11institutetext: The CHARA Array of Georgia State University, Mount Wilson
Observatory, Mount Wilson, CA 91023, USA 22institutetext: Institute of
Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
33institutetext: Institut de Planétologie et d’Astrophysique de Grenoble,
Grenoble 38058, France 44institutetext: European Southern Observatory, Karl-
Schwarzschild-Str. 2, 85748 Garching, Germany 55institutetext: University of
Michigan, Department of Astronomy, 1085 S. University Ave; West Hall 323; Ann
Arbor, MI 48109 66institutetext: Royal Observatory of Belgium, Avenue
Circulaire/Ringlaan 3, B-1180, Brussels, Belgium 77institutetext: Space
sciences, Technologies, and Astrophysics Research (STAR) Institute, University
of Liège, Quartier Agora, 19c, Allée du 6 Août, B5c, B-4000 Sart Tilman,
Belgium 88institutetext: Astrophysics Group, School of Physics and Astronomy,
University of Exeter, Stocker Road, Exeter, EX4 4QL, UK 99institutetext:
European Southern Observatory, Casilla 19001, Santiago 19, Chile
correspondence<EMAIL_ADDRESS>
# Multiplicity of northern bright O-type stars with optical long baseline
interferometry

Results of the pilot survey

C. Lanthermann 112233 J.-B. Le Bouquin 33 H. Sana 22 A. Mérand 44 J. D.
Monnier 55 K. Perraut 33 A.J. Frost 22 L. Mahy 66 E. Gosset 77 M. De Becker 77
S. Kraus 88 N. Anugu 11 C. L. Davies 88 J. Ennis 55 T. Gardner 55 A. Labdon 99
B. Setterholm 55 T. ten Brummelaar 11 G. H. Schaefer 11

(November 2022)

###### Abstract

Context.  The study of the multiplicity of massive stars gives hints on their
formation processes and their evolutionary paths, which are still not fully
understood. Large separation binaries (¿50 milliseconds of arc, mas) can be
probed by adaptive-optics-assisted direct imaging and sparse aperture masking,
while close binaries can be resolved by photometry and spectroscopy. However,
optical long baseline interferometry is mandatory to establish the
multiplicity of Galactic massive stars at the separation gap between 1 and 50
mas.

Aims.  In this paper, we aim to demonstrate the capability of the new
interferometric instrument MIRC-X, located at the CHARA Array, to study the
multiplicity of O-type stars and therefore probe the full range of separation
for more than 120 massive stars ($H<7.5$ mag).

Methods.  We initiated a pilot survey of bright O-type stars ($H<6.5$ mag)
observable with MIRC-X. We observed 29 O-type stars, including two systems in
average atmospheric conditions around a magnitude of $H=7.5$ mag. We
systematically reduced the obtained data with the public reduction pipeline of
the instrument. We analyzed the reduced data using the dedicated python
software CANDID to detect companions.

Results.  Out of these 29 systems, we resolved 19 companions in 17 different
systems with angular separations between $\sim 0.5$ and 50 mas. This results
in a multiplicity fraction $f_{\text{m}}=17/29=0.59\pm 0.09$, and an average
number of companions $f_{\text{c}}=19/29=0.66\pm 0.13$. Those results are in
agreement with the results of the SMASH+ survey in the Southern Hemisphere.
Thirteen of these companions have been resolved for the first time, including
the companion responsible for the nonthermal emission in Cyg OB2-5 A and the
confirmation of the candidate companion of HD 47129 suggested by SMASH+.

Conclusions.  A large survey on more than 120 northern O-type stars ($H<7.5$)
is possible with MIRC-X and will be fruitful.

##  1 Introduction

Massive stars are key components of the evolution of their host galaxy. They
are the main producers of heavy elements, and the momentum and kinetic energy
involved in their death have an influence on a large part of their galaxy
(Zinnecker & Yorke, 2007). They are also the progenitors of the compact
objects that, when they merge, produce gravitational wave bursts that we can
currently detect (Abbott et al., 2016).

However, their short lifetime (a few million years) and their rapid formation
process ($10^{5}$ years) make the observation of their early ages difficult
(Tan et al., 2014). Indeed, their lifetime makes them rare, and so to observe
a large number of massive stars (¿ 100), one needs to look for them at
significant distances, typically 1 to 3 kpc. In addition, the majority of
young massive stars are still embedded in a cloud of gas and dust when they
finish their formation process (Zinnecker, 2006), making the observation of
this formation step even harder. In consequence, the formation process of
massive stars is still actively discussed.

Historically, the standard models of star formation could not explain the
formation of stars with masses significantly higher than about 10 M☉. The main
difficulty is overcoming the radiation barrier emitted by the protostar as
soon as it starts burning nuclear fuel. So, specific formation models need to
explain how massive stars can form. There are currently three main scenarios:
1) the core accretion (Terquem, 2001; Yorke, 2002), which uses a massive
accretion disk to accrete more matter; 2) the competitive accretion (Larson,
1978; Zinnecker, 1982; Bonnell & Bate, 2002; Bonnell et al., 2003) for which
close protostar cores use the combined gravitational potential to attract
matter from further away than with each individual gravitational potential;
and 3) the collision (Binney et al., 1988; Bonnell & Bate, 2005; Dale &
Davies, 2006) in which intermediate-mass stars collide to merge and form a
more massive star. The outcomes of these three different formation models
predict different multiplicity parameters. Hence, the study of the
multiplicity of massive stars, after their formation process, should provide
relevant constraints on these formation models.

Another motivation for the investigation of the multiplicity of massive stars,
especially in the range of periods considered in this study, is the
investigation of physical processes driven by the colliding winds. In
particular, such systems are well suited for particle acceleration, hence the
class of particle-accelerating colliding-wind binaries (PACWBs, De Becker &
Raucq (2013); De Becker et al. (2017)). Such systems, mainly revealed by
synchrotron radio emission, are likely contributors to the population of lower
energy Galactic cosmic rays. Appropriate knowledge of their orbit is required
to interpret their behavior and model their shock physics.

To probe the full range of orbital separations of systems situated at a
typical distance of 2 kpc, one needs to use different observational
techniques. The close companions (up to 0.5 milliseconds of arc, mas, Mahy et
al., 2020) can be probed by photometry (eclipsing binaries) or spectroscopy
(radial velocity, Sana et al., 2012, 2013; Barbá et al., 2017), while wide
companions (separation ¿ 50 mas) can be probed with techniques such as
adaptive-optics-assisted direct imaging, aperture masking, speckle imaging,
and coronography (Turner et al., 2008; Mason et al., 2009; Reggiani et al.,
2022). For separations between 1 and 50 mas, the only technique we can use is
optical long baseline interferometry (OLBI) (see Fig. 1 in Sana (2017)). But
until recently, this technique was limited by its sensitivity and could only
be applied to a modest sample of massive stars.

The advent of the PIONIER (Precision Integrated-Optics Near-infrared Imaging
ExpeRiment) instrument at the very large telescope interferometer (VLTI) (Le
Bouquin et al., 2011) enabled the southern massive stars at high angular
resolution (SMASH+), the first systematic interferometric large survey on
massive stars in the Southern Hemisphere (Sana et al., 2014), probing the
missing range of separation to have a complete statistical study of the
multiplicity of massive stars. With this survey, Sana et al. (2014) observed
96 southern O-type star systems, nearly reaching the 100 targets required to
get a statistical error ¡ 5% over the entire range of the multiplicity
fraction. The observational constraints brought by the SMASH+ survey,
especially the abundance of companions with a separation smaller than 100 AU,
are qualitatively in overall agreement with the core accretion model leading
to disk fragmentation. However, the statistic on subgroups of stars, such as
masses or evolutionary stage, is too low to obtain a robust conclusion.
Therefore, we aim to perform a similarly large survey (120 objects) in the
Northern Hemisphere to double the total statistic.

To observe more than 100 O-type stars in the Northern Hemisphere, one needs to
reach a limiting magnitude in the J-band (the spectral band available in the
GOSC catalog, Maíz Apellániz et al. 2013) of $J=7.5$, as shown in Fig. 1. In
this figure, the limit of declination ¿ $-20^{\circ}$ corresponds to the limit
of observability of the CHARA (center for high angular resolution astronomy)
Array. Thanks to the recent implementation of the MIRC-X (Michigan InfraRed
Combiner-eXeter) instrument (Kraus et al., 2018; Anugu et al., 2020;
Lanthermann et al., 2019) at the CHARA Array (ten Brummelaar et al., 2016),
located at Mount Wilson observatory, USA, this magnitude is now reachable in
the H-band with the OLBI technique in the Northern Hemisphere. As O-type stars
are hot stars and under typical reddening conditions, their magnitudes remain
relatively the same in all the infrared spectral bands (Martins & Plez, 2006),
meaning that the limit on the magnitude of 7.5 in the J-band required to
observe ¿100 O-type objects remains valid in the H-band.

Figure 1: Cumulative histogram of the number of O-type stars as a function of
their magnitude in the J-band. In blue, for the whole sky. In orange, for a
declination greater than $-20^{\circ}$ to be reachable with the CHARA Array.
Data from the Galactic O-star catalog (GOSC) (Maíz Apellániz et al., 2013).

In this paper, we present the results of the pilot survey performed on 29
systems, with the goal to demonstrate the feasibility of a large survey of
more than 100 O-type stars with the CHARA/MIRC-X instrument. We present the
observations in Section 2, with the definition of the sample, the description
of the observation campaign, and the data reduction process. We then describe
the data analysis that we performed in Section 3. Section 4 presents our
results. We perform a statistical analysis of the results in Section 5. We
finally discuss the results in Section 6 and conclude in Section 7.

##  2 Observations

###  2.1 Observation sample

We built our sample using the Galactic O-star catalog (GOSC Maíz Apellániz et
al., 2013). We selected every O-star with a declination DEC ¿ $-20^{\circ}$
and with a magnitude in the J-band registered in GOSC of $J<7.0$ mag. We chose
the J-band criterion for several reasons. The first one is that the magnitude
criteria available in GOSC are either in the B-band or the J-band. As we used
the MIRC-X instrument, working in the H-band, the J-band is the nearest one of
the two available. We adopted the threshold value of 7.0 or brighter because,
during this pilot study, the official limiting magnitude offered by MIRC-X was
$H=6.5$ mag. As only the Rayleigh-Jeans tail of the O-type stars is observed
in the J- and H-bands, their magnitudes are comparable in both bands. We took
an extra 0.5 magnitude as a margin to be sure that our sample contains all
targets observable with MIRC-X. We then looked for the H-band magnitude of the
selected systems in the 2MASS All-Sky Catalog of Point Sources (Cutri et al.,
2003) and performed the last selection on stars with a magnitude $H<6.5$ to
comply with the MIRC-X limiting magnitude. Our input sample is therefore
magnitude limited. We note that some of the targets in our sample overlap with
targets already observed by SMASH+, which can be used to validate our results.

###  2.2 Observation campaign

Table 1: List of O-type stars observed with good quality data during the pilot
survey.

Name | Spectral type | $H$ | $d$ | SC | SIC | IC | WC | Total
---|---|---|---|---|---|---|---|---
|  | (mag) | (kpc) | (¡0.5 mas) | (0.5 - 50 mas) | (0.05″-8″) |
Cyg OB2-5 A (BD+40 4220A) | O7Iafep | 4.745 | 1.748 | 1 | 0 | 2 | 2 | 5
Cyg OB2-9 (HIP 101419) | O4.5If | 5.897 | 1.788 | 0 | 1 | 0 | 1 | 2
Cyg OB2-10 (BD+41 3804) | O9.7Iab† | 5.839 | 1.376 | 0 | 0 | 1 | 3 | 4
HD 17505 A | O6.5IIIn(f) | 6.177 | 2.258 | 1 | 0 | 1 | 1 | 3
HD 19820 (CC Cas) | O8.5III(n)((f)) | 6.003 | 1.135 | 1 | 0 | 2 | 0 | 3
HD 24431 | O9III | 5.845 | 0.922 | 0 | 0 | 1 | 1 | 2
HD 28446 A (1 Cam A) | O9.7IIn | 5.459 | 0.760 | 1 | 0 | 1 | 1 | 3
HD 30614 ($\alpha$ Cam) | O9Ia | 4.242 | 1.717 | 1 | 0 | 0 | 0 | 1
HD 34078 (AE Aur) | O9.5V | 5.355 | 0.382 | 0 | 0 | 1 | 0 | 1
HD 36861 ($\lambda$ Ori A) | O8III((f)) | 3.769 | 0.438 | 0 | 0 | 1 | 1 | 2
HD 45314 | O9:npe | 5.761 | 0.864 | 0 | 0 | 1 | 0 | 1
HD 47129 | O8I+O7.5III‡ | 5.806 | 1.283 | 1 | 0 | 1 | 2 | 4
HD 47432 (V689 Mon) | O9.7Ib | 5.949 | 1.596 | 0 | 0 | 0 | 1 | 1
HD 47839 (15 Mon AaAb) | O7V+B1.5/2V⋆ | 5.322 | 3.974 | 0 | 0 | 0 | 1 | 1
HD 167971 (MY Ser AaAb) | O8Iaf(n)+O4/5 | 5.315 | 1.339 | 1 | 0 | 1 | 0 | 2
HD 188001 (9 Sge) | O7.5Iabf | 6.166 | 1.833 | 0 | 0 | 0 | 0 | 0
HD 193322 AaAb | O9IV(n) | 5.688 | 1.001 | 1 | 0 | 1 | 3 | 5
HD 195592 | O9.7Ia | 4.911 | 1.729 | 1 | 0 | 0 | 0 | 1
HD 201345 | ON9.2IV | 8.171 | 1.828 | 0 | 0 | 0 | 1 | 1
HD 202214 AaAb | O9.5IV | 5.505 | 1.032 | 1 | 0 | 1 | 1 | 3
HD 206183 | O9.5IV-V | 7.193 | 0.901 | 0 | 0 | 0 | 2 | 2
HD 206267 AaAb | O6.5V((f))+O9/B0V | 5.254 | 0.789 | 1 | 0 | 0 | 4 | 5
HD 207198 | O8.5II | 5.318 | 0.978 | 0 | 0 | 1 | 1 | 2
HD 209975 (19 Cep) | O9Ib | 4.935 | 0.959 | 0 | 0 | 0 | 4 | 4
HD 210809 | O9Iab | 7.401 | 3.661 | 0 | 0 | 0 | 0 | 0
HD 210839 ($\lambda$ Cep) | O6.5I(n)fp | 4.618 | 0.832 | 0 | 0 | 0 | 0 | 0
HD 217086 | O7Vnn((f))z | 6.100 | 0.830 | 0 | 0 | 0 | 2 | 2
HD 228779 | O9Iab† | 5.834 | 1.653 | 0 | 0 | 0 | 0 | 0
HD 229196 | O6II(f) | 6.079 | 1.720 | 0 | 0 | 1 | 0 | 1

111The first column provides the identifier of the star. The second column
contains the spectral type, with the ones marked with a $\dagger$ coming from
Maíz Apellániz et al. (2016), the one marked wit a $\ddagger$ coming from Mahy
et al. (2011), and the one marked with a $\star$ coming from Skiff (2013), the
others coming from Sota et al. (2011). The third column displays the magnitude
in the H-band as found in the 2MASS All-Sky Catalog of Point Sources (Cutri et
al., 2003). The fourth column gives the distance that separates us from the
system according to Bailer-Jones et al. (2021), except for HD 202214 for which
the distance comes from Megier et al. (2009). The fifth to eighth columns give
the number of already known spectroscopic companions (SC), spectroscopic
companions resolved by interferometry (SIC), interferometric companion (IC),
and wide companion (WC), respectively. The references for already known
companions can be found in the star-by-star description in Sect. 4. The ninth
column gives the total number of known companions after this study.

The MIRC-X beam combiner operates in the J- and H-band. The observations
presented in this paper are performed only in the H-band (1.65 $\mu$m) because
the J-band mode was still experimental during the pilot survey and only uses
four telescopes. The six telescopes provide sufficient coverage of the uv-
plane to constrain the multiplicity of a star in a single snapshot. This can
also be done for data that combine only five telescopes when the conditions
(weather, technical, operational) would not permit a six-telescope
observation. The MIRC-X combiner allows different spectral resolutions. Our
data have been taken with the PRISM-50 configuration, allowing a spectral
resolving power of $R\sim 50$. This configuration was chosen to optimize the
sensitivity of the beam combiner and because it brings the Outer Working Angle
(OWA) of MIRC-X to:

$OWA=R\frac{\lambda}{B}=2.7\times 10^{-7}\leavevmode\nobreak\ \text{rad}\simeq
55\leavevmode\nobreak\ \text{mas}$ (1)

where $\lambda$ is the central wavelength which in the H-band is equal to
$1.6\times 10^{-6}$ m, and $B$ is the length of the baseline, equal to 330 m
for the longest baseline at CHARA. This OWA allowed us to fill the gap in
angular separation that other techniques cannot reach. We note that detection
of companions with a separation larger than the OWA is still possible, but the
flux ratio will be biased by the bandwidth smearing, hence, hampering accurate
measurement of the contrast (Hummel et al., 2016).

We note that the Inner Working Angle is the angular resolution of the
instrument, meaning that a binary separated by less than this angle would not
be resolved, and is defined by:

$IWA=\frac{\lambda}{2B}\simeq 0.55\leavevmode\nobreak\ \text{mas}.$ (2)

This angular resolution is about a factor of two to three smaller than the
SMASH+ survey owing to the larger baseline $B$ of CHARA compared to the VLTI.

For the calibration strategy, we alternated a calibrator with a science
target. The calibrator was chosen with the tool searchcal (Chelli et al.,
2016a), developed by the JMMC222https://www.jmmc.fr/english/tools/proposal-
preparation/search-cal/. The selection criterion was the calibrators needed to
be at most 1.5 magnitudes brighter and 0.5 magnitudes fainter than the science
target it would calibrate, and situated at a maximum angular distance of 3
degrees on the sky. Most of our calibration stars are of spectral type KIII,
for which a sufficiently accurate diameter (a few percent) can be estimated
from the apparent photometry (Chelli et al., 2016b).

The observations with MIRC-X have been carried out during five runs spread
over three observation semesters from 2018 to 2019. The observation time was
obtained through NOAO333https://noirlab.edu (now called NOIRLab) community
access time (program IDs: 2018A-M12/NOAO2, 2018B-M17/NOAO4, 2019A-M16/NOAO4;
PI: C. Lanthermann). We also used one night that studied O-type stars during
which O-type stars were observed as backup targets because the original
program could not be executed, in December 2017 (PI: S. Kraus).

During this campaign, we could obtain good quality data on 29 O-type stars,
listed in Table 1 with information on the spectral type, distance, and the
number of detected companions in various separation ranges, from the
literature as well as those detected by this study.

Figure 2: Histogram of the H-band magnitude of our observed sample in green,
the original sample planned for this pilot survey in orange, and the planned
sample for the large survey in blue.

Figure 2 shows the histogram of O-type star systems for which we obtained
good-quality data as a function of their magnitude in the H-band. As the
official magnitude limit in typical conditions is $H=6.5$ mag, the bulk of
observed objects is around this limit. But as we advanced in time, the
improved knowledge of the MIRC-X instrument acquired during commissioning
allowed us to push for fainter targets, beyond the initial magnitude limit of
the instrument. Ultimately, observing an O-type star with a magnitude up to
$H=8.1$ mag was possible in excellent seeing conditions, as well as a couple
of systems around $H=7.5$ mag in normal seeing conditions. These latter
observations are important to demonstrate that one can observe a large number
of O-type stars with MIRC-X. Indeed, as shown in Fig. 1, we can observe up to
120 systems if a magnitude limit of $H=7.5$ mag can be reached.

Usually, to calibrate a science target with the OLBI technique, we use
”CAL1-SCI-CAL2” sequences, meaning that we observe a first calibrator (CAL1),
then the science target (SCI), and finally a second calibrator (CAL2). To
choose CAL1 and CAL2, we take unresolved targets within a reasonable distance
and a similar apparent brightness to the science target, as explained above.
It appears that two consecutive science targets observed in this program are
close enough in the sky and in magnitude that CAL2 of one science target can
be used as CAL1 of the next science target. Therefore, we chose to follow an
observing sequence such as ”CAL1-SCI1-CAL2-SCI2…,” using each best-suited
calibrator for each science target. This allows us to reduce the error due to
calibration. When the same calibrator was best suited for two science targets
observed one after the other (ex: SCI1 and SCI2), we preferred to use another
calibrator for the second science target instead of using the same calibrator
for both science targets (CAL1-SCI1-CAL1-SCI2). This reduces the risk that the
results might be affected by a bad calibrator. A list of the calibrators
observed but discarded because suspected to be actually multiple systems can
be found in Appendix A.

###  2.3 Data reduction

We used the MIRC-X data reduction
pipeline444https://gitlab.chara.gsu.edu/lebouquj/mircx_pipeline (Anugu et al.,
2020). We set the maximum integration time (max-integration-time keyword in
the pipeline) for one calibrated file to 220 seconds. The max-integration-time
set the maximum time one reduced file will cover, with one file giving one
constituent of the calibrated parameters. This means that one file will give
the average calibrated parameters over the given maximum integration time.
This time allows us to bin our data recording sequences of about 10 minutes
into three files with a similar signal-to-noise ratio (S/N). This is needed
because the change of the uv-coordinates due to the rotation of the Earth
affects the observed squared visibility (V2). V2 can indeed change
significantly in a timescale of 300 seconds for binaries at the limit of the
OWA (see Fig. 3 for an example).

Figure 3: Example of change in the uv-plane modeled with the ASPRO2 software.
Left: global view of the uv-plane. Different colors are for different pairs of
telescopes (baselines). Right: zoom on the change in the uv-plane for the
fastest moving baseline. Each straight black line indicates the uv-coordinate
for this baseline for an instant snapshot, and each snapshot is separated by 5
minutes. The regularly spaced, orange lines display the V2 values modeled for
a binary with a separation of 50 mas.

To get rid of some outlier points due to bad S/N data, we applied a threshold
on the S/N of four instead of the default value of 3. This limit allows us to
select only data with high enough quality, while at the same time preserving
as much data as possible. To increase the quality of the reduced data, one
would like to coherently sum the data over as long a time as possible.
However, the atmospheric conditions limit the amount of time one can
coherently integrate, as the phase induced by the atmosphere blurs the
fringes, therefore reducing the quality of the data. The optimum time interval
over which we can sum data for V2 and closure phase (CP) can however be
different. To find this optimum value, we reduced the data for different
values of the coherent integration time (ncoherent keyword in the reduction
pipeline), which is the number of frames we add together to increase photon
S/N, a frame being one recorded image of the detector. The pipeline produces a
measurement of the calibrated parameters for each of these coherently added
frames, and it is these coherently added frames that are incoherently averaged
in the final calibrated file. Then, for each baseline and each target, we
plotted the mean value over the files of the V2 S/N and the CP error as a
function of the coherent integration time. We finally merged the V2 of the
files with the higher S/N on V2 and the CP of the files with the lower error
on CP, for most of the baselines or triplets. For the V2 we chose the same
coherent integration time throughout the night. For the CP we took the best
coherent integration time for each target. The number of coherently added
frames for every target is specified in Table 5, each frame integrating the
flux for about 3 ms.

The data reduction pipeline provides two options to unbias the CP. We chose
the option that computes an estimation of the bias as it does not require
tuning any extra parameters (in opposition to the second method). This
unbiasing method is explained in Appendix B of Anugu et al. (2020).

##  3 Data analysis

To analyze the reduced data, and look for companions in the interferometric
signal, we used the CANDID555https://github.com/amerand/CANDID software
(Gallenne et al., 2015). CANDID is a tool developed to look for binarity
signals in interferometric data as well as to determine the position and flux
ratio of the companion(s). For nondetections, CANDID also provides upper
limits on the contrast of potential companions. More information about the
algorithms and methods can be found in Gallenne et al. (2015). To streamline
the analysis of the data given the relatively large size of our sample, we
established an automated procedure to analyze all the data consistently and
uniformly.

This procedure is summarized here. First, for each observation of a star, we
input all the reduced data to CANDID. We then perform a first search for a
companion, fixing the maximum separation to 50 mas, which is approximately our
OWA (see Eq.1). We fixed the step of the search grid to 1.0 mas. This step
size is fine enough to find the global minimum in the range of separation we
are looking for, while it is large enough to preserve reasonable computation
time (approximately an hour per observation). If a companion is detected
(n$\sigma$ ¿5, with n$\sigma$ being the significance of the binary model
compared to a uniform disk model fitting the data), we use the bootstrap
function of CANDID around the position of the found companion. This gives us
errors on the position and flux ratio of the companion that are more realistic
than those computed by the initial grid search method. Then, if a first
companion is detected, we analytically remove the signal of this first
companion from the interferometric data, and we perform a search for a second
companion, using the same parameters as for the first search. We note that the
detection of a second companion is made with an indirect method assuming the
signal of the first companion is perfectly analytically removed, with no
residual. Therefore, these detections should be taken with caution and would
need further observations to confirm them. Finally, we determine the upper
limiting $\Delta$magnitude of a companion detectable in the data. If no
companion is detected, we compute this limit on the reduced data directly. It
gives us the limit in $\Delta$magnitude for which we would detect a companion.
If a first companion is detected, we perform this computation on the data with
the signal of the first companion analytically removed. It then gives us the
limit in $\Delta$magnitude for which we would detect a second companion. We
note that we can only remove the signal of one companion, so, the results of
this detection limit might be biased if the signal of a second companion is
present in the data.

Given the distance of these systems, even optical interferometry with 330 m
baselines is not resolving the diameter of the stars in those systems. Hence,
we consider them as a point source in CANDID, reducing the number of free
parameters in the search for companions.

##  4 Results

A summary of the results is shown in Table 2 for the first companion search
and Table 3 for the search of a second companion, with parameters that
characterize the systems.

###  4.1 New detections

We here summarize the newly detected companions.

Cyg OB2-5 A / BD+40 4220A / Schulte 5: This system includes a short 6.6 d
period binary, along with other components on wider orbits (Rauw et al., 1999,
2019). Two distant companions were already known at separations of 0.93″ and
5.55″ (Maíz Apellániz, 2010; Caballero-Nieves et al., 2014, 2020), which is
largely outside the OWA of our observations. Cyg OB2-5 A is a known PACWB,
with the nonthermal radio emission mainly associated with a wide orbit with a
period of about 6.7 years (Kennedy et al., 2010). We detect a companion in
both observations of June 2018 and June 2019, at a mean separation of
12.18$\pm 0.35$ mas and a mean $\Delta H=1.63\pm 0.3$ mag, and a second
companion in the observation of June 2019 at a separation of 6.51$\pm 0.26$
mas and a $\Delta H=4.13\pm 0.01$ mag. The computed detection limit for the
search of a second detection for the observation of June 2018 is 4 magnitudes
fainter than the primary component, while the detected second companion in
June 2019 is 4.13 magnitudes fainter. This could explain why we did not detect
it in the June 2018 data, but further observations are necessary to confirm
this second companion. This is the first direct detection for both companions.
The wind-wind collision between the combined wind of the inner system and the
one of the newly detected companions is likely the cause of the synchrotron
radio emission. Long-term monitoring should allow us to determine which is
associated with the 7-year period.

Cyg OB2-10 / 2MASS J20334610+4133010 / Schulte 10: Three companions have
already been observed previously at separations of 0.21″, 0.74″ and 4.16″ with
$\Delta K=2.80\pm 0.78$, $5.24\pm 0.05$, and $6.03\pm 0.07$ mag (Caballero-
Nieves et al., 2020). In the observation of June 2018, we detected a companion
at a separation of 7.35$\pm 0.20$ mas and $\Delta H=2.45\pm 0.03$ mag, but we
do not detect it again in the observation of June 2019. More observations
could be useful to confirm this new companion detection.

HD 17505: This object is known as a hierarchical triple system (Hillwig et
al., 2006; Sota et al., 2014). The system includes a close binary with an
orbital period of 8.571 days, separated from the primary component by 2.161”
(Maíz Apellániz et al., 2019). We detect an additional companion at a
separation of 15.43$\pm 0.02$ mas from the primary component and $\Delta
H=0.35\pm 0.04$ mag in two different observations separated by 1 day. This
companion is detected for the first time, making this system a quadruple one.

HD 19820: This system is a known spectroscopic binary (SB) with a period of
3.36 days (Hill et al., 1994). We detect a companion at a mean separation of
13.87$\pm 0.03$ mas and $\Delta H=2.57\pm 0.01$ mag in two different
observations separated by 1 day, and another companion at a separation of
6.96$\pm 0.11$ mas and $\Delta H=4.16\pm 0.01$ mag in only one of these
observations. The detection of this second companion is made with an indirect
method assuming the signal of the first companion is perfectly analytically
removed, with no residual. Therefore, this detection should be taken with
caution and will necessitate further observations to be confirmed.

HD 24431: This system has a companion situated at 0.72” (Mason et al., 1998;
Turner et al., 2008). We detect a new companion with a separation of 9.74$\pm
0.02$ mas and $\Delta H=1.37\pm 0.01$ mag.

HD 28446: This system is supposed to be an SB2 (double line spectroscopic
binary) with a period of 1.31 days in Mayer et al. (1994) but has not been
confirmed since. A third component is known at a separation of 10” (Eggleton &
Tokovinin, 2008). We detect a fourth companion in both our observations of
February 2018 and June 2018 with a mean separation of 26.16$\pm 0.13$ mas and
a mean $\Delta H=1.35\pm 0.08$ mag.

HD 34078: This star is a known runaway (Hoogerwerf et al., 2001). Candidate
companions have been detected by direct imaging at a separation of 8.4″ (Mason
et al., 1998) and 0.35″ (Turner et al., 2008), but both those detections are
suspected to be field stars observed in the line of sight of this star. We
detected a new companion in two different observations, at a separation of
6.85$\pm 0.07$ mas and $\Delta H=2.76\pm 0.02$ mag in December 2017 and a
separation of 1.74$\pm 0.20$ mas and $\Delta H=3.29\pm 0.03$ mag in September
2018.

HD 36861: This star ($\lambda$ Ori A) is known to be variable (Fullerton et
al., 1996), and part of a wide binary (HD 36861J). The components A and B of
the system $\lambda$ Ori may not be physically bound (Lindroos, 1985; Mason et
al., 1998). $\lambda$ Ori A had no detected companion yet (Mason et al.,
2009), but we detect a companion in our observation of February 2018, with a
separation of 10.13$\pm 0.05$ mas and a $\Delta H=3.30\pm 0.02$ mag. This
companion has not been detected again in our observation of June 2018, despite
the computed limiting magnitude of detection being $\Delta H=5.03$ mag. The
reason for this nondetection on the second observation is unknown. A new
observation of this system could confirm this new companion.

HD 47129: This is Plaskett’s star. It is a known SB2 with a period of 14.4
days (Linder et al., 2008). There are also two known visual companions at
0.78” and 1.12” (Turner et al., 2008). The SMASH+ survey resolved a faint
companion at 36 mas with $\Delta H\sim 4.0$ mag, with the NACO/SAM instrument,
but it was too faint to be confirmed by PIONIER and the uncertainties on the
separation found by NACO/SAM were large. We detect a companion at a separation
of 32.29$\pm 0.06$ mas and $\Delta H=4.6\pm 0.01$ mag. This detected companion
is a confirmation of the candidate by NACO/SAM, providing compelling evidence
for the existence of this companion. Interestingly enough, this long-period
companion is compliant with the likely membership of this system to the
category of PACWBs, based on radio results published by Kurapati et al.
(2017).

HD 207198: This system has a known companion at a separation of 17.64″ (Mason
et al., 2004). We detect for this system a companion at a separation of
41.07$\pm 0.04$ mas and $\Delta H=4.68\pm 0.01$ mag. This companion is
detected for the first time. We note that this detection is close to the OWA.

HD 229196: We detect for the first time in this system a companion, situated
at a separation of 5.88$\pm 0.02$ mas and a mean $\Delta H=2.80\pm 0.04$ mag
in two different observations separated by 1 day.

###  4.2 Already detected

We here summarize the redetection of companions that were already known from
other techniques or previous optical interferometric observations.

Cyg OB2-9 / HIP 101419: This PACWB is a known very excentric SB2 (Blomme et
al., 2013; Maíz Apellániz et al., 2019; Caballero-Nieves et al., 2020) with a
period estimated at 2.4 years and an excentricity of 0.713 (Nazé et al., 2010,
2012) with another companion at a separation of 21″ (Maíz Apellániz, 2010). We
detect a companion at a mean separation of 0.77$\pm 0.01$ mas and a mean
$\Delta H=0.42\pm 0.04$ mag in two observations separated by two days. With
the orbital parameters in Blomme et al. (2013) we derive a minimum projected
separation of $\sim 2.04$ AU with the known SB2 companion. Taking the distance
of the system and the angular separation we detect our companion, we compute a
projected separation of $\sim 1.38$ AU. Taking the uncertainties into account,
our detection is probably the SB2 component observed close to its periastron.
Further observations could confirm it.

HD 47839 / 15 Mon: This system has a known companion at $\simeq$ 0.1″ with a
difference of magnitude of 1.6 in the visible (Hutter et al., 2021) and a
third component at a wider (3 ″) separation (Mason et al., 1998; Sana et al.,
2014). We detect a companion with a separation of at least 49.19$\pm 0.32$ mas
and $\Delta H=1.81\pm 0.01$ mag. This detection is at the limit of the OWA,
which means that it is probable that the companion detected is further out, as
discussed in Sect. 6.1. This companion is probably the known companion around
100 mas, as the differences in magnitude are compatible and as the separation
close to the OWA cannot rule out this known companion.

HD 167971: This system is a known hierarchical triple system (Leitherer et
al., 1987; De Becker et al., 2012; Le Bouquin et al., 2017; Sanchez-Bermudez
et al., 2019), that also turns out to be the brightest synchrotron-emitting
O-type PACWB in the catalog (De Becker & Raucq, 2013). The central binary has
an orbital period of 3.3 days and the third component is orbiting the inner
binary on a timescale of 21.4 years. We detect a companion at 19.89$\pm 0.01$
mas and $\Delta H=0.61\pm 0.01$ mag. The separation of the detected companion
is compatible with the one of the outer component of the system measured in De
Becker et al. (2012) and Le Bouquin et al. (2017).

HD 193322: This is a complex multiple system. The A component consists of a
single star Aa orbiting around a 312-day binary Ab in 35 years (ten Brummelaar
et al., 2011). Three other components are also known, with a separation of
2.6″ for the closest (Turner et al., 2008). We detect a companion at a
separation of at least 47.33 mas and maximum $\Delta H=0.06^{+0.06}_{-0.05}$
mag in our three observations of this system in June 2018, in September 2018,
and in June 2019. These detections are at the limit of the OWA, which means
that it is possible that the companion is somewhat further out, as discussed
in Sect. 6.1. The detected companion is most likely the already known pair Aa
and Ab due to its separation being compatible with the known pair reported in
ten Brummelaar et al. (2011).

HD 202214: One close companion is already known from spectroscopy, with an
orbital period of 81.30 days (Mante, 2002). The system also has two wider
companions, one at a separation of 0.071″ (Mante, 2002) and a $\Delta V=0.6$
(Mason et al., 2009) mag and one at 1.0″ with a $\Delta V=0.3$ (Mason et al.,
2009) mag. We detect a companion at a separation of 47.27$\pm 0.05$ mas and
$\Delta H=0.03^{+0.03}_{-0.04}$ mag. This detection is at the limit of the
OWA, which means that it is probable that the detected companion is actually
further out, as discussed in Sect. 6.1. We, therefore, cannot rule out that
the detected companion is the known one at 71 mas. The difference between our
magnitude difference and the one from Mason et al. (2009) could then be
explained by the separation potentially being larger than our OWA, introducing
bias in our detection, and by the fact that our observing setup is not
optimized for companions outside of the OWA. The derived contrast might
therefore be systematically biased.

HD 206267: This system is a high order multiple system (Maíz Apellániz et al.,
2019; Maíz Apellániz & Barbá, 2020). The central component (AaAb) is composed
of an SB2 (Aa) with a period of 3.71 days (Raucq et al., 2018) and another
companion (Ab) separated from Aa by 0.1″ and a difference in magnitude of
1.63$\pm$0.3 at a wavelength of $\lambda=0.91\leavevmode\nobreak\ \mu$m (SDSS
z
filter666https://skyserver.sdss.org/dr1/en/proj/advanced/color/sdssfilters.asp)
(Maíz Apellániz et al., 2020). A third component (B) is situated at a
separation of 1.7″ with a difference of 5.72$\pm$0.13 in magnitude at
$\lambda=0.91\leavevmode\nobreak\ \mu$m. Two other companions (C and D) are
situated within 25″. We detect a companion at a separation of at least
49.52$\pm 0.22$ mas with a difference of 1.64$\pm 0.02$ mag in the H-band.
This detection is at the limit of the OWA, which means that it is probable
that this detected companion is further out, as discussed in Sect. 6.1. We,
therefore, cannot rule out that this detection can be the known companion at
0.1″; the magnitude differences are compatible one with each other.

###  4.3 No detection

We do not detect interferometric companions around HD 30614 (SB1 system with a
period of 3.68 days; Zeinalov & Musaev, 1986), HD 47432 (one known companion
at 0.78″; Turner et al., 2008), HD 188001 (single runaway star; Trigueros Páez
et al., 2021), HD 195592 (spectroscopic binary with a period of a few days; De
Becker et al., 2010), HD 201345 (one known wide companion at 7.38″; Turner et
al., 2008), HD 206183 (two known wide companions at separations of 6.6″ and
11.6″; Mason et al., 1998), HD 209975 (four known wide companions at 3.79″,
4.14″, 19.8″, and 60.4″; Mason et al., 1998; Turner et al., 2008), HD 217086
(2 known companions at 2.8″ and 3.1″; Mason et al., 1998; Turner et al.,
2008), and HD 228779.

###  4.4 Candidates

Some of our observations resulted in candidates with only a marginally
significant detection criterion ($3<n\sigma<5$). Those systems are HD 45314
(Oe star Rauw et al., 2015), HD 210809, and HD 210839. More observations will
be needed to validate or reject the presence of a companion. The position of
those candidates can be found in Table 2.

Table 2: Summary of the results for the first companion search with CANDID.

Target’s name | DATE-OBS | n$\sigma$ | sep | P.A. | emax | emin | P.A. emax | $\Delta H$ | det. lim.
---|---|---|---|---|---|---|---|---|---
| MJD |  | [mas] | [deg] | [mas] | [mas] | [deg] | [mag] |  $\Delta$mag(H)
Cyg OB2-5 A | 58279.353 | 6.46 | 13.35 | 97.45 | 0.35 | 0.11 | $-3.03$ | 1.91 ${}^{+0.02}_{-0.02}$ | –
… | 58657.396 | 8.03 | 11.00 | 107.12 | 0.00 | 0.00 | 26.56 | 1.38 ${}^{+0.00}_{-0.00}$ | –
Cyg OB2-9 | 58386.154 | 8.03 | 0.76 | 148.90 | 0.01 | 0.00 | $-13.26$ | 0.38 ${}^{+0.02}_{-0.02}$ | –
… | 58388.197 | 8.03 | 0.78 | 152.99 | 0.01 | 0.01 | 81.50 | 0.45 ${}^{+0.01}_{-0.01}$ | –
Cyg OB2-10 | 58281.491 | 5.75 | 7.35 | $-21.47$ | 0.20 | 0.03 | 38.96 | 2.45 ${}^{+0.03}_{-0.03}$ | –
… | 58657.446 | 2.96 | – | – | – | – | – | – | 3.24
HD 17505 | 58386.393 | 8.03 | 15.43 | $-141.24$ | 0.02 | 0.01 | 40.24 | 0.35 ${}^{+0.04}_{-0.03}$ | –
… | 58387.358 | 8.03 | 15.43 | $-141.22$ | 0.01 | 0.00 | 52.60 | 0.34 ${}^{+0.02}_{-0.03}$ | –
HD 19820 | 58386.331 | 8.03 | 13.89 | 82.35 | 0.03 | 0.01 | 1.55 | 2.57 ${}^{+0.01}_{-0.01}$ | –
… | 58387.424 | 8.03 | 13.85 | 82.56 | 0.02 | 0.02 | 36.70 | 2.56 ${}^{+0.01}_{-0.01}$ | –
HD 24431 | 58385.388 | 49.96 | 9.74 | 146.19 | 0.02 | 0.01 | $-82.80$ | 1.37 ${}^{+0.01}_{-0.00}$ | –
HD 28446 | 58157.339 | 47.82 | 25.06 | $-45.64$ | 0.13 | 0.02 | $-86.04$ | 1.42 ${}^{+0.02}_{-0.01}$ | –
… | 58385.363 | 49.96 | 27.25 | $-56.15$ | 0.01 | 0.01 | $-52.32$ | 1.28 ${}^{+0.01}_{-0.01}$ | –
HD 30614 | 58386.439 | 1.34 | – | – | – | – | – | – | 4.32
HD 34078 | 58100.407 | 5.62 | 6.85 | 172.83 | 0.07 | 0.06 | 77.06 | 2.76 ${}^{+0.02}_{-0.02}$ | –
… | 58384.400 | 5.29 | 1.74 | 171.17 | 0.20 | 0.04 | $-61.50$ | 3.29 ${}^{+0.03}_{-0.03}$ | –
HD 36861 | 58156.175 | 6.51 | 10.13 | $-11.06$ | 0.05 | 0.04 | 59.92 | 3.3 ${}^{+0.02}_{-0.02}$ | –
… | 58387.479 | 0.96 | – | – | – | – | – | – | 5.03
HD 45314 | 58386.497 | 3.25 | 27.80 | 167.42 | 0.09 | 0.04 | $-21.81$ | 4.24 ${}^{+0.00}_{-0.01}$ | –
HD 47129 | 58385.529 | 5.01 | 32.39 | 37.50 | 0.06 | 0.03 | $-73.35$ | 4.6 ${}^{+0.01}_{-0.01}$ | –
HD 47432 | 58387.523 | 0.66 | – | – | – | – | – | – | 4.91
… | 58388.512 | 0.00 | – | – | – | – | – | – | 4.99
HD 47839 | 58386.535 | 17.76 | 49.19∗ | $-72.92$ | 0.32 | 0.17 | 86.62 | 1.81 ${}^{+0.01}_{-0.01}$ | –
HD 167971 | 58658.289 | 49.96 | 19.89 | $-98.40$ | 0.01 | 0.00 | $-20.18$ | 0.61 ${}^{+0.01}_{-0.01}$ | –
HD 188001 | 58387.135 | 2.23 | – | – | – | – | – | – | 4.25
HD 193322 | 58281.321 | 49.96 | 47.33∗ | 15.78 | 0.24 | 0.13 | 10.57 | 0.06 ${}^{+0.06}_{-0.05}$ | –
… | 58388.146 | 49.96 | 48.70∗ | 148.78 | 0.27 | 0.08 | $-17.21$ | 0.01 ${}^{+0.1}_{-0.05}$ | –
… | 58658.367 | 49.96 | 49.18∗ | 148.12 | 0.11 | 0.05 | $-25.95$ | $-0.01^{+0.00}_{-0.00}$ | –
HD 195592 | 58280.337 | 1.89 | – | – | – | – | – | – | 3.63
HD 201345 | 58661.420 | 2.82 | – | – | – | – | – | – | 4.38
HD 202214 | 58658.412 | 49.96 | 47.27∗ | $-129.68$ | 0.05 | 0.04 | 71.07 | 0.03 ${}^{+0.03}_{-0.04}$ | –
HD 206183 | 58661.470 | 0.67 | – | – | – | – | – | – | 5.83
HD 206267 | 58660.442 | 8.03 | 49.52∗ | $-145.71$ | 0.22 | 0.06 | 0.38 | 1.64 ${}^{+0.02}_{-0.01}$ | –
HD 207198 | 58658.449 | 7.10 | 41.07∗ | $-32.93$ | 0.04 | 0.02 | $-34.19$ | 4.68 ${}^{+0.00}_{-0.01}$ | –
HD 209975 | 58278.401 | 0.76 | – | – | – | – | – | – | 5.16
HD 210809 | 58660.490 | 3.14 | 4.45 | 70.72 | 0.09 | 0.04 | $-64.87$ | 4.02 ${}^{+0.01}_{-0.02}$ | –
HD 210839 | 58657.486 | 4.93 | 6.72 | 79.36 | 0.08 | 0.02 | $-60.61$ | 5.92 ${}^{+0.00}_{-0.00}$ | –
HD 217086 | 58387.243 | 0.10 | – | – | – | – | – | – | 4.69
HD 228779 | 58660.400 | 2.50 | – | – | – | – | – | – | 4.97
HD 229196 | 58385.195 | 8.03 | 5.88 | 13.52 | 0.03 | 0.01 | 77.55 | 2.76 ${}^{+0.00}_{-0.00}$ | –
… | 58388.244 | 8.03 | 5.88 | 14.02 | 0.03 | 0.02 | 89.62 | 2.84 ${}^{+0.01}_{-0.01}$ | –

777The first column is the system name and the second column is the MJD date
of the observations. The third column is the significance of the detection of
a companion by CANDID. The fourth and fifth columns are respectively the
separation and the position angle (P.A.) of the detected companion. The P.A.
is defined as the angle between the north direction and the companion
direction with respect to the central element counted positively toward the
east. The separations noted with an ∗ symbol are close to the OWA, and should
only be considered as a lower limit. The sixth, seventh, and eighth columns
give respectively the semi-major axis and the semi-minor axis, and the P.A.
between the semi-major axis direction and the north direction of the error’s
ellipse on the position of the detected companion. The ninth column is the
magnitude difference between the main component and the detected companion in
the H-band. The tenth column is the $\Delta$magnitude limit for which we
should be able to detect a companion computed by CANDID. We note that for the
systems with no companion detected, we only give the result of the detection
limiting magnitude, and we do not give them for the systems with candidates or
detected companions, as we give them in Table 3.

Table 3: Same as Table 2 but for the second detection.

Target’s name | DATE-OBS | n$\sigma$ | sep | P.A. | emax | emin | P.A. emax |  $\Delta$H | det. lim.
---|---|---|---|---|---|---|---|---|---
| MJD |  | [mas] | [deg] | [mas] | [mas] | [deg] | [mag] |  $\Delta$mag(H)
Cyg OB2-5 A | 58279.353 | 0.74 | – | – | – | – | – | – | 4.06
… | 58657.396 | 8.03 | 6.51 | $-85.06$ | 0.26 | 0.04 | 85.05 | 4.15 ${}^{+0.01}_{-0.01}$ | –
Cyg OB2-9 | 58386.154 | 0.76 | – | – | – | – | – | – | 4.98
… | 58388.197 | 0.67 | – | – | – | – | – | – | 5.88
Cyg OB2-10 | 58281.491 | 1.62 | – | – | – | – | – | – | 3.51
HD 17505 | 58386.393 | 3.72 | – | – | – | – | – | – | 4.19
… | 58387.358 | 0.7 | – | – | – | – | – | – | 1.56
HD 19820 | 58386.331 | 8.03 | 6.96 | 91.45 | 0.11 | 0.05 | 89.91 | 4.16 ${}^{+0.01}_{-0.01}$ | –
… | 58387.424 | 0.99 | – | – | – | – | – | – | 4.29
HD 24431 | 58385.388 | 1.83 | – | – | – | – | – | – | 4.77
HD 28446 | 58157.339 | 0.81 | – | – | – | – | – | – | 3.28
… | 58385.363 | 1.81 | – | – | – | – | – | – | 4.72
HD 34078 | 58100.407 | 4.74 | – | – | – | – | – | – | 3.33
… | 58384.4 | 2.13 | – | – | – | – | – | – | 4.31
HD 36861 | 58156.175 | 1.18 | – | – | – | – | – | – | 4.83
HD 45314 | 58386.497 | 2.0 | – | – | – | – | – | – | 4.74
HD 47129 | 58385.529 | 0.78 | – | – | – | – | – | – | 5.28
HD 47839 | 58386.535 | 6.66 | – | – | – | – | – | – | 3.34
HD 167971 | 58658.289 | 1.17 | – | – | – | – | – | – | 3.78
HD 193322 | 58281.321 | 4.52 | – | – | – | – | – | – | 3.03
… | 58388.146 | 2.33 | – | – | – | – | – | – | 3.16
… | 58658.367 | 6.72 | – | – | – | – | – | – | 3.07
HD 202214 | 58658.412 | 15.7 | – | – | – | – | – | – | 2.86
HD 206267 | 58660.442 | 4.62 | – | – | – | – | – | – | 3.08
HD 207198 | 58658.449 | 0.82 | – | – | – | – | – | – | 5.78
HD 210809 | 58660.49 | 1.03 | – | – | – | – | – | – | 5.05
HD 210839 | 58657.486 | 2.98 | – | – | – | – | – | – | 5.51
HD 229196 | 58385.195 | 3.07 | – | – | – | – | – | – | 4.38
… | 58388.244 | 1.24 | – | – | – | – | – | – | 4.42

888The detection’s limiting $\Delta$magnitude of systems with a second
companion detected is not accurate as the data are polluted by the signal of
the second companion.

##  5 Statistical analysis

Among the 29 systems observed with good-quality data, we confirm the detection
of 19 companions for 17 multiple systems (see Sections 4.1 and 4.2). Out of
these 19 companions, 13 are detected for the first time. This gives us a
multiplicity fraction $f_{\text{m}}=17/29=0.59\pm 0.09$, and a companion
fraction of $f_{\text{c}}=19/29=0.66\pm 0.13$ in the range of separations to
which we are sensitive. The uncertainty for the multiplicity fraction is
obtained with a binomial uncertainty and the companion fraction uncertainty is
obtained with a Poisson uncertainty.

We note that 38% of our sample corresponds actually to multiple systems with
at least three components and that in 28% of the sample, the interferometric
companion constitutes the detection of the outer orbit in a hierarchical
triple system. This proportion of hierarchical triple systems should allow us
to study the Kozai-Lidov effect (Naoz, 2016), by studying their orbits.

###  5.1 Comparison with SMASH+

The multiplicity fraction in this study is marginally higher than the one in
SMASH+ ($0.41\pm 0.05$). This difference could be explained by the fact that
our preliminary magnitude limit ($H<6.5$ mag) was brighter than the one of
SMASH+ ($H<7.5$ mag). This would push the observational bias to observe a
larger fraction of multiple systems.

By taking into account all known companions, summarized in Table 1, the total
multiplicity fraction ($0.86\pm 0.07$) and the total companion fraction
($2.10\pm 0.27$), are consistent with the one of SMASH+ (respectively $0.91\pm
0.03$ and $2.1\pm 0.2$). We also find that in our sample, $38\pm 9$% of the
systems contain spectroscopic binaries, which is marginally lower than in the
SMASH+ sample ($49\pm 5$%).

###  5.2 Estimated mass ratio distribution

We define the mass ratio $q$ as:

$q=M_{\text{comp}}/M_{\text{primary}}$ (3)

where $M_{\text{comp}}$ is the mass of the detected companion and
$M_{\text{primary}}$ is the mass of the primary component of the system. This
mass ratio can be estimated using the flux ratio between the two components.
In this study, we use the same relation used in Le Bouquin et al. (2017) and
derived from Martins et al. (2005), which gives a good approximation of the
mass ratio for main-sequence stars:

$q=(f_{H})^{0.7}$ (4)

where $f_{H}$ is the flux ratio in the H-band, given by the CANDID analysis.
We note that if the central component is an unresolved binary, this method of
computing the mass ratio is using the combined flux of both components, hence
the estimated mass ratio will be biased.

Figure 4: Histogram of detected companions as a function of the estimated mass
ratio $q$, when taking into account only the first detected companions (blue),
and when adding the second companions detected (orange).

Figure 4 displays the distribution of the estimated mass ratio of the detected
companions. In this figure, we can see that the distribution seems to be bi-
modal, with a lack of companions between $q=0.4$ and $0.6$, and favoring a
lower mass ratio. The bi-modality could be explained by the small statistic we
are using here, with only 17 companions. However, we ran a Kuiper test to
compare the estimated mass ratio distribution with a uniform distribution. The
result of this test is a value of D $=0.41$, and a probability of obtaining
the value D from a uniform distribution of 2.7%. From this low probability, we
can conclude that the actual mass ratio distribution is most probably not
uniform.

The distribution favoring low mass ratios goes against the observational bias
of the survey being magnitude limited. This bias should favor the inclusion of
binaries with bright companions, therefore, with a flux ratio, hence a mass
ratio, close to 1. So, this tendency seems to come from the intrinsic O-type
stars’ mass ratio distribution. The results of the survey of the massive stars
in the Orion region (GRAVITY collaboration et al., 2018) show a similar trend,
with a mass ratio distribution following a power law $\propto q^{\alpha}$ with
$\alpha=1.7$.

###  5.3 Projected separation distribution

In the absence of any estimate of the inclination of the orbit, the absolute
physical separation cannot be determined. Rather, we determined the projected
separation of the detected companions, using the distances published by
Bailer-Jones et al. (2021).

Figure 5: Histogram of detected companions as a function of the projected
separation in Astronomical Unit (AU). The distribution in blue takes into
account only the first companions. The distribution in orange considers all
companions.

Figure 5 shows the distribution of the separation of the companions detected
in this study. The distribution seems to favor the middle and high part of the
probed separation, from 10 to 100 AU. We note that the companions detected
close to the OWA may actually be located further out, meaning that the real
distribution could have a tail at larger separations. This figure only shows
the companions that were (re)detected in this study.

###  5.4 Estimated mass ratio as a function of the projected separation

Figure 6: Estimated mass ratio as a function of the projected separation in AU
of the detected companions. We note that some error bars are hidden by the
size of the markers. Error bars on separation ending with an arrow pointing
right are to distinguish the companions detected close to the OWA. The black
points are for known companions detected with other observational techniques.

Figure 6 shows the estimated mass ratio $q$ as a function of the projected
separation of the companions detected in this study. Error bars on separation
ending with an arrow pointing right are to distinguish the companions detected
close to the OWA, meaning that the physical separation on the plot is only a
lower limit. The black points are for the companions detected with other
techniques for which the mass ratio and physical separation are known or can
be determined from the literature.

We notice the higher number of companions with an estimated mass ratio $q<0.6$
as described in Sect. 5.2. However, we cannot discern any correlations in this
plot between the estimated mass ratio $q$ and the physical separation for the
companions detected in this study as the companions seem relatively
homogeneously distributed in the figure.

Furthermore, taking into consideration the companions previously detected by
other techniques, a correlation seems to appear, with $q$ being anticorrelated
with the separation. This anticorrelation would be in favor of the competitive
accretion formation process (GRAVITY collaboration et al., 2018). But one
should note that this result could be due to the difference of biases in the
detection of companions by the different techniques. A further study taking
into account the different biases is necessary to bring a stronger conclusion.

We caution that the plot is affected by some factors that deserve a few
comments. First of all, we certainly need a greater statistical sample if we
want to be sure that there is or is not a correlation between these two
parameters for massive star systems. For subsequent developments, we stress
that we should ideally base our discussion on absolute physical separations,
and not on projected ones, which requires knowledge about the inclination.
This can be obtained through a suitable interferometric follow-up to derive
the relative astrometric orbit of the systems. Finally, the best test for a
potential (lack of) correlation with the mass ratio should rely on an estimate
of the semi-major axis, and not on the measured separation at one specific
epoch. The available measurements have been obtained at any orbital phase, and
in the case of a significantly eccentric orbit, the measured separation is not
necessarily a good proxy for the semi-major axis.

##  6 Discussion

###  6.1 Outer working angle

As we limited our search for companions to OWA, the results for the companions
found close to this limit (separation ¿ 40 mas, HD 47839, HD 193322, HD
202214, HD 207198, and HD 206267) might correspond to a local minimum of
$\chi^{2}$, while the global minimum may not be probed in our search. The
detection of those companions is still valid, as the interferometric signal
still favors the presence of a companion compared to a uniform disk, but the
found separation should be considered as a lower limit. Further observations
with a wider OWA could confirm the real separation of those companions, but
this requires a higher spectral resolution, which is doable with MIRC-X,
however, it would reduce the sensitivity of the instrument. It can be achieved
only for the brightest systems. Alternative methods such as sparse aperture
masking may thus be preferred.

###  6.2 Candidates for orbital parameter measurements

While the statistical analysis will require the large survey data, the
currently detected companions can already give us good candidates for follow-
up orbital parameter measurements. To be a good candidate for follow-up with
interferometry, we take here a limit on the orbital period of a maximum of 10
years, which is a reasonable time scale for follow-up observations.

To obtain an estimation of the orbital period of the detected companions, we
use the Kepler’s third law:

$P^{2}=\frac{a^{3}}{M_{1}+M_{2}}$ (5)

where $P$ is the period in years, $a$ is the semi-major axis of the orbital
ellipse in AU, and $M_{1}$ and $M_{2}$ are the masses of the two objects
orbiting each other, in solar mass.

For our estimation of $P$, we approximate the semi-major axis $a$ with the
projected separation that we computed earlier. This will lead to an
overestimate of $a$, hence $P$, for eccentric systems as companions spend a
larger fraction of the orbit at separations $>a$ (Kepler’s law). For the mass
of the two objects, we use the $m_{\text{evol}}$ in table 4 of Weidner & Vink
(2010), which gives a theoretical mass of O-type stars as a function of their
spectral type. We used the spectral types of our objects listed in Table 1 to
get an estimation of the mass for the central object, and we used the
estimated mass ratio $q$ for the detected companion mass.

With the flux ratio, separation, and estimated mass ratio, we could estimate
also the shift of the photo-center of our binary systems. This estimated shift
could give us candidates of systems for which we could determine the orbital
parameters with Gaia, as discussed in Le Bouquin et al. (2017). From equation
five in that paper we can determine that:

$\mu=\frac{a(q-f)}{(f+1)(q+1)}$ (6)

For our estimation of $\mu$, we used the separation of our detected companions
as an estimation of $a$, the estimated mass ratio $q$, and the detected flux
ratio $f$.

Figure 7: Estimated photo-center shift $\mu$ in mas as a function of the
estimated orbital period in years. The red lines show the limit of capability
of Gaia to measure the orbital parameters of a system, with the hatched area
being not accessible by Gaia.

Figure 7 displays the estimated photo-center shift $\mu$ in mas as a function
of the estimated orbital period in years. The detection limit on $\mu$
detectable by Gaia is set to 0.1 mas or higher. This value comes from the fact
that Gaia needs a shift of at least three times the Gaia accuracy of a
transit, which is 0.034 mas on bright targets ($G<12$, see Sect. 4 of Perryman
et al. (2014)), which is the case for all our targets. The conservative limit
in the period for which Gaia can determine the orbital parameters is set to 6
years. This limit is the one for which Gaia will be able to determine orbital
parameters from a detectable astrometric shift of the photo-center in almost
any case. But this limit is for the nominal mission period of 5 years. Now
Gaia has observed for 7.8 years and the anticipated mission lifetime is now at
least 10 years. So we estimate the expected limit on Fig. 7 at 10 years, which
corresponds also to the period we set for the interferometric survey.

First, we see that eight companions have an estimated orbital period of less
than 10 years, which makes them suitable to be followed up by interferometry
directly. Then, we see that Gaia should be able to obtain the orbital
parameters of seven of our systems, which have an estimated orbital period of
approximately 6 years or less and an estimated photo-center shift of more than
0.1 mas. For the periods larger than 10 years, the orbital parameters will not
be well constrained by Gaia, but combined with the data from interferometry,
it should be possible to constrain orbital parameters well. Furthermore, the
orbital parameters with Gaia are interesting because, in combination with the
information from interferometry, one could measure the individual masses of
each component of a multiple system. Currently interferometry needs to be
combined with spectroscopy to measure individual masses (e.g., Le Bouquin et
al. 2017; Mahy et al. 2018; Fabry et al. 2021; Sanchez-Bermudez et al. 2022).
The technique with Gaia would not need spectroscopy because it will provide
the distance, which with the orbit size from interferometry would provide the
total mass of the system, and by combining the orbit size and the orbit size
of the photo-center provided by Gaia, one would obtain the mass ratio of the
components of the system. Combining both total mass and mass ratio would
provide the individual masses of these components. Gaia would also probe a
different range of separation than the spectroscopy. These two techniques
would then be complementary. In addition, one would be able to compare the
results of the two methods and remove the potential biases that each of these
methods could present, as the range of masses estimated by spectroscopy alone
shows discrepancies with the measured masses by combining spectroscopy and
interferometry (Le Bouquin et al., 2017).

##  7 Conclusion

From the results of this pilot study, we can conclude that a large survey to
study the multiplicity of northern O-type stars can be performed with the
instrument MIRC-X at the CHARA Array. Indeed, we demonstrated that we can
constrain the multiplicity of O-star systems with a magnitude in the H-band
around 7.5 mag, in good atmospheric conditions. This magnitude allows the
observation of more than 120 northern O-type stars. From the experience gained
with this pilot survey, we can observe six to eight science targets per night
with normal conditions. Taking into account an average loss of 25% of the
night due to bad atmospheric conditions weather or technical issues, we
estimate that the large program will require approximately 25 nights to be
completed.

This study also detected 19 companions in 17 different systems, including 13
companions detected for the first time, notably the companion responsible for
the nonthermal emission in Cyg OB2-5 A, and the confirmation of the candidate
companion of HD 47129 previously suggested by SMASH+. The preliminary
statistical study gives us a multiplicity fraction $f_{\text{m}}=17/29=0.59\pm
0.09$, and a companion fraction of $f_{\text{c}}=19/29=0.66\pm 0.13$. Those
results are consistent with the results of the southern large survey already
performed, SMASH+.

We also demonstrated that a number of the detected systems are suitable for
follow-up studies for orbital parameter measurement, either by interferometry
(8) and/or with Gaia (7). The results obtained in this study are promising in
terms of scientific returns of a more ambitious project focusing on a large
sample, and involving repeated observations spread over several years.

###### Acknowledgements.

We would like to thank Carine Babusiaux, from IPAG, for her help in
determining the capability of Gaia to help in the constraint of orbital
parameters and Laetitia Rodet in her explanation of the relevance of the study
of the Kozai-Lidov cycle. We also thank the referee for their constructive
comments that resulted in a better paper. L.M. and E.G. acknowledge the
European Space Agency (ESA) and the Belgium Federal Science Policy Office
(BELSPO) for their support in the framework of the prodex programme. This work
is based upon observations obtained with the Georgia State University Center
for High Angular Resolution Astronomy Array at Mount Wilson Observatory. The
CHARA Array is supported by the National Science Foundation under Grant No.
AST-1636624 and AST-2034336. Institutional support has been provided from the
GSU College of Arts and Sciences and the GSU Office of the Vice President for
Research and Economic Development. Time at the CHARA Array was granted through
the NOIRLab community access program (NOIRLab 2018A-0158, 2018B-0123,
2019A-0080; PI: C. Lanthermann). S.K., N.A., and C.L.D. acknowledge support
from an ERC Starting Grant (Grant Agreement No. 639889), ERC Consolidator
Grant (Grant Agreement ID 101003096), and STFC Consolidated Grant
(ST/V000721/1). A.L. received funding from STFC studentship No. 630008203.
J.D.M. acknowledges funding for the development of MIRC-X (NASA-XRP
NNX16AD43G, NSF-AST 1909165) and MYSTIC (NSF-ATI 1506540, NSF-AST 1909165).
This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(Grant agreement No. DLV-772225: MULTIPLES). This research has made use of the
Jean-Marie Mariotti Center Aspro service 999Available at
http://www.jmmc.fr/aspro. This work was supported by the Programme National de
Physique Stellaire (PNPS) of CNRS/INSU co-funded by CEA and CNES. This work
has been partially supported by the LabEx FOCUS ANR-11-LABX-0013. This
research has made use of the SIMBAD database, operated at CDS, Strasbourg,
France.

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##  Appendix A Calibrators

In this section, we list the stars that we used as calibrators in data
reduction in Table LABEL:tab:cal-used. In addition, we observed eight targets
to use them as calibrators but ended up showing resolved features such as
nonconstant closure phases, or obvious multiplicity signal. These targets are
2MASS J21472749+5746367, HD 47415, HD 167882, HD 194479, HD 237112, HD 239737,
HD 281311, and SAO 49700: they will be reported and added into the bad
calibrator list101010https://www.jmmc.fr/badcal/ of the JMMC.

1]

Table 4:  Calibrator observed and used to reduce the data.  Calibrator’s name | Diameter [mas] | Error [mas] | Science target | Observing dates
---|---|---|---|---
2MASS J19524977+4836263 | 0.46 | 0.03 | HD 188209 | 2018-06-09
2MASS J20295613+4137570 | 0.31 | 0.01 | Cyg OB2-9 | 2018-09-23
… | … | … | HD 193322 | 2018-06-12
… | … | … | HD 34078 | 2017-12-13
2MASS J20473119+3629045 | 0.2 | 0.01 | HD 201345 | 2019-06-27
2MASS J21281481+6005284 | 0.52 | 0.03 | HD 209975 | 2018-06-09
HD 21820 | 0.48 | 0.03 | HD 24534 | 2018-09-23, 2018-09-27
HD 22269 | 0.58 | 0.03 | HD 24534 | 2018-09-27
HD 24688 | 0.37 | 0.03 | HD 24431 | 2018-09-24
HD 26311 | 1.64 | 0.03 | HD 24534 | 2018-02-08
HD 30111 | 0.562 | 0.03 | HD 34078 | 2017-12-13
HD 30793 | 0.53 | 0.03 | HD 34078 | 2018-09-23, 2018-09-27
HD 32518 | 0.816 | 0.03 | HD 30614 | 2018-09-25
HD 35238 | 1.03 | 0.05 | HD 34078 | 2018-09-27
HD 42618 | 0.377 | 0.03 | HD 34078 | 2017-12-13
HD 45089 | 0.61 | 0.03 | HD 41129 | 2018-09-23, 2018-09-24
… | … | … | HD 45314 | 2018-09-25
HD 46714 | 0.86 | 0.03 | HD 47432 | 2018-09-27
HD 48596 | 0.53 | 0.03 | HD 47432 | 2018-09-26, 2018-09-27
HD 49019 | 0.89 | 0.03 | HD 36861 | 2018-02-07
HD 52961 | 0.232 | 0.02 | HD 34078 | 2017-12-13
HD 77250 | 0.8 | 0.04 | HD 34078 | 2017-12-13
HD 87828 | 0.78 | 0.03 | HD 89353 | 2018-02-07
HD 150470 | 0.45 | 0.01 | HD 150193∗ | 2019-06-24
HD 155524 | 0.49 | 0.03 | Cyg OB2-5 A | 2018-06-10
… | … | … | HD 157214∗ | 2018-06-11
HD 165480 | 0.44 | 0.01 | HD 166737 | 2019-06-24
HD 185663 | 0.64 | 0.03 | HD 188001 | 2018-09-26
HD 186962 | 0.41 | 0.01 | HD 188001 | 2018-09-26
HD 189942 | 1.15 | 0.05 | HD 193237∗ | 2018-06-24
HD 193217 | 1.57 | 0.03 | Cyg OB2-5 A | 2018-06-10
HD 195647 | 0.42 | 0.03 | HD 229196 | 2018-09-24
… | … | … | Cyg OB2-9 | 2018-09-27
… | … | … | Cyg OB2-8 | 2018-06-12
… | … | … | Cyg OB2-10 | 2019-06-23
HD 196134 | 0.71 | 0.06 | Cyg OB2-5 A | 2019-06-23
HD 196360 | 0.6 | 0.03 | Cyg OB2-9 | 2018-09-24
… | … | … | HD 229196 | 2018-09-27
HD 200060 | 0.516 | 0.03 | Cyg OB2-11 | 2018-09-25
HD 204050 | 0.42 | 0.03 | HD 203064 | 2018-06-10
HD 204721 | 0.6 | 0.06 | HD 207198 | 2019-06-24
HD 211982 | 0.57 | 0.02 | HD 202214 | 2018-06-09
… | … | … | HD 210839 | 2018-06-09
HD 212289 | 0.48 | 0.03 | HD 203064 | 2018-06-10
… | … | … | HD 214686 | 2018-06-11
HD 217711 | 0.67 | 0.03 | HD 2018086 | 2018-09-26
HD 228660 | 0.58 | 0.01 | HD 228779 | 2019-06-26
HD 228721 | 0.31 | 0.01 | HD 229202 | 2019-06-27
HD 228852 | 0.54 | 0.03 | Cyg OB2-9 | 2018-09-24
… | … | … | HD 193322 | 2018-09-27, 2019-06-24
HD 232948 | 0.68 | 0.03 | HD 36861 | 2018-02-08
… | … | … | HD 28446 | 2018-09-24
HD 235757 | 0.43 | 0.01 | HD 210809 | 2019-06-26
HD 235872 | 0.34 | 0.01 | HD 218915 | 2019-06-27
HD 237032 | 0.76 | 0.03 | HD 17505 | 2018-09-25, 2018-09-26
HD 237036 | 0.5 | 0.03 | HD 17505 | 2018-09-26
HD 239636 | 0.36 | 0.01 | HD 202214 | 2018-06-09, 2019-06-24
HD 239760 | 0.61 | 0.02 | HD 206267 | 2019-06-22
HD 240211 | 0.34 | 0.03 | HD 217086 | 2018-09-26
HD 246454 | 0.6 | 0.03 | HD 36861 | 2018-09-26
HD 254874 | 0.51 | 0.03 | HD 45314 | 2018-02-07
HD 261683 | 0.56 | 0.03 | HD 47839 | 2018-09-25
SAO 50079 | 0.4 | 0.03 | Cyg OB2-10 | 2018-06-12
SAO 50138 | 0.38 | 0.03 | HD 199579 | 2018-06-11
SAO 50258 | 0.27 | 0.03 | LS III +46 11 | 2018-06-24
Table 4: continued. 111111The first column is the calibrator name. The second
column is the diameter of the calibrator in the H-band in mas as stated in the
JSDC catalog (Bourges et al. 2017). The third column is the associated error
in mas. The fourth column is the science target it has calibrated. The fifth
column gives the observing dates at which the calibrator was used for this
science target. We note that science targets noted with the symbol $\ast$ are
non O-type stars observed during the observing runs: their calibrators were
still used for the data reduction. Concerning O-type star science targets
present in this table that were observed with the associated calibrator, but
had not good enough quality data, thus them not being present in the results,
their calibrator was still used for the data reduction.

##  Appendix B Coherent time used in the data reduction

In this section, we display the number of frames that we coherently add to
optimize the quality of the data in Table 5.

Table 5: Number of frames coherently added for V2 and CP for each observation.

Target’s name | DATE-OBS | V2 | CP
---|---|---|---
| (YYYY-MM-DD) | (n coadd) | (n coadd)
Cyg OB2-5 A | 2018-06-10 | 8 | 11
… | 2019-06-23 | 8 | 9
Cyg OB2-9 | 2018-09-27 | 11 | 3
Cyg OB2-10 | 2018-06-12 | 15 | 11
HD 17505 | 2018-09-26 | 9 | 3
HD 19820 | 2018-09-26 | 9 | 3
HD 24431 | 2018-09-24 | 3 | 3
HD 28446 | 2018-02-08 | 12 | 9
… | 2018-09-24 | 3 | 3
HD 30614 | 2018-09-25 | 11 | 3
HD 34078 | 2017-12-13 | 10 | 10
… | 2018-09-27 | 11 | 3
HD 36861 | 2018-02-07 | 8 | 5
… | 2018-09-26 | 9 | 3
HD 45314 | 2018-09-25 | 11 | 3
HD 47129 | 2018-09-24 | 3 | 3
HD 47432 | 2018-09-27 | 11 | 3
HD 47839 | 2018-09-25 | 11 | 3
HD 167971 | 2019-06-24 | 9 | 5
HD 188001 | 2018-09-26 | 9 | 3
HD 193322 | 2018-06-12 | 15 | 10
… | 2019-06-24 | 9 | 5
HD 195592 | 2018-06-11 | 15 | 15
HD 201345 | 2019-06-27 | 8 | 9
HD 202214 | 2019-06-24 | 10 | 15
HD 206183 | 2019-06-27 | 8 | 9
HD 206267 | 2019-06-26 | 8 | 15
HD 207198 | 2019-06-24 | 9 | 5
HD 209975 | 2018-06-09 | 15 | 10
HD 210809 | 2019-06-26 | 8 | 8
HD 210839 | 2019-06-23 | 8 | 11
HD 217086 | 2018-09-26 | 9 | 3
HD 228779 | 2019-06-26 | 8 | 9
HD 229196 | 2018-09-27 | 11 | 3
121212The first column gives the identifier of the system. The second column
gives the UT date the data have been taken. The third and fourth columns are
the number of frames coherently added for respectively V2 and CP.

In Figure 8, we show an example of S/N of V2 as a function of the number of
frames added coherently, for HD 210809, for the date 2019-06-26.

Figure 8: V2 S/N as a function of the number of frames added coherently, for
HD 210809, for the different baselines.

In Figure 9, we show an example of the error on the CP as a function of the
number of frames added coherently, for HD 210809, for the date 2019-06-26.

Figure 9: CP error as a function of the number of frames added coherently, for
HD 210809, for the triplets of telescopes.