambda$ 4057 as
well as the N iv $\lambda$ 6381 line. As there are no metal lines that solely
can be attributed to the secondary, we use the prominent He i $\lambda$ 6875
and the He i $\lambda$ 7065 line. The projected rotational velocities of the
primary and secondary component are best described with ${\varv_{1}\sin
i=135\pm 10\ \mathrm{km\ s^{-1}}}$ and ${\varv_{2}\sin i=185\pm 10\
\mathrm{km\ s^{-1}}}$, respectively.

Most of the observed lines are formed in the rotating photosphere of a star,
while fewer but still important lines in the UV are formed within the static
(non-rotating) wind. To account for this, the synthetic PoWR models used in
this work are calculated with a rigidly rotating photosphere and a non-
rotating wind, as described in Shenar et al. (2014).

####  4.2.2 Luminosity, temperature, and surface gravity

To constrain the luminosity of each binary component, we carefully looked at
the ratios of isolated and blended helium and metal lines. One of the key
diagnostic lines was the C iii $\lambda$ 1175 in the UV, which originates
purely from the secondary, giving an extra constraint on the luminosity ratio.
A selected set of the lines used is illustrated in Fig. 5. Determining the
luminosity ratio is an iterative process and is revisited after each modelling
change, as changes in temperature and surface gravity also affect the shape of
key diagnostic lines. The luminosity of each component is ${\log(L_{1}\ /\
L_{\odot})=5.75}$ and ${\log(L_{1}\ /\ L_{\odot})=5.78}$ for the primary and
secondary, respectively.

Figure 5: Close-ups on the carbon and helium lines used to constrain the
luminosity ratio (solid blue) compared to the combined synthetic model (dotted
red). Left: Observed FUSE spectra (ID 01). The weighted synthetic spectra of
the primary and secondary components are shown as a dotted black and green
line. Right: Observed X-Shooter spectra (ID 09 and 31). The unweighted
synthetic spectra of the primary and secondary components are shown as a
dotted black and green line.

The surface gravity of each of the component stars is determined by fitting
the wings of the Balmer lines in the spectra with the biggest RV shifts. We
find that the primary and the secondary have similar surface gravities of
$\log g=3.7\pm 0.1$ (see Fig. 6).

Figure 6: Close-ups on the Balmer lines in the X-Shooter spectrum (ID 09;
solid blue) compared to the combined synthetic model (dotted red). The
unweighted synthetic spectra of the primary and secondary components are shown
as dotted black and green line.

The temperatures of the stars are derived using the ratio between the He I and
He II lines associated with each component (see Table 12). To get a more
accurate constraint on the primary’s temperature, the ratio between the
different observed nitrogen lines are used, namely N iv
$\lambda\lambda\lambda$ 3479, 3483, 3485, N iv $\lambda$ 4058, N v
$\lambda\lambda$ 4604, 4620, N iii $\lambda\lambda$ 4634, 4641, and N iv
$\lambda\lambda\lambda$ 6212, 6216, 6220. We find for the primary
$T_{\mathrm{eff,\,1}}=$43.6\pm 2\text{\,}\mathrm{k}\mathrm{K}$$, while the
secondary is best fit with $T_{\mathrm{eff,\,2}}=$38.7\pm
2\text{\,}\mathrm{k}\mathrm{K}$$.

Table 7: Abundances and ionisation stages employed in the PoWR models. Element | Primary | Secondary
---|---|---
| mass fr. | ion. stages | mass fr. | ion. stages
H | 0.60 |  i, ii | 0.7375 |  i, ii
He | 0.39 |  i, ii, iii | 0.26 |  i, ii, iii
C | $1\text{\times}{10}^{-5}$ |  ii – v | $21\text{\times}{10}^{-5}$ |  ii – v
N | $138\text{\times}{10}^{-5}$ |  ii – vi | $40\text{\times}{10}^{-5}$ |  ii – vi
O | $4\text{\times}{10}^{-5}$ |  ii – vii | $110\text{\times}{10}^{-5}$ |  ii – vii
Mg | $10\text{\times}{10}^{-5}$ |  ii, iii, iv | $10\text{\times}{10}^{-5}$ |  ii, iii, iv
Si | $1.3\text{\times}{10}^{-5}$ |  iii – viii | $1.3\text{\times}{10}^{-5}$ |  iii – vi
P | $8.3\text{\times}{10}^{-7}$ |  iv, v, vi | $8.3\text{\times}{10}^{-7}$ |  iv, v, vi
S | $4.4\text{\times}{10}^{-5}$ |  iii – vi | $4.4\text{\times}{10}^{-5}$ |  iii – vi
Fe | $3.5\text{\times}{10}^{-4}$ |  ii – ix | $3.5\text{\times}{10}^{-4}$ |  ii – ix

####  4.2.3 Surface abundances

During the determination of the temperature of the primary, we find that it is
possible to match the ratio of the He I and He II lines, but these lines are
systematically too weak. Hence, we lowered the primary’s surface hydrogen
abundance to $X_{\mathrm{H,\,1}}=0.60\pm 0.1$. Furthermore, to fit the
observed nitrogen lines, which are also crucial for the temperature
determination, we find that the nitrogen abundance of the primary is enhanced
to $X_{\mathrm{N,\,1}}=138^{+10}_{-30}\times 10^{-5}$ (i.e. $2\,N_{\odot}$).

In addition, the spectrum contains carbon and oxygen lines that show clear
contributions from the primary. To constrain its surface oxygen abundance, we
used the O iv $\lambda\lambda\lambda$ 1337-1343-1344 triplet in the UV, the O
iv multiplet around $\sim 3000$ Å, and the O iii lines in the range from
$1409\text{\,}\AA 1412\text{\,}\AA$. We find that oxygen in the primary’s
atmosphere is depleted with $X_{\mathrm{O,\,1}}=4^{+6}_{-3}\times 10^{-5}$.
Regarding the carbon abundance, we used C iv $\lambda$ 1169 in the UV and the
C iv $\lambda\lambda$ 5801, 5812 doublet in the optical, yielding a surface
carbon abundance of $X_{\mathrm{C,\,1}}=1^{+9}_{-0}\times 10^{-5}$ in the
primary.

Determining the surface abundance of the secondary is more complicated as it
shows little contribution to the observed metal lines. We can see in some
spectra that the secondary contributes to the N iii $\lambda\lambda$ 4634,
4641 doublet. Hence, we tried to use this as a constraint on its surface
nitrogen abundance and find the best fit with
$X_{\mathrm{N,\,2}}=60^{+20}_{-10}\times 10^{-5}$. We can also see a
contribution to the C iv $\lambda\lambda$ 5801, 5812 doublet in the optical,
and the C iii $\lambda$ 1175 in the UV. These lines can be well reproduced
with the initial carbon abundance of $X_{\mathrm{C,\,2}}=21^{+0}_{-5}\times
10^{-5}$. Unfortunately, we cannot see a clear contribution of the secondary
to the oxygen lines. As the nitrogen abundance is increased and theory
predicts that the amount of CNO material should be
$X_{\mathrm{CNO}}\approx{137\times 10^{-5}}$ for stars in the SMC (Kurt &
Dufour, 1998), we scaled down the oxygen abundance of the secondary to
$X_{\mathrm{O,\,2}}=$80\text{\times}{10}^{-5}$$. We note that this does not
have any impact on the quality of our fit.

Figure 7: Close-up on the iron forest of the HST FOS (ID 03) spectrum (solid
blue) compared to the combined synthetic model flux (dashed red). The weighted
synthetic model spectra of the primary and secondary are shown as a dotted
black and green line, respectively. The iron forest is used to check the iron
abundance and to constrain the microturbulence within the stellar atmosphere.
Figure 8: Close-ups on the metal lines in the X-Shooter spectrum (ID 09 and
31; solid blue) compared to the combined synthetic spectrum (dashed red). The
unweighted synthetic spectra of the primary and the secondary component are
shown as a dotted black and green line, respectively.

Figure 8 shows the all-important metal lines used to fit the abundances of the
primary and secondary. The changed surface abundances of the primary,
especially the lower surface hydrogen abundance and the increased nitrogen,
hint at previous binary interaction that stripped off parts of the envelope
(see Sect. 6).

####  4.2.4 Spectroscopic stellar masses

Given the fundamental stellar parameters ($T_{\mathrm{eff}}$, $\log g$, $L$)
of each binary component, we can calculate the spectroscopic masses. We find
that the mass of the primary component is
${M_{\mathrm{spec,\,1}}=32^{+19}_{-13}\,M_{\odot}}$, surprisingly low for its
luminosity. The mass of the secondary is
${M_{\mathrm{spec,\,2}}=55^{+32}_{-21}\,M_{\odot}}$. The low mass of the
primary strengthens our argument that the binary components must have
interacted in the past.

To further strengthen this hypothesis, we calculated the Roche radius, using
the results from the orbital analysis in combination with the spectroscopic
masses and find that both stars are currently slightly overfilling their Roche
lobe with ${R_{1}/R_{\mathrm{RL}}=1.01}$ and ${R_{2}/R_{\mathrm{RL}}=1.03}$.
This strongly suggests that the system interacted in the past, and that both
stars are still currently in contact.

####  4.2.5 Wind velocities and mass-loss rates

So far only photospheric lines were considered in the spectroscopic analysis.
However, in the spectra there are several lines that are sensitive to wind
parameters, like the N v $\lambda\lambda$ 1239, 1243 and C iv $\lambda\lambda$
1548, 1551 doublets in the UV, and H$\alpha$ and He ii $\lambda$ 4686 in the
optical. Both stars are very bright, massive, and hot, meaning that both of
them are expected to contribute to the wind diagnostic lines. Within the FUV
FUSE observation, no measurable P v or S IV wind resonance lines are present.
This is consistent with our composite model.

The primary motion is reflected by the emission parts of H$\alpha$ and He ii
$\lambda$ 4686, while the secondary’s motion is evident from the absorption
components of the same lines. We conclude that the primary must have a
stronger mass-loss rate compared to the secondary. We used the H$\alpha$ and
He ii $\lambda$ 4686, in combination with N v $\lambda\lambda$ 1239, 1243 and
C iv $\lambda\lambda$ 1548, 1551, to calibrate the primary’s mass-loss rate to
${\log(\dot{M}_{1}/({\,M_{\odot}\,\mbox{yr}^{-1}}))=-5.4\pm 0.1}$. With this
mass-loss rate, the resonance doublets in the UV were fully saturated in the
synthetic spectrum of the primary, yet the observed profiles were not fully
saturated. The secondary contributes roughly 60% of the UV flux, so we fit the
combined spectra with a partially saturated secondary wind. The secondary is
fit with a mass-loss rate of ${\log(\dot{M}_{2}\ /\
({\,M_{\odot}\,\mbox{yr}^{-1}}))=-7.3\pm 0.1}$, which results in the combined
synthetic spectrum matching the observed spectrum (Fig. 9).

The terminal wind velocity of the primary is adjusted to match the blue edge
of the N v $\lambda\lambda$ 1239, 1243 absorption trough, giving
${\varv_{\infty,\,1}=$2500\pm
100\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$}$. For the secondary, we
experimented with different values of $\varv_{\infty}$ to see how the slope of
the C iv $\lambda$ 1548,1551 resonance doublet changes. The best fit that
matches the profile in the STIS and FOS spectrum was obtained when using the
same terminal wind velocity for the secondary as for the primary
(${\varv_{\infty,\,2}=$2500\pm
300\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$}$).

Figure 9: Close-ups on the key wind diagnostic lines (solid blue) in the FUV,
UV and optical spectra overplotted by the combined synthetic model (dashed
red). In the upper panels the weighted and in the lower panels the unweighted
synthetic spectra of the primary and secondary components are shown as dotted
black and green line, respectively. Upper left: The O VI line of the FUSE (ID
1) spectrum. This line is sensitive to X-rays. Upper middle: The N V resonance
doublet in the HST FOS (ID 3) spectrum. Upper right:  The C IV resonance
doublet in the HST FOS (ID 3) spectrum. Lower left: The He ii $\lambda$ 4686
line in the X-Shooter spectrum (ID 9), showing strong wind emission features
from the primary. Lower right: $\mathrm{H}\alpha$ of the X-Shooter spectrum
(ID 31), again, the primary dominates the wind emission of this line.

####  4.2.6 Required X-ray flux

The O vi $\lambda\lambda$ 1032, 1038 resonance doublet in the FUV shows weak
indications of a P Cygni profile, which cannot be modelled by default in a
stellar atmosphere model. Cassinelli & Olson (1979) were the first to suggest
that these high ionisation stages must be ‘super-ionised’ by a hot X-ray
plasma that originates from within the wind.

We include, in our primary and secondary, a hot plasma that is smoothly
distributed throughout the wind, starting at $1.1\,R_{\ast}$ and having a
temperature of $T_{\mathrm{X}}=$3\text{\,}\mathrm{M}\mathrm{K}$$. We find that
the O vi $\lambda\lambda$ 1032, 1038 resonance doublet (Fig. 9) can be
explained with an X-ray luminosity of
$\log(L_{\mathrm{X,\,1}}/(\mathrm{erg\,s}^{-1}))=32.4$ and
$\log(L_{\mathrm{X,\,2}}/(\mathrm{erg\,s}^{-1}))=32.1$ for the primary and
secondary, respectively. This is much lower than the X-Ray luminosity observed
from the core of NGC 346 and comparable to X-rays needed for other O stars
(Nebot Gómez-Morán & Oskinova, 2018).

Table 8: Stellar parameters derived from the spectroscopic analysis, compared
to those of the best-fitting MESA model

| Spectroscopic fit | MESA model | Unit
---|---|---|---
| SSN 7a | SSN 7b | mass donor | mass gainer |
$\log\,L$ | $5.75\pm{0.15}$ | $5.78\pm{0.15}$ | $5.76\pm{0.1}$ | $5.74\pm{0.1}$ | $[L_{\odot}]$
$T_{\mathrm{eff}}$ | $43.6\pm{1.0}$ | $38.7\pm{1.0}$ | $43.6\pm{1.5}$ | $38.8\pm{1.5}$ | $[\mathrm{kK}]$
$\log\,g$ | $3.7\pm{0.1}$ | $3.7\pm{0.1}$ | $3.68\pm{0.05}$ | $3.7\pm{0.05}$ | $[\mathrm{cm\ s}^{-2}]$
$\varv\sin i$ | $135\pm 10$ | $150\pm 10$ | - | - | $[\mathrm{km\,s^{-1}}]$
$\varv_{\mathrm{rot}}$ | - | - | $222\pm{10}$ | $274\pm{10}$ | $[\mathrm{km\,s^{-1}}]$
$\log\dot{M}$ | $-5.4\pm 0.1$ | $-7.3\pm 0.4$ | $-5.87\pm{0.1}\,^{(a)}$ | $-5.75\pm{0.1}\,^{(a)}$ | $[M_{\sun}\,\textrm{yr}^{-1}]$
$\varv_{\infty}$ | $2500\pm 100$ | $2500\pm 300$ | - | - | $[\mathrm{km\,s^{-1}}]$
$R$ | $13.2\pm 1.7$ | $17.3\pm 2.1$ | $13.5\pm{0.3}$ | $16.3\pm{0.5}$ | $[R_{\odot}]$
$R_{\mathrm{RL}}\,^{(b)}$ | $13.1^{+3.8}_{-2.3}$ | $16.8^{+4.8}_{-3.3}$ | $13.5\pm{0.3}$ | $16.3\pm{0.5}$ | $[R_{\odot}]$
$R/R_{\mathrm{RL}}$ | $1.01$ | $1.03$ | $1$ | $1$ |
$M$ | $32^{+19}_{-13}$ | $55^{+32}_{-21}$ | $33\pm{2}$ | $50\pm{5}$ | $[M_{\odot}]$
$X_{\mathrm{H}}$ | $0.60\pm 0.05$ | 0.7375 | $0.51\pm 0.1$ | $0.71\pm 0.02$ | $[\mathrm{mass\,fr.}]$
$X_{\mathrm{He}}$ | $0.39\pm 0.05$ | 0.26 | $0.50\pm 0.1$ | $0.28\pm 0.02$ | $[\mathrm{mass\,fr.}]$
$X_{\mathrm{C}}\times 10^{5}$ | $1^{+1}_{-0}$ | $21\pm 5$ | $2\pm 2$ | $26\pm 2$ | $[\mathrm{mass\,fr.}]$
$X_{\mathrm{N}}\times 10^{5}$ | $138^{+10}_{-30}$ | $40^{+20}_{-10}$ | $138\pm 2$ | $43\pm 5$ | $[\mathrm{mass\,fr.}]$
$X_{\mathrm{O}}\times 10^{5}$ | $4^{+6}_{-1}$ | 80(c) | $4\pm 2$ | $80\pm 5$ | $[\mathrm{mass\,fr.}]$

555 (a) Only wind mass-loss rates, according to the wind recipe used in our
calculations. (b) Calculated using the period $P=$3.07\text{\,}\mathrm{d}$$,
as from the orbital analysis (see Sect. 3), and using the spectroscopic mass
ratio. (c) Set to fulfil
${\Sigma\,\mathrm{CNO}_{\mathrm{i}}\approx\mathrm{const.}=$137\text{\times}{10}^{-5}$}$.

##  5 Stellar evolution modelling

In the previous sections we determine the stellar and wind parameters of the
binary components, and refine the binary period, and we establish that the
system is most likely in contact. With this information at hand, we proceed to
model the past, present, and future evolution of this remarkable system.

The evolution of SSN 7 in this work is modelled using the Modules for
Experiments in Stellar Astrophysics (MESA; Paxton et al., 2011, 2013, 2015,
2018, 2019) code (v.15140). Our aim is to understand, from the predictions of
the stellar evolutionary models, the current evolutionary stage of our target
rather than finding a perfect fine-tuned fit for our empirically derived
parameters. The orbital and spectroscopic parameters (Sect. 4.1 and Sect. 3.1)
limit the possible previous evolutionary paths. To find a fitting model, we
explore a parameter space in the following ranges: donor masses in the range
${M_{1,\,\mathrm{i}}=$45\text{\,}\mathrm{M}_{\odot}65\text{\,}\mathrm{M}_{\odot}$}$,
initial accretor masses with
${M_{2,\,\mathrm{i}}=$30\text{\,}\mathrm{M}_{\odot}55\text{\,}\mathrm{M}_{\odot}$}$,
and initial orbital periods in the range
${P_{\mathrm{i}}=$2\text{\,}\mathrm{d}7\text{\,}\mathrm{d}$}$.

###  5.1 Stellar and binary input physics

The employed binary evolutionary models are constructed using the input files
provided by Marchant et al.
(2016).666https://github.com/orlox/mesa_input_data/tree/master/2016_binary_models
A brief summary of the assumed input physics follows.

In the binary models, following the work of Brott et al. (2011), tailored
initial abundances are used. The initial abundances are
$X_{\mathrm{H}}=0.7460$, $X_{\mathrm{He}}=0.2518$, and $Z=0.0022$, with $Z$
being the total metal fraction. The individual initial metal abundances are
listed in Table 7. The abundances are comparable to fit in our atmospheric
model (see Table 7).

Table 9: Initial chemical abundances of our stellar evolutionary models.

element | mass fraction | reference
---|---|---
$\mathrm{C}$ | $20.82\times 10^{-5}$ | Kurt & Dufour (1998)
$\mathrm{N}$ | $3.28\times 10^{-5}$ | Kurt & Dufour (1998)
$\mathrm{O}$ | $113.07\times 10^{-5}$ | Kurt & Dufour (1998)
$\mathrm{Mg}$ | $9.32\times 10^{-5}$ | Trundle et al. (2007)
|  | Hunter et al. (2007)
$\mathrm{Si}$ | $1.30\times 10^{-5}$ | Trundle et al. (2007)
|  | Hunter et al. (2007)
$\mathrm{Fe}$ | $33.74\times 10^{-5}$ | Venn (1999)
777All elements that are not listed here correspond to the solar abundances
from Asplund et al. (2005) scaled down by a factor of $1/5$.

Figure 10: Evolutionary tracks of the donor (left) and the accretor (right)
colour-coded by their surface H-abundance. The track of the mass gainer is
only colour-coded until the primary dies and then continues as a solid white
line, assuming that the binary is not disrupted by a supernova explosion. The
tracks are overlayed by black dots that show equidistant time steps of
$30\,000\text{\,}\mathrm{y}\mathrm{r}$ to highlight phases in which the stars
spend most of their time. The spectroscopic results are shown as green and red
triangles surrounded by error ellipses. Start and end phases of fast and slow
Case A, as well as Case AB mass-transfer are indicated by arrows. The iso-
contours of equal radii are indicated in the background as dashed grey lines.

Mixing is included as follows. Convection is modelled as standard mixing
length theory (MLT, Böhm-Vitense, 1958) using the Ledoux criterion and
$\alpha_{\mathrm{mlt}}=1.5$. Semiconvective mixing is assumed to be efficient
with $\alpha_{\mathrm{sc}}=1$ (Langer et al., 1983; Schootemeijer et al.,
2019). For core hydrogen-burning stars, the step overshooting is assumed to be
up to $0.335H_{\mathrm{P}}$ (Brott et al., 2011; Schootemeijer et al., 2019).
Furthermore, rotational mixing is included as a diffuse process, including
dynamical shear, secular shear, and Goldreich-Schubert-Fricke instabilities,
as well as Eddingtion-Sweet circulations Heger et al. (2000). The efficiency
parameters are set to $f_{c}=1/30$ and $f_{\mu}=0.1$. Thermohaline mixing is
modelled with $\alpha_{\mathrm{th}}=1$ (Kippenhahn et al., 1980). Lastly, the
models take into account momentum transport originating from a magnetic field
as expected from a Taylor-Spruit dynamo (Spruit, 2002).

To avoid numerical complications in the late evolutionary stages of the star,
the evolution of both components is only modelled until core helium depletion.
Furthermore, for core helium burning stars with core masses above
$>14\,M_{\odot}$ a more efficient mixing theory, MLT++ (section 7.2 of Paxton
et al., 2013), is employed.

Mass-loss via a stellar wind is included in the models in the following way.
For hydrogen-rich ($X_{\mathrm{H}}\geq 0.7$) OB stars, the recipe of Vink et
al. (2001) is used. As soon as the temperature of any model drops below the
bi-stability jump (Vink et al., 2001, their equations 14 and 15), the maximum
of the mass-loss rate of Vink et al. (2001) or Nieuwenhuijzen & de Jager
(1990) is taken. During the WR stage, when the surface hydrogen abundance
drops below $X_{\mathrm{H}}\leq 0.4$, the mass loss rates of Shenar et al.
(2019, 2020b) are used. For surface abundances between
${0.7>X_{\mathrm{H}}>0.4}$, the mass-loss rate is linearly interpolated
between the mass-loss rates of Vink et al. (2001) and Shenar et al. (2019,
2020b).

To reduce the free parameter space, it is presumed that the components of SSN
7 are initially tidally locked and that the orbit is circularised. This is a
reasonable approach for a binary with a period as short as
$3.1\text{\,}\mathrm{d}$.

Mass transfer by Roche-lobe overflow is modelled implicitly using the contact
scheme of the MESA code. The mass transfer is modelled conservatively as long
as the mass-gainer is below critical rotation. Whenever the mass-gainer spins
up to critical rotation, it will stop the accretion, and we assume that the
material is directly lost from the system. In addition to the mass transfer by
Roche-lobe overflow, mass accretion from the stellar wind is taken into
account.

At the instance of time when the donor star depletes helium in its core, its
model is stopped. It is assumed that the primary directly collapses into a BH
without a supernova explosion and without a kick. Further mass transfer via
Roche-lobe overflow and wind from the companion onto the BH accretion onto the
BH is limited by the Eddington accretion rate.

###  5.2 Resulting binary models

The best fit of the empirically derived fundamental stellar parameters of both
binary components is achieved with an initial primary mass of $52\,M_{\odot}$,
an initial secondary mass of $38\,M_{\odot}$, and an initial orbital period of
$2.7\text{\,}\mathrm{d}$. The corresponding tracks of the mass donor and mass
gainer in the Hertzsprung–Russell diagram (HRD) are shown in Fig. 10. The
binary evolutionary model that matches the spectral fit parameters best
predicts that the observed stars are currently in contact in a slow Case A
mass-transfer phase. This prediction would make SSN 7 the most massive Algol-
like system known so far, making it an ideal laboratory to study the ongoing
effects and efficiencies of mass transfer in binaries hosting massive stars.

The parameters of the closest fitting binary evolution model are listed in
Table 5. Errors quoted are sophisticated guesses on the uncertainties of the
binary evolutionary models from the experiences we gained when tailoring the
evolutionary models to match the empirically derived stellar parameters. For
more accurate error margins, a fine grid of detailed stellar evolution models
is needed.

The empirically derived fundamental stellar parameters as well as the observed
period of $3.1\text{\,}\mathrm{d}$ can be explained by our binary evolutionary
model. Our favourite model predicts that the binary has an age of
$4.2\text{\,}\mathrm{M}\mathrm{y}\mathrm{r}$. The only discrepancy found is
between the predicted and observed rotation rates. We discuss this in detail
in Sect. 6.2.2.

It is predicted that the primary, after it depletes the hydrogen in its core,
expands and initiates another more rapid mass-transfer phase, also called Case
AB mass-transfer. During this phase it strips off large fractions of its
H-rich envelope and evolves bluewards in the HRD towards the regime where WR
stars can be found. During its WR phase, our model is predicted to have some H
remaining in the envelope (${X_{\mathrm{H}}\sim 0.2}$). During this time, the
secondary, which will be rejuvenated from mass accretion, is still core
hydrogen burning.

After the primary, which is the current mass donor, depletes the helium in its
core, we assume that it directly collapses into a BH. The formed BH has a mass
of $25.5\,M_{\odot}$, which should be considered as an upper limit since we
assumed a direct collapse. However, this assumption allows us to make
predictions about the future evolution of the secondary. Our model predicts
that the secondary will evolve off the main sequence and will initiate mass
transfer on the BH, stripping parts of its H-rich envelope
(${X_{\mathrm{H}}\sim 0.4}$). This star does not evolve bluewards to the WR
regime and the Of/WNh population. This is linked to the increased envelope-to-
core mass ratio, leading to the formation of a steep chemical gradient (Pauli
et al., 2023; Schootemeijer & Langer, 2018). After a short time (of the order
of a few hundred thousand years), the remaining star will also collapse to a
BH with a mass of $25\,M_{\odot}$. The two black holes orbit each other every
$4.85\text{\,}\mathrm{d}$. Following Peters (1964) we calculated the merger
timescale of the binary to be
$\tau_{\mathrm{merger}}=$18.5\text{\,}\mathrm{G}\mathrm{y}\mathrm{r}$$. This
is longer than the age of the Universe. We note that our estimated value
should be considered a lower limit as the BH masses of the individual
components could be lower, which would result in even longer merger
timescales.

##  6 Discussion

###  6.1 Orbital, spectroscopic, and stellar evolutionary masses

The most reliable mass estimate is the projected orbital mass of the system
(see Sect. 3). Since we do not have a light curve available, it is only
possible to compare it with the spectroscopic result by choosing an
inclination. However, this introduces additional uncertainties and makes the
orbital masses inaccurate. A better way to compare the results is by using the
derived mass ratios.

In Section 3 we obtained $q_{\mathrm{wilson}}=1.34\pm 0.07$ using the fitting
method from Wilson (1941) and $q_{\mathrm{PHOEBE}}=1.47^{+0.13}_{-0.09}$ when
modelling the RV curve in detail with the PHOEBE code. From our spectroscopic
analysis, we derived a somewhat higher mass ratio of
$q_{\mathrm{spec}}=1.7^{+2.9}_{-1.0}$. The large error margins arise from the
uncertainties from fitting the surface gravity and from the uncertainties
introduced in the multiple solutions that can be found for the luminosity
ratio (i.e. ${M_{\mathrm{spec}}\propto R^{2}\propto L}$). Hence, it could be
that the spectroscopic mass ratio is overestimated. However, the conclusion
that the primary component is more massive than the secondary component
remains.

During the tailoring process of our evolutionary model towards the empirically
derived stellar parameters, we exploited various combinations of the mass
ratio of the two components. In these models, the mass and the position of the
primary were always only explainable when it was in a slow Case A mass-
transfer phase. The secondary in these models had different initial masses,
and thus the mass during the Case A mass transfer was also different (i.e.
lower) compared to our best-fitting model.

Figure 11: Observed mass-loss rates of O stars in NGC 346 (including SSN 7) as
a function of stellar luminosity compared to theoretical and empirical
relations. The position of both binary components of SSN 7 are marked by black
stars. The data is complemented by O stars from Rickard et al. (2022).
Apparently single stars are shown as filled blue squares and known muliple
systems as open blue squares. In the background the empirical relation of
main-sequence O-type stars from Rickard et al. (2022) is included as dashed
black line. In addition, we show the theoretical relations of Vink et al.
(2001) and Björklund et al. (2022) for main-sequence stars as dashed yellow
and dashed red line, respectively.

###  6.2 Effects of the inclination on the final parameters

####  6.2.1 Fundamental stellar and wind parameters

As discussed in the previous section, the orbital mass ratio and the
spectroscopic mass ratio agree within their respective uncertainties. This
agreement enabled us to estimate the inclination of the system to be
${i_{\mathrm{orb}}=$16\pm 1\text{\,}{}^{\circ}$}$ (see Sect. 3.3.2). This
implies that we must be looking at the system pole-on. Given our estimates on
the rotational velocities and the fact that the two stars are in contact, they
must be oblate and deformed. Hence, the stellar parameters of these stars
might no longer be uniform over the surface of the star.

Under the assumption of a star rotating close to break-up velocity, the
effective surface gravity at the equator is ${g_{\mathrm{equator}}\approx 0}$
as the gravitational and centrifugal forces cancel each other out. On the
other hand, the effective surface gravity on the pole must be rather
unperturbed and is mostly affected by gravity. Since we are looking at the
pole region of the star, we conclude that our estimate on the surface gravity
is reliable within its uncertainties, and hence also our estimate on the
inclination.

Due to the effect of gravity darkening, an ellipsoidal star is cooler at the
equator and hotter at the poles. Abdul-Masih (2023) studied the effect of
rotation and inclination on the determined effective temperature by using
synthetic models created with the spamms code on a three-dimensional surface.
He concluded that in the case of rapid rotation and low inclination, the
star’s temperature can be overestimated by $10\%$. This means that both of our
stars actually might be
$3\text{\,}\mathrm{k}\mathrm{K}4\text{\,}\mathrm{k}\mathrm{K}$ cooler.
Furthermore, Abdul-Masih (2023) finds that the surface helium abundance of a
rapidly rotating pole-on star can be underestimated by as much as $60\%$,
which would account for the discrepancy between the observed helium abundance
and the helium abundance from the binary evolutionary models.

Given the ellipsoidal shape and hence the different radii and temperatures, it
might be evident that the star’s luminosity also depends on the inclination
angle. We calculated the expected luminosity of our target at the pole and the
equator and find a difference ${\Delta\log L/L_{\odot}\approx 0.15}$, which is
within our given uncertainties. The impact of a somewhat lower luminosity on
our final results is too small to impact our final conclusions.

Due to the different effective surface gravities between the poles and the
equator, wind parameters vary with inclination. The wind is slower and weaker
in the equatorial regions, while it is faster and more powerful at the poles.
An average mass-loss rate for the whole star would thus be lower than any
measured from a low inclination angle, such as in our case. We would therefore
treat our stated mass-loss rates as upper limits.

####  6.2.2 Discrepancy between observed and predicted rotation velocity

The binary evolutionary models agree with almost all spectroscopically derived
stellar parameters, except the rotational velocity. Under the assumption that
the inclination determined from the orbital analysis (see Sect. 3) is
reliable, the observed rotation velocities of the binary components
(${\varv_{1}=$490\pm 47\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$}$ and
${\varv_{2}=$544\pm 49\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$}$) are a
factor of two higher than those predicted by the binary evolutionary models.

Given that we are looking at the binary pole-on, and that both stars are
deformed due to their fast rotation, this means that the assumption of
spherical symmetry breaks down in the evolutionary models. Zahn et al. (2010)
have shown this for a uniformly rapidly rotating star
${R_{\mathrm{equator}}\approx 1.5R_{\mathrm{pole}}}$. Hence, under the
assumption that ${R\approx R_{\mathrm{pole}}}$, the rotation rates of the
binary model need to be corrected to
${\varv_{\mathrm{mod,\,\,1}}\approx$325\pm
45\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$}$ and
${\varv_{\mathrm{mod,\,\,2}}\approx$425\pm
50\text{\,}\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$}$. This brings observations
and predictions closer together, but still shows some discrepancy. We note
that our target is a contact binary, meaning that the stars are tear-drop
shaped rather than ellipsoidal. This makes an estimate of the rotation rates
even more complicated.

On the other hand, it is worth mentioning that in our stellar atmosphere
calculations we neglect additional broadening mechanisms such as
macroturbulence and asynchronous rotation (e.g. introduced by differential
rotation). These effects are compensated for in our estimate of the projected
rotational velocity $\varv\sin i$, and hence might lead to an overestimation,
which can explain the observed discrepancy.

###  6.3 Empirical mass-loss rates

From our spectroscopic analysis (Sect. 4.2.5) we derived that the primary
dominates most of the wind lines
(${\log\,(\dot{M}_{1}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-5.4}$), while the
secondary still has a significant and noticeable contribution in the wind UV
lines (${\log\,(\dot{M}_{2}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-7.3}$). In
the following we want to determine whether the chosen mass-loss rates agree
with observations and theoretical expectations.

Following Rickard et al. (2022), we would expect from a star that has evolved
in isolation and has a current luminosity of $\log(L/L_{\odot})=5.75$ a mass-
loss rate of only
${\log\,(\dot{M}_{\mathrm{Rickard}}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-7.35}$.
This is two orders of magnitude lower than that derived for the primary from
empirically spectroscopic analysis. However, the primary has lost a huge
amount of mass and has an unusual $L/\/M$ ratio that is not considered in
their relation. On the other hand, theoretical mass-loss recipes take into
account several parameters, such as luminosity, mass, temperature and
metallicity. For comparison, we calculated the mass-loss rate predicted with
the frequently used Vink et al. (2001) to be ${\log\,(\dot{M}_{\mathrm{Vink,\
1}}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-5.9}$. A more updated recipe for
O-type stars is from Björklund et al. (2022). Their mass-loss recipe predicts
${\log\,(\dot{M}_{\mathrm{Bj\"{o}rklund\ 2022,\
1}}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-6.6}$, which is one order of
magnitude lower than the observed mass-loss rate. However, these mass-loss
rates are calculated for H-rich ($X_{\mathrm{H}}>0.7$). The primary has
already lost a significant amount of its envelope, and its surface H-abundance
already dropped to $X_{\mathrm{H}}\approx 0.6$ (see Table 5). For
completeness, we calculated the corresponding WR mass-loss rates according to
Shenar et al. (2019, 2020b) for stars with $X_{\mathrm{H}}>0.4$, yielding
${\log\,(\dot{M}_{\mathrm{Shenar,\
1}}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-5.5}$ and being in agreement with
the empirically derived values.

The secondary seems to be more well behaved. Its empirically derived mass-loss
rates agrees well with the expectations from other O stars in the SMC (Rickard
et al., 2022). The theoretical predicted rates from Vink et al. (2001) and
Björklund et al. (2022) are ${\log\,(\dot{M}_{\mathrm{Vink,\
2}}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-6.2}$ and
${\log\,(\dot{M}_{{\mathrm{Bj\"{o}rklund\ 2022}},\
1}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-7.1}$, respectively. Only the latter
agrees within the error margins of the observed mass-loss rates. For
comparison, we illustrate in Fig. 11 the expected mass-loss rates from other
O-type stars in NGC 346 compared to our spectroscopically fit values,
alongside theoretical prescriptions.

###  6.4 SSN 7 and its role in NGC346

In the recent paper of Rickard et al. (2022), it is noted that the massive
giant NGC 346 SSN 9 (MPG 355, O2III(f *), Walborn et al. 2000) is the major
ionising source of the core region. In their work it is stated that the star
outshines the remaining O-star population and is responsible for 50% of the
hydrogen ionising flux (($\log{Q}_{\mathrm{H,\,SSN\,9}}=49.98$). However, in
their analysis SSN 7 was neglected because of its binary nature. According to
our stellar atmosphere models, we find that the two early-type stars in the
binary have a combined hydrogen ionising flux of
$\log{Q}_{H,\,\mathrm{SSN7\,a+b}}=49.88$. This makes SSN 7 one of the two
major contributors to the H ionising flux of the core of NGC 346. We stated in
Rickard et al. (2022) that the morphology of the ionising front within images
of NGC 346 centre upon SSN 9. The location of SSN 7 is directly ‘behind’ SSN 9
from the position of the ionising front (Fig. 1).

We compared the calculated H ionising photon count of both components of SSN 7
to other massive stars within both the SMC and LMC (Fig. 12). The predicted
ionising flux is consistent with the spectral types assigned to each component
by Walborn et al. (2000), even though the primary has an outstanding L/M ratio
and the secondary that is suspected to have accreted several solar masses.

For helium ionising photons, the model of the primary gives
$\log{Q}_{\mathrm{He\,I,\,SSN\,7a}}=48.98$ and
$\log{Q}_{\mathrm{HeII,\,SSN\,7a}}=40.81$, while the secondary model gives
$\log{Q}_{\mathrm{He\,I,\,SSN\,7b}}=48.58$ and
$\log{Q}_{\mathrm{HeII,\,SSN\,7b}}=43.14$. Combined, the helium ionising
fluxes of the two components of the binary combined are
$\log{Q}_{\mathrm{\mathrm{HeI,\,SSN7\,a+b}}}=49.12$ and
$\log{Q}_{\mathrm{\mathrm{HeI,\,SSN7\,a+b}}}=43.14$, or 25% and 0.04% of the
total of the O stars analysed in the core of NGC 346 between this paper and
Rickard et al. (2022). This is compared to
$\log{Q}_{\mathrm{HeI,\,SSN\leavevmode\nobreak\ 9}}=49.41$ and
$\log{Q}_{\mathrm{HeII,\,SSN\leavevmode\nobreak\ 9}}=46.50$, or 31% and 99%.
This is notable because the combined He i ionising flux for the binary is
comparable to that of SSN 9, but not for the He ii ionising flux, where SSN 9
dominates.

Figure 12: $\log Q_{H}$ to spectral type. SMC sample stars analysed by
Ramachandran et al. (2019) are included (red diamonds) as well as LMC stars
from Ramachandran et al. (2018) (blue diamonds) and O stars from the core of
NGC 346 from Rickard et al. (2022) (black diamonds). The two components of the
SSN 7 binary are shown separately.

###  6.5 Age of the NGC 346 O-star population

During our evolutionary analysis it was revealed that the system of SSN 7 has
an age of $4.2\text{\,}\mathrm{M}\mathrm{y}\mathrm{r}$ (see Sect. 5.2).
Meanwhile, much younger ages for NGC346 have been estimated in previous works,
such as $1\leavevmode\nobreak\ -\leavevmode\nobreak\ 2.6$ Myr (Dufton et al.,
2019) and $1\leavevmode\nobreak\ -\leavevmode\nobreak\ 2$ Myr (Walborn et al.,
2000). In Fig. 13 we compare the empirically derived stellar parameters of SSN
7 and other O stars (Rickard et al., 2022) to isochrones from Georgy et al.
(2013). According to these isochrones, the age of the primary should be
$2\text{\,}\mathrm{M}\mathrm{y}\mathrm{r}$, while the secondary would be
$3\text{\,}\mathrm{M}\mathrm{y}\mathrm{r}$ old. This mismatch between the age
predicted through evolutionary modelling and the age compared to single-star
isochrones is not an isolated example and could lead to false conclusions on
the age of the cluster.

When inspecting Fig. 13 in more detail we can see that most of the luminous O
stars in NGC 346 are known binaries, or higher order multiple systems, with
the one exception of SSN 9. However, this star is unusually luminous and hot
and undermassive for its position in the HRD, hinting towards a binary nature.
Taking into account only the apparent single O stars in this cluster, we
conlcude the age of the O-star population, according to single-star evolution
isochromes, to be $4\text{\,}\mathrm{M}\mathrm{y}\mathrm{r}$, which is
consistent with the age derived from our binary models.

With evidence that the core of NGC 346 has not yet been affected by any
supernova explosion (Danforth et al., 2003), the fate of more massive stars
within NGC 346 comes into question. Either none had formed yet, or those that
did have imploded into BHs directly.

Figure 13: HR diagram showing the position of the two components of SSN 7 as
determined by our spectrographic analysis. Black stars are the two SSN 7
components. Blue symbols are the other O stars within the central core of NGC
346 (Rickard et al., 2022). Open symbols are noted spectral binaries (Dufton
et al., 2019). Dotted lines are isochrones with $Z=0.002$ (Georgy et al.,
2013) and an initial rotation of ${100\ \mathrm{km\ s^{-1}}}$.

###  6.6 Luminosity class and spectral type

In the previous work of Walborn (1978), SSN 7 was classified as O4 III(n)(f),
but it was not known to be a binary. In a recent work, Dufton et al. (2019)
propose that the presence of He i $\lambda$ 4471 absorption and weak He ii
$\lambda$ 4686 emission suggest that the primary should be a O4 If star. With
the new insights gained from the detailed multi-epoch observations, we assign
the He i $\lambda$ 4471 absorption mainly to the secondary component, meaning
that the primary has an earlier type.

Here we want to use the newly gained insights from the spectral analysis to
reclassify the primary and secondary star. It is evident that the primary in
our model shows only a very weak contribution to the He i $\lambda$ 4471 line
(see Fig. 5), meaning that it must be of very early type (O2-3.5). Following
Walborn et al. (2002) it is suggested to use for such early-type stars the
ratio of N iv $\lambda$ 4058 to N iii $\lambda$ 4640 emission. The multi-epoch
observations have shown that the N iii $\lambda$ 4640 emission line is a blend
of the primary and secondary components, while the N iv $\lambda$ 4058 purely
originates from the primary (see Fig. 8 and Table 12). Guided by our stellar
atmosphere models we find that N iv $\lambda$ 4058 $>$ N iii $\lambda$ 4640,
while we see very weak or no absorption in He i $\lambda$ 4471, implying a
spectral type of O3.

According to our spectral analysis we find that in the primary nitrogen is
enhanced, while carbon and oxygen are deficient. Therefore, we add the
qualifier ‘N’ to the spectral type. Following the classification criteria of
Sota et al. (2011) and taking into account that the N iv $\lambda$ 4058
emission feature is greater than the N iii $\lambda$ 4640 emission and that
the He ii $\lambda$ 4686 is also in emission we suggest adding the suffix
‘f∗’. In Sota et al. (2014) the luminosity classes are linked to the spectral
type as a function of the f phenomenon, suggesting a luminosity class I for
the primary. Because of the high temperature of the star, combined with the
low Si iv abundance ($\sim\,2\%$ solar), no Si iv $\lambda\lambda$ 1394, 1403
P Cygni lines are observed (Crowther et al., 2002), so the presence or absence
of this line cannot contribute to our luminosity classification. The final
spectral type we assign to the primary is ON3 If∗.

Observational counterparts with similar spectral type at low metallicity are
sparse. Galactic examples are Cyg OB2-7 and Cyg OB2-22A. By comparison of
their observed spectra to the synthetic spectrum of our primary we find a good
agreement between the morphology of the lines, supporting our choice on the
spectral type.

For the secondary, we limit its spectral type to O4-8 as it shows He i
$\lambda$ 4471 in absorption, while He ii $\lambda$ 4542$\,>\,$He i $\lambda$
4388 and He ii $\lambda$ 4200$\,>\,$He i $\lambda$ 4144, and it lacks Si III
$\lambda 4552$, which can be seen in the earliest O-type stars. Hence, we
follow Conti & Alschuler (1971) and use the logarithmic ratio of the
equivalent widths of He i $\lambda$ 4471 and He ii $\lambda$ 4542\.
Unfortunately, the He ii $\lambda$ 4542 line is blended by the companion.
Therefore, we decided to use the equivalent widths of the synthetic spectrum
of the secondary, yielding $\log(\mathrm{EW}(4471)/\mathrm{EW}(4542))=-0.45$.
This corresponds to a spectral type of O5.5. As mentioned above, the N iii
$\lambda$ 4640 emission line is a blend from the primary and secondary
component. As the secondary does not contribute to the N iv $\lambda$ 4058
line and shows strong He ii $\lambda$ 4686 absorption we add the suffix
‘((f))’ (Sota et al., 2011). Following Sota et al. (2014), given the spectral
type and the f phenomenon, the star should have a luminosity class V. We use
the criterion for the luminosity class estimation introduced by Martins
(2018). The criterion is based on the equivalent width of He ii $\lambda$ 4686
absorption line in the synthetic model of the secondary. With an equivalent
with of ${\mathrm{EW}(4868))=0.74}$, this star is confirmed to have a
luminosity class V. The final spectroscopic classification of the binary is
ON3 If∗+O5.5 V((f)).

##  7 Conclusions

We have conducted the first consistent multi-wavelength multi-epoch spectral
analysis of the SB 2 contact binary SSN 7 located in the NGC 346 cluster in
the SMC. The detailed analysis revealed that SSN 7 is a system with two binary
components that have comparable luminosity ($\log(L/L_{\odot})\approx 5.75$),
while having divergent stellar and wind parameters. The primary is the hotter
($T_{\mathrm{eff,\,1}}=$43.6\text{\,}\mathrm{k}\mathrm{K}$$) but less massive
($M_{1}=32\,M_{\odot}$) component. We revealed that the surface hydrogen
abundance is $X_{\mathrm{H}}=0.6$, and that it has CNO values close to those
of the CNO equilibrium. The mass-loss rate of the primary,
${\log\,(\dot{M}_{1}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-5.4}$, is
exceptionally high for its luminosity. The secondary is slightly cooler
($T_{\mathrm{eff,\,2}}=$38.7\text{\,}\mathrm{k}\mathrm{K}$$), but more massive
($M_{2}=55\,M_{\odot}$). The secondary has a mass-loss rate of
${\log\,(\dot{M}_{2}\,/\,({\,M_{\odot}\,\mbox{yr}^{-1}}))=-7.3}$, which is in
agreement with other O stars within the SMC that have similar luminosity. The
findings suggest that the two binary components exchange mass. Based on the
newly gained insights we reclassified the system as ON3 If∗+O5.5 V((f)).

The multi-epoch RV analysis of 19 separated observations, including 11 spaced
over ten days, allowed us to constrain the orbital parameters. The best fit is
achieved with a period of ${P=$3.07\text{\,}\mathrm{d}$}$ and a circular
orbit. The orbital analysis confirms a mass ratio of ${q_{\mathrm{orb}}=1.5}$,
favouring the secondary to be more massive and supporting the theory of a
binary interaction. Furthermore, given the orbital and stellar parameters, we
calculated the Roche radius and found that both components are filling their
Roche lobes and must be in contact.

From initial abundances consistent with NGC 346, we have modelled possible
stellar evolution pathways that explain the empirically derived stellar and
orbital parameters of SSN 7. Our favourite model predicts that the system has
an age of $\sim 4$ Myr. In this context, we review the age of the O-star
population within the core of NGC 346 and see that no single star (except for
the peculiar massive object SSN 9) is to the left of the 4 Myr isochrone. We
postulate that the age of the O-star population within the core of NGC 346 is
older than $\gtrsim 4$ Myr.

The binary evolutionary models are capable of explaining the currently
observed contact phase and predict that both stars are still undergoing slow
Case A mass transfer. This makes SSN 7 the most massive Algol-like system
known to date, enabling the study of the physics of binary interactions in a
way previously unavailable. This will shape our understanding of post-
interaction massive binaries, binary BHs, and ultimately, the progenitors of
GW events.

###### Acknowledgements.

DP acknowledges financial support by the Deutsches Zentrum für Luft und
Raumfahrt (DLR) grant FKZ 50 OR 2005. MJR and DP acknowledge Prof. Wolf-Rainer
Hamann, Prof. Lida Oskinova, Dr. Rainer Hainich, and Dr. Heldge Todt of the
Institut für Physik und Astronomie, Universität Potsdam. Dr. Andreas Sander
and Dr. Varsha Ramachandran of Zentrum für Astronomie der Universität
Heidelberg, Astronomisches Rechen-Institut, and Dr. Tomer Shenar of the
Institut for Astronomy, University of Amsterdam, and all other contributors to
the PoWR code. This publication has benefited from a discussion at a team
meeting sponsored by the International Space Science Institute at Bern,
Switzerland.

## References

  * Abbott et al. (2016) Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2016, ApJ, 832, L21
  * Abbott et al. (2019) Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2019, Phys. Rev. D, 100, 122002
  * Abdul-Masih (2023) Abdul-Masih, M. 2023, A&A, 669, L11
  * Asplund et al. (2005) Asplund, M., Grevesse, N., & Sauval, A. J. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 336, Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis, ed. T. G. Barnes III & F. N. Bash (San Francisco: Astronomical Society of the Pacific), 25
  * Batten (1989) Batten, A. H. 1989, Space Sci. Rev., 50, 1
  * Baym et al. (2018) Baym, G., Hatsuda, T., Kojo, T., et al. 2018, Reports on Progress in Physics, 81, 056902
  * Björklund et al. (2022) Björklund, R., Sundqvist, J. O., Singh, S. M., Puls, J., & Najarro, F. 2022, arXiv e-prints, arXiv:2203.08218
  * Böhm-Vitense (1958) Böhm-Vitense, E. 1958, ZAp, 46, 108
  * Bonanos et al. (2010) Bonanos, A. Z., Lennon, D. J., Köhlinger, F., et al. 2010, AJ, 140, 416
  * Brott et al. (2011) Brott, I., de Mink, S. E., Cantiello, M., et al. 2011, A&A, 530, A115
  * Burbidge et al. (1957) Burbidge, E. M., Burbidge, G. R., Fowler, W. A., & Hoyle, F. 1957, Reviews of Modern Physics, 29, 547
  * Cassinelli & Olson (1979) Cassinelli, J. P. & Olson, G. L. 1979, ApJ, 229, 304
  * Conroy et al. (2020) Conroy, K. E., Kochoska, A., Hey, D., et al. 2020, ApJS, 250, 34
  * Conti & Alschuler (1971) Conti, P. S. & Alschuler, W. R. 1971, ApJ, 170, 325
  * Crowther et al. (2002) Crowther, P. A., Hillier, D. J., Evans, C. J., et al. 2002, ApJ, 579, 774
  * Danforth et al. (2003) Danforth, C. W., Sankrit, R., Blair, W. P., Howk, J. C., & Chu, Y.-H. 2003, ApJ, 586, 1179
  * de Mink et al. (2007) de Mink, S. E., Pols, O. R., & Hilditch, R. W. 2007, A&A, 467, 1181
  * Dufton et al. (2019) Dufton, P. L., Evans, C. J., Hunter, I., Lennon, D. J., & Schneider, F. R. N. 2019, A&A, 626, A50
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306
  * Gaia Collaboration et al. (2022) Gaia Collaboration, Vallenari, A., Brown, A. G. A., et al. 2022, arXiv e-prints, arXiv:2208.00211
  * Georgy et al. (2013) Georgy, C., Ekström, S., Eggenberger, P., et al. 2013, A&A, 558, A103
  * Gräfener et al. (2002) Gräfener, G., Koesterke, L., & Hamann, W. R. 2002, A&A, 387, 244
  * Hainich et al. (2015) Hainich, R., Pasemann, D., Todt, H., et al. 2015, A&A, 581, A21
  * Hainich et al. (2014) Hainich, R., Rühling, U., Todt, H., et al. 2014, A&A, 565, A27
  * Hamann & Gräfener (2004) Hamann, W. R. & Gräfener, G. 2004, A&A, 427, 697
  * Heger et al. (2003) Heger, A., Fryer, C. L., Woosley, S. E., Langer, N., & Hartmann, D. H. 2003, ApJ, 591, 288
  * Heger et al. (2000) Heger, A., Langer, N., & Woosley, S. E. 2000, ApJ, 528, 368
  * Hilditch et al. (2005) Hilditch, R. W., Howarth, I. D., & Harries, T. J. 2005, MNRAS, 357, 304
  * Hillier & Miller (1999) Hillier, D. J. & Miller, D. L. 1999, ApJ, 519, 354
  * Hollenbach & Tielens (1999) Hollenbach, D. J. & Tielens, A. G. G. M. 1999, Reviews of Modern Physics, 71, 173
  * Horvat et al. (2018) Horvat, M., Conroy, K. E., Pablo, H., et al. 2018, ApJS, 237, 26
  * Hunter et al. (2007) Hunter, I., Dufton, P. L., Smartt, S. J., et al. 2007, A&A, 466, 277
  * Jones et al. (2020) Jones, D., Conroy, K. E., Horvat, M., et al. 2020, ApJS, 247, 63
  * Kajino et al. (2019) Kajino, T., Aoki, W., Balantekin, A. B., et al. 2019, Progress in Particle and Nuclear Physics, 107, 109
  * Kasen et al. (2017) Kasen, D., Metzger, B., Barnes, J., Quataert, E., & Ramirez-Ruiz, E. 2017, Nature, 551, 80
  * Kippenhahn et al. (1980) Kippenhahn, R., Ruschenplatt, G., & Thomas, H. C. 1980, A&A, 91, 175
  * Kipping (2013) Kipping, D. M. 2013, Monthly Notices of the Royal Astronomical Society: Letters, 434, L51
  * Kurt & Dufour (1998) Kurt, C. M. & Dufour, R. J. 1998, in Revista Mexicana de Astronomia y Astrofisica Conference Series, Vol. 7, Revista Mexicana de Astronomia y Astrofisica Conference Series, ed. R. J. Dufour & S. Torres-Peimbert, 202
  * Langer et al. (1983) Langer, N., Fricke, K. J., & Sugimoto, D. 1983, A&A, 126, 207
  * Li et al. (2022) Li, F. X., Qian, S. B., & Liao, W. P. 2022, AJ, 163, 203
  * Mac Low et al. (2005) Mac Low, M.-M., Balsara, D. S., Kim, J., & de Avillez, M. A. 2005, ApJ, 626, 864
  * Marchant et al. (2016) Marchant, P., Langer, N., Podsiadlowski, P., Tauris, T. M., & Moriya, T. J. 2016, A&A, 588, A50
  * Martins (2018) Martins, F. 2018, A&A, 616, A135
  * Massey et al. (2021) Massey, P., Neugent, K. F., Dorn-Wallenstein, T. Z., et al. 2021, ApJ, 922, 177
  * Massey et al. (1989) Massey, P., Parker, J. W., & Garmany, C. D. 1989, AJ, 98, 1305
  * Matzner (2002) Matzner, C. D. 2002, ApJ, 566, 302
  * Miller-Jones et al. (2021) Miller-Jones, J. C. A., Bahramian, A., Orosz, J. A., et al. 2021, Science, 371, 1046
  * Moe & Di Stefano (2017) Moe, M. & Di Stefano, R. 2017, ApJS, 230, 15
  * Mokiem et al. (2007) Mokiem, M. R., de Koter, A., Evans, C. J., et al. 2007, A&A, 465, 1003
  * Nascimbeni et al. (2016) Nascimbeni, V., Piotto, G., Ortolani, S., et al. 2016, MNRAS, 463, 4210
  * Nazé et al. (2002) Nazé, Y., Hartwell, J. M., Stevens, I. R., et al. 2002, ApJ, 580, 225
  * Nebot Gómez-Morán & Oskinova (2018) Nebot Gómez-Morán, A. & Oskinova, L. M. 2018, A&A, 620, A89
  * Nelson & Eggleton (2001) Nelson, C. A. & Eggleton, P. P. 2001, ApJ, 552, 664
  * Niemela & Gamen (2004) Niemela, V. & Gamen, R. 2004, New A Rev., 48, 727
  * Niemela et al. (1986) Niemela, V. S., Marraco, H. G., & Cabanne, M. L. 1986, PASP, 98, 1133
  * Nieuwenhuijzen & de Jager (1990) Nieuwenhuijzen, H. & de Jager, C. 1990, A&A, 231, 134
  * Orosz et al. (2011) Orosz, J. A., McClintock, J. E., Aufdenberg, J. P., et al. 2011, ApJ, 742, 84
  * Oskinova et al. (2011) Oskinova, L. M., Todt, H., Ignace, R., et al. 2011, MNRAS, 416, 1456
  * Paczyński (1967) Paczyński, B. 1967, Acta Astron., 17, 355
  * Paczyński (1971) Paczyński, B. 1971, ARA&A, 9, 183
  * Pauldrach et al. (1986) Pauldrach, A., Puls, J., & Kudritzki, R. P. 1986, A&A, 164, 86
  * Pauli et al. (2022a) Pauli, D., Langer, N., Aguilera-Dena, D. R., Wang, C., & Marchant, P. 2022a, A&A, 667, A58
  * Pauli et al. (2023) Pauli, D., Oskinova, L. M., Hamann, W. R., et al. 2023, arXiv e-prints, arXiv:2303.03989
  * Pauli et al. (2022b) Pauli, D., Oskinova, L. M., Hamann, W. R., et al. 2022b, A&A, 659, A9
  * Paxton et al. (2011) Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3
  * Paxton et al. (2013) Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4
  * Paxton et al. (2015) Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS, 220, 15
  * Paxton et al. (2018) Paxton, B., Schwab, J., Bauer, E. B., et al. 2018, ApJS, 234, 34
  * Paxton et al. (2019) Paxton, B., Smolec, R., Schwab, J., et al. 2019, ApJS, 243, 10
  * Peters (1964) Peters, P. C. 1964, Physical Review, 136, 1224
  * Pignatari et al. (2010) Pignatari, M., Gallino, R., Heil, M., et al. 2010, ApJ, 710, 1557
  * Pols (1994) Pols, O. R. 1994, A&A, 290, 119
  * Price-Whelan et al. (2017) Price-Whelan, A. M., Hogg, D. W., Foreman-Mackey, D., & Rix, H.-W. 2017, ApJ, 837, 20
  * Prša et al. (2016) Prša, A., Conroy, K. E., Horvat, M., et al. 2016, ApJS, 227, 29
  * Prša & Zwitter (2005) Prša, A. & Zwitter, T. 2005, ApJ, 628, 426
  * Ramachandran et al. (2018) Ramachandran, V., Hamann, W. R., Hainich, R., et al. 2018, A&A, 615, A40
  * Ramachandran et al. (2019) Ramachandran, V., Hamann, W. R., Oskinova, L. M., et al. 2019, A&A, 625, A104
  * Rauw & Nazé (2016) Rauw, G. & Nazé, Y. 2016, Advances in Space Research, 58, 761
  * Rickard et al. (2022) Rickard, M. J., Hainich, R., Hamann, W. R., et al. 2022, A&A, 666, A189
  * Rogers & Pittard (2013) Rogers, H. & Pittard, J. M. 2013, MNRAS, 431, 1337
  * Sabbi et al. (2007) Sabbi, E., Sirianni, M., Nota, A., et al. 2007, AJ, 133, 44
  * Sana et al. (2013) Sana, H., de Koter, A., de Mink, S. E., et al. 2013, A&A, 550, A107
  * Sana et al. (2012) Sana, H., de Mink, S. E., de Koter, A., et al. 2012, Science, 337, 444
  * Sana et al. (2014) Sana, H., Le Bouquin, J. B., Lacour, S., et al. 2014, ApJS, 215, 15
  * Sander et al. (2015) Sander, A., Shenar, T., Hainich, R., et al. 2015, A&A, 577, A13
  * Schootemeijer & Langer (2018) Schootemeijer, A. & Langer, N. 2018, A&A, 611, A75
  * Schootemeijer et al. (2019) Schootemeijer, A., Langer, N., Grin, N. J., & Wang, C. 2019, A&A, 625, A132
  * Scott et al. (2015) Scott, P., Grevesse, N., Asplund, M., et al. 2015, A&A, 573, A25
  * Shenar et al. (2020a) Shenar, T., Gilkis, A., Vink, J. S., Sana, H., & Sander, A. A. C. 2020a, A&A, 634, A79
  * Shenar et al. (2014) Shenar, T., Hamann, W. R., & Todt, H. 2014, A&A, 562, A118
  * Shenar et al. (2015) Shenar, T., Oskinova, L., Hamann, W. R., et al. 2015, ApJ, 809, 135
  * Shenar et al. (2019) Shenar, T., Sablowski, D. P., Hainich, R., et al. 2019, A&A, 627, A151
  * Shenar et al. (2020b) Shenar, T., Sablowski, D. P., Hainich, R., et al. 2020b, A&A, 641, C2
  * Simón-Díaz & Herrero (2014) Simón-Díaz, S. & Herrero, A. 2014, A&A, 562, A135
  * Smith (2014) Smith, N. 2014, ARA&A, 52, 487
  * Sota et al. (2014) Sota, A., Maíz Apellániz, J., Morrell, N. I., et al. 2014, ApJS, 211, 10
  * Sota et al. (2011) Sota, A., Maíz Apellániz, J., Walborn, N. R., et al. 2011, ApJS, 193, 24
  * Spruit (2002) Spruit, H. C. 2002, A&A, 381, 923
  * Thielemann et al. (2011) Thielemann, F. K., Arcones, A., Käppeli, R., et al. 2011, Progress in Particle and Nuclear Physics, 66, 346
  * Trundle et al. (2007) Trundle, C., Dufton, P. L., Hunter, I., et al. 2007, A&A, 471, 625
  * Udalski et al. (2015) Udalski, A., Szymański, M. K., & Szymański, G. 2015, Acta Astron., 65, 1
  * Vanbeveren & Conti (1980) Vanbeveren, D. & Conti, P. S. 1980, A&A, 88, 230
  * Vanbeveren et al. (1998) Vanbeveren, D., De Loore, C., & Van Rensbergen, W. 1998, A&A Rev., 9, 63
  * Venn (1999) Venn, K. A. 1999, ApJ, 518, 405
  * Vidaña (2018) Vidaña, I. 2018, European Physical Journal Plus, 133, 445
  * Vink et al. (2001) Vink, J. S., de Koter, A., & Lamers, H. J. G. L. M. 2001, A&A, 369, 574
  * Walborn (1978) Walborn, N. R. 1978, ApJ, 224, L133
  * Walborn et al. (2002) Walborn, N. R., Howarth, I. D., Lennon, D. J., et al. 2002, AJ, 123, 2754
  * Walborn et al. (2000) Walborn, N. R., Lennon, D. J., Heap, S. R., et al. 2000, PASP, 112, 1243
  * Weisskopf et al. (2000) Weisskopf, M. C., Tananbaum, H. D., Van Speybroeck, L. P., & O’Dell, S. L. 2000, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 4012, X-Ray Optics, Instruments, and Missions III, ed. J. E. Truemper & B. Aschenbach, 2–16
  * Wellstein & Langer (1999) Wellstein, S. & Langer, N. 1999, A&A, 350, 148
  * Wilson (1941) Wilson, O. C. 1941, ApJ, 93, 29
  * Wilson (1990) Wilson, R. E. 1990, ApJ, 356, 613
  * Zahn et al. (2010) Zahn, J. P., Ranc, C., & Morel, P. 2010, A&A, 517, A7

##  Appendix A Additional tables

Table 10: Radial velocities of different lines associated with the primary.

MJD |  N iv $\lambda\lambda$ 3478 – 3485 |  N iv $\lambda$ 4058 |  N iv $\lambda$ 6381 |  N iv $\lambda\lambda$ 7103 – 7129 |  N v $\lambda\lambda$ 4604, 4620 |  He ii $\lambda$ 6683(a) |  mean RV(b)
---|---|---|---|---|---|---|---
| $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$
52249.01198 | $\,\,\,\,\,\,7\pm\,\,\,6$ | $\,\,\,18\pm 7$ | $\,\,\,\,\,\,9\pm 15$ |  — |  — |  — | $\,\,\,11\pm 10$
53277.25739 |  — | $\,\,\,56\pm 7$ |  — |  — |  — |  — | $\,\,\,56\pm\,\,\,7$
53277.25939 |  — | $\,\,\,51\pm 7$ |  — |  — |  — |  — | $\,\,\,51\pm\,\,\,7$
53277.26022 |  — | $\,\,\,42\pm 6$ |  — |  — |  — |  — | $\,\,\,42\pm\,\,\,6$
53277.28112 |  — | $\,\,\,48\pm 6$ |  — |  — |  — |  — | $\,\,\,48\pm\,\,\,6$
53280.19821 |  — |  — |  — |  — | $\,\,\,18\pm 15$ |  — | $\,\,\,18\pm 15$
53292.06195 |  — |  — |  — |  — | $-57\pm 15$ |  — | $-57\pm 15$
57611.32930 |  — |  — | $\,\,\,97\pm 15$ | $100\pm 15$ |  — | $\,\,\,96\pm 13$ | $\,\,\,98\pm 14$
57613.24630 |  — |  — | $-74\pm 15$ | $-75\pm 15$ |  — | $-86\pm 14$ | $-78\pm 15$
57613.28829 |  — |  — | $-82\pm 15$ | $-75\pm 15$ |  — | $-73\pm 13$ | $-77\pm 14$
57617.23463 |  — |  — | $\,\,\,54\pm 15$ | $\,\,\,61\pm 14$ |  — | $\,\,\,51\pm\,\,\,8$ | $\,\,\,55\pm 13$
57618.10327 |  — |  — | $\,\,\,84\pm 15$ | $\,\,\,61\pm 15$ |  — | $\,\,\,70\pm\,\,\,8$ | $\,\,\,72\pm 13$
57620.14865 |  — |  — | $\,\,\,39\pm 15$ | $\,\,\,38\pm 14$ |  — | $\,\,\,31\pm\,\,\,8$ | $\,\,\,36\pm 13$
57620.19042 |  — |  — | $\,\,\,40\pm 15$ | $\,\,\,45\pm 14$ |  — | $\,\,\,32\pm\,\,\,8$ | $\,\,\,39\pm 13$
57620.23262 |  — |  — | $\,\,\,45\pm 15$ | $\,\,\,46\pm\,\,\,8$ |  — | $\,\,\,41\pm\,\,\,8$ | $\,\,\,43\pm 11$
57621.20640 |  — |  — | $\,\,\,62\pm 15$ | $\,\,\,68\pm 15$ |  — | $\,\,\,62\pm\,\,\,8$ | $\,\,\,64\pm 13$
57621.24834 |  — |  — | $\,\,\,55\pm 15$ | $\,\,\,45\pm 10$ |  — | $\,\,\,48\pm\,\,\,8$ | $\,\,\,49\pm 11$
57622.14718 |  — |  — | $-81\pm 15$ | $-80\pm 15$ |  — | $-94\pm\,\,\,9$ | $-85\pm 13$
59216.11133 | $\,\,\,98\pm\,\,\,6$ | $\,\,\,97\pm 6$ | $\,\,\,82\pm 22$ | $\,\,\,93\pm 22$ | $\,\,\,92\pm 16$ | $\,\,\,95\pm\,\,\,8$ | $\,\,\,92\pm 15$

888 (a) The line shows a clear but distinguishable contribution of the
secondary. It can be used as a cross-check for the quality and self-
consistency of the secondary’s RV fit.

Table 11: Radial velocities of different lines associated with the secondary.

MJD |  He i $\lambda$ 4471 |  He i $\lambda$ 4713 |  He ii $\lambda$ 6683(a) |  C iv $\lambda\lambda$ 5801, 5812(a) |  mean RV(b)
---|---|---|---|---|---
| $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$ | $[$\mathrm{k}\mathrm{m}\,\mathrm{s}^{-1}$]$
52249.01198 | $\,\,\,18\pm\,\,\,9$ | $\,\,\,\,\,\,6\pm 31$ |  — | $\,\,\,\,\,\,7\pm 16$ | $10\pm 21$
53277.25739 | $-34\pm\,\,\,7$ |  — |  — |  — | $-34\pm\,\,\,7$
53277.25939 | $-32\pm\,\,\,9$ |  — |  — |  — | $-32\pm\,\,\,9$
53277.26022 | $-39\pm\,\,\,7$ |  — |  — |  — | $-39\pm\,\,\,7$
53277.28112 | $-39\pm\,\,\,7$ |  — |  — |  — | $-39\pm\,\,\,7$
53280.19821 |  — | $-12\pm 29$ |  — |  — | $-12\pm 29$
53292.06195 |  — | $\,\,\,41\pm 27$ |  — |  — | $41\pm 27$
57611.32930 |  — | $-48\pm 22$ | $-62\pm 20$ | $-60\pm 13$ | $-57\pm 19$
57613.24630 |  — | $\,\,\,57\pm 28$ | $\,\,\,69\pm 25$ | $\,\,\,77\pm 14$ | $67\pm 23$
57613.28829 |  — | $\,\,\,71\pm 21$ | $\,\,\,71\pm 19$ | $\,\,\,77\pm 23$ | $73\pm 21$
57617.23463 |  — | $-19\pm 20$ | $-24\pm 23$ | $-22\pm 14$ | $-22\pm 19$
57618.10327 |  — | $-30\pm 25$ | $-35\pm 23$ | $-38\pm 17$ | $-34\pm 22$
57620.14865 |  — | $-34\pm 25$ | $-32\pm 23$ | $-35\pm 16$ | $-34\pm 22$
57620.19042 |  — | $-32\pm 23$ | $-40\pm 23$ | $-29\pm 14$ | $-34\pm 22$
57620.23262 |  — | $-32\pm 18$ | $-31\pm 31$ | $-34\pm 14$ | $-32\pm 22$
57621.20640 |  — | $-21\pm 26$ | $-29\pm 22$ | $-22\pm 16$ | $-24\pm 22$
57621.24834 |  — | $-28\pm 25$ | $-30\pm 20$ | $-31\pm 16$ | $-30\pm 20$
57622.14718 |  — | $\,\,\,71\pm 22$ | $\,\,\,70\pm 25$ | $\,\,\,75\pm 16$ | $72\pm 21$
59216.11133 | $-55\pm\,\,\,8$ | $-57\pm 25$ | $-55\pm 25$ | $-52\pm 11$ | $-55\pm 19$

999 (a) The line shows a clear but distinguishable contribution of the
primary.

Table 12: List of used lines. Includes which component the lines are attributed to based on relative position to other lines and shifts at different epochs. Line |  Wavelength ($\AA$) | Components source and description
---|---|---
O vi | 1031.9, 1037.6 | Absorption, predominately from primary
P v | 1118.0 | Both components show absorption
P v | 1128.0 | Both components show absorption
C iv | 1169.0 | Both components show absorption
C iii | 1175.3 | Secondary absorption
N v | 1238.8, 1242.8 doublet | Resonance wind lines with absorption and emission for both
O iv | 1338.6, 1343.0, 1343.5 triplet | Both components show absorption
O v | 1371.0 | Both components show absorption
O iii | 1408.6, 1409.8, 1410.8, 1410.9, 1412.1 | Both components show absorption
Fe v-vi |  Range $\sim 1412-1475$ | Iron forest lines, both components show absorption
N iv | 1483.3, 1486.5 | Both components show absorption
Si v | 1502.0 | Both components show absorption
C iv | 1548.2, 1550.8 doublet | Resonant wind line showing contribution of both components
He ii | 1640.5 | Primary P-Cygni with emission, secondary absorption
N iv | 3478.7, 3483.0, 3484.9 triplet | Both components show absorption
He i | 3964.7 | Primary absorption
He ii | 3970.1 | Both components show absorption
He ii | 4025.6 |  Overlapping with He i $\lambda$ 4026.2 for both primary and secondary
He i | 4026.2 |  Overlapping with He ii $\lambda$ 4025.6 for both primary and secondary
N iv | 4057.8 | Primary emission
He ii | 4100.7 | Both components show absorption
He ii | 4199.9 | Both components show absorption
He ii | 4338.7 | Both components show absorption
He i | 4471.5 | Secondary absorption
He ii | 4541.6 | Both components show absorption
N v | 4603.8, 4619.9 doublet | Absorption, predominately from primary
N iii | 4634.1, 4640.6 doublet | Both components show emission
O ii | 4650.0 |  Primary emission, overlapped by primary He ii $\,\lambda\,4686\AA$ emission
He ii | 4685.8 | Primary emission, secondary absorption
He i | 4713.2 | Secondary absorption
He ii | 4859.3 | Both components show absorption
He i | 4921.9 | Secondary absorption
He i | 5015.7 | Absorption, predominately secondary
He ii | 5411.5 | Both components show absorption
C iv | 5801.3, 5812.0 doublet | Primary emission, secondary absorption
He i | 5875.4, 5875.5, 5875.8 triplet | Both components show absorption
He i | 6170.7 | Both components show absorption
N iv | 6212.4, 6215.5, 6219.9 triplet | No observations. Model of primary shows emission
He i | 6233.8 | Both components show absorption
N iv | 6380.8 | Primary absorption
He ii | 6527.1 | Both components show absorption
He ii | 6560.1 | Primary emission, secondary absorption
He ii | 6678.1, 6679.6 doublet | Secondary absorption
He ii | 6683.2 | Both components show absorption
He ii | 7065.3 | Absorption, predominately Secondary
N iv |  ${7102{-}7129}$ multiplet | Emission, predominately from primary

##  Appendix B Light curve modelling with PHOEBE

Although it is in the survey region of the Optical Gravitational Lensing
Experiment (OGLE, Udalski et al. 2015) catalogue, to date no light curve of
this object has been reported. In addition, the resolution of the Transiting
Exoplanet Survey Satellite (TESS) is
$21\text{\,}\mathrm{\SIUnitSymbolArcsecond}\,\mathrm{p}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l}^{-1}$,
not fine enough to disentangle the light curve of our target from the other O
stars in NGC 346. To demonstrate if detectable photometric variations based on
our results are expected at all, we employed the PHOEBE code (used in Sect.
3.3.2) to create a synthetic light curve.

Typically light curves are observed in the optical. Hence, we decided to
create the synthetic light curve (shown in Figure 14) in the Johnson V band.
In the PHOEBE model we used the stellar parameters of the binary components
obtained from our spectroscopic analysis (see Sect. 4.1) as input parameters.
Furthermore, we assume that gravitational darkening can be approximated by a
power law with a coefficient of $\beta_{\mathrm{grav}}=1$, as typically used
for hot stars with radiative envelopes. The atmospheres of both components are
approximated by a black body, when compared to the SED of our atmospheric
model it is a valid approximation for the V-band flux. Limb darkening is
modelled by using a quadratic approximation and using coefficients
${a_{1}=0.2694}$ and ${b_{1}=-0.003}$ for the primary and ${a_{2}=0.1751}$ and
${b_{2}=0.0871}$ for the secondary, obtained from the emergent flux
distribution of our stellar atmosphere models. The effect of reflections and
resulting heating in the binary is modelled using the build in the Horvat
scheme that includes Lambert scattering as well as the reflection scheme of
Wilson (1990). It is assumed that $90\%$ of the incident flux will be
reflected.

For a better understanding on how the different photometric variations are
linked to the orbital configuration of the binary, we depict the orbital
configurations of the stars in the lower part of Fig. 14. It is evident that
the expected maximum photometric variation of the binary components is
$18\text{\,}\mathrm{m}\mathrm{m}\mathrm{a}\mathrm{g}$. The shape of the light
curve is only caused by ellipsoidal variability and not by eclipses.

Given the expected low variability, we conclude that only the upcoming
powerful telescopes, such as the ELT, will be able to detect this kind of
variability. Hence, we can say that our derived low inclination angle is
consistent with the lack of published light curve data.

Figure 14: Synthetic predicted light curves of SSN 7 for an inclination angle
of $i=$16\text{\,}{}^{\circ}$$ and the orbital configuration of the binary
components in the plane of sky at different phases. Upper panel: Phased
synthetic light curve in the Johnson V band. Lower panel: Orbital
configuration of the binary components at phases $\phi=-0.5$, $-0.25$, $0.0$,
$0.25$, and $0.5$. The models are colour-coded by effective temperature,
taking into account the physical effect mentioned in the text.