Shedding Light on the Isolation of Luminous Blue Variables

Selecting unevolved massive stars photometrically is complicated. There are two problems, both related to their high temperatures. First, the optical colors of unevolved massive stars change very little over the relevant effective temperature range of 30000 K (a B0 star) to 50000 (the hottest O-type stars), and yet the bolometric corrections change very significantly (∼1.5 mag) over this range (see, e.g., Massey et al. 1989b). Thus, from optical photometry alone, one cannot infer effective temperatures or bolometric luminosities to determine masses from evolutionary tracks with any precision.⁷ Second, as a massive star ages, it cools slightly, with the absolute visual magnitude getting much brighter as the flux distribution shifts to longer wavelengths. Thus, during its main-sequence evolution, a $25\,{M}_{\odot }$ star will evolve from an O6 V star with M_V = −3.8 to a B0 I with M_V = −5.4 (see Table 1 in Massey et al. 2017). Although we would like to define photometric criteria for the identification of unevolved massive stars as a V limit as a function of color (or, preferably, a reddening-free index), the relative insensitivity of optical colors to effective temperature (and the lack of reliable synthetic colors from model atmospheres) renders this impractical given finite errors in the photometry.

Instead, we have adopted a broad-brush approach by using the photometry of Zaritsky et al. (2004) of the LMC to select high-mass stars, following Neugent et al. (2018). Our goal is to select the highest-mass stars. We adopt a magnitude cut-off of V < 13.9 to restrict the sample to stars with M_V < −5 for an apparent distance modulus of 18.9, based upon a distance of 50 kpc (van den Bergh 2000) and a typical reddening of the OB stars of $E(B-V)=0.13$ (Massey et al. 1995, 2007b). We construct the standard reddening-free index Q as $(U-B)\,-0.72\times (B-V)$, and then restrict the sample to the hottest stars, Q < −0.88, where Q < −0.88 corresponds roughly to an effective temperature > 35000 K (Massey et al. 1995). In order to exclude stars with unrealistic colors (indicating bad photometry), we further restrict the sample to Q > −1.2, $(U-B)\lt -0.5$, and $B-V\lt 0.2$. For M31 and M33, we will use the LGGS photometry (Massey et al. 2007b, 2016), adopting an approprite V cut-off to achieve the same ${M}_{V}\lt -5$ criterion, and using the same color requirements.

As shown in Figure 1, these samples should be relatively complete for stars of 40 M_⊙ and above (except in crowded regions), but will include stars as low in mass as 25 M_⊙ near the end of core-H burning when they are at their brightest visually, but still within our narrow range of Q. We designate this sample as "bright blue stars" (BBSs); we expect them all to be high-mass stars, primarily of O-type (with some high-mass early B-supergiants), although certainly not all O-type stars will be in our sample, as stars of $15\,{M}_{\odot }$ are late-type O stars early in their lives (see Table 1 in Massey et al. 2017) and are too faint and not intrinsically blue enough to be included. These lower-mass O-type stars are not expected to have an LBV phase by standard single-star evolutionary theory, but should instead evolve into RSGs. Therefore, by selecting only the highest-mass stars, we are looking at those that evolve into LBVs according to the standard model.

Zoom In Zoom Out Reset image size

Smith & Tombleson (2015), Humphreys et al. (2016), and Richardson & Mehner (2018) all disagree on exactly which stars should be considered LBVs and LBV candidates. This has been an issue since the very beginning of the terminology of "luminous blue variable" (see Bohannan 1997), and remains controversial today. The stars that were originally used by Conti (1984) to define the class included S Dor, P Cyg, η Car, and the Hubble-Sandage variables. However, the "sanctification" of LBV candidates (luminous blue stars which are spectroscopically similar to confirmed LBVs but which have not shown spectacular photometric outbursts) is contentious (see, e.g., discussion in Massey et al. 2007a; Clark et al. 2012; Humphreys et al. 2014, 2017) and there is even disagreement on what constitutes a valid LBV candidate with some stars being dismissed as merely "warm hypergiants" (Humphreys et al.2017).

This disagreement resulted in Humphreys et al. (2016) removing six stars that Smith & Tombleson (2015) had included as being LBVs, leaving a total of 10 stars that both Smith & Tombleson (2015) and Humphreys et al. (2016) agreed upon. The Richardson & Mehner (2018) catalog includes these 10 agreed-upon LBVs and 17 additional LBVs and LBV candidates. Stars in Richardson & Mehner (2018) were included as candidate LBVs if they had been described as having spectra that were similar to established LBVs; see, for example, Massey et al. (2007a). The LBVs from each source are listed in Table 1.

Since one of the disagreements between the isolation studies is over which LBVs should be included, we looked at the projected angular separation from their nearest BBS neighbor for each of the three LMC sets (Smith & Tombleson 2015, Humphreys et al. 2016, and Richardson & Mehner 2018) of LBVs, which is displayed in Figure 2. Visually, distributions of these LBV sets do not appear significantly different from each other.

Zoom In Zoom Out Reset image size

In order to evaluate whether the sets can be considered as coming from the same parent distribution a Kolmogorov–Smirnov (KS) test (see, e.g., Press et al. 1992) was implemented. The KS test outputs a p-value, which if less than 5%, suggests that the two samples are from different parent distributions. Large values are consistent with the samples being from the same parent population, but of course this does not prove that they are. We find that the p-value between the sets Humphreys et al. (2016) and Smith & Tombleson (2015) is 82%, between the sets Richardson & Mehner (2018) and Smith & Tombleson (2015) is 100%, and between the sets Humphreys et al. (2016) and Richardson & Mehner (2018) is 47%. Since all three KS tests have p-values that are well in excess of the 5% criterion described above, there is no evidence of the three LBV samples having different distributions of projected offsets from the BBS sample. Thus, since the Richardson & Mehner (2018) catalog is the most up-to-date list of LBVs and LBV candidates, we have drawn our LBV samples from it. We will use this same source for our choice of M31 and M33 LBV candidates. (Note that we will henceforth refer to these stars as "LBVs," although many are only "candidates" based upon their spectroscopic similarity to the more classical LBVs.)

We will also compare the separation of the LBVs with respect to WRs and RSGs. One of the most intriguing results to come from the Smith & Tombleson (2015) study was that the separations of LBVs from the nearest spectroscopically confirmed O-type star was significantly greater than that of the O-type stars themselves or that of WRs. If confirmed, this would demonstrate that LBVs could not be a transitional phase between O-type stars and WRs.

All three galaxies (LMC, M31, and M33) have been subject to recent surveys of WRs which are believed to be complete at the 5% or better level (Neugent & Massey 2011; Neugent et al. 2012a, 2018).

For RSGs, spectroscopically identified samples are available for all three galaxies (Drout et al. 2012; Neugent et al. 2012b; Massey & Evans 2016), but we know that these samples are not complete, and so we used photometry to select our RSG samples. For the LMC, we are using the same criteria as used successfully by Neugent et al. (2012b), using the 2MASS catalog (Cutri et al. 2003) with the cuts of $1.2\geqslant (J-K)\,\gt 0.9$ and K ≤ 10.2. For a typical RSG with with a spectral type of M1-1.5, the effective temperature will be 3700 K and have a bolometric correction at K of +2.8 mag (Levesque et al. 2006). This corresponds to a bolometric luminosity of about $\mathrm{log}L/{L}_{\odot }=4.1$, or about $9\,{M}_{\odot }$ and above. For M31 and M33, we use V < 20 and $V-R\gt 0.6$ to select our photometric sample, and then use color cuts in B-V to remove foreground stars, following Massey (1998a). The V < 20 criteria corresponds to a $\mathrm{log}L/{L}_{\odot }=4.5$ when applying a bolometric correction at V of −1.5 mag, or about $12\,{M}_{\odot }$ and above.

Given our use of photometric selection, what do we expect by way of foreground contaminations in this study? Low-luminosity Galactic stars can be confused with extragalactic supergiants of similar colors, i.e., nearby red dwarfs and extragalactic red supergiants. Our previous studies have used the Besançon model of the Milky Way (Robin et al. 2003) to examine the extent of foreground contamination in the color–magnitude diagram in the direction of the Magellanic Clouds (Figure 1 in Neugent et al. 2010), M31 (Figure 1 in Drout et al. 2009), and M33 (Figure 2 in Drout et al. 2012). We expect little or no contamination from foreground objects for the BBSs, where the only low-luminosity stars hot and blue enough would be white dwarfs and sdOs (subdwarf O stars). Using the photometric criteria defined above, the Besançon model does not predict a single such contaminant in either the LMC sample of BBSs, or in the combined M31/M33 data set. Our extensive spectroscopy in M31/M33 (Massey et al. 2016) has actually found seven foreground white dwarfs (three of these meet the photometric criteria we are using), reinforcing the fact that the space density of white dwarfs is not particularly well known locally, although progress is being made in this area (see, e.g., Bianchi et al. 2018). As for red stars, we have found that using proper motions was an effective tool to eliminate contamination of the LMC sample (see Neugent et al. 2012b), while for M31 and M33 we have successfully employed two-color diagrams to separate foreground stars and RSGs (Massey 1998a; Drout et al. 2012; Massey & Evans 2016). Here we use utilize Data Release 2 (DR2) Gaia parallaxes for the first time to eliminate foreground stars seen toward the LMC.

For stars in the LMC, we check for foreground contamination in our photometrically selected samples of BBSs and RSGs using proper motions (μ_α, μ_δ) and parallaxes (π) from the Gaia DR2. To identify probable members of the LMC and likely foreground stars we follow a procedure based on that described in Gaia Collaboration et al. (2018). In brief: we first download Gaia sources within a 5° radius of the LMC center (5:15:20 –69:20:10). Restricting ourselves to sources with relative parallax error π/σ_π < 5 and magnitudes G < 17.5 mag, we determined the median proper motions and median parallax for the sample. As in Gaia Collaboration et al. (2018), we then further eliminated any sources whose μ_α or μ_δ were more than four times the robust scatter estimate. Using this sample, we then determined the covariance matrix μ of μ_α, μ_δ, and π and defined a filter on proper motion and parallax, requiring that the transpose of μ with σ⁻¹ times μ (${\mu }^{T}{\sigma }^{-1}\mu$) is greater than 12.8 (corresponding to the 99.5% confidence region) for classification as a probable foreground star. We then applied this filter to the samples of the LMC BBSs and RSGs described above, after cross matching with the Gaia database.

For the M31 and M33 samples, DR2 does not go quite faint enough to be useful, and so we rely upon photometric means to separate the foreground contamination for the extragalactic sample. For the M31/M33 BBS samples, we rely upon the expectation that there will be little or no contamination for very blue stars.

Since we are relying upon ground-based photometry to select our BBS sample (using the Zaritsky et al. 2004 catalog) and our RSG sample (using 2MASS), we decided to exclude stars from all of our samples which lay within 10 arcmin of the center of 30 Dor, as crowding is severe there, particularly in the core R136 region.

BBS: With that exclusion, there are 688 stars in our BBS. After removing 22 Gaia-selected foreground stars, our reference sample is left with 666 stars. LBVs: The exclusion region around 30 Dor requires that we remove R143, leaving 26 LBVs and LBV candidates. WRs: The WR stars were selected based on "The Fifth Catalog of LMC Wolf–Rayet Stars" given in Neugent et al. (2018), excluding R127 and HDE  269582, the two former "slash" stars that are currently in an LBV state (Walborn et al. 2017). After excluding stars near 30 Dor, we have 117 WRs in our sample. RSGs: We selected candidate RSGs using the 2MASS list, as described above. The initial list contained 1288 stars. Our Gaia study then eliminated 105 (9%) of these sources as likely foreground, leaving us with 1183.⁸ As described above, this sample will be dominated by stars with masses of 9–15 M_⊙.

Our initial motivation for using the photometric catalog rather than spectroscopically identified O-type stars was that we were concerned about the spotty coverage of previous spectroscopic surveys in the LMC, where observers have typically concentrated on probing the stellar content of particular OB associations (see, e.g., Massey et al. 1989a; Garmany et al. 1994; Massey et al. 2000, 1995). Even in the era of wide-field multi-fiber surveys, such studies have concentrated on specific regions, e.g., the VLT-FLAMES Tarantula Survey of the 30 Dor region (Evans et al. 2011 and the subsequent papers in this series). Furthermore, the SIMBAD database used by Smith & Tombleson (2015) and Humphreys et al. (2016) are constantly evolving and incorporating new data, and there is no way of knowing which stars were included at the time of those studies. We can investigate the spectroscopic completeness question here by using the current updated version of the Skiff (2014) on-line catalog of spectral types, only some of which would have been incorporated into SIMBAD at the time of the (Smith & Tombleson 2015) study.

Of the 666 BBS (excluding foreground stars in the 30 Dor region), only 135 (20%) have been identified spectroscopically as O-type stars. Another 140 (21%) are luminous early B-type supergiants, and the remainder (59%) have no spectral types. The presence of very early B-type supergiants in our sample is to be expected, considering stellar evolution and our use of a magnitude-limited sample, as early B-type supergiants can be more massive than many O-type stars are; only stars of 40 M_⊙ and above are expected to bypass the early B supergiant phase in their evolution (again, see Table 1 in Massey et al. 2017). Conversely, a late-type O star may be as low in mass as 15 M_⊙. However, the early B-type supergiants will be brighter visually as their bolometric corrections are not as significant: a 25 M_⊙ B0 I star will be as bright visually as a 60 M_⊙ O3 V star. This raises another problem with the methodology utilized in previous papers on the subject, as only the "nearest O-type" stars were considered, excluding B-supergiants that may have been more massive.

We note that with some irony that of the 22 BBS that were eliminated as "probable foreground," about half had been spectroscopically confirmed as O-type stars, and therefore members of the LMC. Possibly our method for eliminating stars based upon Gaia was a bit too aggressive, due, perhaps, to errors in Gaia proper motions/parallaxes for stars in dense regions or multiple systems or unusual kinematics for a small set of massive LMC stars. Alternatively, it could be that some prior spectral classifications mistook sdO stars for the real thing. Given the predictions of the Besançon model and individual examination of the discrepant stars, we suspect the former. We have run the samples both with and without these Gaia-selected foreground stars included with indistinguishable results.

As shown in Figure 3, the projected separation of LBVs and WRs from the nearest BBS are very similar to the projected separation of the BBSs themselves. In contrast, the RSGs are significantly more isolated. Numerically, the median projected separation for each BBS star from its nearest BBS neighbor is 129'' (31 pc). The LBVs have a median projected separation from the nearest BBS star of 181'' (43 pc), and the WRs have a median projected separation from the BBS sample of 175'' (42 pc). By contrast, the separation for the RSGs from the BBS sample is about twice as large, with a median projected separation of 316'' (76 pc).

Zoom In Zoom Out Reset image size

A KS test yields a p-value of 96% between the LBV and BBS projected separations, a p-value of 56% between the LBV and the WR projection separations, while the RSG and the LBV projected separations have a p-value of only 0.3%. Since the LBV–RSG KS agreement is well below 5%, we can reject at high confidence the possibility that the LBV and RSG distributions are from the same parent distribution. This is consistent with RSGs evolving from lower-mass stars than the LBVs or WRs.

Although this method does not lend itself to a formal analysis, we can at least test the robustness of our results by seeing if the same results hold by using the second-closest neighbor as a measure of isolation. The results are shown in Figure 4. We find that the projected separations have similar distributions as before. The median projection separations of BBSs is 213'' (51 pc); for LBVs, it is 302'' (72 pc); for WRs, it is 319'' (77 pc); and for RSGs, it is again almost double that at 506'' (121 pc). The results of a KS test between the LBV distribution and the BBS distribution for the second closest BBSs is 26%, for WR distribution and the LBVs it is 73%, and for RSG distribution and the LBVs it is 0.1%. This shows that the second closest BBS projected separations have similar results to that of the closest BBS projected separations, and the conclusions hold.

Zoom In Zoom Out Reset image size

Another piece of evidence regarding the connection between LBVs and high-mass stars (i.e., the BBS sample) comes from examining their membership in OB associations. In Table 1, we list the membership status for LBVs in or near the LMC's OB associations (Lucke & Hodge 1970), using the same criteria as Neugent et al. (2018) did for WR stars.⁹ Recall that the OB associations were defined by Lucke & Hodge (1970) in the usual way (see, e.g., Hodge 1986), namely based primarily on visual inspection of blue and red pairs of images to identify collections of blue stars (see, e.g., Humphreys & Sandage 1980 for a more complete description of the process). In other words, the identification of OB associations is not dependent upon the completeness of spectroscopic information. We also calculated the membership rates for our RSG sample and for the BBSs themselves. Excluding stars in 30 Dor, 65% of LBVs are in or near an OB association, compared to 52% for BBSs, 68% for WRs, and 23% for RSGs. Thus, most BBSs, LBVs, and WRs are found in OB associations, while far fewer RSGs are members, as we would expect from their lower masses and greater ages. We note that a similar conclusion can be drawn from Table 1 of Walborn et al. (2017), where they find that five of their six active LBVs in the LMC are members of clusters or OB associations.

The comparison sample of BBSs was found using the LGGS photometry of M31 and M33 (Massey et al. 2007b, 2016). In order to stay consistent with Section 3, the cuts for the sample were kept at ${M}_{V}\lt -5.0$, $(U-B)\lt -0.5,B-V\lt 0.2$, and −1.2 < Q < −0.88. The apparent distance modulus for M31 is 24.8 and for M33 is 25.0 (Massey et al. 2007b and references therein); therefore, the V magnitude cuts became V < 19.8 and V < 20.0 for M31 and M33, respectfully. We expect there will be regions in M31 and M33, like their nuclei, where incompleteness will be an issue, but we expect to find few massive stars there of any kind.

As with the LMC, the LBVs for M31 and M33 were taken from Richardson & Mehner (2018). The RSGs were identified using the LGGS photometry adopting V − R > 0.6, V < 20. As discussed above, this should extend down to a $\mathrm{log}L/{L}_{\odot }$ of 4.5, or about 12 M_⊙. The WRs were selected based on the classifications from Neugent & Massey (2011), Neugent et al. (2012a), and Massey et al. (2016).

Our experience with identifying RSGs in M31 and M33 shows that about half of the red stars in the right magnitude-color range are foreground stars. As discussed earlier, we have been successful in separating the bona fide extragalactic RSGs from foreground red dwarfs using a two-color plot. For cool stars, B − V becomes primarily a surface gravity indicator due to the effects of line-blanking in the blue, while V − R remains primarily a temperature indicator, as first discovered by Massey (1998a) and subsequently utilized in our studies of RSGs of M31 (Massey et al. 2009; Massey & Evans 2016) and M33 (Drout et al. 2012). Therefore, we have applied a cut-off of $B-V\gt -1.599\,\times (V-R)+4.18\times (V-R)-0.83$ to select supergiants.

However, our radial velocities studies have shown that while this method is mostly effective, there are invariably some foreground stars misidentified as RSGs, and some RSGs misidentified as foreground stars. A quick check of the Gaia DR2 confirms that a substantial number of our photometrically identified stars are missing in the DR2 as they are too faint. For the stars with nonnegligible parallaxes, most uncertainties are similar to the size of the parallax itself. We have decided then to include a second sample of RSGs, namely those that have been identified spectroscopically in the LGGS on the basis of their radial velocities. This is a considerably smaller sample (626 stars), and the distribution does not cover all of M31 as there is the "alligator jaws" region in the NE where radial velocities cannot distinguish M31 stars from foreground (Drout et al. 2009). However, the selection is otherwise non-clumpy; i.e., it does not suffer from the same selection effects we expect from the LMC O-type star sample. As we will see that although neither RSG sample is perfect, they yield very similar results.

In M31, there are only six confirmed LBVs (Table 2), and in M33, there are only five confirmed LBVs (Table 3). To avoid small number statistics for the LBVs and to provide a complete picture of the spatial distributions, the LBVs, WRs, BBSs, and RSGs from M31 were combined with their counterparts in M33, resulting in a combined list of the M31 and M33 data for each type of star. There are 1824 BBSs, 50 LBVs and LBV candidates, 374 WRs, and 4243 photometrically defined RSGs, and 626 spectroscopically confirmed RSGs.

The projected separations relative to the BBS sample are shown in Figure 5 for the BBSs, the LBVs, the WRs, and the two RSG samples. We see immediately that the projected separation of the LBVs from BBSs is similar to that of the BBSs themselves and that of the WRs, while the RSGs have a much larger average separation from the BBSs, as was the case for the LMC.

Zoom In Zoom Out Reset image size

The median projected separations from BBSs for the BBSs themselves is 17'' (∼65 pc). The LBVs have a median projected separation of 18'' (∼68 pc), and the WRs have a median projected separation of 19'' (∼72 pc). The photometrically defined RSGs have a median projected separation of 120'' (∼456 pc), over five times as large as the other median projected separations. Even the spectroscopically defined RSGs have a median projected separation of 52'' (∼198 pc), twice as large as the other samples.

A KS test shows that the distribution of the LBVs and the BBSs have a p-value of 95%, the LBVs and the WRs have a p-value of 100%. In contrast, the KS test provides p-values well below 0.1% for both RSG distributions. We can thus reject the hypothesis that the LBVs and RSGs come from the same parent distribution. Once again, we find that the LBV isolation is similar to that of the BBSs and WRs, but unlike that of the RSGs.

The second closest BBS from the different types of stars was again evaluated and the corresponding projected separations are shown in Figure 6. When we look at the second closest BBS, we find that, like in the LMC, the separations have similar relative distributions compared to the closest BBS projected separation. The median separation of BBSs is 32'' (122 pc), that of the LBVs is also 32'', for WRs it is 30'' (114 pc), and for RSG photometric sample it is again around five times that at 167'' (635 pc). The spectroscopic sample of RSG has a projected separation of 83'' (315 pc). The results of a KS test between the LBVs and the second closest BBSs is 80%, for WRs it is 52%, and for RSG it is ≪0.1%. The distributions are once again are similar to the closest projected separation for M31/M33, supporting our original results.

Zoom In Zoom Out Reset image size

The M31/M33 results are in agreement with what we found for the LMC, namely that the LBVs show a similar degree of isolation to massive unevolved stars and WRs, and are less isolated than RSGs.