*2.2. Disk Dynamics and Structure*

Determination of the kinematics within dense circumstellar environments requires the use of reliable tracers. High-resolution near-infrared spectroscopic observations have revealed that the band heads of the CO emission from B[e]SGs typically display a characteristic shape, consisting of a blue-shifted shoulder and a red-shifted maximum. For the generation of such a band head profile, the individual CO rotation-vibration lines, superimposing within the region of the band head, must display double-peaked profiles (see Figure 2). Such line profiles can originate either from a circumstellar ring of gas expanding with constant velocity (constant outflow), or from rotational motion of a ring of gas around the central object. To discriminate between the two scenarios, complementary tracers are needed.

**Figure 2.** Sketch of the generation of the typical CO band head profile. (**a**) Spectrum around the (2-0) band head of the CO first-overtone bands for a hot gas with velocity dispersion of a few km s<sup>−</sup>1. (**b**) Profile of a single line from a rotating gas ring with a velocity, projected to the line of sight, of 66 km s<sup>−</sup><sup>1</sup> as seen with a spectral resolution of 6 km s<sup>−</sup>1. (**c**) Total synthetic CO band head spectrum resulting from the convolution of the band transitions in (**a**) with the profile of the ring in (**b**). (**d**) CO band head observations of the Galactic B[e]SG CPD-57 2874 [58].

The SiO band emission seen in four Galactic B[e]SGs displays a similar shape of the band heads. Detailed modeling revealed that in each object the SiO bands required a slightly lower value of the velocity [45] than the CO bands. The SiO molecule is less stable than CO, meaning that it can form and persist only at lower temperatures. This fact naturally places the region where SiO molecules are expected to form, and hence the SiO band emitting region, at slower orbital velocities and greater distances from the central object.

As CO is the most stable molecule, its formation and emission region marks the inner edge of the molecular disk. Closer to the star, tracers for the kinematics need to be found from line emission of the atomic gas. Here, the lines from forbidden transitions are most suitable, because their emission is optically thin, so that their profile shapes contain the full velocity information of their formation region [56,57]. Of particular interest are hereby the [O I] lines, because they are one of the defining characteristics of the B[e] phenomenon and hence observed in all B[e]SGs. The ionization potential of O I is about the same as the one for H I, which means that within the [O I] line forming regions, hydrogen should be basically neutral as well, restricting the formation region of the [O I] line emission to the neutral regions within the circumstellar disk. While recombination in the equatorial region close to the star might be achieved, e.g., with the model of a latitude dependent wind [70–72], the requirement of a hydrogen neutral environment severely limits the number of free electrons that will be available to collisionally excite the levels within O I from which the forbidden transitions emerge. Consequently, the [O I] lines arise in regions with high total density, but low electron density.

The profiles of the [O I] lines often display double-peaks, in line with their formation in the disk. Typically, the [O I] *λ*5577 line, which arises from a higher level than the *λλ*6300,6364 lines, is broader, indicating spatially distinct formation regions of the emissions, with the [O I] *λ*5577 line being formed at higher velocities and higher densities and hence closer to the star than the other two lines.

With the identification of the lines of [Ca II] *λλ*7291,7324 in the spectra of numerous B[e]SGs, a further highly valuable tracer for the disk kinematics has been found. These lines typically display double-peaked profiles as well, with velocities comparable to or even greater than the one traced by the [O I] *λ*5577 line [53,57,58]. This implies that they form in the same region, or at least very close to each other, which is in agreemen<sup>t</sup> with their comparably high critical density. Since the [O I] *λ*5577 line is not always detectable, the [Ca II] lines thus provide a suitable, complementary benchmark for the dynamics within the disks of B[e]SGs.

In summary, the optical and near-infrared spectra provide emission features from several species, which are suitable to pin down the kinematics within the disks of B[e]SGs at various distances from the star, and Table 2 includes the information on the detection of the individual tracers in the MC sample. Based on the physical constraints outlined above, the logical order of the appearance of the divers tracers from inside out would be: [Ca II], [O I], CO bands and SiO bands. The velocity information carried by these species thereby implies a decrease with increasing distance from the star. While an equatorial, outwards decelerating outflow might be able to explain some of the observed line profiles [56], the velocity patterns seem to be in better agreemen<sup>t</sup> with (quasi-)Keplerian rotation. In this respect, it is interesting to note that Keplerian rotation has been made directly discernible by means of spectro-interferometric observations. The rotational motion of the CO gas has been derived based on the differential phase spectrum [38,52], and the rotational motion of the ionized gas based on the spatially resolved Br*γ* emission [49].

While, in general, the rotational motion of the material within the circumstellar disks of B[e]SGs seems now to be well established, possibly in connection with a (very) slow outflow component [57], recent investigations of the spatial distribution of the circumstellar gas revealed that it is more likely accumulated in multiple rings, partial rings, and possible spiral arm-like structures rather than in a smooth disk [43,44,58]. These rings might result from multiple mass ejection phases caused by (pulsational) instabilities acting in the outer layers of these luminous objects (e.g., [73–75]), or from binary interaction in close systems, as seems to be the case for some of the Galactic objects [58], in which the rings are circumbinary rather than circumstellar. Other disk-forming mechanisms that have been proposed in the literature over the years include equatorial mass-loss from a critically rotating star [76,77], the rotationally induced bi-stability mechanism [78], the slow-wind solution [79], and the combination of the latter two [80]. For an overview including a detailed description of the various models and their limitations, see [81].

The circumstellar material of many MC objects appears durable. This is evidenced by their emission features and their infrared photometry that both display no considerable variability over several decades, in combination with chemically processed dust displaying emission from crystalline silicates [82]. It is tempting to imagine that in such an environment even minor bodies might have formed from the long-lived disk material, creating gaps within the disk in radial direction and hence leading to the formation of the presumed ring structures [43]. These minor bodies or possible planets can also stabilize the neighboring rings, in analogy to the shepherd moons in planetary systems. However, thus far, there is insufficient observational evidence that might support the validity of such a scenario.

### *2.3. Current Evolutionary State of B[e]SGs*

The formation mechanism of the observed gaseous and dusty rings or disk-like structures around B[e]SGs is certainly one of the most important ye<sup>t</sup> unsolved issues. Equally important questions arise: What is the evolutionary phase of B[e]SGs? What is their evolutionary connection to other evolved massive stars? Does such a connection exist at all? While the question on the relation between B[e]SGs and other evolved objects is beyond the scope of this review, we briefly elucidate the current knowledge about the evolutionary status of B[e]SGs. Considering the MC sample, it is obvious from Figure 1 that all objects have evolved off the main sequence. Whether this occurred only recently, or whether B[e]SGs might be on a blue loop or blueward evolution after having passed through the turning point on the cool edge of their track, is still an open issue, in particular, since we lack clear methods for age determinations of these emission-line objects, which only very rarely are detected in clusters2.

In this regard, the detection of clear signs of the 13C isotope in the form of 13CO band emission from a number of MC B[e]SGs ([41,86], see Table 2) was one major step forward. The appearance of these bands has been predicted based on theoretical model computations for a variation of the carbon isotope ratio 12C/13C [87]. As surface abundance calculations have shown, this ratio will drop during the evolution of massive stars from an initial, interstellar value of ∼90 down to values <5, depending on the initial mass of the star and its initial rotation speed. The surface material enriched in 13C is transported via winds to the environments, where it will cool and condense into 13CO molecules, whose emission can be observed in the K-band, together with the emission from the main isotope, 12CO (see Figure 3). Hence, the detected amount of 13CO is a measure for the stellar surface enrichment in 13C at the time the material, which is currently traced in the molecular emission, has been released from the stellar surface.

**Figure 3.** Synthetic spectra of the combined emission from 12CO and 13CO for different values of the 12C/13C ratio. The computations have been performed for the following physical parameters: a 12CO column density of 2 × 10<sup>21</sup> cm<sup>−</sup>2, a gas temperature of 3000 K, a line-of-sight rotational velocity of 66 km s<sup>−</sup>1, and a spectral resolution of 50 km s<sup>−</sup>1.

From the MC sample of 15 objects, seven have been found to display CO band emission, and all of them display clear indication of enrichment in 13C (see Table 2). Interestingly, all these objects with CO emission cluster in the same region of the HR diagram, as indicated by the dotted black square in Figure 1, i.e., in the luminosity range log *L*/*L* = 5.0–5.8. None of the three most luminous stars (S 22, S 111, and S 127) or of the four low-luminosity objects (S 23, S 59, S 93, and S 137) displays clear signs of CO emission. One outlier in the luminosity domain occupied by the CO emitting B[e]SGs is the star S 89, which also has no detectable CO band emission [41].

The absence of measurable CO band emission might have different reasons. Either the intensity of the emission is too low to be detectable against the strong near-IR continuum3, or the density of

<sup>2</sup> Currently, only four B[e]SGs are reported to be cluster members: the two LMC objects LHA 120-S 111 in the compact cluster NGC 1994 [26] and LHA 120-S 35 in SL482 [44], and the two Galactic sources MWC 137 in SH 2-266 [83] and Wd1-9 in Westerlund 1 [84,85].

<sup>3</sup> This spectral region suffers from strong telluric contamination, which is not always easy to remove, so that especially weak CO emission features might be hidden within telluric remnants.

the molecular gas might be very high, resulting in optically thick emission, which no longer has a characteristic band head structure. Another possibility would be that the CO emission from these stars might have variable CO band emission and they have thus far always been observed in phases of no emission. In this context, it is interesting to refer to the SMC object LHA 115-S 65, in which CO band emission suddenly occurred, while observations taken about nine months earlier did not detect any molecular features [40]. Alternatively, since we now know that the material is most probably concentrated in rings, the conditions within the circumstellar environment in terms of density and temperature might not be favorable for the excitation of the first-overtone bands. For those stars, observations in the spectral region of the fundamental bands might therefore be a possibility to search for cooler CO gas.

The measured 12C/13C isotope ratios of the MC B[e]SGs are all very similar, spreading from 9 to 20. This might point towards a similar formation history of the circumstellar material, i.e., a similar phase in the evolution (considering they are single stars or at least unaffected by a possible companion) when the enriched material was ejected. Considering that stars are typically born with some intrinsic rotation velocity, rotational mixing in combination with enhanced mass-loss may drive the enrichment of the stellar surface with 13C already in early stages of the evolution of massive stars. This can be seen in Figure 4, where the evolutionary tracks of a 32 M star with solar metallicity [88] and for a variety of initial rotation velocities are shown. The covered rotation speeds spread from *<sup>v</sup>*/*<sup>v</sup>*crit = 0 to *<sup>v</sup>*/*<sup>v</sup>*crit = 0.4, which correspond to values of Ω/Ωcrit from 0 to 0.568. The interpolation of the tracks has been performed with the SCYCLIST tool<sup>4</sup> provided by the Geneva group.

**Figure 4.** Evolution of the 12C/13C isotope ratio along the solar metallicity tracks of a star with initial mass of 32 M and initial rotation speeds *<sup>v</sup>*/*<sup>v</sup>*crit ranging from 0 to 0.4 (corresponding to Ω/Ωcrit = 0.0; 0.1; 0.2; 0.3; 0.4; 0.5; 0.568). The individual tracks have been obtained from the interpolation tool SCYCLIST provided by the Geneva group. For clarity of the plot, we truncated the evolutionary tracks within the red supergiant regions. Included are the positions of the MC B[e]SG sample from Table 2 with known 12C/13C ratio, following the same color coding as for the tracks. The Galactic objects are excluded due to their highly uncertain luminosities. Depending on the initial rotation speed of the star, the observed ratio can be reached either in the pre-RSG (moderate rotator) or post-RSG (slow rotator) phase.

The color coding along the tracks refers to the values of the 12C/13C isotope ratio on the stellar surface. Figure 4 also includes the positions of the seven MC B[e]SGs with known values of the

<sup>4</sup> https://www.unige.ch/sciences/astro/evolution/en/database/syclist/.

12CO/13CO isotope ratios. Their colors correspond to the same color coding as the evolutionary tracks. Obviously, the observed ratios for the sample stars might be reached either along or after the main-sequence evolution for stars rotating initially with rates Ω/Ωcrit ≥ 0.3. However, they might also be reached during or after the red supergiant stage for stars rotating initially with rates smaller than Ω/Ωcrit ≤ 0.3. As we do not know the initial rotation speeds of the progenitor stars of these B[e]SGs, the measured values of the 12CO/13CO isotope ratio alone cannot solve the issue with the current evolutionary state of the objects.

If B[e]SGs represent a specific phase in the evolution of massive stars, then these objects should also exist in other environments with high content of massive stars. Searching for representatives of B[e]SGs in other galaxies and studying their properties and number statistics at various metallicities might help to unveil their disk/ring formation mechanism, to pin down their evolutionary phase (preversus post-RSG), and to set constraints on the evolution of massive stars in general.

### **3. Identification of B[e] Supergiants in the Local Universe**

Identifying and classifying B[e]SGs is a tedious job, whether in the Milky Way, where we face large amounts of foreground extinction and the issue with the often unknown distances, or in other galaxies, where we have strong contamination with foreground sources, often crowded regions, and the faintness of the objects. While the first B[e]SGs have been found rather accidentally, nowadays dedicated surveys can make use of the established classification criteria. As mentioned in Section 2, there are basically four characteristics a star should fulfill to be classified as B[e]SGs [18,25]. It should display:


Despite these defining criteria, the identification of extragalactic B[e]SGs is not as straightforward, because suitable candidates need first to be found based on other means. These candidates can then be further investigated to search for these, mostly spectroscopic, characteristics.

A suitable approach is to search for B[e]SG candidates among the luminous, blue objects identified in imaging surveys that have been performed for several galaxies over the past ∼30 years. For instance, the early photographic and photometric surveys of M31 [89,90] and M33 [91] revealed (amongst many other objects) the most luminous hot stars and the brightest blue supergiants, which could then be studied spectroscopically to obtain indications for their possible nature (e.g., [92]). A milestone for the identification of evolved massive stars was certainly the Local Group Galaxies Survey (LGGS) project [93,94], which resulted in the discovery of numerous putative emission-line stars in M31, M33, and seven more dwarf galaxies. Spectroscopic follow-ups were used to sort out H II regions, and to match the remaining objects with the various known categories of evolved massive stars. A major result of this survey was the identification of numerous objects that were dubbed as luminous blue variable (LBV) candidates [6,95], based on the appearance of their blue emission-line or P Cygni-type spectra that resemble confirmed LBVs in quiescence. Since the blue optical spectra of LBVs in their

<sup>5</sup> We would like to stress that the high-luminosity B[e]SGs barely display photospheric absorption lines, whereas the low-luminosity B[e]SGs typically do.

quiescence state display a number of common characteristics with B[e]SGs [95–97], it was expected that this sample contains a number of B[e]SGs.

Surprisingly, when analyzed in more detail [97–99], this bunch of newly identified LBV candidates in M31 and M33 turned out to be a mixed bag containing not only B[e]SGs candidates, but also so-called Fe II emission stars (with neither [O I] nor [Fe II] emission and lacking warm dust), and warm hypergiants (with lots of dust, possible [O I] and/or [Fe II] but of spectral type A–F), with only a few objects left to be considered as LBV candidates (with no [O I] emission and lacking hot dust).

As both LBVs and B[e]SGs are luminous blue supergiants, they share the same optical colors. Hence, one step to distinguish these two groups of objects is to inspect their location in infrared color–color diagrams (e.g., [16,20,41,97,99]). The hot ( ∼1000 K) circumstellar dust of B[e]SGs results in significantly increased near-IR emission. On the other hand, LBVs can be associated to cold, dusty environments such as the circumstellar shells recently discovered around many LBVs and LBV candidates with the Spitzer Space Telescope at 24 μm ( e.g., [100,101]). The separation of B[e]SGs from quiescent LBVs, based on their diverse IR properties, is demonstrated in Figure 5 for the known samples of MC objects, limiting to the confirmed and generally accepted LBVs in the LMC [102] and including one confirmed object from the SMC (R40, [103]). Shown are two different color–color diagrams (J–H versus H–K and W1–W2 versus W2–W4). The IR colors of the objects are listed in Table 3. They result from the JHK-band magnitudes obtained from the 2MASS point source catalog<sup>6</sup> [104], and from the mid-IR magnitudes (W1, W2, W4) collected with the Wide-field Infrared Survey Explorer<sup>7</sup> (WISE [105]). From the many possibilities of near- and mid-IR color–color diagrams, these two show the clearest separation between the two groups of objects.

**Figure 5.** Demonstration of the separation of the B[e]SGs from the quiescent LBVs within the near-IR (J–H versus H–K diagram (**left**)) and the WISE diagram (W1–W2 versus W2–W4 (**right**)). Shown are the positions of the classical MC B[e]SG sample and of the MC LBV sample. IR colors of the objects are provided in Table 3. The solid line represents the positions of regular supergiants with empirical colors taken from [106] for solar metallicity stars.

Another clear distinctive feature between B[e]SGs and LBVs is the S Dor cycle of the latter, while B[e]SGs are typically not undergoing this type of variability. However, to identify such S Dor excursions of the stars within the HR diagram is a time-consuming (though important) task, because it requires regular monitoring of the whole sample.

<sup>6</sup> http://cdsarc.u-strasbg.fr/viz-bin/cat/II/246.

<sup>7</sup> http://cdsarc.u-strasbg.fr/viz-bin/cat/II/311.

In addition, dedicated spectroscopic observations are required to search for the characteristic forbidden emission lines of [O I] and possible [Ca II] in the red portion of the optical spectra, and to search for possible molecular emission of CO in their near-IR spectra, because LBVs typically do not show these sets of forbidden lines and CO band emission<sup>8</sup> [21,35,41].


**Table 3.** IR colors of Magellanic Cloud B[e]SGs and LBVs.

Note: IR photometry for all objects is taken from the 2MASS point source catalog (J, H, and K [104]), except for the stars LHA 120-S 111 [21] and LHA 120-S 89 [108], and from the WISE All-Sky Data Release (W1, W2, and W4 [105]). a Despite of the lack of WISE colors, the presence of warm dust is proven by its IR excess seen in the Spitzer data, and its IR spectrum that looks like a twin of the one of LHA 120-S 73 (see [82]).
