The First High-contrast Images of X-Ray Binaries: Detection of Candidate Companions in the γ Cas Analog RX J1744.7-2713

RX J1744.7−2713 (R.A.: 17^h44^m457659; decl.: −27^d13^h44477) is located at a distance of 1.22 ± 0.04 kpc (Gaia Collaboration et al. 2021) and was first identified as a HMXB by Israel et al. (1997). The distance above is based upon geometric parallax inversion and includes a zero-point offset correction of −0.0348 mas according to the algorithm described in Lindegren et al. (2021). Its optical component—HD 161103—has been spectroscopically characterized in Motch et al. (1997) and Lopes de Oliveira et al. (2006), and is classified as a Be star.

RX J1744.7−2713 has similar properties to γ Cassiopeiae (also known as 2S 0053+604; e.g., Raguzova & Popov 2005; Shrader et al. 2015) and has an X-ray luminosity of (3.08 ± 0.49) × 10³² erg s⁻¹ (Naze & Motch 2018). Although the origin of X-ray emission in RX J1744.4−2713 is still debated, it may point to accretion onto a white dwarf (WD; Lopes de Oliveira et al. 2006).

It should be noted that in the case of Be stars, the star's massive outflows lead to a diffuse and gaseous circumstellar disk known as a decretion disk (e.g., Kravtsov et al. 2020); however, these disks have radii at sub-au scales, which for RX J1744.7−2713 is well within the inner working angle of the NIRC2 vortex coronagraph.

In the case of RX J1744.4−2713, Coleiro & Chaty (2013) estimated the age of the system to be ∼60 Myr by investigating the expected offset between the position of the Galaxy's spiral arms and HMXBs. However, considering the uncertainties (e.g., see their Figure 13), the age of RX J1744.4−2713 is likely to be anywhere between a couple Myr to 80 Myr (95% confidence). Given these uncertainties, we consider the range of 5–60 Myr throughout this study and note that even if we were to consider an age outside this range, our conclusions remain the same.

Furthermore, the system has proper motions of −0.955 ±0.100 mas yr⁻¹ and −2.062 ± 0.077 mas yr⁻¹ in R.A. and decl., respectively, and is located in the Galactic plane, as most of the HMXBs in our galaxy (e.g., Tauris & van den Heuvel 2006).

The Keck/NIRC2 vortex coronagraph (Mawet et al. 2005; Serabyn et al. 2016) was used to observe RX J1744.7−2713 in pupil-tracking mode—with the narrow-field camera (9.971 ±0.004 mas/pixel; Service et al. 2016)—in $L^{\prime}$-band in 2017 (λ = 3.776 μm, Δλ = 0.700 μm; PI: Mawet) and in both $L^{\prime}$-band and K_s -band in 2020 (λ = 2.146 μm, Δλ = 0.311 μm; PI: Fogarty). Observations were adaptive-optics-assisted with the Keck II Shack-Hartmann wave-front sensor in 2017, which performs wave-front sensing in R, and the infrared pyramid wave-front sensor (PyWFS) in 2020, which performs wave-front sensing in H (Wizinowich et al. 2000; Bond et al. 2018). Given the R and H magnitudes of RX J1744.7−2713 (R ∼ 9; Cutri et al. 2003, H ∼ 7; Zacharias et al. 2012), the performances of the two wave-front sensors are comparable; however, we chose to use the PyWFS for our 2020 observations since sensing in H is advantageous for several extremely red HMXBs in our 2020 survey sample. Tip-tilt adjustments were performed with Quadrant Analysis of Coronagraphic Images for Tip-tilt sensing (Huby et al. 2017) in order to keep the star well centered on the vortex focal plane mask.

Individual exposure times, coadds, total number of frames and total integration times obtained for each observation are summarized in Table 1.

Table 1. Keck/NIRC2 Observing Log for RX J1744.7−2713 ^a

UT Date	2017 Sep 8	2020 Jul 11	2020 Jul 12
Filter	$L^{\prime}$	$L^{\prime}$	Ks
WFS	SH	py	py
Int. Time (s)	0.5	0.5	0.6
Coadds	60	60	45
Total frames	40	120	92
P. A. cov. (o)	14.3	38.3	39.6

Note.

^a Abbreviations: wave-front sensor (WFS), parallactic angle coverage (P. A. cov.)

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In our 2017 observations, we only obtained ∼14° of field rotation, but in our 2020 observations we obtained ∼40° of rotation in both bands to enable reduction using angular differential imaging (ADI; Marois et al. 2006). Additional frames taken with RX J1744.7−2713 moved off-axis were taken throughout each run to sample the evolution of the point-spread function (PSF) throughout the run and to obtain photometric measurements of RX J1744.7−2713.

Data reduction (flat fielding, bad pixel masking, sky removal, image registration and selection, and centering via speckles) was performed using the Vortex Image Processing (VIP) package (Gomez Gonzalez et al. 2017). The frames were then derotated and mean combined, and a Principal Component Analysis (PCA) annular ADI algorithm from VIP was applied to obtain the high-contrast images (see Figure 1). Note that the number of principal components (n_comp) for each individual source was chosen to reach an optimal signal-to-noise ratio (S/N), by testing many values ranging from 1 to 50. We then generated the S/N and significance (signal in terms of σ; Mawet et al. 2014) maps to identify sources with a S/N greater than 5 (which results in a signal greater than 4σ for all of our sources). This also provided estimates of the sources' coordinates.

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To calculate the full width at half maximum (FWHM) of the PSF for both filters, we fit a Gaussian profile to the median-collapsed PSF data cube. We obtained a FWHM of 83.2 milliarcseconds (hereafter mas) and 47.5 mas for $L^{\prime}$ and K_s , respectively. Note that we also generated a 2D synthetic PSF for $L^{\prime}$ flux fitting—using a Gaussian model and the corresponding FWHM—because of an artifact caused by thermal background noise from the primary mirror that has been folded back on-axis by the vortex phase mask. However, the use of a synthetic PSF does not affect the flux fitting much, as we get consistent results in the error bars when we test our K_s data with both real and synthetic PSFs.

Using the reduced data cube and the normalized and centered synthetic PSF, we injected fake companions with an inverse flux into the science data cube to estimate the photometric counts, coordinates, and errors (Lagrange et al. 2010) of any detected source with a S/N > 5 in the $L^{\prime}$ S/N map. This process uses a Nelder–Mead optimization algorithm to find the coordinates and the flux of a source in a given aperture (a radius of 3 FWHM). We then divided the counts of the sources by the counts of the HMXB's median-collapsed PSF data cube—measured in the same aperture as the sources—in order to obtain the flux of the candidate companion relative to the X-ray binary (i.e., the contrast).

Knowing the apparent magnitudes of RX J1744.7−2713 ($L^{\prime}$ = 5.809 ± 0.077 mag and K_s = 6.507 ± 0.023 mag; Cutri et al. 2003), the contrast can be converted to apparent magnitudes and absolute magnitudes (using the known distance in parsec), and then to mass using a model from MESA Isochrones and Stellar Tracks (MIST; Paxton et al. 2011, 2013, 2015, 2018; Choi et al. 2016; Dotter 2016; Faherty et al. 2016).

Servillat et al. (2012) reported that there is no significant variability in the light curve of HD 161103 (Be star in RX J1744.7−2713). However, large timescale (∼50–100 yr) variability could still occur. We therefore injected a 5% additional error to the magnitudes to occur for any large timescale variability, and adding even larger errors does not change our results. As for the line-of-sight interstellar reddening E(B − V), Schlafly & Finkbeiner (2011) estimated it to be E(B − V) ∼ 3.4. Since the extinction A(V) is related to E(B − V) via A(V) = 3.2E(B − V), we have A(V) ∼ 10.9, and assuming a typical extinction power law varying as A(V) ∝ λ^−1.75 (Draine 1989; and see Doherty et al. 1994; Viehmann et al. 2005; Dong et al. 2017; Uyama et al. 2020 for examples of papers that use that technique), we obtain A(K_s ) ∼ 0.85 and $A(L^{\prime} )\sim 0.32$ (via a simple cross product). Therefore, K_s and $L^{\prime}$ are not strongly impacted by dust reddening; such an extinction results in a color shift of ∼0.5 mag for ${K}_{s}-L^{\prime}$ and a magnitude shift of ∼0.3 for $L^{\prime}$. These corrections have been applied to our results; by adding them to the K_s and $L^{\prime}$ magnitudes.

In order to estimate the errors on the parameters—the flux and the position (i.e., the separation from the XRB in mas and the parallactic angle in degrees)—obtained with the optimization process, we proceeded by injection recovery. We first injected fake companions with known values for the parameters, and then ran the optimization code to compare the outputs with the known inputs. For each parameter, we tested this method for 90 different values, with a range covering the values of the true candidate companions of the system. We found that the errors were relatively stable while increasing the values of the parameters, meaning they are more significant for smaller values within the range. Averaging the results, we obtained errors of the order of ∼0.5 mas for the separation and ∼0.01^o for the parallactic angle. As for the flux, we considered only the errors explained in Section 2.4, as they are dominant and physically significant.

The injection/recovery method gives relatively small errors, but other types of error must be included (e.g., the error when determining the center of the vortex coronagraph within the different frames). As our 2020 $L^{\prime}$ and Ks observations are spaced out by only one day, the astrometry parameters should be the same. Therefore, we also considered the difference between our 2020 $L^{\prime}$ and Ks results as part of astrometry errors, which are greater than the injection/recovery errors.

The left panel of Figure 1 presents the $L^{\prime}$ high-contrast image of RX J1744.7−2713, while the right panel shows the K_s image, both from the 2020 observation runs. The $L^{\prime}$ image from 2017 is shown in Figure A1 in the Appendix, in which only three sources are detected. With deeper observations in 2020 (unlike the poor parallactic coverage for angular differential imaging in 2017), it revealed a then-unresolved ∼450 au candidate companion from the central X-ray binary. We therefore only consider the 2020 observations for the remainer of the paper, except for a preliminary proper motion analysis in Section 3.4.

Using the $L^{\prime}$ S/N map, we find a total of 21 sources that have a S/N > 5. These sources are labeled from B to V in Figure 1 and are also detected in the K_s image with a S/N > 5. Moreover, as the K_s image is more sensitive (more sources), note that we only considered the sources detected in $L^{\prime}$ when measuring the magnitudes, since potential substellar companions are usually brighter in $L^{\prime}$ (Faherty et al. 2016). The projected separations from RX J1744.7−2713, estimated using the distance and the plate scale, range from ∼450 to ∼5500 au. In the next sections, we examine the nature of these sources via different analyses.

3.2.1. TRILEGAL

3.2.2. Probability of Chance Alignment

In addition to TRILEGAL, we derived a probability of chance alignment—i.e., the likelihood that the candidates are not bound to the system—using the Two Micron All-Sky Survey (2MASS) Point Source Catalog (PSC; see Correia et al. 2006; Lafrenière et al. 2008, 2014 for examples of that technique). More specifically, we retrieved all the sources in a $15^{\prime} \times 15^{\prime}$ field surrounding RX J1744.7−2713, and we constructed a cumulative distribution of the number of sources as a function of the apparent K_s magnitude. We then divided this result by the area (in arcsec²) to obtain a surface density Σ that depends on the limiting magnitude of the candidate, i.e., Σ = Σ(K_s < Ks_candidate). Assuming a random uniform Poisson distribution of unrelated objects across the chosen area, the probability that a candidate is not related to the system is given by:

$$\begin{eqnarray}&&{P}_{\mathrm{unrelated}}({\rm{\Sigma }},{\rm{\Theta }})=1-\exp (-\pi {\rm{\Sigma }}{{\rm{\Theta }}}^{2})\end{eqnarray} \tag{ 1 }$$

where Θ is the projected separation from RX J1744.7−2713 (in arcsec). Table 2 shows the Σ, Θ, and 1 − P_unrelated(Σ, Θ) values for all sources (B to V).

Table 2. Probability of Unrelation with RX J1744.7−2713 for All the Sources (B to V in Figure 1), as Estimated from 2MASS PSC

Source	Σ	Θ	1 − Punrelated(Σ, Θ)
	(arcsec−2)	(arcsec)	(%)
B	3.24 × 10−2	0.37	98.6
C	2.11 × 10−2	1.18	91.2
D	7.14 × 10−3	1.25	96.6
E	1.66 × 10−2	3.02	62.3
F	2.47 × 10−2	3.19	45.5
G	2.43 × 10−2	4.51	21.2
H	3.29 × 10−2	4.23	15.8
I	3.29 × 10−2	3.37	30.9
J	3.29 × 10−2	1.96	67.3
K	3.29 × 10−2	3.93	20.2
L	3.29 × 10−2	2.85	43.2
M	3.29 × 10−2	4.42	13.4
N	3.29 × 10−2	2.80	44.4
O	3.29 × 10−2	4.29	14.9
P	3.29 × 10−2	1.83	70.6
Q	3.29 × 10−2	2.18	61.3
R	3.29 × 10−2	1.91	68.6
S	3.29 × 10−2	3.74	23.6
T	3.29 × 10−2	4.02	18.9
U	3.29 × 10−2	3.69	24.5
V	3.29 × 10−2	2.48	53.1

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This table shows that sources B, C, D have a high probability of not being unrelated to the system, respectively, of 98.6%, 91.2%, and 96.6%, which is consistent with Figure 5. Moreover, sources E, J, P, Q, and R have high but less convincing probabilities, while the remaining sources are likely to be background stars since their probability is lower than 60%.

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Since both $L^{\prime}$ and K_s observations were taken, we were able to construct a color–magnitude diagram, as has been done in previous studies to estimate the physical properties of companions (e.g., Rameau et al. 2013; Salaris & Bedin 2018; Jones et al. 2021). Figure 3 presents the absolute magnitude in $L^{\prime}$ versus ${K}_{s}-L^{\prime}$ for the 21 potential companions to RX J1744.7−2713. The track from MIST at 10 Myr is overlaid, as well as the extinction vector (see Section 2.4).

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From this diagram, the fainter sources (H to L and O to V) could be coherent with low-mass stars (M- or K-type), while B and M could be G-type stars. Moreover, B, C, E, F, and G have estimated masses potentially coherent with massive A- or B-type stars. Due to their offset ${K}_{s}-L^{\prime}$ color, the other sources (F, G, M) seem to be inconsistent with being substellar or stellar companions, and may therefore be unrelated background objects such as extincted background stars or artifacts.

A table with the position, the $L^{\prime}$ and K_s magnitudes, the estimated mass, and the projected separation of the 21 sources companion candidates is presented in the Appendix (see Table A1). Note that the masses were estimated from the 5–60 Myr stated in Section 2.1 and that we did not apply the extinction correction for this table.

Thus, RX J1744.7−2713 does not currently show evidence of exoplanet-mass companions, as the candidate companions have masses from ∼0.2 to 6 M_⊙. However, we reached excellent S/N and we detected sources down to $L^{\prime} \sim 16.5$. Another way to gather more information on the sources is via additional bands (e.g., H) or via spectroscopic characterization.

To confirm more robustly that the sources are bound, a proper motion analysis could be conducted (e.g., Marois et al. 2008). Given the distance (∼1 kpc) and proper motion of RX J1744.7−2713 (see Section 2.1), a >3σ detection will only be possible in ∼5–10 yr. However, considering that there is a three-year interval between our 2017 and 2020 sets of observations, a preliminary proper motion analysis was conducted for sources C, D, and J. The plots of astrometric positions (position angle in degrees, separation in mas, and relative separations in R.A. and decl.) for each of these sources relative to the X-ray binary can be found in the Appendix (see Figure A2). Accounting for the errors from Section 2.5, we conclude that both scenarios—stationary background or comoving with RX J1744.7−2713—are possible for sources D and J at this current epoch. We note that the position of source C is offset from the tracks, which indicates that it could be a nonstationary background object.

The 21 sources detected in RX J1744.7−2713 at high S/N would have wide projected separations (from ∼450 to ∼5500 au), which raises concerns as to whether potential companions could be gravitationally bound to the system. However, very large separations have been observed in many known systems including companions white dwarfs or other evolved systems (e.g., 2000 au for GU Psc b; Naud et al. 2014; 2985 au for WISE 2005+5424; Mace et al. 2013; 16 500–26 500 au for LSPM 1459+0857 AB; Day-Jones et al. 2011). Baron et al. (2019) reported that the occurrence of substellar companions at very large orbits are rare. However, in RX J1744.7−2713 the mass ratios are small (from q ∼ 0.003 to ∼0.08), and such ratios have yet to be studied in detail. Despite the large separations, the large mass of the central system (i.e., the X-ray binary) implies a high binding energy. Assuming a total mass M_XRB of ∼18 M_⊙ for RX J1744.7−2713 (typical masses for WD and Be stars) and a mass M_c of ∼80 M_Jup as a lower limit for the companions, we can estimate the binding energy of the system via the following equation (assuming circular orbits):

$$\begin{eqnarray}&&{E}_{{\rm{b}}{\rm{i}}{\rm{n}}{\rm{d}}}\sim -\displaystyle \frac{{GM}_{{\rm{X}}{\rm{R}}{\rm{B}}}{M}_{c}}{1.27r}.\end{eqnarray} \tag{ 2 }$$

Here, 1.27 is the average projection factor between r and the semimajor axis, assuming a random viewing angle (e.g., Brandeker et al. 2006). We obtain E_bind ∼ −4.3 × 10⁴³ erg and E_bind ∼ −3.2 × 10⁴² erg for the closest (450 au) and farthest (5500 au) candidates, respectively. In both cases, the binding energy is higher than in many known bound systems (e.g., ∼10⁴¹ erg; Naud et al. 2014).

Therefore, it is not unreasonable that the multiple stellar companion candidates, if confirmed with proper motion analysis, are gravitationally bound to the HMXB despite their wide separations. However, it is important to note that it is unlikely that all these sources would be bound due to dynamic instability. In fact, although we do not have detailed information on their potential orbital motion yet, candidate companions C and D have similar separations from RX J1744.7−2713, and simulations show that this configuration can be unstable (e.g., Kiseleva et al. 1994). On the contrary, a scenario of a triple system—composed of the X-ray binary (considered as one system here), candidate companion B, and candidate companion C, D, E or J—is more plausible according to basic N-body simulations.

The discovery of multiple probable stellar candidate companions in RX J1744.7−2713 implies that it would be a multiple-star system. In fact, high order multiplicity increases with primary mass (e.g., Peter et al. 2012), and although surveys are incomplete, they suggest that stellar multiplicity is frequent in high-mass stars, such as young B stars (see Duchêne & Kraus 2013 for a review on stellar multiplicity). More precisely, if we consider only the confirmed companions, the multiplicity frequency would be ≥ 80% for stars with a mass ≥16 M_⊙ (e.g., Chini et al. 2012). Regarding the companion frequency (i.e., the average number of companion per target in a population), it is ≈130 ± 20% for high-mass stars (Duchêne & Kraus 2013). Moreover, the frequency N(n) of multiplicity n roughly follows a geometric distribution N(n) ∝ 2.3⁻ⁿ (up to n = 7; Eggleton & Tokovinin 2008) for solar-type stars; however, there is currently no derived relation for massive stars. As RX J1744.7−2713 is already a known high-mass binary system, the complete sample of this project could therefore enable us to better understand if X-ray binaries are likely to stellar multiplicity, as well as probing stellar multiplicity at mass ratios below ∼0.1.

In addition, RX J1744.7−2713 is a γ Cassiopeiae analog, and the latter has two faint optical companions (e.g., Mason et al. 2001). Therefore, it suggests that Be stars might be more favorable to stellar multiplicity. As γ Cassiopeiae is a HMXB candidate (e.g., Haberl 1995), it also means that stellar companions could be common in X-ray binaries.

In the case of X-ray binaries, companions are believed to form (1) from the direct fragmentation of a collapsing prestellar core, i.e., roughly at the same time as the stars that will eventually form the X-ray binary (e.g., Bate 2012), (2) from the circumbinary disk surrounding the initial binary system (i.e., preexplosion of the then-compact object; e.g., Kratter et al. 2010), or (3) from the supernova fallback disk surrounding the X-ray binary (postexplosion; e.g., Wolszczan & Frail 1992). Note that fallback disks could lead to the formation of substellar companions, but they are not massive enough to allow star formation. However, this work does not show evidence of such disks, so we can not conclude how the candidate companions have formed. Furthermore, if companions are formed under the last scenario, then they must be younger than the X-ray binary; their age could be lower than 5 Myr (the lower limit for RX J1744.7−2713's age stated in Section 2.1). Overall, X-ray binaries could host multigeneration companions that form at different epochs through the evolution of the binary. This work explores the idea that the interactions between X-ray binaries and their surroundings might be complex, leading to multiple companions and hierarchical orbits. Moreover, it opens up the discussion on how substellar and stellar formation could occur even in the most extreme environments.