The Red Supergiant Binary Fraction of the Large Magellanic Cloud

We began by selecting sources from the 2MASS point-source catalog (Skrutskie et al. 2006) within 210′ of the center of the LMC, taken to be α_J2000 = 05:18:00 and δ_J2000 = −68:45:00, chosen to match the same field used for the recent survey for WR stars in the LMC (Massey et al. 2014; Neugent et al. 2018b) and encompassing the entire optical disk of the galaxy. We kept only objects with the best 2MASS photometry, i.e., with quality flags of “AAA,” and “artifact contamination” flags of “000.” Our initial selection was restricted to stars with K_s ≤ 13 and J − K_s ≥ 0.5. This left us with a sample of 87,637 stars.

These magnitude and color limits were chosen to be extremely generous. A K_s = 13 star in the LMC would have $\mathrm{log}L/{L}_{\odot }\sim 3.0-3.3$, adopting a distance to the LMC of 50.0 kpc, and the equations given in Table 4 of Neugent et al. (2020). This is much smaller than our completeness goal of $\mathrm{log}L/{L}_{\odot }\sim$ 4.0. Similarly, a lightly reddened J − K_s = 0.5 star will have an effective temperature (T_eff) of 5000 K (using Equation (1) from Neugent et al. 2012b), much warmer than the ∼4200 K upper temperature limit for RSGs we will employ below.

In Figure 1(a), we show the CMD of the sample of 87,637 stars. In the next two sections, we will demonstrate how we refine these to select only the RSGs.

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The majority of the very red stars in the LMC will be members, as previously shown by radial velocity studies (see, e.g., Neugent et al. 2012b), but a few will be foreground, and as we approach the warmer temperatures and yellower colors, there will be increasing contamination from Galactic stars. Indeed, in the color regime for YSGs, Galactic contamination becomes even more overwhelming. Fortunately, Gaia data (Gaia Collaboration et al. 2018) provide the means to identify these foreground objects through the judicious analysis of proper motions and parallaxes. We say “judicious” as there is a known systematic offset in Gaia DR2 astrometric measurements and the formal uncertainties provided do not represent the total error (Lindegren et al. 2018).

To assess the probability of LMC membership, we adopted a procedure similar to that described in Gaia Collaboration et al. (2018). First, we select a large set of highly probable LMC stars in order to define the distributions of astrometric parameters that are expected for true members. We initially select all sources overlapping the LMC with Gaia G < 18 mag. In order to minimize any foreground contamination in this baseline sample, we then exclude all sources with either yellow colors (0.7 mag < G_bp − G_rp < 1.1) or parallax measurements greater than 4σ as well as any remaining sources whose parallaxes or proper motions deviated from the rest of the sample by >4σ. The red 2MASS stars identified above are then compared to this sample in order to assess their consistency with the kinematics of the LMC. If the proper motions and parallax of a given star fall outside the region that contains 99.5% of the comparison sample, we flag it as a probable foreground star. Conversely, if a star falls within the region that contains 75% of the comparison sample, we consider it a likely LMC member. Stars that fall in between are flagged as having “ambiguous” membership based on astrometry alone. Further details of our application of this method can be found in Aadland et al. (2018). Figure 2 shows where our LMC members, probable foreground stars, and ambiguous results fall in proper motion and parallax space.

There were eight photometrically selected RSGs (as defined below) whose proper motions were consistent with LMC membership, but have quoted Gaia DR2 parallax measurements that are more negative than our comparison sample of LMC stars. A large negative parallax is nonphysical but suggests that these objects may not be foreground stars. We therefore retained these stars in our sample, but changed their status from “probable foreground” to “ambiguous” results. This included one star, 05300119–6956382, that had been previously identified in Neugent et al. (2019) as an RSG + B-star binary.

Two other RSG + B binaries from Neugent et al. (2019), 05274747–6913205 and 05292143–6900202, would have also been dismissed as nonmembers were it not for the spectroscopic information. In the case of 05274747–6913205, the Gaia parallax of 0.5561 ± 0.0746 mas has a quoted significance of >7σ and is consistent with a distance of 1.8 kpc (Bailer-Jones et al. 2018), but the proper motions and radial velocity (280 km s⁻¹) are in excellent agreement with membership in the LMC. The spectrum is that of a cool star with strong TiO bands, consistent with its J – K colors; Balmer lines are clearly present. We retain this star but flag the Gaia results as ambiguous. As for 05292143–6900202, Gaia does not robustly detect a parallax (0.4757 ± 0.1604); the proper motions are slightly outside the accepted spread we have adopted for membership, but the errors are large. Both its ground-based and Gaia radial velocities (also 280 km s⁻¹) suggest membership in the LMC. The spectrum is consistent with its colors, a late K or early M, with clear upper Balmer lines. We also retain this star, describing its membership as ambiguous. We note that Gaia parallaxes can be impacted by both binarity and variability, both of which may be common in our sample.

One other star labeled as an RSG + B binary in Neugent et al. (2019), 05065284–6841123, shows up as a foreground star. Further inspection of the unpublished AAT spectrum showed that there were reduction problems, and we no longer consider this star an RSG binary.

After cross-matching with Gaia (and making these small adjustments), out of the 87,637 red stars, 73,361 (83.7%) were probable members, 3585 (4.1%) had ambiguous results, 9651 (11.0%) were probable foreground stars, and 1040 (1.2%) either had no match with Gaia or did not have Gaia parallax data that could be used to determine membership.

At this point, we removed the probable foreground stars from our sample but left the probable members as well as those with either ambiguous results or incomplete Gaia data. How the addition of the ambiguous results might alter our calculated binary fraction is discussed below. In Figure 1(b) we show the CMD after the foreground stars were removed. Note that the vast majority of these stars were those with lower J − K_s values, consistent with our statement above that the contamination in our sample is primarily at the warmer temperatures. The green points are the stars for which there were incomplete or no Gaia data.

Contamination by AGBs has long been the bane of RSG population studies. AGB stars are evolved low- to intermediate-mass stars, which are in their He- and H-shell burning phase. These stars overlap in luminosity with RSGs below $\mathrm{log}L/{L}_{\odot }$ of 4.9 as noted by Brunish et al. (1986). Using optical photometry, one’s only recourse was to limit RSG population studies to higher luminosities.

However, AGBs are cooler than RSGs because the Hayashi limit shifts cooler at lower masses (Hayashi & Hoshi 1961). Yang et al. (2019) used a (J − K_s, K_s) CMD to separate RSGs and AGBs in the SMC following the work of Cioni et al. (2006) and Boyer et al. (2011). Neugent et al. (2020) adapted this method for their recent identification of RSGs in part of M31. They found that the color of the AGB/RSG boundary shifted in M31 relative to that of the SMC in the manner expected from the shifting of the Hayashi limit to cooler temperatures at higher metallicities, demonstrating that cuts must be established for each galaxy separately.

Here we repeat the same process for the LMC. Figure 3 shows the same CMD as shown previously, but now with the sequences labeled and probable foreground stars removed. The tip of the red giant branch (TRGB) is striking at K_s = 12, or about M_K = −6.5.⁷ The location of the oxygen-rich, carbon-rich, and “extreme” AGBs are shown, based upon the nomenclature of Boyer et al. (2011); see, in particular, their Figure 4, based on a combination of 2MASS and Spitzer data.

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The realm of the RSGs is fairly easy to separate from these other stars, and we have drawn in the envelope of what we consider to be the RSG sequence. The locations are intermediate in color between what Yang et al. (2019) adopted for the SMC and what Neugent et al. (2020) adopted for M31; this is consistent with the LMC having a metallicity that is intermediate between the two. (Note that the SMC and LMC metallicities are usually taken to be 1/3 and 1/2 solar, respectively—see Russell & Dopita 1990; while M31's metallicity is about 1.5× solar—see Sanders et al. 2012.) In Table 1 we provide the color relationships we use to define the RSG region of the LMC CMD. Next we will describe how we defined our K_s and J − K cuts.

The red giant branch (RGB) and the RSG sequences begin to merge at K_s = 12.5 and fainter, which corresponds to $\mathrm{log}L/{L}_{\odot }\sim 3.3$. Because these diagrams go much fainter than our desired completeness limit of $\mathrm{log}L/{L}_{\odot }=4$, we cut our RSGs at K_s = 12, roughly the TRGB, similar to the approach adopted by Yang et al. (2019) for the RSGs in the SMC. This still allows completeness to $\mathrm{log}L/{L}_{\odot }\sim 3.6$ using the transformations in the next section, still considerably lower than the lowest luminosity we are concerned about.

After defining a faintness limit for K_s, we next investigated the best way of determining the lower value for J − K as a function of K_s. When selecting RSGs in M31, Neugent et al. (2020) chose to make their low (yellow) J − K_s limit parallel to the high (red) J − K_s limit following previous studies (e.g., Boyer et al. 2011). In their case, there were a substantial number of yellow stars without Gaia data, and they were concerned with removing yellow foreground contamination. However, here we do not have this issue and placing similar cuts would impose unrealistic requirements on the temperatures of the brightest stars. Using the transformations in the next section, a T_eff of 4200 K corresponds to an observed J − K_s = 0.917, where we assume a visual extinction A_V = 0.75 mag as argued below. We therefore have modified the low (yellow) J − K_s limit as shown in Figure 3 compared to what Neugent et al. (2020) used in M31 and as documented in Table 1. The scarcity of stars to the left of the low J − K_s line is consistent with evolutionary theory: stars zip across the HRD to the RSG phase, spending very little time as YSGs, of order tens of thousands of years (see discussion in Drout et al. 2009 and Neugent et al. 2012b). The tilt of this line at lower luminosities in essence says that higher-luminosity RSGs are cooler than lower-luminosity RSGs; this is consistent with what the evolutionary tracks say as well (Ekström et al. 2012; Stanway & Eldridge 2018).

Finally, we decided to relax the color requirement on the upper J − K values at the brightest magnitudes, as there should no longer be any AGB contamination. Again, this is consistent with what Neugent et al. (2020) did in M31 and Yang et al. (2019) did for the SMC. This allows for the fact that the higher-luminosity RSGs could be more heavily reddened by circumstellar dust, an effect confirmed by Neugent et al. (2020) in their M31 study.

To put our derived binary fraction in context, it is helpful to understand the physical properties of the stars probed; in addition, our LMC RSG sample will likely be used by ourselves and others for a variety of studies. We therefore provide here the transformations from the CMD to the physical HR diagram of T_eff and the log of the luminosity relative to that of the Sun ($\mathrm{log}L/{L}_{\odot }$). Our procedure closely parallels that of Neugent et al. (2020).

The typical OB star in the LMC has an extinction in the visual bandpass of A_V = 0.40 mag (Massey et al. 2007), but in general, RSGs have larger extinction due to circumstellar dust (Levesque et al. 2005; Massey et al. 2005). The typical A_V for RSGs in the LMC is 0.75 mag based upon the spectrophotometric fits of 36 stars done by Levesque et al. (2006). This is the same as what we adopted for RSGs in M31 (Neugent et al. 2020) based upon the spectrophotometric fits of Massey et al. (2009). In M31, we found a clear trend in A_V with luminosity for the highest luminosity stars, not surprising given that those stars are likely to suffer higher mass loss (see, e.g., Ekström et al. 2012) as they approach the Eddington limit or develop late-stage pulsations at high luminosities (van Loon et al. 2005; Davies et al. 2008; Bonanos et al. 2010). Thus, we adopt A_V = 0.75 for the entire sample except for the few brighter stars (K_s < 8.5). For those stars, we determine the extra extinction in such a way as to match the average K_s versus J − K_s relation along a reddening vector. The relevant equations are given in Table 1. These higher reddenings affected only 45 stars in our sample of 4090 RSGs (1.1%) and had values that ranged from A_V = 1.34 mag to 3.37 mag. RSGs with considerably larger amounts of circumstellar extinction are known both in the Galaxy (Massey et al. 2005) and the LMC (Levesque et al. 2009). The impact of these higher extinction values on the derived luminosities is relatively minor: as noted in Table 1, the equivalent A_K values are only 12% of the A_V values, and at most the extra extinction we deduce increases $\mathrm{log}L/{L}_{\odot }$ by 0.1 dex. Given the luminosity dependence on these higher mass-loss events, we do not believe we are missing a population of lower-luminosity RSGs with higher-than-expected reddening values.

Before applying any extinction correction, we first transform the 2MASS J − K_s colors and K_s brightness to the standard J − K and K system (Bessell 1990) using the transformations determined by Carpenter (2001); these equations are given in Table 1. The transformation from J − K to T_eff is then determined by first de-reddening the color assuming E(J − K) = A_V/5.79 (Schlegel et al. 1998), and then using the MARCS stellar atmosphere models (Plez et al. 1992) computed for LMC metallicity described by Levesque et al. (2006) to relate the intrinsic (J − K)₀ colors to T_eff. The typical errors on T_eff are 150 K, where this value is dominated not by the photometric uncertainties but rather by assuming an uncertainty of ±0.5 mag on our value for A_V. The relationship is quite linear over the relevant color range. To determine the bolometric luminosity, we first correct the K-band photometry for extinction (A_K = 0.12A_V; Schlegel et al. 1998). The bolometric correction then comes from the adopted T_eff, and we determine the bolometric magnitude using a distance modulus of 18.50 (50 kpc; van den Bergh 2000). The relevant equations are given in Table 1.

We note explicitly that our reddening correction makes the assumption of a normal Cardelli et al. (1989) reddening law with a ratio of total-to-selective extinction R_V = 3.1. However, we also note that our use of NIR photometry makes this assumption relatively benign and our results robust. We have used A_V to characterize the amount of reddening both for convenience and because the 0.75 mag value came out of fitting the optical spectrophotometry by Levesque et al. (2006). However, as shown in Table 1, we actually correct the photometry by A_K (for luminosity) and by E(J − K) for effective temperature and bolometric corrections to the luminosity. The relationships between these and A_V come from Schlegel et al. (1998), who adopted the Cardelli et al. (1989) law, which would be generally applicable in the optical and NIR to the interstellar dust found in the Milky Way and Magellanic Clouds. However, we know little about the dust properties of grains in the circumstellar environments of RSGs. As discussed by Massey et al. (2005), Galactic RSGs with abnormally large extinction compared to neighboring OB stars show a correspondingly large UV excess compared to stellar models, primarily indicative of scattering, but that large grains may also play a role. Indeed, the recent dimming of Betelgeuse seems like it was caused by a dust episode with grains that are so large that the extinction was nearly gray (Levesque & Massey 2020). What we do know from multiple SED fittings is that the Cardelli, Clayton, and Mathis law (Cardelli et al. 1989) works well at wavelengths beyond the near-UV; see, e.g., Levesque et al. (2005, 2006, 2007), even in cases of extremely high extinction, such as WOH G64 with A_V = 6.8 mag (Levesque et al. 2009). Thus, the assumption that the circumstellar reddening in the optical and NIR is similar to that of interstellar dust appears to be borne out empirically. In addition, the use of NIR photometry makes the issue of reddening relatively moot, given that the extinction in A_K is only 12% that of A_V, and thus an uncertainty even of 1 mag in A_V would affect our M_K value by only 0.12 mag. As mentioned above, such a mistake would affect the derived luminosity by 0.13 dex when the effect on both the extinction and bolometric correction was taken into account. It is indeed partially for this reason that we chose to use NIR photometry.

Table 2 contains the coordinates, 2MASS J and K colors, and derived temperatures and luminosities for the 4090 RSGs in the LMC. We note that the color limits imposed in the CMD require a T_eff as a function of $\mathrm{log}L/{L}_{\odot }$. For $4.0\leqslant \mathrm{log}L/{L}_{\odot }\leqslant 4.25$, T_eff has a minimum of $5300\mbox{--}362\mathrm{log}L/{L}_{\odot }$ and a maximum of $5333\mbox{--}362\mathrm{log}L/{L}_{\odot }$. For $\mathrm{log}L/{L}_{\odot }\gt 4.25$, T_eff has a minimum of 4200 K and a maximum of $5333\mbox{--}362\mathrm{log}L/{L}_{\odot }$.

While 2MASS NIR colors are helpful for identifying RSGs, we needed additional information about the RSGs’ flux in the bluer wavelengths to determine if they have B-star companions. For this information, we used Zaritsky et al. (2004), which contains U, B, V, and I photometry for most of our survey region of 4090 stars. After cross-matching our list of LMC RSGs with Zaritsky et al. (2004) using a 1″ radius, we found that 3870 (95%) had U-band photometry, 3992 (98%) had both B and V, and 3579 (88%) had I. The remaining 98 stars had no match in Zaritsky et al. (2004), primarily due to crowding (over half of such stars were located in the inner bar).

Because RSGs with B-star companions will have smaller U − B colors (and thus higher flux at bluer wavelengths) than those without, we focused on observing RSGs with small U − B colors. As discussed in Neugent et al. (2019), we previously identified RSG + B-star binaries in the Magellanic Clouds using archival spectra. Of the 23 we identified, 8 have U − B < 0, and all but 2 have U − B < 1. Thus, as we will discuss when we calculate the binary fraction, we believe that the majority of RSG + B-star binaries have U − B colors less than 1 so we focused the majority of our spectroscopic observing efforts on those stars. However, we still observed a few candidates with U − B colors between 1 and 2 to better characterize the binary fraction at slightly higher U − B values and attempt to define a U − B color “cutoff” above which RSG + B-star binaries are not found.

Of the 95% of LMC RSGs with U and B photometry, 127 (3%) have U − B < 0, 388 (10%) have 0 < U − B < 1, and 2870 (74%) have 1 < U − B < 2. However, to maximize the number of stars observed, we focused on the brighter targets (generally those with U brighter than 16th). This decreased our initial target list to 107 stars with U − B < 0, 142 with 0 < U − B < 1, and 25 with 1 < U − B < 2. We then attempted to observe a subset of those with a wide range of U − B values to determine the binary fraction as a function of U − B.

Candidate RSG + B-star binaries were observed with the Magellan Echellette (MagE; Marshall et al. 2008) instrument on the Baade 6.5 m telescope at Las Campanas Observatory over two dedicated observing runs in 2019 and 2020 and an engineering run in 2019. The first two-night run occurred on UT 2019 September 7–8 when we observed both SMC and LMC targets and were plagued by atrocious seeing that varied between 20 and 40. We were still able to achieve adequate signal-to-noise ratio (S/N) by simply increasing our exposure times thanks to our objects’ bright magnitudes (U ∼ 14.6, B ∼ 14.3, V ∼ 12.9). The seeing was somewhat improved during our second run on UT 2020 January 14–15 with seeing that started out at 10 and degraded to 22. On the second run, just LMC targets were observed. Additionally, 14 LMC targets were observed with MagE during engineering time on UT 2019 September 12–13 with 10 seeing. On all runs, we used a 1″ slit and exposure times ranged between 300 for the brightest targets to 1200 for the dimmest targets obtained during poor seeing. The MagE instrument gives a wavelength coverage of 3400 Å to 1 μm at R ∼ 4100, allowing us to observe both the upper Balmer lines between 3700 and 4000 Å and the TiO bands redwards of 6000 Å simultaneously. We additionally observed spectrophotometric standards throughout the night to assist with flux calibration. The data were extracted using both the iraf echelle package and mtools routines designed by Jack Baldwin for the reduction of spectra obtained with another one of Las Campanas’ instruments, the Magellan Inamori Kyocera Echelle.

Our goal when observing was both to spectroscopically confirm single and binary RSGs but also to get a sense of how the binary fraction might change with respect to increasing U − B colors. To do this correctly, we had to be confident in our classifications and not, for example, mistakenly classify a single RSG as single when really we just had not observed long enough to detect the faint upper Balmer lines of its companion. Thus, our exposure times were dictated by our desire to either observe or conclusively rule out the presence of the upper Balmer lines. Based on previous observations described by Neugent et al. (2018a), we determined that an S/N greater than 100 at our spectral resolution of R ∼ 4100 was needed to definitively rule out the presence of upper Balmer lines coming from the faintest possible B star (a 15,000 K B dwarf; M_V = −1.5). We therefore first observed each target with a short (5–10 minute) exposure and checked the S/N of the spectra in real time. We additionally performed quick-look reductions which were completed just a few minutes after each spectrum had read out. If the star showed upper Balmer lines, we moved on. If it did not and the S/N was below 100, we continued observing the candidate until we either detected the upper Balmer lines or the S/N reached 100. Given this observing strategy, we are confident that the stars we have labeled as single do not have hidden B-star companions with M_V > −1.5, which should encompass all B-type stars.

Overall, the photometry of the spectroscopically confirmed binary and single stars was as expected with stars with lower U − B colors being binaries. We observed 27 candidates with U − B < 0 and 74% of them were RSG + B-star binaries (the remaining 7 stars being single RSGs). We found a similar percentage of binaries (71%) for the 24 stars we observed with 0 < U − B < 1. For the remaining 12 stars we observed with U − B > 1, only one was an RSG + B binary. As discussed extensively in Section 2.3.1 in Neugent et al. (2019), likely reasons for single RSGs having anomalously blue U − B colors include the possibility of dust scattering that produces a blue reflection nebula or even the much simpler explanation of poor initial photometry.

While our overall goal was to determine the binary fraction of RSGs in the LMC, our first observing run was scheduled in early September and the LMC was not above 2 airmasses until around halfway through the night. Thus, we started off each night by observing a few candidates in the SMC based upon stars with U − B < 1 and U brighter than ∼16th from the RSG sample presented in Yang et al. (2019) and cross-matched with Zaritsky et al. (2002) for U, B, V, and I colors. Overall, we observed 22 new candidates and confirmed 14 as single RSGs and 8 as new RSG + B binaries. Because we were not able to observe a statistically significant sample of candidates, we are not comfortable estimating a binary fraction for RSGs in the SMC yet. While we hope to be able to expand on this research more in the future, at this point we have chosen to simply include our findings on these 22 stars as part of this paper in Table 3. A further discussion on deriving the physical properties of these stars can be found in the Appendix.

Table 3.  Spectroscopically Observed SMC Stars

2MASS	α2000	δ2000	Ks	σKs	J − Ks	${\sigma }_{J-{Ks}}$	U	B	V	Class.	RSG Component
											Teff [K]	${\sigma }_{{T}_{\mathrm{eff}}}$	Type
00473688–7304441	00 47 36.886	−73 04 44.18	8.319	0.024	1.147	0.033	15.603	14.734	12.736	RSG	3525	25	M2
00503842–7319359	00 50 38.420	−73 19 35.95	10.206	0.025	0.963	0.032	16.018	15.547	14.054	RSG + B	3825	100	K5-M0
00523496–7226017	00 52 34.968	−72 26 01.73	10.023	0.023	0.855	0.033	15.073	14.574	13.256	RSG	3875	100	K5-M0
00523564–7251053	00 52 35.650	−72 51 05.32	9.745	0.023	0.854	0.031	15.553	14.594	13.096	RSG	3875	100	K5-M0
00531772–7246072	00 53 17.729	−72 46 07.20	9.271	0.023	1.005	0.033	14.103	13.884	12.836	RSG	3800	100	K5-M0
00532528–7215376	00 53 25.290	−72 15 37.68	9.758	0.023	0.942	0.033	15.293	14.744	13.296	RSG + B	3850	100	K5-M0
00534156–7215268	00 53 41.563	−72 15 26.83	9.590	0.023	0.954	0.033	14.953	14.624	13.226	RSG	3900	100	K2-3
00534451–7233192	00 53 44.517	−72 33 19.21	9.462	0.020	1.021	0.030	14.563	14.464	13.226	RSG + Be	3725	25	K5-M0
00562532–7228182	00 56 25.324	−72 28 18.26	10.032	0.021	0.888	0.030	14.823	14.634	13.376	RSG	3950	100	K2-3
00585831–7213429	00 58 58.310	−72 13 42.93	9.837	0.021	0.923	0.032	13.463	13.894	13.066	RSG	3900	100	K2-3
00595187–7243351	00 59 51.870	−72 43 35.15	9.528	0.019	0.981	0.029	15.703	14.824	13.236	RSG + B	3875	100	K5-M0
01004445–7159389	01 00 44.454	−71 59 38.96	9.911	0.026	0.963	0.039	15.545	14.944	13.531	RSG + B	4050	100	K2-3
01012693–7201414	01 01 26.930	−72 01 41.43	9.235	0.024	0.991	0.034	14.863	14.434	12.926	RSG	3900	100	K2-3
01014357–7238252	01 01 43.579	−72 38 25.29	9.358	0.021	1.005	0.031	14.323	14.364	13.076	RSG + B	3900	100	K2-3
01020407–7226109	01 02 04.076	−72 26 10.90	9.420	0.023	1.035	0.033	14.623	14.614	13.286	RSG	3775	100	K5-M0
01024480–7201517	01 02 44.801	−72 01 51.75	9.386	0.021	0.954	0.030	15.613	14.634	12.986	RSG	3900	100	K5-M0
01033730–7158448	01 03 37.301	−71 58 44.88	9.598	0.020	0.962	0.030	15.013	14.484	13.096	RSG + B	3825	100	K5-M0
01033984–7239059	01 03 39.849	−72 39 05.93	10.362	0.021	0.969	0.032	16.065	15.436	13.955	RSG + B	3850	100	K5-M0
01034536–7207490	01 03 45.360	−72 07 49.03	9.639	0.025	0.959	0.034	14.963	14.764	13.386	RSG	3850	100	K5-M0
01061197–7214380	01 06 11.970	−72 14 38.00	10.072	0.019	0.901	0.029	14.633	14.484	13.346	RSG	4000	100	K2-3
01064766–7216118	01 06 47.669	−72 16 11.85	8.312	0.019	0.929	0.031			11.870	RSG	3750	25	K5-M0
01081478–7246411	01 08 14.787	−72 46 41.10	9.174	0.023	0.955	0.033	15.263	14.314	12.696	RSG	3850	100	K5-M0

Note. J and K photometry from 2MASS. U, B, V photometry from Zaritsky et al. (2002).

A machine-readable version of the table is available.

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To produce the initial estimate of the binary fraction of RSGs with B-type companions based upon archival photometry and our spectroscopically observed LMC stars, we relied on a k-NN approach. This method is based upon the idea that stars with bluer colors and/or UV signal are more likely to be binary RSGs, which is something we have confirmed spectroscopically. The k-NN algorithm assigns probabilities of binarity to each of the remaining candidate stars that we did not spectroscopically observe by looking at how close they are in color–color space to the stars that have been spectroscopically confirmed. It follows that candidates with colors similar to known binaries are more likely to be binaries than those with colors similar to known single RSGs. This method allows us to calculate the percentage likelihood that each individual candidate is a binary RSG.

The input columns to the k-NN algorithm were all based on archival photometry including U, B, V, and I photometry from Zaritsky et al. (2004) as well as the calculated U − B and B − V values. We opted not to include the 2MASS J and K photometry because the single and binary RSGs were evenly distributed throughout the CMD and thus the NIR colors did not provide any additional information that could help classify the stars. We additionally included a flag related to the brightness of the star in the NUV based upon survey data from the GALEX (Martin & GALEX Team 2005; Morrissey et al. 2007; Bianchi 2009). RSG + B-star binaries should be bright in the UV given the B-star companion while single RSGs should not be. Thus, we hoped that the presence of NUV signal would help identify binaries. To determine whether the GALEX data is sensitive to the lowest luminosity B companions, we determined whether we would detect the flux of a reddened LMC A0V with a typical magnitude of 21.3 in the GALEX NUV filter. According to Simons et al. (2014), the GALEX NUV detection limit in the LMC is 22.7 mag, and thus, we are sensitive to even the lowest-mass B-star companions.

NUV images for each of the 4090 LMC RSGs were downloaded from the Mikulski Archive for Space Telescopes (MAST) and then simple aperture photometry was run to obtain an estimate of the star’s brightness. The stars were then grouped into four categories based on their aperture photometry: no data at the specified coordinates (24%), data but no NUV signal detected (63%), dim NUV signal (6%), medium NUV signal (3%), and bright NUV signal (2%). The 76% with aperture photometry were then visually checked to confirm that the category (none, dim, medium, or bright) matched what was found in the images. While the GALEX data proved to be very useful when used in combination with the Zaritsky et al. (2004) photometry as part of the k-NN algorithm, it should be noted that there are issues present within the data set. These are discussed in great detail in Simons et al. (2014) but revolve around the GALEX resolution being quite large at 5″ and thus inadequate in the crowded OB associations. Thus, we have used the GALEX data as one small piece of our overall method of determining binarity, and not as the determining factor. Still, we do find that confirmed RSG + B-star binaries are brighter in GALEX than the confirmed RSG single stars with 68% of the binaries with data showing either medium or bright NUV signal and 70% of the single RSGs showing either dim or no NUV signal. Additionally, as discussed above, not all photometry (including Zaritsky et al. 2004) is perfect. By using the k-NN approach and using inputs from different data sets in different passbands, we decrease the overall weight being placed on any individual measurement. Thus, we hope this will decrease erroneous results due to a single poor measurement of a star, for example.

To implement the k-NN algorithm, we relied on Python’s SCIKIT-LEARN machine-learning package. Our total number of spectroscopically confirmed RSG + B binaries included the 36 described in this paper, as well as the 10 discussed in Neugent et al. (2019), 4 found by Levesque et al. (2006), and 5 found by Dorda et al. (2018), bringing the total up to 55. For single stars, we included the 23 described here, as well as 217 other spectroscopically confirmed single RSGs described in Neugent et al. (2019), Levesque et al. (2006), Dorda et al. (2018), and our own unpublished AAT data described in Neugent et al. (2019). Thus, we had 295 stars we could use to both train and test our data. We first scaled our data using SCIKIT-LEARN's RobustScaler to account for the fact that our features (magnitudes/colors and flags) are in different units. We then used k-fold cross-validation to train and test our model. We found that splitting our data up into eight folds (as opposed to the default five) achieved the highest accuracy when rerun against the test data set. Thus, each of the 8 test sets contained around 7 binaries and 27 single RSGs. During testing, we found that we had the highest success using a k-NN search that looked at the nearest 26 neighbors weighted based on distance. Using this method, we achieved an accuracy of 93.5%.

We applied the k-NN algorithm to the 1457 stars in our sample with both $\mathrm{log}L/{L}_{\odot }\gt 4.0$ (our completeness limit) and a minimum of B and V photometry from Zaritsky et al. (2004). Figure 4 shows a color–color plot of both the original input sample of 295 spectroscopically observed stars and the results from the k-NN classification run. It has been color-coded to reflect the percent likelihood of each star being a binary, with the bluer points representing binaries and the redder points representing single stars. Note that the “transitional zone” is around U − B = 1, which is what we had concluded empirically during our observations. Stars with U − B colors smaller than 1 are more likely to be RSG binaries while stars with U − B colors higher than 1 are more likely to be single RSGs. The input data and final percentage likelihoods for each star are shown in Table 4.

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Because we assigned a percent likelihood of binarity to each individual candidate star, we could then get a first estimate of the binary fraction before taking any biases into account. By simply summing up the percent likelihood of each star being in a binary system and dividing by the percent likelihood of each star being a single RSG, we can estimate the binary fraction of RSG + B stars with $\mathrm{log}L/{L}_{\odot }\gt 4$ ($M\gt \sim 9\ M\odot$). After adding in the 295 spectroscopically confirmed stars and taking the 93% accuracy rate of the k-NN algorithm into account, we arrive at a binary percentage of ${13.5}_{-6.67}^{+7.56} \%$ where the errors were calculated by assuming the most extreme scenarios given the 93% accuracy rate. However, as we discuss next, there are other factors to take into account that will increase this percentage slightly.

We additionally must consider eclipsing binaries as the majority of our binary fraction estimate is based upon single-epoch photometry. Take, for example, the Galactic RSG + B-star binary system, VV Cep, which has a 20.3 yr orbit and is in secondary eclipse for 18 months, or around 7% of the time (Bauer & Bennett 2000). If there are systems like VV Cep in our sample and the companion was behind the RSG when the photometry was obtained, these systems would not show up as binaries. Thus, we must account for this bias. If we had orbit determinations for our binaries, it would be possible to calculate this probability directly. However, because our classifications are based upon single-epoch spectroscopy, this is not possible. Instead, we must make some assumptions about RSG binary systems and their orbits to determine what percentage of them are eclipsing at any given time. In the future, this calculation could hopefully be done independent of any modeling either by obtaining U, B, and V photometry at another epoch (in essence, repeating the work of Zaritsky et al. 2004), or a detailed analysis of the orbital parameters of our discovered RSG binaries. But at this point, this is outside the scope of the current work and thus cannot be done observationally.

Instead, we turned to the BPASS models (v2.2.1) from Eldridge et al. (2017) and Stanway & Eldridge (2018). We are grateful to J.J. Eldridge for help providing a program that allowed us to easily estimate the percentage of RSGs that would be in eclipse at any given moment. BPASS uses the findings of Moe & Di Stefano (2017) as initial conditions and then evolves the binary systems to populate appropriate binary companions to RSGs and determines (along with a host of physical properties) their periods, mass ratios, and separations at an LMC-like metallicity of z = 0.008. The maximum angle of inclination for eclipses is then computed based on the RSG’s radius and the separation of the stars, and then, for those that could possibly eclipse, the eclipse duration is determined. Simple Poisson errors were also estimated based on the number of eclipsing binaries. Based upon these calculations and the types of binaries we are sensitive to detecting, we estimate that 3.61% ± 0.01% of our targets that appear to be single RSGs are actually eclipsed binaries. (Note: further information on how we ran BPASS to most closely align with our observations is discussed in Section 5). This increases the binary fraction slightly, but not substantially.

One possible contaminant in our survey is line-of-sight pairings. These are stars where both the RSG and B-star are genuine LMC members, but the B star is not gravitationally bound to the RSG and instead just happens to exist in our line of sight to the RSG. In general, we expect these cases to be rare given the photometric quality checks we went through when selecting the original list of RSG candidates in 2MASS (stars with poor photometry flags, and thus possible visual pairings, were ignored), but the presence of a faint B star in the LMC foreground or background could still contribute Balmer lines to a spectrum. (For example, take LGGS J004453.06 + 412601.7, which Neugent et al. 2012a classified as a WN+TiO. We originally thought this might be the first example of an RSG + WR binary system, but based on archival imaging, we determined it is actually an M31 WR + foreground M dwarf pairing). To determine the probability that each of our spectroscopically confirmed RSG + B-star binaries is actually a line-of-sight pairing, we ran a simple Monte Carlo simulation that took into account the OB-star density around each of our confirmed RSG binaries.

Overall, the process worked as follows: for each of our confirmed LMC RSG + B-star binaries, we found the locations of the OB stars within a 5′ radius of the binary using B and V photometry from Zaritsky et al. (2004). We then ran a simulation that randomly placed an RSG within this region and checked to see if it fell within 1″ of one of the OB stars. If it did, we flagged it as a line-of-sight pairing. The value of 1″ comes from the size of our slit while observing on Las Campanas.

We opted to include both O stars as well as B stars in our simulation because, as described below, they are possible RSG binary companions, even if the likelihood is small. Also, given that we were relying on B and V photometry from Zaritsky et al. (2004), it is difficult to distinguish O and B stars from one another because their B − V colors are nearly identical due to being on the tail end of the Rayleigh–Jeans distribution after having peak flux in the UV. To select the stars within the 5′ radius of the binary, we removed everything redder than an A0V by using a cut at (B − V) < 0.0. We then took the average reddening of the LMC to be 0.13 from Massey et al. (2007) and set the brightness limit of V = 21 because spectroscopically, we would not be able to observe the upper Balmer lines from OB stars fainter than that.

After running the simulation 10,000 times, we found that there was a 1.9% ± 2.0% chance that any of the observed RSG + B-star binaries was actually a line-of-sight pairing (with 0% being the minimum and 10% being the maximum for any individual system). We additionally ran the program on the spectroscopically confirmed single RSGs and found a very similar distribution with a 1.6% ± 1.7% chance that any of the single RSGs could have a line-of-sight companion (again, 0% was the minimum and 10% was the maximum). Given both the similarity between these two results and their low values, we believe that line-of-sight pairings have a negligible impact on the overall binary fraction.

In Neugent et al. (2018a, 2019), we argue that RSGs will primarily have B-type companions from an evolutionary point of view because longer-lived main-sequence stars (A, G, K, and M stars) will not have formed by the time an RSG is created. However, what about the shorter lived or non-main-sequence stars such as O stars, YSGs, RSGs, WRs, etc.? From an evolutionary point of view, these systems are certainly possible. However, so far, none have been observed and the lifetimes of such companion stars are so short that finding such a system is statistically unlikely. Here we delve deeper into each of these pairings and how their occurrence could alter our calculated RSG binary fraction.

The most likely system other than an RSG + B-star binary is an RSG + O-star binary, simply due to the longer duration of of an O star’s time on the main sequence (a few million years) as compared to the later evolutionary stages (YSGs, RSGs, WRs, etc.), which last only tens to hundreds of thousands of years. Such a system would exist for a short period of time if two nearly equal-mass stars were born together and one evolved into an RSG while the other was still on the main sequence. In terms of these stars biasing our calculated binary fraction, due to our photometric detection method, if any O-star binaries do exist in the LMC, we have likely already detected them. The U − B colors of O stars are nearly identical to that of B stars, so they would show up as candidates based on our k-NN algorithm (possibly even as higher-likelihood candidates due to their lower U − B values). We additionally would have been sensitive to them as spectroscopic candidates. Even though their upper Balmer lines have smaller equivalent widths, the stars themselves are brighter in U and their strong He i and He ii lines would have shown up prominently. While none of our spectroscopically confirmed binaries appear to have O-type companions, our method of calculating the binary fraction is sensitive to such pairings.

Continuing on a massive star’s evolutionary path are the even shorter-lived YSG and RSG stages. We admit that such systems would be difficult to detect and would likely only be observable if eclipsing or as a spectroscopic binary with some of the narrow metal lines (such as the Ca ii triplet) appearing double. Again, because these pairings are statistically unlikely and have never been observed, we do not think they will affect our calculated binary fraction. However, we do point out that our method of detecting RSG binaries is not sensitive to such systems.

Next up are WR+RSG binary systems. We can confidently say that none of these have been detected in any of the nearby galaxies and furthermore, we do not expect to find any since the population of WRs in the LMC is thought to be complete (Neugent et al. 2018b). Because the discovery method for finding the WRs was based on their strong emission lines, any WR+RSG binaries would have been found as part of these galaxywide searches.

Finally, let us consider RSGs with neutron star or, in the case of more massive primaries, black hole companions. Such systems can occur if the RSG is originally the less massive of the two stars and the binary is not disrupted when the primary explodes as an SN. If the post-SN separation is too small, the systems will subsequently interact, potentially merging to create a Thorne–Żytkow object such as the candidate recently found in the SMC (Levesque et al. 2014). However, if the post-SN separation is wide enough, the secondary can expand into the RSG phase. While to the best of our knowledge no RSG + compact object binaries have yet been confirmed, and the majority of known high-mass X-ray binaries in the Magellanic Clouds have periods too short to allow the secondary to expand to the RSG phase (Antoniou & Zezas 2016; Haberl & Sturm 2016), there are a number of observational biases against detecting long-period systems. Indeed, RSGs have been identified as candidate counterparts/donor stars to several ultraluminous X-ray sources (Heida et al. 2016; López et al. 2017) and recent high-cadence time-domain surveys are now facilitating the detection of noninteracting compact object systems (e.g., Thompson et al. 2019). Theoretically, both the rate of binary disruptions and the post-SN separation distribution are highly dependent on uncertain SN kick prescriptions (e.g., Bray & Eldridge 2018). However, using BPASS v2.2.1 as described above, we estimate that 2.42% ± 0.01% of RSGs have compact object companions.

We are now in the position to estimate the final binary fraction of RSGs in the LMC. We initially planned our observations to be sensitive to RSG + B-star companions given that B-type stars should dominate the sample based on evolutionary constraints. However, we additionally point out that our selection criteria is sensitive to the less common O-type companions as well. Using the k-NN approach described above, we observationally estimate the RSG + OB-star binary fraction as ${13.5}_{-6.67}^{+7.56} \%$. We then used BPASS to estimate both the fraction of eclipsing binaries (3.61% ± 0.01%) and RSG + compact companions (2.42% ± 0.01%) that we were not sensitive to in our search. Overall, we reach a final percentage of ${19.5}_{-6.7}^{+7.6} \%$ for RSGs with $\mathrm{log}L/{L}_{\odot }\gt 4$. These values are shown in Table 5. We stress that we are not including RSG + protostars in this calculation and that we are not sensitive to RSG + RSG or RSG + YSG systems, though from an evolutionary standpoint, these should be extremely rare. We expect from first principles that in order for an RSG + RSG system to exist even momentarily would require the two stars to be born with masses within 5% of each other; for the RSG + RSG to last for the majority of the RSG phase of the higher-mass star, it would require an initial mass ratio q of 0.98–1.02. A more exact calculation is beyond the scope of the present paper, but will be discussed in future work. In the next section, we compare our results to expectations from BPASS for the total population as well as the binary fraction of other types of massive stars.

As discussed in the Introduction, the binary fraction of long-period, noninteracting OB-star systems could be between 70% and 100% (Gies 2008; Sana et al. 2012) with the short-period binary fraction being closer to 30%–35% (Garmany et al. 1980; Sana et al. 2013). Because RSGs evolve primarily from OB stars, why is our calculated binary fraction of ${19.5}_{-6.7}^{+7.6} \%$ so much lower?

The key thing to remember is that RSGs have radii that are hundreds to even thousands of times the radius of the Sun. Two main-sequence stars less than 30 M_⊙ in a binary system must have separations on the order of thousands of solar radii to not interact at some point before the more massive star turns into an RSG, thus creating an RSG binary system. As discussed in Sana et al. (2012), binaries with orbital periods up to around 1500 days will exchange mass throughout their lifetime, and all except for one of the binary systems they measured had periods less than 1000 days (note: some of their rarity is a selection effect as long-period systems are more difficult to detect spectroscopically, but even in the “corrected” sample set, there were few binaries with periods longer than 1000 days). Thus, the majority of these systems will interact before the more massive component turns into a RSG. When they interact, a few different things can occur. In close systems, RLOF will prevent the more massive star from ever turning into an RSG and a merger of the two OB-type stars might occur. In slightly more separate systems, the more massive star will turn into an RSG but then a merger between the evolved RSG and the unevolved companion might occur.

In short-period systems, the two stars will begin interacting as the more massive star evolves and grows in radius. However, RLOF will eventually occur and the more massive star will be stripped of its entire envelope, losing much of its original mass. The secondary will then gain mass and angular momentum but neither will evolve into the RSG stage. As discussed in Sana et al. (2012), it is estimated that 40%–50% of O-star binaries will have their evolution altered due to RLOF.

In the case of a merger at the RSG phase, the binary system starts off with two main-sequence stars. Over time, the more massive star evolves first and eventually turns into an RSG with a companion. If the two stars are close enough, they will influence each other’s orbits, begin spinning up, and transfer angular momentum. Once they merge, the RSG will photometrically appear single (though with a much higher rotational velocity). From photometry alone, a merged single star will generally be indistinguishable from an always-single star. While an RSG merger has not been directly observed, it has been hypothesized as an explanation for why one of the most famous RSGs is spinning so fast. Betelgeuse has a projected rotational velocity of around 15 km s⁻¹, much higher than that of a normal RSG. Wheeler et al. (2017) suggest that this increased velocity could be due to a past merger with a smaller mass companion. Sana et al. (2012) estimate that 20%–30% of massive, apparently single stars, are actually the result of mergers.

Taking an initial O-star binary fraction of 70% and considering both mergers (20%–30% of binaries) and RLOF (40%–50% of binaries), our estimated binary fraction of ${19.5}_{-6.7}^{+7.6} \%$ is well in accord with the broad model predictions done by Sana et al. (2012). Additionally, if we look at Figure 1 (left) in Sana et al. (2012), we see that ∼15% of O-star systems have periods longer than 1000 days and thus would likely turn into RSG binary systems after the more massive star has evolved. This percentage is very well aligned with our findings.

As discussed in Section 4, we used BPASS v2.2.1 (Eldridge et al. 2017; Stanway & Eldridge 2018) to calculate the percentage of eclipsing binaries and RSG + compact companions. Here we go into a bit more detail about these BPASS simulations and compare the binary fraction we found to the BPASS results.

To ensure a fair comparison between our results and those of BPASS, we used our photometric selection criteria transformed to T_eff and $\mathrm{log}L/{L}_{\odot }$ (as described in Section 2.4) to select model RSGs. We additionally placed a minimum mass constraint (M > 8 M_⊙) on the RSG and a minimum luminosity of $\mathrm{log}L/{L}_{\odot }\gt 4$. Using these two selection methods, we believe we have separated out the AGB stars in the BPASS models at least as well as we have done photometrically. Given these constraints, the BPASS models predict that 31% are single RSGs, 25% are merged RSGs, 2% are RSGs + compact objects (as discussed above), and the remaining 42% are RSG + main-sequence star binaries (all percentages have Poisson errors <1%) at an LMC-like metallicity of z = 0.008. So, why the factor of 2 discrepancy?

The primary reason is that BPASS is a stellar evolution and population synthesis code and does not deal with star formation (yet!). Thus, all stars arrive on the ZAMS at the same time, regardless of their mass. When taking the types of stars that might exist in binary systems with RSGs into account, BPASS uses the prescription given by Moe & Di Stefano (2017) without considering whether these stars would have arrived on the ZAMS by the time the RSG was formed. Due to the initial mass function (IMF) favoring lower-mass stars, this adds a significant number of low-mass companions.

Using the BPASS models, we can plot an HR diagram of the companions, as is shown in Figure 5. From Cox (2000) we know that a B8V has $\mathrm{log}L/{L}_{\odot }\sim 2.5$ and a B0I has $\mathrm{log}L/{L}_{\odot }\sim 5.5$. Thus, we can make cuts in the BPASS companions to determine the percentage of binaries with O, B, and less-luminous companions. We find that, as expected based on lifetimes alone, O-type companions are exceedingly rare and make up just 1% of the binaries. The majority (74%) are B-type stars, and the remaining 25% are stars that would not have reached the ZAMS before the formation of an RSG. Thus, we can conclude that 25% of the RSG binaries estimated by BPASS are most likely single RSGs. This brings the BPASS-estimated binary fraction down to 32%, which includes RSGs with O- and B-type companions, compact companions, and eclipsing systems. Because our calculated fraction is lower, this may suggest (again) that either the merger fraction is underestimated or the initial OB binary fraction is overestimated.

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As described in the Appendix, we additionally obtained estimates of T_eff, luminosities, and radii for the 63 LMC RSGs we observed on Magellan. We can additionally estimate the radii of our entire sample of k-NN classified RSGs using the photometrically calculated temperatures and luminosities, as shown in Figure 6. Because stars with larger radii will interact with a larger fraction of binary companions, it is interesting to examine both the average radii of single versus binary stars and the binary fraction of large versus small radius stars. Because these parameters will be impacted by a variety of factors, from the initial binary fraction as a function of mass to the IMF, we compare these parameters found for our sample to the same parameters from the BPASS models.

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First, we can compare the physical properties of the 25 single RSGs to those of the 38 binaries we observed spectroscopically. One might expect that the average radii of the binaries will be smaller because RSGs with larger radii are more likely to have merged with their companions. As the temperatures of RSGs are relatively constant because they sit at the Hayashi limit, it follows that the average luminosities of RSGs in binary systems might be lower as well. However, simply averaging the temperatures, luminosities, and radii for both the single and binary systems shows that there is no difference between the two sets. The average T_eff, $\mathrm{log}L/{L}_{\odot }$, and R for the spectroscopically confirmed binaries are 3710 ± 80 K, 4.75 ± 0.25, and 610 ± 220R_⊙, respectively. For spectroscopically confirmed single stars, it is 3700 ± 100 K, 4.78 ± 0.25, and 640 ± 210R_⊙.

We can also divide the k-NN classified sample into two bins, each with around 730 stars: those with a small RSG radius (R < 300R_⊙) and those with a large RSG radius (R > 300R_⊙). A simple calculation reveals that, surprisingly, the binary fraction is much higher (36% versus 4%) for RSGs with larger radius. Overall, we would expect that larger radii RSGs should have a higher incidence of mergers, but this might also be balanced out by the steep dependence on the IMF. If we do a similar study with the BPASS RSG + OB binary systems, we find that there is almost no dependence on RSG radius, and in both bins (small and large RSG radius), the binary fraction is around 30%. As we continue to spectroscopically observe more single and binary systems, we will find out whether our observed results are due to small number statistics or whether the two populations really differ that drastically.

There were six additional stars we observed spectroscopically that were not included in the binary fraction calculations for various reasons. Each of these reasons points to a possible completeness issue (field size, 2MASS flag requirements, and color cuts), which we discuss in detail below. However, we believe that each of these issues will simply lower our sample’s overall completeness of RSGs in the LMC but should in all cases impact binaries and single stars in the same manner, thus having a negligible impact on our final binary fraction.

As described in Section 2.1, we chose to select RSGs within a well-defined region of the LMC centered on ${\alpha }_{{\rm{J}}2000}$ = 05:18:00 and δ_J2000 = −68:45:00 and extending in radius by 210′. This region was chosen based on our previous survey of WRs in the LMC and because it covers the entire optical disk of the galaxy. However, while we believe this region encompasses the majority of RSGs within the LMC, there are certainly a few outside of this region. Two such examples are 2MASS stars 04415417–6727202, a confirmed RSG + B-star binary, and 05535411–6647126, a single RSG. As discussed recently by Nidever et al. (2019), the size of the LMC is an ongoing topic, with fainter stellar streams being found continuously. While our radius selection means that we have missed some of the RSGs on the outskirts, there is no physical reason why we would be missing single stars or binaries preferentially and thus, this does not alter the determined binary fraction.

When selecting candidates using 2MASS, we additionally only kept those with the best photometry (quality flags of “AAA” and “artifact contamination” flags of “000”). However, based on lists included in Dorda et al. (2018), we observed two candidates with lower quality flags. The 2MASS star 05254453–6616228 had a flag of EAA and turned out to be an RSG + B binary, and 05402532–6915302 had a “ddd” flag and is a single RSG. As with our size selection, our method of choosing flags will hinder our completeness as we will miss a few RSGs with substandard quality flags, but binaries and single stars will be equally incomplete and thus this will not change the binary fraction.

Finally, there are two stars that fell outside our color cuts in K and J − K. These cuts are always going to be difficult to execute perfectly due to uncertain star-by-star reddening values, and thus, it is not unexpected that there will be a few RSGs a bit redder than our cut or even one or two a bit bluer, such as the early K-type stars. Two examples are the single RSG 05312818–6703228, which was slightly too blue with a J − K of 0.916 instead of the required 0.917, and the binary RSG 05401638–6659303, which was a little too red. To verify that our J − K cuts were not altering our overall binary fraction, we measured the fraction as a function of J − K and found it to be constant to within our errors.

We also wanted to assess whether the ambiguous Gaia data might have changed our completeness rate or the binary fraction. There were initially 3,585 stars in our sample with ambiguous results (4.1%). After filtering out AGBs and making the appropriate color cuts, only four stars remained in our sample with log L/L_⊙ > 4. Two of them were spectroscopically confirmed LMC RSGs and the remaining two were classified as single RSGs by the k-NN algorithm. The classification of these two stars, even if they turn out to be foreground red dwarfs, will not change our final binary fraction.