ON THE SOCIAL TRAITS OF LUMINOUS BLUE VARIABLES

Luminous blue variables (LBVs) or S Doradus variables have attracted attention in recent years for two mutually independent reasons. Normal hot-star winds cannot account for sufficient mass loss (Fullerton et al. 2006); thus, another form of mass loss, perhaps in LBV events, is required for them to become W-R stars; see also Humphreys & Davidson (1994). Second, the nonterminal supernova (SN) impostors resemble extreme LBV outbursts (Van Dyk & Matheson 2012), and certain types of SNe were observed to have experienced prior high-mass-loss events that have been likened to LBVs.

Unfortunately, serious confusion has arisen because disparate objects are often mixed together and collectively called "LBVs." In a recent paper, Smith & Tombleson (2015) argue that LBVs are not generically associated with young massive stars. They suggest that LBVs gained mass from more massive companions in interacting binary systems and subsequently moved away from their birth sites when the companions became SNe. This would contradict traditional views in which evolved massive hot stars experience periods of enhanced mass loss, in transition to a W-R star. Their argument is based on their failure to find LBVs closely associated with young O-type stars in the Milky Way and the Magellanic Clouds. As we explain in Section 4.2, however, Smith and Tombleson's statistical sample is a mixed population, with at least three physically distinct types of objects. When they are separated, the statistics agree with standard expectations. We mention this example because it illustrates the need to distinguish between giant eruptions, classical LBVs, less luminous LBVs, LBV candidates, and others such as B[e] stars that occupy the same part of the H-R diagram. In this paper we explore those distinctions.

Since there are numerous misunderstandings of this subject, a careful summary of the background is useful. LBV/S Dor variables are evolved massive stars, close to the Eddington limit, with a distinctive spectroscopic and photometric variability. There are two classes with different initial masses and evolutionary histories, as we explain later. In its quiescent or normal state, an LBV spectrum resembles a B-type supergiant or Of-type/WN star. During the "eruption" or maximum visible light stage, increased mass loss causes the wind to become optically thick, sometimes called a pseudo-photosphere, at T ∼ 7000–9000 K, with an absorption-line spectrum resembling an F-type supergiant. Since this alters the bolometric correction, the visual brightness increases by 1–2 mag while the total luminosity remains approximately constant (Wolf 1989; Humphreys & Davidson 1994 and numerous early references therein) or may decrease (Groh et al. 2009). Such an event can last for several years or even decades.

There are two recognized classes of LBV/S Dor variables based on their position on the H-R diagram (Humphreys & Davidson 1994). The classical LBVs, with bolometric magnitudes between −9.7 and −11.5 (log L/L_⊙ ≳ 5.8), have clearly evolved from very massive stars with M_ZAMS ≳ 50 M_⊙. Their high mass loss prevents them from becoming red supergiants (RSGs; Humphreys & Davidson 1979). The less luminous LBVs with M_Bol ≃ −8 to −9.5 mag had initial masses in the range of ∼25–40 M_⊙ or so and can become RSGs.

Some factor must distinguish LBVs from the far more numerous ordinary stars with similar T_eff and L, and L/M is the most evident parameter. LBVs have larger L/M ratios than other stars in the same part of the H-R diagram. Their Eddington factors Γ = L/L_Edd are around 0.5 or possibly higher.³ This is not surprising for the very massive classical LBVs. But how can the less luminous LBVs have such large L/M ratios? The simplest explanation is that they have passed through an RSG stage and moved back to the left in the H-R diagram (Humphreys & Davidson 1994). Meynet & Maeder (2005) showed that stars in the 22–45 M_⊙ initial mass range, evolving back to warmer temperatures, will pass through the LBV stage. Recent evolutionary tracks, with mass loss and rotation (Ekstrom et al. 2012), show that these stars will have shed about half of their initial mass. Having lost much of their mass, they are now fairly close to (L/M)_Edd. Although empirical mass estimates are uncertain, the low-luminosity LBVs are close to their Eddington limit with Γ ≈ 0.6 (Vink 2012). Hence, the evolutionary state of less luminous LBVs is fundamentally different from those of classical LBVs.

To illustrate this, in Figure 1 we show the evolution of L/M for two different masses representing the two LBV/S Dor classes. It shows a simplified Eddington factor, ${{\rm{\Gamma }}}_{{\rm{s}}}=(L/{L}_{\odot })/(43000M/{M}_{\odot })$, as a function of time in four evolution models reported by Ekstrom et al. (2012) for rotating and nonrotating stars with M_ZAMS = 32 and 60 M_⊙. The 32 and 60 M_⊙ models have $\mathrm{log}L\sim 5.6$ and 6.0, respectively, when they are in the LBV instability strip (see Figures 2 and 3). Three critical evolution points are marked in the figure: (1) the end of central H burning, (2) the farthest major excursion to the red side of the H-R diagram, and (3) the end of central He burning. For the 60 M_⊙ star, Γ_s ≳ 0.5 as it leaves the main sequence, but the 32 M_⊙ star must pass through yellow supergiant and/or RSG stages before its Γ_s reaches 0.5. Of course, these examples depend on the input parameters and assumptions of the models. Other recent evolution models with mass loss and rotation generically agree on the main point stated here; see, for example, Chen et al. (2015).

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Therefore, we should expect that only the classical LBVs should be associated with young objects such as O-type stars. The less luminous LBVs, more than 5 × 10⁶ yr old, will have moved 50–100 pc and are also old enough for their neighbors to evolve out of the O star class. Among other results in this paper, we find that the data agree with this expectation.

One of the distinguishing characteristics of LBV/S Dor variability is that during quiescence or minimum light, the stars lie on the S Dor instability strip first introduced by Wolf (1989) and illustrated here in Figures 2 and 3. The more luminous, classical LBVs above the upper luminosity boundary have not been RSGs, while those below are post-RSG candidates. Thus, LBVs with very different initial masses and different evolutionary histories occupy the same locus in the H-R diagram.

No single cause is generally accepted as the origin for the LBV/S Dor enhanced mass loss/optically thick wind events. Most proposed explanations invoke the star's proximity to its Eddington limit due to previous high mass loss. Proposed models include an opacity-modified Eddington limit, subphotospheric gravity-mode instabilities, super-Eddington winds, and envelope inflation close to the Eddington limit (see Section 5 in Humphreys & Davidson 1994; Glatzel 2005; Owocki & Shaviv 2012; Vink 2012).

In a giant eruption, represented by objects like η Car in the 1840s and P Cygni in the 1600s, the star greatly increases its total luminosity with an increase in its visual magnitude typically by 3 mag or more. Giant eruptions should not be confused with the normal LBV/S Dor variability described above. The energetics of the outburst and what we observe are definitely different. Unfortunately, many authors do not make the distinction especially with respect to the SN impostors and the progenitors of SNe IIn.

Few confirmed LBVs are known in our Galaxy due to their rarity, uncertainties in distance, and the infrequency of the LBV "eruption." There are only six confirmed LBVs in the LMC and one in the SMC. Thus, even the Magellanic Clouds do not provide a large enough sample to confidently determine their relative numbers and group properties relative to other massive star populations. In this paper we examine the spatial distribution of the LBVs and candidate LBVs in M31 and M33 based on our recent discussion of the luminous stars in those galaxies that included the discovery of a new LBV in M31 (Humphreys et al. 2013, 2014b, 2015). In the next section we show that the majority of these LBVs are found in or near associations of young stars, and although spectra are not available for nearby neighbors, their magnitudes and colors support the classification of most of them as hot supergiants.

It must be emphasized that LBVs are evolved massive stars. We should not necessarily expect to find them closely associated with young O stars. This is especially true for the less luminous LBVs. The appropriate comparison population should be those supergiants found near the quiescent temperature and luminosity of the LBVs on the H-R diagram, that is, the evolved massive stars presumably of similar initial mass. In the Milky Way (Section 3), it is equally important that they be at the same distance. The Smith and Tombleson Magellanic Cloud sample was a mixed population; they combined the classical LBVs with log L/L_⊙ ≥ −5.8 and the less luminous LBVs. In Section 4 we reassess their analysis, separating the LBVs into the two groups based on their positions on the H-R diagram. Their spatial distribution and their kinematics lead to significantly different conclusions, which are summarized in the final section.

The LBVs in M31 and M33 were originally known as the Hubble–Sandage variables. In their paper on the "brightest variables," Hubble & Sandage (1953) indentified one star in M31 (V19 = AF And) and four in M33 (Vars. A, B, C, and 2) based on their long-term light curves from ≈1920s to 1950.⁴ There are now five confirmed LBVs in M31: AF And (Hubble & Sandage 1953; Humphreys 1975), AE And (Humphreys 1975), Var 15 (Hubble 1929; Humphreys 1978), Var A-1 (Rosino & Bianchini 1973; Humphreys 1978), and the newly recognized J004526.62+415006.3 (Humphreys et al. 2015; Sholukhova et al. 2015). The four in M33 are Variables B, C, and 2 (Hubble & Sandage 1953; Humphreys 1975) and Var 83 (Humphreys 1978).

These stars plus a few candidate LBVs are listed in Table 1 with their luminosities and temperature estimates for their quiescent state and their corresponding references. LBVs have one important advantage over other supergiants. During the LBV enhanced mass loss state, with the cool, dense wind, the bolometric correction is near zero, allowing us to determine its bolometric luminosity once corrected for interstellar extinction. This is the case for Var B, Var C, and the new LBV, J004526.62+415006.3. Other luminosities and temperatures in Table 1 are primarily from Szeifert et al. (1995) or Humphreys et al. (2014b). The adopted corrections for interstellar extinction are from Humphreys et al. (2014b). The LBVs and candidates are shown on an H-R diagram in Figure 2.

Most of the known and candidate LBVs in these galaxies are in known stellar associations mapped previously by Hodge (1981) for M31 and by Humphreys & Sandage (1980) in M33, and a few are also in or near H ii regions. The association designation (A) and number from these references are given in the comments column in Table 1. To compare their space distribution with the luminous star populations in these galaxies, we show images in the Appendix of their environments made from the Local Group Galaxy Survey (Massey et al. 2006). The LBVs and representative nearby stars listed in Table 2 are identified in each image. Although spectra are not available for these neighboring stars, their magnitudes and colors included in Table 2 indicate that most are hot stars or other supergiants. We use the Q-method (Hiltner & Johnson 1956; Johnson 1958) to estimate the intrinsic $B-V$ colors, color excess, and visual extinction (A_v) with R = 3.2 for the candidate OB-type stars in Table 2. Their absolute visual luminosities, M_v, are determined using distance moduli of 24.4 and 24.5 mag for M31 and M33, respectively (Scowcroft et al. 2009; Riess et al. 2012).

2.1. Comments on Individual Stars

2.2. Spatial Distribution and Kinematics

There are very few confirmed LBVs in the Milky Way due to the infrequency of the LBV eruption and, of course, to the uncertainty in the distances. Smith and Tombleson list 10 LBVs and candidate LBVs and discuss some of the better-studied examples. A few deserve some comments and cautionary remarks. As has been acknowledged for some time, the giant eruption η Car is clearly associated with a population of luminous massive stars, including several O3-type stars (Davidson & Humphreys 1997). At its presumed initial mass of 150–200 M_⊙, it is at most about (2–3) × 10⁶ yr old and has not have moved far from its place of birth.

Smith and Tombleson emphasize that most of the other Galactic LBVs are relatively isolated from O stars. But most are also much less massive and will be older. For example, the well-studied, classic stellar wind star and survivor of a giant eruption, P Cygni, is in the Cyg OB1 association. At its distance, the two nearest B-type supergiants of similar temperature and luminosity are about 30 pc away. The same is true of an O star. At its position on the H-R diagram, P Cyg had an initial mass of ≈50–60 M_⊙ and is past core H burning, with a current mass of 23–30 M_⊙ (Lamers et al. 1983; Pauldrach & Puls 1990). It is therefore at least (4–5) × 10⁶ yr old based on models by, e.g., Ekstrom et al. (2012), with and without rotation. With a velocity dispersion of 10 km s⁻¹ for the extreme Population I, P Cyg will have moved 35–44 pc or more. So its spatial separation from similar stars is what would be expected.

AG Car is a well-studied classical LBV. At its high luminosity and presumed initial mass of ≈80 M_⊙, one would expect to find an associated population of massive stars. Smith and Tombleson argue that there are no nearby O stars. However, at its large kinematic distance of ≈6 kpc (Humphreys et al. 1989; Groh et al. 2009), AG Car must be compared with the stellar population at the same distance. Since our line of sight to AG Car at l = 289° is directly down the Carina spiral arm, the cataloged O stars are most likely in its foreground.

HR Car is in a similar situation at ∼5 kpc in the Carina arm (van Genderen et al. 1991). HR Car, HD 160529, and HD 168607 are confirmed LBVs, but belong to the less luminous, less massive group of LBVs with ages of roughly 6 × 10⁶ yr or more—enough time for them to move 30–100 pc away from their original locations even at low random speeds. We would not expect them to be closely associated with O stars.

In all cases these stars need to be compared with stars at the same distance and in the same part of the H-R diagram. That is, of course, the advantage of studying these stars in nearby galaxies and especially in the Magellanic Clouds.

Smith and Tombleson included 19 stars in the Magellanic Clouds in their analysis. However, six of the LMC stars in their list are neither LBVs nor candidates. This does not mean that these stars, described below, are not interesting or that someday they may be shown to have LBV characteristics, but they should not be included in a survey to set limits on the spatial distribution of the known LBVs. The six confirmed LMC LBVs (S Dor, R71, R127, R143, R110, R85) and four candidates (S61, S119, Sk −69°142a, Sk −69°279) are listed in Table 3 with their observed parameters. They also list three stars in the SMC, but R40 is the only confirmed LBV/S Dor variable (Szeifert et al. 1993). The very luminous HD 5980 is a complex triple system that may be an example of a giant eruption, as we describe below. R4 is a B[e] star. The confirmed LBVs are shown on an H-R diagram in Figure 3. The three most luminous LBVs, R127, S Dor, and R143, are the classical LBVs (Humphreys & Davidson 1994), and the remaining four belong to the less luminous group.

4.1. The LBV Candidates in the LMC and SMC

4.2. The Spatial Distribution and Kinematics of the Magellanic Cloud LBVs

Here we reassess the Smith and Tombleson analysis of spatial correlations in the LMC and SMC. For each star in a set, e.g., WN stars, RSGs, or LBVs, they measured the projected distance D1 to the nearest O-type star and plotted the cumulative fraction of the stars in that set that have D1 less than a given value. This is illustrated in Figure 4, where we reproduce their Magellanic sample from their Table 1, together with the late O-type stars, WN stars, and RSGs. The O-type stars, for example, tend to exist in groups, so naturally they have small values of D1. We would conclude from this figure that the RSGs have a spatial distribution uncorrelated with O stars. The stars in the Smith and Tombleson sample fall in between.

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We repeat this analysis for the seven confirmed LBVs in Table 3. The seven stars discussed in Section 4.1 that have no clear relation to LBVs are removed, and the four "candidates" are discussed below. We show the cumulative distributions for the classical and less luminous LBVs in Figure 5, plotted respectively as LBV1 and LBV2.⁵ The three most luminous stars (LBV1) in the sample were originally identified as classical LBVs by Humphreys & Davidson (1994) and were not merely chosen in relation to Smith and Tombleson's arguments. They have an average D1 of only 7 pc, and, as Figure 5 shows, their distribution is statistically indistinguishable from the late O-type stars. The four stars in LBV2 are all substantially fainter than the M_bol ≈ −9.7 criterion. As expected for these less massive, highly evolved objects, they parallel the RSG distribution in Figure 5. Formal statistical tests are doubtful for such a small sample; but if one attempts to apply any such test (e.g., Kolmogorov–Smirnov), the result is excellent consistency between set LBV2 and the RSG distribution. This is obvious in the figure.

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Moreover, elementary statistics support the distinction between classical and less luminous LBVs. Among the seven confirmed LBVs, the three classical LBVs have the three smallest values of D1. The ab initio probability of this outcome would be 2.9% if all seven represent the same population; so, in this sense, the difference between the two classes is significant with a 97% confidence. Two aspects of this statement are worth noting: (1) Given only seven objects, 97% is the highest confidence level that can be attained without additional information.⁶ (2) In terms of standards for judging scientific evidence, the above result is useful because it was not known at the time when the two classes of LBVs were defined.

Just as important, their velocities do not suggest that any of the LBVs are runaways or have exceptionally high velocities. Their heliocentric velocities are included in Table 3 with the references. The emission-line velocities are given for the RAVE measurements (Munari et al. 2009) except for R143.⁷ The published average velocities for the Magellanic Clouds range from 262 to 278 km s⁻¹ for the LMC and from 146 to 160 km s⁻¹ for the SMC (Richter et al. 1987; McConnachie 2012). The LBV velocities are all consistent with their membership, and for the LMC stars, with their position based on the H I rotation curve available at NED (from Kim et al. 1998). The only exception is the candidate LBV, S119, with a possible systemic velocity based on the center of its expanding nebula (Weis et al. 2003) that is much lower than expected at its position in the LMC. Thus, S119 is a candidate for a runaway star.

In addition, a runaway star with a high velocity would be expected to alter the morphology of its circumstellar ejecta, the LBV nebula. Runaway stars are commonly known to have an arc-like bow shock nebula due to interaction with the interstellar medium (Brown & Bomans 2005). The stars in M31 and M33 are too distant to search for bow shocks, but several confirmed LBVs and candidates in the Milky Way and LMC have associated circumstellar nebulae that are either spherical or bipolar in shape (Weis 2011). They are not bow shocks. The only nebula that has a signature, an embedded arc in the surrounding nebulosity, that could be attributed to a bow shock is S119, which may be a runaway.

The distribution of the four LBV candidates in the LMC (Figure 6) interestingly follows that of the less luminous LBVs. Three of the four are considered candidates because of their circumstellar nebulae. The origin of their very extended ejecta may be a prior giant eruption or numerous earlier S Dor-like events, but their low expansion velocities (14–27 km s⁻¹) are a puzzle compared with the outflow velocities of LBV winds and giant eruptions.⁸ They may be due to deceleration with the ISM or the product of mass loss in a previous state with lower ejection velocities. Their published luminosities are very similar, and except for Sk −69°279, they lie in or near the LBV instability strip. Based on their position on the H-R diagram, they may be post-RSGs, or, given their rather high luminosities, former warm hypergiants like IRC +10420 or Var A in M33.

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In M31 and M33 we conclude that except possibly for AE And, which may be a post-RSG, the LBVs and candidates are associated with luminous young stars and supergiants appropriate to their luminosities and positions on the H-R diagram. Their measured velocities are also consistent with their positions in their respective galaxies. There is no evidence that they are runaway stars that have moved away from their place of origin.

In the Magellanic Clouds, separating the LBVs by luminosity removes the apparent isolation of the LBVs claimed by Smith and Tombleson. The more luminous and more massive classical LBVs have a distribution similar to the late-type O stars and the WN stars, while the less luminous ones have a distribution like the RSGs, an evolved lower-mass population of supergiants. In both the Magellanic Clouds and in M31 and M33, none of the sample of 16 confirmed LBVs have high velocities or are candidate runaway stars.

One positive result is especially notable: since the LBV2 distribution in Figure 5 is indistinguishable from the RSGs, evidently the less luminous LBVs are not young. This fact strongly supports the interpretation outlined in Section 1, i.e., those objects have evolved back to the blue in the H-R diagram.

It is not necessary to invoke an exotic explanation such as "kicked mass gainers" from binary systems to explain the LBVs. Some LBVs and candidates are indeed binaries (Lobel et al. 2013; Rivinius et al. 2015; Martayan et al. 2016), but this binarity contradicts the Smith and Tombleson scenario of the LBV, the primary in these systems, as the mass gainer. Thus, the results of our discussion and analysis support the accepted description of LBVs of all luminosities as evolved massive stars that have shed a lot of mass, whether as hot stars or as RSGs, and are now close to their Eddington limit.

Research by R.H., K.D., and M.G. on massive stars is supported by the National Science Foundation AST-1109394.

The blue and Hα images of the LBVs and candidate LBVs shown here are from the Local Group Galaxy Survey (Massey et al. 2006). Their survey used the standard UBVRI filters plus narrowband filters with the Mosaic CCD Camera on the KPNO 4 m Mayall telescope. The reduced images have a scale of 027 pixel⁻¹. Details of the reductions can be found in the paper and at the LGGS website. The authors quote 1%–2% photometry for stars expected to be above 20 M_⊙. The dashed grid on the images reproduced here is 10''. At the distances of M31 and M33, 10'' is approximately 37 pc.

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