# The First High-Contrast Images of Near High-Mass X-Ray Binaries with
Keck/NIRC2

M. Prasow-Émond Department of Earth Science and Engineering, Imperial College
London, Prince Consort Rd, London SW7 2BP, United Kingdom  Département de
Physique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, QC
H3C 3J7, Canada  Trottier Institute for Research on Exoplanets, Université de
Montréal, Département de Physique, C.P. 6128 Succ. Centre-ville, Montréal, QC
H3C 3J7, Canada  J. Hlavacek-Larrondo Département de Physique, Université de
Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, QC H3C 3J7, Canada  K.
Fogarty Division of Physics, Math, and Astronomy, California Institute of
Technology, Pasadena, CA, USA  NASA Ames Research Center, Moffett Field, CA
94035, USA  É. Artigau Trottier Institute for Research on Exoplanets,
Université de Montréal, Département de Physique, C.P. 6128 Succ. Centre-ville,
Montréal, QC H3C 3J7, Canada  D. Mawet Division of Physics, Math, and
Astronomy, California Institute of Technology, Pasadena, CA, USA  Jet
Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109,
USA  P. Gandhi Department of Physics and Astronomy, University of Southampton,
Highfield, Southampton, SO17 1BJ, United Kingdom  J. F. Steiner Harvard-
Smithsonian Center for Astrophysics, Cambridge, MA 02138, United States  J.
Rameau Trottier Institute for Research on Exoplanets, Université de Montréal,
Département de Physique, C.P. 6128 Succ. Centre-ville, Montréal, QC H3C 3J7,
Canada  Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France  D.
Lafrenière Département de Physique, Université de Montréal, C.P. 6128, Succ.
Centre-Ville, Montréal, QC H3C 3J7, Canada  Trottier Institute for Research on
Exoplanets, Université de Montréal, Département de Physique, C.P. 6128 Succ.
Centre-ville, Montréal, QC H3C 3J7, Canada  A. Fabian Institute of Astronomy,
Cambridge University, Madingley Road, Cambridge CB3 0HA, United Kingdom  D. J.
Walton Centre for Astrophysics Research, University of Hertfordshire, College
Lane, Hatfield AL10 9AB, United Kingdom  R. Doyon Département de Physique,
Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, QC H3C 3J7,
Canada  Trottier Institute for Research on Exoplanets, Université de Montréal,
Département de Physique, C.P. 6128 Succ. Centre-ville, Montréal, QC H3C 3J7,
Canada  B. B. Ren Division of Physics, Math, and Astronomy, California
Institute of Technology, Pasadena, CA, USA

###### Abstract

Although the study of X-ray binaries has led to major breakthroughs in high-
energy astrophysics, their circumbinary environment at scales of
$\sim$100–10,000 astronomical units has not been thoroughly investigated. In
this paper, we undertake a novel and exploratory study by employing direct and
high-contrast imaging techniques on a sample of X-ray binaries, using adaptive
optics and the vortex coronagraph on Keck/NIRC2. High-contrast imaging opens
up the possibility to search for exoplanets, brown dwarfs, circumbinary
companion stars, and protoplanetary disks in these extreme systems. Here, we
present the first near-infrared high-contrast images of 13 high-mass X-ray
binaries located within $\sim$2–3 kpc. The key results of this campaign
involve the discovery of several candidate circumbinary companions ranging
from sub-stellar (brown dwarf) to stellar masses. By conducting an analysis
based on galactic population models, we discriminate sources that are likely
background/foreground stars and isolate those that have a high probability
($\gtrsim 60-99\%$) of being gravitationally bound to the X-ray binary. This
publication seeks to establish a preliminary catalog for future analyses of
proper motion and subsequent observations. With our preliminary results, we
calculate the first estimate of the companion frequency and the multiplicity
frequency for X-ray binaries: $\approx$0.6 and 1.8 $\pm$ 0.9 respectively,
considering only the sources that are most likely bound to the X-ray binary.
In addition to extending our comprehension of how brown dwarfs and stars can
form and survive in such extreme systems, our study opens a new window to our
understanding of the formation of X-ray binaries.

stars: abundances — infrared: planetary systems — binaries: general

††journal: ApJ

##  1 Introduction

X-ray binaries are semidetached binary systems in which a compact object
(white dwarf; WD, neutron star; NS, or stellar-mass black hole; BH) accretes
material from a donor star. These systems undergo several extreme physical
phenomena, such as processes acting predominantly in soft X-rays (e.g.,
Khargharia et al. 2010; Tetarenko et al. 2021), and detectable X-ray
pulsations (e.g., Lutovinov et al. 2005).

The variations in physical processes among different X-ray binaries are
directly linked to the mass of the donor star. Over 90% of these systems can
be classified into two distinct categories: high-mass X-ray binaries (HMXB;
$M_{\mathrm{donor}}\gtrsim$ 8 $M_{\odot}$) and low-mass X-ray binaries (LMXB;
$M_{\mathrm{donor}}\lesssim$ 1,5 $M_{\odot}$; e.g., Tauris & van den Heuvel
2006). LMXBs are relatively old systems ($>10^{9}$ yr) harboring a K-M
spectral type donor star, where the process of mass transfer is believed to be
triggered by Roche-lobe overflow (RLO; e.g., Savonije 1978). RLO is triggered
either by stellar evolution or by angular momentum loss (e.g., Paczyński 1967;
Verbunt & Zwaan 1981; Strohmayer 2002; Justham et al. 2006; Chen &
Podsiadlowski 2016; Seto 2018; Van et al. 2019). The transferred mass then
agglomerates to form an accretion disk around the compact object, giving rise
to transient accretion and X-ray emission (e.g., Charles & Coe 2006).

As for HMXBs, they are generally thought to be younger systems ($\lesssim
10^{7}$ yr) harboring a massive O-B spectral type donor star. The transferred
and accreted matter is thought to predominantly come from the capture of a
fraction of the stellar winds ejected from the donor star (e.g., Mohamed &
Podsiadlowski 2007; Abate et al. 2013; El Mellah et al. 2019). There are two
sub-categories of HMXBs relevant to this work. Firstly, we emphasize Be/X-ray
binaries (BeXRB), wherein the donor star is a fast-rotating Be star. In these
systems, the X-ray emission is mainly triggered by the compact object passing
through a diffuse and gaseous circumstellar disk surrounding the Be star
(known as a decretion disk; e.g., Okazaki et al. 2002; Martin et al. 2011;
Rímulo et al. 2018; Kravtsov et al. 2020). Secondly, we highlight supergiant
fast X-ray transients (SFXT; Negueruela et al. 2006), characterized by the
presence of a supergiant donor star, and by fast transient X-ray flaring
activity within the system (likely induced by a NS; e.g., Sidoli 2013; Ducci
et al. 2019).

X-ray binaries are important touchstone objects for high-energy phenomena in
astrophysics. They have been widely used to study several high-energy
astronomical phenomena, including accretion physics (e.g., Done et al. 2007;
Kara et al. 2019) and outflow/jet processes (e.g., Markoff et al. 2001; Fender
et al. 2004; Mooley et al. 2018). However, the immediate surroundings of X-ray
binaries, at the scale of $\sim$100-10,000 astronomical units (hereafter au),
have been poorly studied. This paper undertakes a pioneering exploration of
the circumstellar environments of X-ray binaries through the application of
adaptive optics (AO) and direct/high-contrast imaging techniques. The goal is
to probe a variety of phenomena ranging from protoplanetary disks to debris
disks and fallback disks, and particularly to search for wide-orbiting
circumbinary companions (CBCs) – be they exoplanets, brown dwarfs, or stars.

Considering the discovery of planetary-mass CBCs orbiting both binary systems
(e.g., Bakos et al. 2007; Desidera & Barbieri 2007; Eriksson et al. 2020) and
compact objects (WD or pulsars; e.g., Wolszczan & Frail 1992; Sigurdsson et
al. 2003; Spiewak et al. 2018; Vanderburg et al. 2020; Blackman et al. 2021),
it is not unfounded to expect CBCs orbiting X-ray binaries. A recent study
argued that X-ray binaries could host planetary systems in close orbits
detectable via X-ray eclipses (Imara & Di Stefano, 2018). In this paper, we
explore wider orbits ($\sim$100–10,000 au), as the increased number of
interactions within the system could lead to the ejection of potential CBCs
from the direct environment of the X-ray binary (e.g., Bonavita et al. 2016).

In Prasow-Émond et al. (2022), we presented the first set of observations from
a pilot study aiming to survey all X-ray binaries amenable for direct imaging
within $\sim$3 kpc. We first targeted a $\gamma$ Cassiopeiae-like X-ray binary
harboring a Be donor star, RX J1744.7$-$2713, for which we had observations
from two different bands and two epochs. We unveiled the presence of three
potential CBCs within this system, exhibiting a strong likelihood of being
stellar-mass CBCs. Here, we present the first $L^{\prime}$-band high-contrast
images of 13 other systems and conduct a preliminary statistical analysis
derived from the results of the first epochs of observations.

The paper is organized as follows: Section 2 presents the sample and how it
was constructed. Section 3 presents the near-infrared observations, and the
data reduction and processing. Section 5 presents the first high-contrast
images of the observed X-ray binaries. In Section 6, we analyze the images and
explore the nature of the detection. Finally, in Section 7, we discuss our
results and their implications.

##  2 The Sample

Despite the ongoing active search for new X-ray binaries both within and
beyond our Galaxy (e.g., Gandhi et al. 2022), their presence remains
relatively scarce. Our Galaxy hosts $\sim$300 identified X-ray binaries known
to date (Liu et al., 2006, 2007). We drew upon this list of X-ray binaries as
our initial dataset; however, not all of these systems are suitable for direct
imaging with Keck/NIRC2. In order to build a sample of X-ray binaries that
would yield optimal statistical constraints and mitigate potential biases, we
used four selection criteria:

  1. 1.

Distance. The system must be close enough to resolve the direct environment at
$\sim 100-10,000$ au scales. We chose a distance limit of $\sim$3 kpc within
our Galaxy, which enables the detection of structures and objects located
within a couple of thousands of au from the X-ray binary. The outer limit
(10,000 au) corresponds to the approximate limit of the Keck/NIRC2 field of
view (foV).

  2. 2.

Brightness and Adaptive optics. The donor star must be bright enough ($I<9-10$
mag) for the AO loop to be closed.

  3. 3.

Age. We targeted young ($\lesssim$ 100 Myr) X-ray binaries to favor the
detection of sub-stellar CBCs, considering the steep decline in planet
brightness with time (e.g., Burrows et al. 2001). This limited us to bright
LMXBs, and HMXBs with a massive O/B donor star.

  4. 4.

Visibility. We selected X-ray binaries visible from the W. M. Keck Observatory
at the time of our observations (Keck Observatory Semesters 2017B and 2020A).

Applying these criteria narrowed down the initial list from $\sim$300 X-ray
binaries to 19, out of which 14 were observed between 2017 and 2020 using
Keck/NIRC2 (see Section 3.1 for more details). Our sample includes both HMXBs
and LMXBs (e.g., MAXI J1820+070, V404 Cyg, 1A0620-00); however, we have only
observed HMXBs to date due to observational constraints. Note that X-ray
binary surveys are far from complete, as X-ray binaries can be undetectable in
quiescence (e.g., Bird et al. 2007; Belczynski & Ziolkowski 2009). New X-ray
binaries have also been discovered since we did our sampling (Avakyan et al.,
2023; Neumann et al., 2023). Nonetheless, we assume that our sample is as
complete as possible and that our results accurately represent the known
population of X-ray binaries.

Figure 1 displays the position of the 14 observed targets onto the sky (Aitoff
projection). It also indicates the distance from the observer (in kpc) and, if
known, the nature of the system’s compact object. In Section 4, we present a
brief literature review for each of the observed X-ray binaries. Table 1
summarizes the known relevant physical properties of the systems, namely the
X-ray binary type, X-ray emission class, donor star spectral type and compact
object type. Additional relevant physical properties can be found in the
Appendix (see Table 5).

Figure 1: Position of the 14 observed X-ray binaries on the sky with equatorial coordinates and Aitoff projection, color coded with distance from the observer in kpc. The nature of the compact object is illustrated with different markers: squares for white dwarfs, crosses for neutron stars, asterisks for black holes and circles for cases where the nature is either unavailable or uncertain. The red dotted line shows the approximate coordinates of the galactic plane. Table 1: Information on the binary nature for the 14 observed X-ray binaries. The columns are: 1. Name of the target; 2. Sub-class/type of the X-ray binary, as found in Bird et al. (2016); 3. Class of X-ray emission, as found in Krimm et al. (2013); 4. The spectral type of the donor star and 5. the reference; 6. The nature of the compact object and 7. the reference. †Indicates an uncertain nature. Reference code: (1) Sarty et al. (2011), (2) Lopes de Oliveira et al. (2006), (3) Chaty et al. (2008), (4) Torrejón et al. (2010), (5) Sguera et al. (2007), (6) Moffat et al. (1973), (7) Raguzova & Popov (2005), (8) Postnov et al. (2017), (9) Walter & Zurita Heras (2007), (10) Simon et al. (2019), (11) Negueruela & Reig (2001), (12) Torrejón et al. (2004), (13) Sota et al. (2014), (14) Reynolds et al. (1999), (15) Pellizza et al. (2006), (16) Giménez-García et al. (2016), (17) Bikmaev et al. (2017), (18) in’t Zand (2005), (19) Motch et al. (1997), (20) Sota et al. (2011), (21) Bolton (1972a), (22) Lyubimkov et al. (1997), (23) White et al. (1977), (24) Popper (1950), (25) Liu et al. (2006), (26) Jaschek & Jaschek (1963), (27) Popov et al. (2018), (28) Hiltner et al. (1972). Target | Type | Class | Donor star | Ref. | Compact Object | Ref.
---|---|---|---|---|---|---
RX J1744.7$-$2713 | HMXB | N/A | B0.5 V-IIIe | (1) | WD† | (2)
BeXRB
$\gamma$ Cas analog
IGR J18483$-$0311 | HMXB | Outburst | B0.5-BI/B0-1 Iab | (3, 4) | NS | (5)
SFXT
XP
$\gamma$ Cas | HMXB | Steady | B0.5 IVe | (6, 7) | WD† | (8)
BeXRB
SAX J1818.6$-$1703 | HMXB | Variable | B0.5 Iab | (4) | NS† | (9)
SFXT
1H2202+501 | HMXB | N/A | B3Ve | (10) | N/A |
BeXRB†
4U 2206+543 | HMXB | Variable | O9.5 V | (11) | NS | (12)
4U 1700$-$377 | sgHMXB | Variable | O6Iafpe | (13) | NS | (14)
IGR J17544$-$2619 | HMXB | Flaring | O9Ib/O9IV-V | (15, 16, 17) | NS | (18)
SFXT
RX J2030.5+4751 | HMXB | N/A | B0.5 III-Ve | (19) | N/A |
BeXRB
$\gamma$ Cas analog
Cyg X-1 | HMXB | Variable | O9.7Iabpvar | (20) | BH | (21)
Microquasar
X Per | HMXB | Variable | B0Ve | (22) | NS | (23)
BeXRB
XP
1H0556+286 | HMXB† | N/A | B5ne | (24) | WD or NS | (25)
RX J0648.1$-$4419 | HMXB | N/A | sdO5.5 | (26) | WD | (27)
XP
Vela X-1 | HMXB | Variable | B0.5 Ib | (28) | NS | (28)
XP

##  3 Observations and Data Reduction

###  3.1 Keck/NIRC2 Observations

On September 8, 2017, we observed four HMXBs from our survey sample using the
Keck/NIRC2 vortex coronagraph (Mawet et al., 2005; Serabyn et al., 2016) in
pupil-tracking mode in $L^{\prime}$-band ($\lambda$ = 3.776 $\mu$m,
$\Delta\lambda$ = 0.700 $\mu$m; PI: Mawet), and with the narrow camera (plate
scale of 9.971 $\pm$ 0.004 mas pixel-1; Service et al. 2016). On January 3,
2018, we observed three additional HMXBs using a similar setting. Due to the
successful and promising preliminary results of this initial campaign, we were
awarded three supplementary nights of observation on July 11, 12, and 13, 2020
(PI: Fogarty). On the first night, we observed one additional target and re-
observed two targets (RX J1744.7$-$2713 and $\gamma$ Cas) using a similar
setting. However, due to saturation, we had to downscale the frame size of
$\gamma$ Cas from 1024$\times$1024 pixel2 to 512$\times$512 pixel2. On July
12, 2020, we obtained data for three other HMXBs in $L^{\prime}$-band, in
addition to re-observing RX J1744.7$-$2713 in $K_{s}$-band ($\lambda$ = 2.146
$\mu$m, $\Delta\lambda$ = 0.311 $\mu$m). Finally, on July 13, 2020, we
obtained data for three other HMXBs, totaling observations for 14 out of the
19 X-ray binaries in the sample.

During the observations, we used the Quadrant Analysis of Coronagraphic Images
for Tip-tilt sensing (QACITS; Huby et al. 2017) to make tip-tilt adjustments
to maintain precise centering of the target on the vortex focal plane mask.
The observations were AO-assisted using the Shack-Hartmann wavefront sensor
(which performs wavefront sensing in $R$-band) in 2017, 2018 and the last
night of 2020. For the first two nights of our 2020 observations, we opted for
the Pyramid wavefront sensor (PyWFS) instead. It performs wavefront sensing in
$H$ (Wizinowich et al., 2000; Bond et al., 2018), which is more advantageous
for the redder targets in our sample.

A summary of the observing log is presented in Table 2.

Table 2: Keck/NIRC2 Observing Log. Acronyms are: wavefront sensor (WFS), Shack-Hartmann (SH), pyramid WFS (py), integration time ($t_{\mathrm{int}}$), number of frames ($N_{\mathrm{frames}}$), parallactic angle coverage (P. A. cov.). UT Date | Target | Filter | WFS |  $t_{\mathrm{int}}$ (s) | Coadds | $N_{\mathrm{frames}}$ | P. A. cov. (o)
---|---|---|---|---|---|---|---
2017 September 8 | RX J1744.7$-$2713 | $L^{\prime}$ | SH | 0.5 | 60 | 40 | 14.3
| Cygnus X-1 | $L^{\prime}$ | SH | 0.5 | 60 | 140 | 60.6
|  $\gamma$ Cassiopeiae | $L^{\prime}$ | SH | 0.18 | 150 | 130 | 61.2
| X Persei | $L^{\prime}$ | SH | 0.5 | 60 | 89 | 43.9
2018 January 3 | X Persei | $L^{\prime}$ | SH | 1 | 45 | 54 | 36.7
| 1H0556+286 | $L^{\prime}$ | SH | 1 | 45 | 50 | 48.6
| RX J0648.1$-$4419 | $L^{\prime}$ | SH | 1 | 45 | 17 | 6.5
| Vela X-1 | $L^{\prime}$ | SH | 1 | 45 | 60 | 26.0
2020 July 11 | RX J1744.7$-$2713 | $L^{\prime}$ | py | 0.5 | 60 | 120 | 38.3
| IGR J18483$-$0311 | $L^{\prime}$ | py | 0.4 | 60 | 125 | 42.6
|  $\gamma$ Cassiopeiae | $L^{\prime}$ | py | 0.0528 | 400 | 150 | 48.1
2020 July 12 | RX J1744.7$-$2713 | $K_{s}$ | py | 0.6 | 45 | 92 | 39.6
| SAX J1818.6$-$1703 | $L^{\prime}$ | py | 0.4 | 60 | 90 | 26.3
| 1H2202+501 | $L^{\prime}$ | py | 0.4 | 60 | 89 | 36.9
| 4U2206+543 | $L^{\prime}$ | py | 0.4 | 60 | 27 | 49.5
2020 July 13 | 4U1700$-$37 | $L^{\prime}$ | SH | 0.4 | 50 | 69 | 15.1
| IGR J17544$-$2619 | $L^{\prime}$ | SH | 0.4 | 50 | 94 | 36.5
| RX J2030.5+4751 | $L^{\prime}$ | SH | 0.4 | 60 | 132 | 53.9
| 4U2206+543 | $L^{\prime}$ | SH | 0.4 | 60 | 149 | 49.5

###  3.2 Data Reduction

Similarly to Prasow-Émond et al. (2022), we performed data reduction using the
Vortex Image Processing (VIP) and NIRC2 Preprocessing packages (Gomez Gonzalez
et al., 2017). To obtain a preprocessed data cube, we proceeded as follows:
(1) flat-fielding of the frames, (2) bad pixel masking using the dark frames,
(3) determination of the vortex center for each frame followed by cropping the
science cube around the mean center, (4) removal of sky contribution via a
Principal Component Analysis (PCA)-based technique, and (5) image registration
to align the quasi-static speckle pattern across frames.

After acquiring the preprocessed data cube, we applied a PCA-based Angular
Differential Imaging (ADI; Marois et al. 2006) algorithm to obtain high-
contrast images. Subsequently, we generated several images using two
algorithms in VIP (annular PCA and full-frame PCA) for a broad range of
principal components (from 1 to 50). This was done to ensure consistency in
the detection of sources within the images (i.e., that the source was detected
regardless of the number of principal components). We then listed sources with
a signal-to-noise ratio (SNR) greater than 5 (or with a signal exceeding
4$\sigma$) and determined the optimal number of principal components
($n_{\mathrm{comp}}$) that maximized the SNR for each source.

###  3.3 Source Magnitude Calculation

To calculate the apparent and absolute magnitudes of the detected sources, we
proceeded as follows: (1) we fit a 2D Gaussian profile to the Point Spread
Function (PSF) cube to obtain the Full Width at Half Maximum (FWHM) in
milliarcseconds (hereafter mas) and to recenter the PSF frames. (2) The PSF
cube was reduced into a single 2D PSF by computing the median of the frames.
(3) We normalized the PSF so that the flux within a radius of 1 FWHM equated
to 1. (4) Given a thermal artifact affecting the quality of the real PSF in
our 2020 observations (as discussed in Prasow-Émond et al. 2022), we generated
a normalized synthetic 2D PSF using the FWHM. (5) From the list of sources
with SNR $>$ 5, we generated a list of approximate coordinates using ds9. (6)
Using the preprocessed cube, the optimal number of principal components, and
the approximate coordinates, we fit the astrometric parameters ($\theta$, the
position angle in degrees and $\rho$, the relative separation from the X-ray
binary in pixels) and photometric parameters ($f_{1}$, the number of counts
within an aperture radius of 3 FWHM, i.e., the relative flux) using a Nelder-
Mead optimization algorithm from VIP. This fitting process, involving the
injection of synthetic sources with a negative flux at source location
(Lagrange et al., 2010), aimed to minimize $\chi^{2}$ residuals. (7) Once the
parameters were determined, the position angle in the images was converted
into the true position angle using the celestial north of NIRC2, which is
0°.262 ± 0°.018 (Service et al. 2016 and see Franson et al. 2022 for an
example and more details). (8) We converted the units of $\rho$ from pixel to
mas using the plate scale (see Section 3.1). (9) To derive the apparent
magnitude of the sources ($m_{\mathrm{cc}}$), we applied the following
equation:

$m_{\mathrm{cc}}=-2.5\log_{10}(f_{1}/f_{2})+m_{\mathrm{XRB}}$ (1)

where $f_{2}$ is the PSF flux within the same aperture as the cube (3 FWHM)
and $m_{\mathrm{XRB}}$ is the apparent magnitude of the X-ray binary (see
Section 3.3.2). (10) Using the known distance in parsec (see Section 3.3.1),
the apparent magnitude of the candidate CBCs ($m_{\mathrm{cc}}$) was converted
to absolute magnitude ($M_{\mathrm{cc}}$) via the distance modulus equation.
(11) Finally, to estimate the mass of the sources, we compared the absolute
magnitude ($M_{\mathrm{cc}}$) with evolutionary models from MESA Isochrones &
Stellar Tracks (MIST; Paxton et al. 2011, 2013, 2018, 2015; Dotter 2016;
Faherty et al. 2016; Choi et al. 2016) at the system’s age (see Section
3.3.3).

Due to the poor quality of the PSF in our 2020 observations, we used the
synthetic 2D PSF for fitting processes related to these observations. However,
we kept the original PSF for our 2017 and 2018 observations. We conducted
tests using both synthetic and real PSFs on the 2017 and 2018 data, yielding
consistent results. Consequently, the use of a synthetic PSF does not affect
significantly the derived parameters.

The upcoming sections detail the acquisition of parameters used in the
magnitude calculations.

####  3.3.1 Determining the Distance from the Observer

The distance from the observer is presented in the second column of Table 5 in
the Appendix. Distances for 1H2202+501, 4U 2206+543, 4U 1700$-$377, IGR
J17544$-$2619, Cyg X-1, X Per and Vela X-1 were obtained from Zhao et al.
(2023), which uses parallax measurements to infer distances either using an
inversion or Bayesian approach for a catalog of X-ray binaries. For the other
X-ray binaries, the distance was estimated through a photogeometric
calculation (Bailer-Jones et al., 2021). It was calculated using the parallax
measurement and its uncertainty (geometric), as well as the $G$ magnitude and
the BP-RP color (photometric) from the Gaia Data Release 3 (DR3; De Angeli et
al. 2023; Montegriffo et al. 2023). Table 3 presents the Gaia DR3 ID for each
target. In cases where an object’s distance was sourced from the literature,
the respective reference is cited in the literature review of Section 2. As
previously mentioned, this study targets X-ray binaries within $\sim$2–3 kpc
accessible with Keck/NIRC2.

Table 3: Gaia DR3 ID for each target. Target | Gaia DR3 ID
---|---
RX J1744.7$-$2713 | 4060784345959549184
IGR J18483$-$0311 | 4258428501693172736
$\gamma$ Cas | 426558460884582016
SAX J1818.6$-$1703 | 4097365235226829312
1H2202+501 | 1979911002134040960
4U 2206+543 | 2005653524280214400
4U 1700$-$377 | 5976382915813535232
IGR J17544$-$2619 | 4063908810076415872
RX J2030.5+4751 | 2083644392294059520
Cyg X-1 | 2059383668236814720
X Per | 168450545792009600
1H0556+286 | 3431561565357225088
RX J0648.1$-$4419 | 5562023884304070000
Vela X-1 | 5620657678322625920

####  3.3.2 Determining the Apparent Magnitude of the Central X-Ray Binary

Observing X-ray binaries in the $L^{\prime}$-band of Keck/NIRC2 is not
standard practice, making the direct determination of the true apparent
magnitudes of the central X-ray binaries ($m_{\mathrm{XRB}}$) unfeasible.
Nonetheless, we leveraged the $W1$ filter from the Wide-field Infrared Survey
Explorer (WISE), which has a central wavelength similar to Keck/NIRC2
$L^{\prime}$-band ($\lambda$ = 3.353 $\mu$m). Using the WISE Source Catalog
(Wright et al., 2010), we approximated $m_{\mathrm{XRB}}$ for all X-ray
binaries. These values are presented in the fifth column of Table 5 in the
Appendix. To account for the differences between the two filters, we
considered an uncertainty of 0.5 mag on $m_{\mathrm{XRB}}$.

####  3.3.3 Determining the Age of the System

Most X-ray binaries in our sample lack age estimates in the literature, except
for RX J1744.7$-$2713 (up to $\sim$60 Myr; Coleiro & Chaty 2013), 4U
1700$-$377 (up to $\sim$80 Myr; Coleiro & Chaty 2013), $\gamma$ Cas (8.0 $\pm$
0.4 Myr; Zorec et al. 2005), Cyg X-1 ($<4$ Myr; Miller-Jones et al. 2021) and
X Per ($\sim$5 Myr; Lyubimkov et al. 1997). For the remaining X-ray binaries,
we established an upper limit using basic evolutionary models and the spectral
type of the donor star (see Table 1). We found the maximum age that the donor
star can reach before exploding in supernovae. However, this approach provides
only an approximate estimation of the age. These values are presented in the
sixth column of Table 5 in the Appendix.

####  3.3.4 Determining the Errors

Errors in the fit parameters ($\theta$, $\rho$, and $f_{1}$) were estimated
using an injection/recovery approach (see Prasow-Émond et al. 2022). This
approach relies on injecting synthetic sources with known parameters into the
images. Subsequently, the same optimization method was applied (see Section
3.3), and the error was determined as the difference between estimated and
known parameters. This method was employed across a range of parameter values
to ensure consistency; it was observed that errors were more pronounced for
smaller offset values (i.e., those closer to the central X-ray binary).
Additional sources of uncertainty were taken into consideration in cases where
the value of a parameter is expected to remain consistent between two sets of
observations, specifically astrometric parameters in two different bands. The
dominant source of uncertainty was defined as the total uncertainty.

##  4 Key properties of the sample

###  4.1 $\gamma$ Cassiopeiae

$\gamma$ Cassiopeiae – also known as 2S 0053+604 (hereafter $\gamma$ Cas) –
harbors a well-studied optical component classified as a Be star (Moffat et
al., 1973). Its X-ray luminosity ($\sim$1032–1033 erg s-1; Raguzova & Popov
2005) is higher than the typical luminosity for O/B stars ($\sim$1030 erg
s-1), but too low to be a Be/NS system ($\sim$1034 erg s-1 in quiescence;
Shrader et al. 2015). The nature of the system can be explained by two
hypotheses: (1) the system is a HMXB, involving accretion onto a WD or a fast-
spinning NS (Postnov et al., 2017); or (2) the excess of X-ray emission stems
from physical processes in the high atmosphere of $\gamma$ Cas (Kubo et al.,
1998; Robinson & Smith, 2000). Though $\gamma$ Cas is not confirmed as being a
HMXB, its resemblance to other sources, referred to as $\gamma$ Cas analogs,
warranted its inclusion in our sample. Located at a distance of 0.19 $\pm$
0.02 kpc, it is the nearest system in our sample. Its proximity and proper
motions (25.7 $\pm$ 0.5 mas/yr in RA, $-$3.9 $\pm$ 0.4 mas/yr in Dec; Perryman
et al. 1997) allowed us to conduct a proper motion analysis within the
interval between our two observation sets (see Section 6.2).

###  4.2 RX J1744.7-2713

RX J1744.7-2713 is classified as a BeXRB (Israel et al., 1997) and is composed
of a B0.5 III-Ve star (Motch et al., 1997; Steele et al., 1999; Lopes de
Oliveira et al., 2006) and a WD. However, the origin of X-ray emission is
still uncertain and debated in the literature (Lopes de Oliveira et al.,
2006). It is also known as a $\gamma$ Cas analog, due to the similarities in
their X-ray properties (e.g., Shrader et al. 2015). The first high-contrast
images of this HMXB were presented in Prasow-Émond et al. (2022), in which
more comprehensive information on the system can be found.

###  4.3 4U 1700$-$377

4U 1700$-$377, discovered with the Uhuru X-ray satellite, is classified as a
HMXB (Jones et al., 1973). The system contains a supergiant donor star of
spectral type O6Iafpe (Sota et al., 2014) and a magnetized NS (e.g., Reynolds
et al. 1999; Bala et al. 2020; van der Meij et al. 2021) exhibiting strong
flaring activity (e.g., Kuulkers et al. 2007). This HMXB was observed with,
e.g., XMM-Newton (van der Meer et al., 2005; Giménez-García et al., 2015),
Chandra (Boroson et al., 2003; Martínez-Chicharro et al., 2021), Hubble Space
Telescope (HST; Hainich et al. 2020), Fiber-fed Extended Range Optical
Spectrograph (FEROS; Hainich et al. 2020), IUE (Dupree et al., 1978), EXOSAT
(Haberl et al., 1989), BATSE (Rubin et al., 1996), and BeppoSAX (Reynolds et
al., 1999). NGC 6231, located within the OB association Sco OB1, has been
recently confirmed as the parent cluster of 4U 1700$-$377 (van der Meij et
al., 2021). Moreover, Coleiro & Chaty (2013) inferred an estimated age of
$\sim$80 Myr for the system, a value we have regarded as an upper limit as in
Prasow-Émond et al. (2022). Its X-ray luminosity can reach up to $\sim$7
$\times$ 1036 erg s-1 (Laurent et al., 1992).

###  4.4 4U 2206+543

Although the nature of its donor star remains uncertain (first believed to be
of spectral type Be; Steiner et al. 1984, then O9.5V; Negueruela & Reig 2001),
4U 2206+543 is a well-studied HMXB harboring a magnetar NS (e.g, Torrejón et
al. 2004; Blay et al. 2005; Reig et al. 2009; Ikhsanov & Beskrovnaya 2010;
Torrejón et al. 2018). First discovered with Uhuru (Giacconi et al., 1972),
the system was subsequently observed with, e.g., EXOSAT (Saraswat & Apparao,
1992), RXTE (e.g., Corbet & Peele 2001), IBIS/ISGRI on INTEGRAL (e.g., Bird et
al. 2004), BeppoSAX (e.g., Masetti et al. 2004), $VLA$ (Blay et al., 2005),
Swift (Corbet et al., 2007) and Suzaku (Finger et al., 2010). Its X-ray
luminosity ranges from $\sim$1033 erg s-1 in quiescence up to $\sim$1035–1036
erg s-1 during more active phases (Ribó et al., 2006).

###  4.5 RX J2030.5+4751

RX J2030.5+4751, also known as BD+47 3129 and SAO 49725, was first discovered
with ROSAT (Motch et al., 1997). It is identified as a BeXRB and $\gamma$ Cas
analog. It has a B0.5 III-Ve spectral type donor star and a maximum X-ray
luminosity of $\sim$1033 erg s-1 (Liu et al., 2006; Raguzova, 2007). XMM-
Newton/EPIC observations have revealed that RX J2030.5+4751 has a hard X-ray
spectrum, suggesting the presence of a dense, large, and stable circumstellar
environment surrounding the system (Lopes de Oliveira et al., 2006). On July
20, 2016, RX J2030.5+4751 underwent type I (i.e., smaller and repetitive)
bursts, reaching its maximum luminosity (progressive weakening since; Steele
2016a, b, c). Regarding the long-term variability, Servillat et al. (2012)
reported a significant non-periodic variability of approximately one magnitude
in the light curve of RX J2030.5+4751 over $\sim$100 years, likely caused by
changes in the properties of the decretion disk.

###  4.6 1H2202+501

1H2202+501 is a poorly-studied HMXB, albeit appearing in some surveys (e.g.,
Wood et al. 1984; Hanson et al. 1996; Liu et al. 2000). It consists of a Be
star of spectral type B3Ve (Simon et al., 2019), and the nature of the compact
object remains uncertain. Its X-ray luminosity is estimated to be $\sim$9
$\times$ 1032 erg s-1 (Chevalier & Ilovaisky, 1998).

###  4.7 SAX J1818.6$-$1703

SAX J1818.6$-$1703 was discovered with BeppoSAX while undergoing a strong
outburst (in ’t Zand et al., 1998). Subsequent observations were carried out
using IBIS/ISGRI onboard INTEGRAL (e.g., Grebenev & Sunyaev 2005; Sguera et
al. 2005; Zurita Heras & Chaty 2009; Sidoli et al. 2016), RossiXTE (Sguera et
al., 2005; Smith et al., 2012) and Swift (e.g., Bird et al. 2009; Sidoli et
al. 2009). The system has similar properties to other SFXT (e.g., Sguera et
al. 2005; Negueruela & Smith 2006; Sidoli et al. 2009; Bozzo et al. 2012), and
its compact object is likely a NS (e.g., Walter & Zurita Heras 2007; Boon et
al. 2016). The donor star of the system, confirmed by Chandra (in’t Zand et
al., 2006), is classified as a supergiant star of spectral type B0.5 Iab
(Torrejón et al., 2010). Also observed using XMM-Newton, SAX J1818.6$-$1703
has a quiescent X-ray luminosity that can drop to values below $\sim$1032 erg
s-1 (as determined by not being detected in Bozzo et al. 2012) and can reach
up to $\sim$8 $\times$ 1035 erg s-1 (Torrejón et al., 2010).

###  4.8 IGR J18483$-$0311

Discovered by IBIS/ISGRI onboard INTEGRAL by Chernyakova et al. (2003), IGR
J18483$-$0311 is a well-studied SFXT (Rahoui & Chaty, 2008) composed of an
X-ray pulsar (Sguera et al., 2007) and a supergiant donor star of spectral
type B0.5 Ia (Chaty et al., 2008) or B0.5-B1 Iab (Torrejón et al., 2010). The
system undergoes multiple short and long outbursts (e.g., Sguera et al. 2007,
2010; Ducci et al. 2013; Sguera et al. 2015), resulting in its X-ray
luminosity ranging from $\sim$1033–1034 erg s-1 in quiescence (Romano et al.,
2010; Sguera et al., 2015) up to $\sim$1036 erg s-1 during its strongest
flares (Torrejón et al., 2010). By considering evolutionary scenarios and
exploring the relationship between spin and orbital periods, Liu et al. (2011)
suggested that the compact object in IGR J18483$-$0311 may originate from an
O-type emission line star rather than an average main-sequence star.

###  4.9 IGR J17544$-$2619

IGR J17544$-$2619 was first discovered near the Galactic Center while
undergoing short (a few hours) outbursts using IBIS/ISGRI onboard INTEGRAL
(Sunyaev et al., 2003; Grebenev et al., 2003, 2004). The system was
subsequently observed with, e.g., XMM-Newton (González-Riestra et al., 2004;
Drave et al., 2014), Chandra (in’t Zand, 2005), EMMI/SOFI/NTT (Pellizza et
al., 2006), Suzaku (Rampy et al., 2009), RXTE (Drave et al., 2012), Swift
(e.g., Romano et al. 2015), and NuSTAR (e.g., Bhalerao et al. 2015). It is
identified as a SFXT (Negueruela et al., 2006), and the optical/NIR
counterpart is a massive star of spectral type O9Ib (25–28 $M_{\odot}$;
Pellizza et al. 2006; Giménez-García et al. 2016) or O9IV-V (23 $M_{\odot}$;
Bikmaev et al. 2017). The compact object is a NS (in’t Zand, 2005), as
inferred by the presence of a cyclotron line at 17 keV and the magnetic field
strength ($\sim 1.5\times 10^{12}$ G, typical for NS in X-ray binaries;
Bhalerao et al. 2015). The change in X-ray luminosity between quiescence and
outburst is significant, ranging from $L_{X}\sim 10^{32}-10^{34}$ erg s-1
(e.g., Bozzo et al. 2016) during quiescence to a maximum of $L_{X}\sim 3\times
10^{38}$ erg s-1 during outburst (Romano et al. 2015).

###  4.10 Cyg X-1

Cygnus X-1 (hereafter Cyg X-1), first discovered in 1964, is one of the most
well-studied astronomical objects (e.g., Fabian et al. 1989; Esin et al. 1998;
Orosz et al. 2011; Tomsick et al. 2014; Parker et al. 2015; Sell et al. 2015;
Walton et al. 2016; Mastroserio et al. 2019). The system’s compact object,
with a mass of 21.2 $\pm$ 2.2 $M_{\odot}$ (Miller-Jones et al., 2021), was the
first observed candidate black hole (Murdin & Webster, 1971; Bolton, 1972a),
leading to significant breakthroughs in the astronomical scientific community.
Cyg X-1 is classified as a HMXB (Bolton, 1972b) and the donor star is
characterized as a massive star of spectral type O9.7Iabpvar (Sota et al.,
2011). The system is fairly young, with an estimated age of 5 $\pm$ 1.5 Myr in
Mirabel & Rodrigues (2003) and $<4$ Myr in Miller-Jones et al. (2021). Cyg X-1
is located at 2.22${}_{-0.18}^{+0.17}$ kpc; its distance from the observer was
precisely estimated in Miller-Jones et al. (2021) based on radio parallax
measurements and validated with Gaia DR3. The microquasar undergoes variable
X-ray emission (Krimm et al., 2013), with a maximum X-ray luminosity of $\sim$
3 $\times$ 1037 erg s-1 (Di Salvo et al., 2001).

###  4.11 Vela X-1

Vela X-1 is a pulsing HMXB discovered with the Uhuru X-ray satellite (Giacconi
et al. 1971) and was observed through multiple surveys and with several
instruments (e.g., Charles et al. 1978; La Barbera et al. 2003; Fürst et al.
2014; Martínez-Núñez et al. 2014). The system is highly variable and undergoes
transient outbursts and X-ray eclipses (e.g., van der Klis & Bonnet-Bidaud
1984). Its X-ray luminosity can be as high as 4 $\times$ 1036 erg s-1
(Kreykenbohm et al. 2008). It is composed of a B0.5 1b donor star (Hiltner et
al. 1972) and of a magnetized NS (e.g., Hiltner et al. 1972; van Kerkwijk et
al. 1995; Kreykenbohm et al. 2002; Diez et al. 2022). A complete review of
this object can be found in Kretschmar et al. (2021).

###  4.12 RX J0648.1$-$4419

RX J0648.1$-$4419 is a unique X-ray pulsating system, as it is the only HMXB
known to date containing a hot sub-dwarf donor star of spectral type O
(sdO5.5; Jaschek & Jaschek 1963; Mereghetti et al. 2009). The compact object
has a mass of 1.28 $\pm$ 0.05 $M_{\odot}$ (Mereghetti et al., 2009) and was
initially believed to be a NS (e.g., Israel et al. 1997; Mereghetti et al.
2016). Popov et al. (2018) suggested that it was likely a young ($\sim$2 Myr)
contracting WD. Over the course of almost 30 years of observations (e.g.,
Mereghetti et al. 2011; La Palombara et al. 2015; Mereghetti et al. 2021), the
X-ray luminosity remained stable, maintaining a value of $\sim$1032 erg s-1.

###  4.13 1H0556+286

1H0556+286 contains a Be star of spectral type B5ne (Popper, 1950). It is a
poorly-studied system; while it is generally thought to be a HMXB (e.g.,
Helfand & Moran 2001; Liu et al. 2006), Torrejón & Orr (2001) presented
BeppoSAX observations in which no X-ray emission was detected. As per these
results, neither the Be/NS nor Be/WD scenarios appear probable, hence the
nature of the system remains unclear.

###  4.14 X Per

X Persei (hereafter X Per), also known as 4U 0352+309, was discovered in 1972
with the Copernicus Observatory (Hawkins et al., 1975; Mason et al., 1976).
The system was subsequently observed with, e.g., the High Energy Astrophysical
Observatory (HEAO 2/Einstein; Weisskopf et al. 1984), RXTE (e.g., Delgado-
Martí et al. 2001; Coburn et al. 2002), INTEGRAL (e.g., Lutovinov et al.
2012), XMM-Newton (e.g., La Palombara & Mereghetti 2007), and Chandra (e.g.,
Valencic & Smith 2013). The system is identified as a HMXB/BeXRB, composed of
a magnetized NS as the compact object (e.g., White et al. 1977; Coburn et al.
2001; Doroshenko et al. 2012; Maitra et al. 2017; Yatabe et al. 2018) and a Be
star of spectral type B0Ve as the donor star (Lyubimkov et al., 1997). In
quiescence, its X-ray luminosity is $\sim$ 1034 erg s-1 (e.g., Coburn et al.
2001). When undergoing strong outburst activity, its X-ray luminosity can
reach up to $\sim$ 2 $\times$ 1035 erg s-1 (Lutovinov et al., 2012). Similarly
to Cyg X-1, the system is also relatively young, with an estimated age of
$\sim$5 Myr (Lyubimkov et al., 1997). Objects with similar properties are
often referred to as X Per analogs.

##  5 High-Contrast Images

###  5.1 $\gamma$ Cas

As discussed in Section 4.1, observations of $\gamma$ Cas in the
$L^{\prime}$-band were initially made on September 08, 2017, and subsequently
revisited almost three years later on July 11, 2020. Figure 2 presents the
$L^{\prime}$-band high-contrast images of $\gamma$ Cas for both epochs. A
bright source, labeled B, was detected with a SNR $\gg$ 5\. A much fainter
source, labeled C, was also detected, with a SNR $\sim$ 3\. In Section 6.2, we
undertake a proper motion analysis to determine whether these sources are more
likely to be bound CBCs or background stars.

Figure 2: Keck/NIRC2 $L^{\prime}$-band high-contrast images of $\gamma$ Cas
acquired on 2017 Sept 08 (up) and 2020 July 11 (bottom), treated and reduced
using a PCA annular ADI algorithm (using VIP; Gomez Gonzalez et al. 2017). The
sources detected with SNR $>$ 3 are labeled B and C. The white X symbol
denotes the approximate position of $\gamma$ Cas, masked by the coronagraph.
The bottom-left insets show zoomed-in high-contrast images with a focus on an
annular region (obtained using the PCA annulus algorithm in VIP), highlighting
the presence of the fainter source (labeled as C).

###  5.2 Other X-ray Binaries

Figure 3 presents a panel of $L^{\prime}$-band high-contrast images of all the
other X-ray binaries, in order: 4U 1700$-$377, 4U 2206+543, RX J2030.5+4751,
1H2202+501, SAX J1818.6$-$1703, IGR J18483$-$0311, IGR J17544$-$2619, Cyg X-1,
Vela X-1, RX J0648.1$-$4419, 1H0556+286, and X Per. The $L^{\prime}$\- and
$Ks$-band images of RX J1744.7$-$2713 can be found in Prasow-Émond et al.
(2022). By inspecting the images, we determined that 4U 2206+543, Vela X-1, RX
J0648.1$-$4419, and 1H0556+286 do not exhibit any potential candidate CBCs.
Consequently, further analysis of these systems will not be pursued, except
for the calculation of companion frequency in Section 6.3. Among the remaining
X-ray binaries, we successfully detected at least one source for each system
with a significantly large SNR ($>$5). These sources are labeled in the
images, starting from the letter B.

Table 6 in the Appendix presents several physical properties of the detected
sources, including the angular separation in mas, the position angle in
degrees, the apparent magnitude in $L^{\prime}$-band and the mass estimated
from evolutionary models.

In the next sections, we analyze the nature of the detected sources and
discuss the implications of the results.

Figure 3: Keck/NIRC2 $L^{\prime}$-band high-contrast images of all observed
X-ray binaries – except RX J1744.7$-$2713 (see Prasow-Émond et al. 2022) and
$\gamma$ Cas (see Fig 2) – acquired on September 8, 2017, January 3, 2018, and
July 11–13, 2020. Images were treated and reduced using a PCA annular ADI
algorithm (using VIP; Gomez Gonzalez et al. 2017). The sources detected with
SNR $>$ 5 when computing the signal-to-noise map are labeled. The white X
symbol denotes the position of the X-ray binary masked by the coronagraph.
North points upwards and East points to the left, as in Fig. 2.

##  6 On the Nature of the Detected Sources

###  6.1 Background Contamination

We used TRILEGAL (Girardi et al., 2005) to discriminate background/foreground
stars from gravitationally-bound CBCs. TRILEGAL is a 3D model employed to
simulate the photometric properties of star fields within the Galaxy (e.g.,
Chun et al. 2015; Dietrich & Ginski 2018; Jones et al. 2021; Williams et al.
2021). We compiled a list of predicted sources within a 1 $\times$ 1 arcmin2
region surrounding the X-ray binary using its RA/Dec coordinates.
Subsequently, we applied a geometric rescaling so that the TRILEGAL foV
matches the foV of the high-contrast images (10.24 $\times$ 10.24 arcsec2) for
statistical consistency. We calculated the cumulative distribution of the
expected number of sources in the foV below an apparent magnitude
($m_{L^{\prime}}$), for the distribution of apparent magnitudes
($\mathcal{L^{\prime}}$). It is denoted as
$n_{\mathrm{foV}}(\mathcal{L^{\prime}}\leq m_{L^{\prime}})$.

Fig. 4 presents $n_{\mathrm{foV}}(\mathcal{L^{\prime}}\leq m_{L^{\prime}})$ as
a function of $m_{L^{\prime}}$ for both TRILEGAL and the detected sources in
the high-contrast images. It includes all X-ray binaries with detected
sources, except $\gamma$ Cas (for which the confirmation of the nature of the
CBCs relies primarily on proper motion analysis) and RX J1744.7$-$2713
(presented in Prasow-Émond et al. 2022). In Table 6, we listed
$n_{\mathrm{foV}}(\mathcal{L^{\prime}}\leq m_{L^{\prime}\,\mathrm{source}})$
for each detected source. This represents the expected number of sources –
based on TRILEGAL simulations – with apparent magnitudes ($m_{L^{\prime}}$)
below the magnitude of the corresponding source
($m_{L^{\prime}\,\mathrm{source}}$) while accounting for errors. If the
calculated value, including the upper limit, was lower than the total number
of sources detected below $m_{L^{\prime}\,\mathrm{source}}$, we reject the
hypothesis of background/foreground contamination for that particular source.

Many sources were not predicted by TRILEGAL. Specifically, all detected
sources in 4U 1700$-$377, RX J2030.5+4751, Cygnus X-1, X Per and 1H2202+501
were not expected from the model given their magnitudes and would thus suggest
that they are bound to the X-ray binary. The foVs of IGR J17544$-$2619 and SAX
J1818.6$-$1703 were expected to be more populated than what we detected,
suggesting that the detected sources are likely background or foreground
contaminants. The disparity between the predicted and observed number of
sources might result from the elimination of stationary sources during the ADI
process or from an insufficient S/N for detection. In the case of IGR
J18483$-$0311, sources B, C, and F might be CBC candidates, but their status
remains uncertain in the current stage of our study.

Figure 4: Cumulative distribution of the number of sources in the foV expected
from TRILEGAL simulations (red) and detected with a SNR $>5$ in the high-
contrast images (green) as a function of the apparent magnitude
$m_{L^{\prime}}$. It includes all X-ray binaries in which sources were
detected except $\gamma$ Cas and RX J1744.7$-$2713 (see Prasow-Émond et al.
2022): 4U 1700$-$377, RX J2030.5+4751, IGR J17544-2619, Cygnus X-1,
1H2202+501, IGR J18483$-$0311, X Per, and SAX J1818.6$-$1703.

We extended our analysis by calculating the probability of chance alignment
for each detected source. This probability represents the likelihood that
these sources are not associated with the X-ray binary system based on the
angular separation and the density on the sky of unrelated objects. This
method assumes that the distribution of unrelated sources across the area
follows a Poisson distribution. Note that this method usually relies on sky
surveys such as the 2MASS Point Source Catalog (e.g., Correia et al. 2006;
Lafrenière et al. 2008, 2014; Prasow-Émond et al. 2022) to establish the
distribution of unrelated objects. However, in this work, we used TRILEGAL as
an alternative due to the absence of available $K_{s}$-band observations.

To calculate the aforementioned probability, we first divided the cumulative
distribution of the number of sources
$n_{\mathrm{TRILEGAL}}(\mathcal{L^{\prime}}\leq m_{L^{\prime}})$ by the area
from which the sources were retrieved (between 6 $\times$ 6 arcmin2 and 15
$\times$ 15 arcmin2 depending on the location of the X-ray binary). This
division enabled us to derive a surface density denoted as $\Sigma$. Using the
angular separation $\Theta$ in arcsec, the probability of a source being drawn
from the TRILEGAL distribution – thus indicating its lack of association with
the central X-ray binary – is given by:

$P_{\mathrm{unrelated}}(\Sigma,\Theta)=1-\exp(-\pi\Sigma\Theta^{2})$ (2)

In Table 6, we listed $1-P_{\mathrm{unrelated}}(\Sigma,\Theta)$ as
percentages. Many sources have high probabilities ($>85\%$) of being
associated with the central X-ray binary. However, some sources have lower
probabilities (between 65% and 75%) which are not as statistically
significant, but we nevertheless identified them as candidate CBCs given the
early stage of the study. Sources with probabilities below 60% (not
statistically significant) were rejected as candidate CBCs.

###  6.2 Proper Motion Analysis: $\gamma$ Cas

Conducting a proper motion analysis is among the most robust methods for
confirming the gravitational association of a source with the system (e.g.,
Bohn et al. 2021). Given the proximity of $\gamma$ Cas and its proper motions
(see Section 4.1), it was possible to conduct a statistically significant
proper motion analysis between the two observed epochs (September 08, 2017,
and July 11, 2020). Figure 5 presents the relative separations between sources
B, C, and $\gamma$ Cas in RA and Dec, alongside the expected position of a
stationary background star. The figure also displays the angular separation
and position angle over time, along with the expected tracks for both comoving
and stationary background objects.

Source B’s trajectory implies an underlying motion that necessitates
additional epochs of observation for validation. In 2020, the angular
separation data point aligns with the comoving track, but the position angle
data point deviates by $\sim 3\sigma$ from the same track. This trajectory
suggests that source B is more likely to be bound to $\gamma$ Cas rather than
an unrelated background or foreground object. Nonetheless, its motion suggests
potential scenarios such as orbital motion, ejection from the system, or the
presence of a non-stationary background or foreground object. Using the mass
of $\gamma$ Cas ($\sim$ 13 $M_{\odot}$; Nemravová et al. 2012) and the radial
separation of source B, we calculated the as
$v_{\mathrm{esc}}=\sqrt{2GM/\rho}\approx 7680$ m/s. Additionally, the
projected velocity between 2017 and 2020 was determined, resulting in the
vector $v_{\mathrm{proj}}\approx(1670\,\hat{\rho}-17964\,\hat{\theta})$ m/s.
Since the norm of the velocity vector is greater than the escape velocity,
source B appears to be physically associated with $\gamma$ Cas, but is not
bound (as also suggested in Hutter et al. 2021). A comprehensive
characterization of this motion using high-contrast imaging necessitates
further epochs of observation.

Source C consistently follows the motion track of an unrelated object across
all three plots. Thus, we excluded it from our list of candidate CBCs with a
$\gg 3\sigma$ confidence level.

Figure 5: Left: Relative separations between source B (top row), C (bottom
row), and $\gamma$ Cas in right ascension ($\alpha$) and declination
($\delta$). The first epoch astrometric point is plotted in blue (September
08, 2017) and the second epoch astrometric point is plotted in red (July 11,
2020). The expected position for a stationary background object is plotted in
yellow, along with its proper motion track. Middle: Separation from $\gamma$
Cas in mas as a function of time. A background object with zero proper motion
would follow the orange track, while a bounded and comoving CBC would lie
within the blue zone. Right: Same as middle, but for the position angle in
degrees.

###  6.3 Frequency of Multiple Systems and Companion Frequency

Two key concepts are commonly defined in the stellar multiplicity literature
(e.g., Duchêne & Kraus 2013): the frequency of multiple systems (MF) and the
companion frequency (CF; i.e., the average number of companions per target).
While a proper motion analysis is required to confirm most of the sources, we
calculated a first estimation of MF and CF for the observed X-ray binaries in
our sample. Among the total of 14 observed X-ray binaries, we have identified
candidate CBCs in eight systems: 4U 1700$-$377, RX J2030.5+4751, Cyg X-1, X
Per, 1H2202+501, $\gamma$ Cas, RX J1744.7$-$2713, and IGR J18483$-$0311\.
Thus, based on these numbers and at this stage of the study, MF for triple or
higher-tier systems would be $8/14\approx 0.6$ ($\sim 60\%$). For CF, it is
important to note that X-ray binaries inherently possess one companion, the
donor star, which is included in our calculation of CF. Based on the status of
the detected sources listed in Table 6, the calculated average number of
companions per compact object is $2.1\pm 1.1$ ($210\pm 110\%$). This means
that, on average, the compact object has two companions (the donor star and
one additional companion). However, this value reduces to $1.8\pm 0.9$
($180\pm 90\%$) when considering only the sources that are most likely to be
gravitationally bound ($1-P_{\mathrm{unrelated}}(\Sigma,\Theta)>85\%$). These
values are subject to change as new observations become available and further
analyses are conducted.

##  7 Discussion

###  7.1 Stellar Multiplicity

The discovery of candidate CBCs would imply that X-ray binaries can still be
produced by multiple-star systems rather than exclusively binary systems. The
total mass (i.e., compact object and donor star) of the HMXBs in our sample
all exceeds $\sim$ 10 $M_{\odot}$, with some reaching up to around 60
$M_{\odot}$, placing them on the higher end of the mass spectrum. Stellar
multiplicity is believed to be common in high-mass star systems (e.g., Chini
et al. 2012; Duchêne & Kraus 2013), and high-order multiplicity is thought to
increase with primary mass (e.g., Peter et al. 2012). However, surveys for
high-mass stars remain incomplete.

For high-mass stars ($\gtrsim$ 16 $M_{\odot}$), MF and CF are estimated to be
$\geq 80\%$ and $130\pm 20\%$, respectively (Chini et al., 2012; Duchêne &
Kraus, 2013). The first estimation of MF for our sample ($\sim 60\%$;
calculated in Section 6.3) falls below this percentage. However, in this
study, MF is constrained by the range of projected separations (up to $\sim
12,000$ au). This implies that increasing this limit could potentially lead to
the discovery of more companions and hence increasing the estimation of MF. As
for CF ($210\pm 110\%$; calculated in Section 6.3), it currently exceeds the
estimate obtained from the literature ($130\pm 20\%$; Chini et al. 2012).
Further observations will likely lead to the rejection of candidate CBCs we
have detected, which would lower the sample’s CF (along with the associated
uncertainty range). In both cases, our preliminary estimations (MF and CF)
seem to be broadly in line with current estimates in the literature.

For solar-type stars, the frequency $N(n)$ of multiplicity $n$ follows a
geometric distribution $N(n)\sim\beta^{-n}$ (up to $n=7$ with $\beta=2.3$ or
$3.4$; Eggleton & Tokovinin 2008). Such a relation has not been derived for
massive stars. Thus, the results from this study could be used to derive one,
allowing us to predict the frequency of multiplicity in X-ray binaries and
high-mass systems. The current sample size may be insufficient to infer a
statistically significant relationship, but these results can still contribute
valuable data to future surveys of high-mass systems.

This pilot study, in addition to showing evidence for potential additional
components in X-ray binaries, could contribute to stellar multiplicity surveys
for massive stars. It could also enable us to probe stellar multiplicity at
low mass ratios (below $\sim 0.1$).

###  7.2 Stability in Wide Orbit

The projected separations within the scope of this study (from $\sim 350$ to
$\sim$ 12,000 au) would suggest that CBCs orbit at very large distances from
the central X-ray binary. Note that CBCs located closer to the X-ray binary
within the 2-3 kpc distance range cannot currently be detected through direct
imaging. To assess whether potential CBCs could be gravitationally bound to
these systems, we calculated the binding energy $E_{\mathrm{bind}}$ for every
source likely to be a CBC. Assuming circular orbits, $E_{\mathrm{bind}}$ is
estimated using the following equation (e.g., Naud et al. 2014; Prasow-Émond
et al. 2022):

$E_{\mathrm{bind}}\sim-\frac{GM_{\mathrm{XRB}}M_{\mathrm{comp}}}{1.27r}$ (3)

where $G$ is the gravitational constant, $M_{\mathrm{XRB}}$ is the total mass
of the central X-ray binary, $M_{\mathrm{comp}}$ is the mass of the CBC, $r$
is the projected separation between the CBC and the X-ray binary and 1.27 is
the average projection factor between $r$ and the semi-major axis assuming a
random viewing angle (e.g., Brandeker et al. 2006).

The binding energies for each candidate CBC range from $\sim-2\times 10^{42}$
erg to $\sim-3\times 10^{44}$ erg. A binding energy of $\sim-10^{41}$ erg was
obtained for the comoving exoplanet GU Psc b around a M3 spectral type star
($\sim$ 0.46 $M_{\odot}$), with a mass of $\sim 9-13$ $M_{\mathrm{Jup}}$ and
located at a distance of $\sim$ 2000 au (Naud et al., 2014). All candidate
CBCs have binding energies largely exceeding this currently known lower limit.
This suggests that these sources, if confirmed as CBCs, would fall within the
gravitational binding range of the X-ray binary.

We must also consider dynamic stability for systems containing more than one
candidate CBC. $N$-body simulations have shown that a configuration of two
CBCs at the same projected separation from the central system can lead to
dynamic instability (e.g., Kiseleva et al. 1994). Thus, in the case of 4U
1700$-$377, where B and C have similar projected separations, configurations
B+D or C+D are more likely than B+C+D. As for RX J2030.5+4751 and IGR
J18483$-$0311, the candidate CBCs have distant projected separations,
suggesting that configurations B+C and B+C+D, respectively, are plausible.

###  7.3 Companion Formation and Capture Scenarios

If our findings are confirmed, we hypothesize that CBCs orbiting X-ray
binaries could originate through two main mechanisms: (1) formation within the
same environment as the central X-ray binary or (2) capture by the system. On
the one hand, as detailed in Prasow-Émond et al. (2022), there are three
scenarios in which CBCs could potentially form in the direct environment of
X-ray binaries, and these scenarios may unfold at different times. Firstly,
CBCs could have formed simultaneously with the initial stars that subsequently
evolved to form the present X-ray binary, resulting from the direct
fragmentation of a collapsing prestellar core (e.g., Bate 2012). Note that
this scenario is unlikely because we would expect companions with a mass
similar to that of the main X-ray binary. Secondly, their formation might have
occurred within the circumbinary disk surrounding the initial binary system,
prior to the supernova explosion of the now compact object (e.g., Kratter et
al. 2010). Thirdly, CBCs could have formed within the supernova fallback disk
arising from the explosion (e.g., Wolszczan & Frail 1992). Note that fallback
disks do not contain enough mass to enable star formation, but they do possess
enough mass for the formation of substellar objects. Additional observations
are needed to detect and characterize such disks (see Section 7.4).

On the other hand, stellar and substellar CBCs could be gravitationally
captured by the X-ray binary. This is analogous to the case of the PSR
B1620-26 system, where a giant exoplanet is thought to have been captured by a
binary system containing a neutron star and a white dwarf (e.g., Sigurdsson et
al. 2003). Given that the HMXBs in our sample are massive ($>10$ $M_{\odot}$)
and located in the galactic plane (see Fig. 1), such events would not be
unlikely.

###  7.4 Follow-Up and Complementary Observations

The findings of our study primarily consist of intermediate results, and
additional observations are necessary to conduct further analyses and confirm
that the CBCs are bound to the system. In this section, we provide a list of
recommendations for follow-up and complementary observations.

First, we recommend re-observing the systems in the same band ($L^{\prime}$)
using the same instrument (NIRC2) at one or multiple additional epochs. This
will allow us to conduct proper motion analysis (see Section 6.2) for all the
candidate CBCs identified in this study. Multi-epoch observations will also
enable us to characterize the orbital motion of these CBCs. Since the HMXBs
presented in this study are located within 2-3 kpc, the time interval between
epochs ranges from a few months to a few years. Table 4 provides an estimate
of the recommended year of re-observation for each system, ensuring a
statistically significant ($>3\sigma$) proper motion analysis.

Second, we recommend observing the remaining 5 sources, such as Scorpius X-1,
1A0620-00, and V404 Cyg, to complete the sample of all X-ray binaries within
2-3 kpc accessible with Keck/NIRC2. This would also enable us to incorporate
LMXBs into the analysis and discussion.

Third, observations in other bands (e.g., $K_{s}$) would allow us to construct
color-magnitude diagrams and employ evolutionary models to estimate the
physical properties of the CBCs with greater constraints (e.g., Prasow-Émond
et al. 2022). Similarly, obtaining the near-infrared spectrum of the candidate
CBCs would enable us to characterize the nature of the source and extract
additional physical properties. Finally, submillimeter observations of the
continuum emission would allow us to detect and characterize potential AU-
scale circumstellar or protoplanetary disks composed of dust and hot gas
(e.g., Coleiro et al. 2013; Iyer & Paul 2017; Waisberg et al. 2019).

Contrast curves for all systems with CBCs can be found in the Appendix to
assess the limit that has been reached during these observations.

Table 4: Recommended year for follow-up observations for every X-ray binary with at least one candidate CBC – calculated using the distance, proper motions, and astrometric errors on the 2020 observations – enabling a proper motion analysis with at a $>3\sigma$ significance level. Target | Recommended Year
---|---
X Per | 2026
Cyg X-1 | 2024
IGR J18483$-$0311 | 2024
1H2202+501 | 2027
4U 1700$-$377 | 2024
RX J2030.5+4751 | 2024

##  8 Summary and Conclusions

In this study, we presented the first $L^{\prime}$-band high-contrast images
of nearby, high-mass X-ray binaries using NIRC2 and the vortex coronagraph on
the W. M. Keck Observatory. A total of 14 systems were observed from a sample
of 19 X-ray binaries within $\sim$ 2-3 kpc and amenable for direct imaging.
One or several sources with a SNR $>$ 5 were found in 8 of the observed X-ray
binaries. To discern the nature of these sources – whether unrelated objects
or candidate CBCs – we employed Galactic population models for all systems,
and proper motion analysis for $\gamma$ Cas. We find that, if confirmed, these
results would imply the presence of stellar and sub-stellar CBCs in the direct
environment of X-ray binaries ($\sim 350-12,000$ au), which opens up the
discussion on the binary nature of these systems. As a pilot study, this work
presents a catalog of photometric and astrometric parameters for the first
epochs of observations. Follow-up observations or additional characterization
(e.g., infrared spectrum) will enable us to conduct proper motion analyses to
discriminate more robustly background/foreground sources from comoving,
gravitationally-bound CBCs.

## Acknowledgments

The data presented herein were obtained at the W. M. Keck Observatory, which
is operated as a scientific partnership among the California Institute of
Technology, the University of California and the National Aeronautics and
Space Administration. The Observatory was made possible by the generous
financial support of the W. M. Keck Foundation. The authors wish to recognize
and acknowledge the very significant cultural role and reverence that the
summit of Mauna Kea has always had within the indigenous Hawaiian community.
We are most fortunate to have the opportunity to conduct observations from
this mountain. We also want to thank V. Christiaens for his help with VIP. We
thank Lauren M. Weiss, Marie-Eve Naud and Anjali Rao for their contribution to
the Keck/NIRC2 proposal.

M.P.E. is supported by the Institute for Data Valorisation (IVADO) through the
M. Sc. Excellence Scholarship, by the Department of Physics of the Université
de Montréal and by the Institute for Research on Exoplanets (iREx). J.H.L. is
supported by the Natural Sciences and Engineering Research Council of Canada
(NSERC) through the Canada Research Chair programs and wishes to acknowledge
the support of an NSERC Discovery Grant and the NSERC accelerator grant.

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This Appendix presents additional data related to the main text. Figure 6
presents the 5$\sigma$ contrast curves for all X-ray binaries with CBCs. Table
5 presents additional relevant physical properties for the 14 observed X-ray
binaries. Table 6 presents the properties of the detected sources in the high-
contrast image, including the status (background/foreground source or
candidate CBC), optimization parameters, physical properties (astrometric and
photometric parameters), and estimated mass.

Figure 6: 5$\sigma$ contrast curves in apparent magnitude (left axis) and estimated mass from the age of the XRB (right axis) for $\gamma$ Cas, Cyg X-1, X Per, 4U 1700$-$377, 1H2202+501, RX J2030.5+4751 and IGR J18483$-$0311\. The curves were generated using VIP for a Gaussian distribution (blue) and with a Student-t correction (red). Table 5: Additional relevant physical properties for the 14 observed X-ray binaries. The columns are: 1. Name of the target; 2. Distance in kpc (see Section 3.3.1); 3. Proper motion in right ascension in mas yr-1; 4. Proper motion in declination in mas yr-1; 5. Apparent magnitude in the $L^{\prime}$-band (see Section 3.3.2); 6. Estimated age of the X-ray binary in Myr (see Section 3.3.3); 7. Value of the extinction and 8. the reference; 9. Observed values of the X-ray luminosity in erg s-1 and 10. the reference; 11. The variability indicator, as found in Bird et al. (2016). Reference code: (1) Schlafly & Finkbeiner (2011), (2) Naze & Motch (2018), (3) Torrejón et al. (2010), (4) Romano et al. (2010), (5) Sguera et al. (2015), (6) Moffat et al. (1973), (7) Raguzova & Popov (2005), (8) Bozzo et al. (2012), (9) Simon et al. (2019), (10) Chevalier & Ilovaisky (1998), (11) Nikolov et al. (2017), (12) Negueruela & Reig (2001), (13) Ribó et al. (2006), (14) Hainich et al. (2020), (15) Laurent et al. (1992), (16) Romano et al. (2015), (17) Bozzo et al. (2016), (18) Liu et al. (2006), (19) Raguzova (2007), (20) Caballero-Nieves et al. (2009), (21) Di Salvo et al. (2001), (22) Lyubimkov et al. (1997), (23) Coburn et al. (2001), (24) Helfand & Moran (2001), (25) Mereghetti et al. (2021), (26) Klare & Neckel (1977), (27) Kreykenbohm et al. (2008).  Target | Distance | PM RA | PM Dec | $m_{\mathrm{L}}$ | Age | $E(B-V)$ | Ref. | $L_{\mathrm{X}}$ | Ref. | Var. ind.
---|---|---|---|---|---|---|---|---|---|---
| (kpc) |  (mas yr-1) |  (mas yr-1) |  ($\pm$ 0.5 mag) | (Myr) |  |  |  (erg s-1) |  |
RX J1744.7$-$2713 |  1.22 $\pm$ 0.04 |  -0.87 $\pm$ 0.02 |  -2.30 $\pm$ 0.02 | 5.809 |  Up to $\sim$60 |  $\sim$3.4 | (1) |  (3.08 $\pm$ 0.49) $\times$ 1032 | (2) | N/A
IGR J18483$-$0311 |  2.6 $\pm$ 0.7 |  -1.7 $\pm$ 0.2 |  -3.7 $\pm$ 0.1 | 7.907 |  Up to $\sim$30-50 |  5.22 $\pm$ 0.02 | (3) |  From $\sim$1033 to 1036 | (3, 4, 5) | N
$\gamma$ Cas |  0.19 $\pm$ 0.02 |  25.7 $\pm$ 0.5 |  -3.8 $\pm$ 0.4 | -0.912 |  8.0 $\pm$ 0.4 | -0.15 | (6) |  $\sim$1032–1033 | (7) | N
SAX J1818.6$-$1703 |  2.3 $\pm$ 0.8 |  -1.6 $\pm$ 0.2 |  -4.6 $\pm$ 0.1 | 8.964 |  Up to $\sim$30–50 |  5.08 $\pm$ 0.05 | (3) |  From $\sim$1032 to 1035 | (3, 8) | Y
1H2202+501 |  1.10 $\pm$ 0.01 |  2.36 $\pm$ 0.01 |  -0.29 $\pm$ 0.01 | 8.285 |  Up to $\sim$130 |  0.36 $\pm$ 0.03 | (9) |  $\sim$9 $\times$ 1032 | (10) | N/A
4U 2206+543 |  3.1 $\pm$ 0.1 |  -4.17 $\pm$ 0.02 |  -3.32 $\pm$ 0.01 | 8.700 |  Up to $\sim$8 |  0.547 $\pm$ 0.066 | (11) |  $\sim$1035–1036 | (12, 13) | N
4U 1700$-$377 |  1.5 $\pm$ 0.1 |  2.41 $\pm$ 0.03 |  5.02 $\pm$ 0.02 | 5.36 |  $\sim$80 |  0.50 $\pm$ 0.01 | (14) |  Up to $\sim$7 $\times$ 1036 | (15) | N
IGR J17544$-$2619 |  2.4 $\pm$ 0.2 |  -0.51 $\pm$ 0.03 |  -0.67 $\pm$ 0.02 | 7.67 |  Up to $\sim$8 | N/A |  |  From $\sim 10^{32}$ to $10^{38}$ | (16, 17) | Y
RX J2030.5+4751 |  2.30 $\pm$ 0.07 |  -2.71 $\pm$ 0.02 |  -4.54 $\pm$ 0.02 | 7.088 |  Up to $\sim$30-50 | N/A |  |  Up to $\sim$1033 | (18, 19) | N/A
Cyg X-1 |  2.1 $\pm$ 0.1 |  -3.81 $\pm$ 0.01 |  -6.31 $\pm$ 0.02 | 6.406 |  5 $\pm$ 1.5 |  1.11 $\pm$ 0.03 | (20) |  $\sim$3 $\times$ 1037 | (21) | N
X Per |  0.6 $\pm$ 0.1 |  -1.28 $\pm$ 0.05 |  -1.87 $\pm$ 0.03 | 4.596 |  $\sim$5 |  $\sim$0.4 | (22) |  $\sim$4 $\times$ 1034 | (23) | N
1H0556+286 |  1.5 $\pm$ 0.1 |  0.63 $\pm$ 0.03 |  -2.19 $\pm$ 0.02 | 7.618 |  Up to $\sim$150 | N/A |  |  Up to $\sim$4 $\times$ 1035 | (24) | N/A
RX J0648.1$-$4419 |  0.52 $\pm$ 0.01 |  -4.16 $\pm$ 0.07 |  5.93 $\pm$ 0.06 | 9.150 | N/A | N/A |  |  $\sim$1032 | (25) | N/A
Vela X-1 |  2.0 $\pm$ 0.1 |  -4.82 $\pm$ 0.02 |  9.28 $\pm$ 0.02 | 5.458 |  Up to $\sim$30-50 |  $\sim$0.8 | (26) |  Up to $\sim$4 $\times$ 1036 | (27) | N
Table 6: Physical properties of the detected sources in the high-contrast images. The columns are: 1. The target; 2. The label of the detected source (S/N $>$ 5); 3. The current status of the source, either background/foreground object (bkg) or candidate CBC (cc); 4. The optimal number of principal components used for the fitting ($n_{\mathrm{comp}}$; 5. The expected number of sources in the foV below the apparent magnitude ($n_{\mathrm{foV}}(\mathcal{L^{\prime}}\leq m_{L^{\prime}})$; see Section 6.1); 6. One minus the probability of being unrelated with the central X-ray binary ($1-P_{\mathrm{unrelated}}(\Sigma,\Theta)$; see Section 6.1); 7. The radial separation from the X-ray binary in mas; 8. The position angle in the image in degrees; 9. The apparent magnitude in the $L^{\prime}$-band (no extinction correction was applied); 10. The mass of the source, in $M_{\odot}$ or $M_{\mathrm{Jup}}$, estimated from evolutionary models (MIST or COND/DUSTY); 11. The projected separation from the X-ray binary in au. Target | Source | Status | $n_{\mathrm{comp}}$ | $n_{\mathrm{foV}}(\mathcal{L^{\prime}}\leq m_{L^{\prime}})$ | $1-P_{\mathrm{unrelated}}(\Sigma,\Theta)$ | $\rho$ | $\theta$ | $m_{L^{\prime}}$ | Est. Mass | Proj. sep.
---|---|---|---|---|---|---|---|---|---|---
|  (S/N $>$ 5) |  |  |  | (%) | (mas) | (deg) | (mag) |  | (au)
X Per | B | cc | 20 |  $\sim$0.1 |  $>$ 99 |  587 $\pm$ 18 |  112.3 $\pm$ 2.0 |  14.4 $\pm$ 0.6 |  $\sim$45$-$110 $M_{\mathrm{Jup}}$ | 350
Cyg X-1 | B | cc | 26 |  $\sim$0.6 |  93 $\pm$ 1 |  1853 $\pm$ 12 |  170.1 $\pm$ 0.6 |  16.2 $\pm$ 0.6 |  $\sim$0.2$-$0.3 $M_{\mathrm{\odot}}$ | 4000
IGR J18483$-$0311 | B | cc | 2 |  0.3$-$0.8 |  90 $\pm$ 4 |  2527 $\pm$ 12 |  291.5 $\pm$ 0.2 |  13.3 $\pm$ 0.8 |  $\sim$2.5 $M_{\mathrm{\odot}}$ | 6440
C | cc | 3 |  0.9$-$1.8 |  89 $\pm$ 4 |  1516 $\pm$ 13 |  21.6 $\pm$ 0.4 |  14.8 $\pm$ 0.8 |  $\sim$1.1$-$1.3 $M_{\mathrm{\odot}}$ | 3865
D | bkg | 7 |  3.4$-$7.0 |  32 $\pm$ 15 |  2787 $\pm$ 14 |  16.9 $\pm$ 0.2 |  16.3 $\pm$ 0.8 | – | 7100
E | bkg | 13 |  4.1$-$8.3 |  14 $\pm$ 10 |  3127 $\pm$ 15 |  13.8 $\pm$ 0.2 |  16.7 $\pm$ 0.8 | – | 7975
F | bkg | 17 |  1.3$-$3.1 |  23 $\pm$ 10 |  4522 $\pm$ 14 |  15.0 $\pm$ 0.1 |  15.3 $\pm$ 0.8 | – | 11530
G | bkg | 25 |  $\sim$7 |  $<$ 5 |  3761 $\pm$ 12 |  69.7 $\pm$ 0.2 |  17.0 $\pm$ 0.8 | – | 9600
H | bkg | 23 |  $\sim$11 |  $<$ 5 |  3358 $\pm$ 13 |  83.3 $\pm$ 0.2 |  17.6 $\pm$ 0.8 | – | 8560
I | bkg | 19 |  $\sim$11 |  $<$ 5 |  3168 $\pm$ 15 |  106.8 $\pm$ 0.2 |  17.6 $\pm$ 0.8 | – | 8080
SAX J1818.6$-$1703 | B | bkg | 3 |  1.5$-$3.5 |  25 $\pm$ 10 |  2820 $\pm$ 11 |  96.9 $\pm$ 0.2 |  18.2 $\pm$ 0.8 | – | 6600
C | bkg | 20 |  $>$ 30 |  $<$ 5 |  4069 $\pm$ 12 |  353.9 $\pm$ 0.2 |  14.9 $\pm$ 0.8 | – | 9525
1H2202+501 | B | cc | 14 |  0.2$-$0.5 |  98 $\pm$ 1 |  1222 $\pm$ 15 |  162.4 $\pm$ 0.5 |  16.4 $\pm$ 0.9 |  $\sim$70 $M_{\mathrm{Jup}}$ to $\sim$0.4 $M_{\mathrm{\odot}}$ | 1370
4U 1700$-$377 | B | cc | 8 |  0.5$-$0.7 |  91 $\pm$ 3 |  2238 $\pm$ 12 |  353.0 $\pm$ 0.3 |  14.0 $\pm$ 0.6 |  $\sim$1.2$-$1.3 $M_{\mathrm{\odot}}$ | 4075
C | cc | 7 |  1.3$-$1.9 |  68 $\pm$ 4 |  2616 $\pm$ 12 |  274.4 $\pm$ 0.2 |  13.4 $\pm$ 0.6 |  $\sim$1.5$-$1.6 $M_{\mathrm{\odot}}$ | 4760
D | cc | 3 |  0.7$-$0.9 |  65 $\pm$ 6 |  4157 $\pm$ 15 |  283.4 $\pm$ 0.1 |  15.4 $\pm$ 0.7 |  $\sim$0.4$-$0.8 $M_{\mathrm{\odot}}$ | 7570
IGR J17544$-$2619 | B | bkg | 5 |  $\sim$48 |  $<$ 5 |  827 $\pm$ 12 |  19.4 $\pm$ 0.7 |  16.9 $\pm$ 0.8 | – | 2350
C | bkg | 12 |  $\sim$13 |  $<$ 5 |  2993 $\pm$ 13 |  10.8 $\pm$ 0.2 |  15.1 $\pm$ 0.8 | – | 8500
D | bkg | 3 |  $\sim$6 |  $<$ 5 |  4099 $\pm$ 11 |  72.5 $\pm$ 0.1 |  13.4 $\pm$ 0.8 | – | 11640
E | bkg | 15 |  $\sim$86 |  $<$ 5 |  3170 $\pm$ 14 |  70.7 $\pm$ 0.2 |  17.3 $\pm$ 0.8 | – | 9000
F | bkg | 11 |  $\sim$14 |  $\sim$7 |  2392 $\pm$ 14 |  103.5 $\pm$ 0.2 |  15.3 $\pm$ 0.8 | – | 6790
G | bkg | 3 |  $\sim$22 |  $<$ 5 |  2947 $\pm$ 12 |  118.7 $\pm$ 0.2 |  16.1 $\pm$ 0.8 | – | 8370
H | bkg | 8 |  $\sim$8 |  $<$ 5 |  3935 $\pm$ 13 |  147.7 $\pm$ 0.1 |  14.1 $\pm$ 0.8 | – | 11180
I | bkg | 10 |  $\sim$68 |  $<$ 5 |  2093 $\pm$ 11 |  235.1 $\pm$ 0.3 |  17.1 $\pm$ 0.8 | – | 5950
J | bkg | 15 |  $\sim$85 |  $<$ 5 |  3537 $\pm$ 15 |  267.1 $\pm$ 0.2 |  17.3 $\pm$ 0.8 | – | 10050
RX J2030.5+4751 | B | cc | 7 |  $\sim$0.1 |  $>$ 99 |  513 $\pm$ 11 |  302.9 $\pm$ 0.9 |  14.8 $\pm$ 0.8 |  $\sim$0.3$-$1.1 $M_{\mathrm{\odot}}$ | 1130
C | cc | 17 |  0.2$-$0.3 |  92 $\pm$ 3 |  3251 $\pm$ 15 |  132.1 $\pm$ 0.3 |  16.1 $\pm$ 0.8 |  $\sim$0.1$-$0.6 $M_{\mathrm{\odot}}$ | 7150
D | cc | 28 |  0.3$-$0.7 |  74 $\pm$ 8 |  4208 $\pm$ 13 |  343.1 $\pm$ 0.3 |  17.1 $\pm$ 0.8 |  $\sim$60$-$400 $M_{\mathrm{Jup}}$ | 9250
$\gamma$ Cas (2017) | B | – | 1 | – | – |  2051 $\pm$ 20 |  242.8 $\pm$ 0.3 | – | – | 390
C | – | 24 | – | – |  1803 $\pm$ 20 |  91.4 $\pm$ 0.3 | – | – | 343
$\gamma$ Cas (2020) | B | cc | 1 | – | – |  2056 $\pm$ 20 |  241.2 $\pm$ 0.3 |  3.1 $\pm$ 0.9 |  $\sim$ 13 $M_{\mathrm{\odot}}$ | 391
C | bkg | 24 | – | – |  1721 $\pm$ 20 |  90.8 $\pm$ 0.3 |  10.4 $\pm$ 0.9 | – | 327