Massive stars contain many of the extremes of astrophysics. Their high
masses result in high luminosities, with energy outputs on the order of
a million times that of the sun. While on the main-sequence as O-type
stars, they have nearly the highest effective temperatures of any stars,
with only white dwarfs being hotter. As Luminous Blue Variables (LBVs),
they show spectacular outbursts, throwing off large amount of material
and brightening by several magnitudes visually. As yellow supergiants
(YSGs), they are among the visually brightest in any galaxy, although,
ironically, their identification is often complicated by the plethora of
foreground Galactic yellow dwarfs. As cool red supergiants (RSGs), they
flirt with the limits of hydrostatic equilibrium, and are physically the
largest stars: if you place one of the biggest at the center of the
solar system, its photosphere would end somewhere between the orbits of
Jupiter and Saturn. As Wolf-Rayets (WRs) they are little more than
stripped stellar cores with such strong stellar winds that they would
lose ten times the mass of the sun in a mere million years, were they to
live that long. Finally, massive stars end their lives as spectacular
supernova, briefly outshining the whole of their host galaxies.
There are two fundamental reasons for studying massive stars amongst the star-forming galaxies of the Local Group. First, these galaxies allow us to perform tests of stellar evolutionary theory in a laboratory where primarily a single variable can be changed, namely the chemical composition of the stars. The physical properties of a massive star will be essentially identical at birth regardless of small changes in the composition. (Recall that the heavier elements represent only a few percent of the overall composition of stars.) But, these trace elements have a large impact on the subsequent evolution of massive stars. On the main-sequence, a massive star's high effective temperature and luminosity result in strong stellar winds, which are driven by radiation pressure on these highly ionized metal atoms, resulting in significant mass loss. A 100 M star could lose half of its mass during its short lifetime! The importance of this mass-loss on mass star evolution was first demonstrated by the early models that attempted to include the effects of mass loss (e.g., de Loore et al. 1977, 1978; Chiosi et al. 1978, 1979; Brunish & Truran 1982). Modern models continue to demonstrate the importance of mass loss to massive star evolution (Meynet & Maeder 2005). Because these winds are driven by radiation pressure acting on highly ionized metal atoms, the mass-loss rates depend upon a star's initial metallicity z, as something like ~ z0.7 (Vink et al. 2001). Thus, over the ~ 20× metallicity difference between WLM (z / z ~ 0.1) to M31 (z / z ~ 2), we expect the main-sequence mass-loss rates to vary by nearly an order of magnitude. Such differences should be (and are) reflected in the relative number of evolved massive stars of various kinds, such as the relative number of Wolf-Rayet stars to red supergiants, or the relative number of WC- and WN-type WRs.
Secondly, these massive stars affect the overall evolution and properties of the galaxies themselves, through three "feedback" mechanisms (see, e.g., Oey & Clarke 2009). First, their ultraviolet radiation heats dust, powering the far-IR luminosities of galaxies, while at the same time providing the ionizing radiation that causes the HII regions (see, e.g., Maeder & Conti 1994). Of course, it is these HII regions which delineate the arms in spiral galaxies, and otherwise reveal where most of the star formation action is occurring in irregular galaxies. Secondly, their strong stellar winds provide significant mechanical energy input into the interstellar medium, as does their eventual disruption as supernovae (Abbott 1982), shock-heating the gas to > 106 K (Oey & Clarke 2009). This mechanical energy feedback is responsible for the creation of superbubbles (Pikel'ner 1968; Weaver et al. 1977; see discussion in Oey et al. 2001). And thirdly, they are responsible for much of the chemical enrichment of galaxies, particularly of the "lighter" elements (atomic weight less than 30), such as carbon, nitrogen, and oxygen (Maeder 1981, Sparke & Gallagher 2000). During their red supergiant phase, massive stars also make a significant contribution to the dust content, particularly for star-burst systems and galaxies at large look-back times where AGBs have not yet formed (Massey et al. 2005a).
In this review, we will first provide an introduction to massive stars, and then follow this with a more detailed description of the current state of our knowledge (and lack thereof) of the content of these stars in Local Group galaxies. A much shorter review on this subject was given by Massey (2010), and an older, but more detailed look, can be found in Massey (2003).
When we talk about the "star-forming galaxies of the Local Group," we are referring to the galaxies listed in Table 1, an updated version of Table 1 from Massey (2003) and Massey et al. (2007b).
|Galaxy||Type||l||b||MV||E(B-V) b||Dist (Mpc)||log O/H+12|
|MW||S(B)bc I-II:||—||—||-20.9?||—||—||8.7 c|
|M31||Sb I-II||121.2||-21.6||-21.2||0.13||0.76||8.9-9.0 d|
|M33||Sc II-III||133.6||-31.3||-18.9||0.12||0.83||8.3-8.9 e|
|NGC 6822||Ir IV-V||25.3||-18.4||-16.0||0.25||0.50||8.1|
|IC 10||Ir IV:||119.0||-3.3||-16.3||0.81||0.66||8.2|
|IC 1613||Ir V||129.7||-60.6||-15.3||0.72||0.05 f||7.9|
|a Data from van den Bergh (2000) and references therein, except as noted.|
|b From Massey et al. (2007b), except as noted.|
|c In the solar neighborhood.|
|d From Sanders et al. (2012) at R = 12 kpc.|
|e From Magrini et al. (2007) but see Bresolin (2011) and discussion in Neugent & Massey (2011).|
|f From Sandage (1971).|
1.2. A Massive Star Primer
Before delving into the primer, it is worth emphasizing that our understanding of massive star properties and evolution derives not from observations or theory alone, but from the combination of the two: even something as basic as a star's luminosity relies not only upon the visual brightness, but also a knowledge of stellar atmospheres in order to relate what is observed to the meaningful physical quantity. Within this review, a lot of the emphasis will be given to the observational side, but it would be horribly remiss not to stress the importance of theory as well. Just as large telescopes and more efficient detectors have made possible observations only dreamed of in the 1960s, so has the improvement in the physics and computational tools improved both the study of stellar atmospheres and stellar evolution. Further, just as observers often go to pains to make their data freely available, our theoretician colleagues have gone to similar efforts to share the results of their modeling and codes. The first non-LTE atmosphere modeling that included only H and He done by Auer & Mihalas (1972) have now evolved to very complex non-LTE codes that include the effects of line-blanketing and stellar winds, such as CMFGEN (Hillier & Miller 1998), a code which is made publicly available by the kindness of D. John Hillier. Similarly, the early evolutionary models that included the effects of mass loss have now evolved to very sophisticated models that include the effects of rotation and mass loss throughout the H-R diagram (e.g., Maeder & Meynet 2000a, 2000b; Meyent & Maeder 2000, 2003, 2005; Ekström et al. 2012; Georgy et al. 2012). The Geneva group has, in particular, always been very generous by making their models publicly available, encouraging direct comparisons (and sometimes confrontations) between predictions and observations.
1.2.1. The main-sequence
Evolution. Massive stars (m > 8M) begin their lives on the main-sequence as O- and early B-type dwarfs. As these stars age, they burn hydrogen in their cores via the CNO cycle. The main-sequence (hydrogen-burning) phase lasts for between 3 Myr (120 M) and 30 Myr (9 M), according to the latest solar-metallicity Geneva models (Ekström et al. 2012). We summarize some of their main-sequence properties in Table 2, where we have assigned spectral types and luminosity classes based upon their evolutionary effective temperatures and surface gravities. There are several things of note:
Figure 1. Evolution of massive stars. The high mass Geneva evolutionary tracks (Ekström et al. 2012) for solar metallicity (z = 0.014) are shown ; these models assume an initial rotation velocity of 40% of the critical break-up speed. The initial masses label the beginning part of each track; for simplicity we have not included the 85 M or 60 M tracks. The bold sections of the tracks show the main-sequence. The general regions of the yellow supergiants and red supergiants are shown.
|ZAMS||Turn-off||Start of He-burning|
|Mass||tH||Teff||Log||Log g||Spect.||Teff||Log||Log g||Spect.||Teff||Log||Log g||Spect.|
|120||3.2||52,000||6.2||4.1||O2-3 V||50,500||6.2||4.0||O2-3 V||29,400||6.0||2.8||B0 I|
|85||3.7||50,000||6.0||4.2||O2-3 V||48,000||6.0||4.0||O2-3 V||21,300||6.3||2.1||B1 I|
|60||4.4||47,000||5.7||4.2||O3 V||45,000||5.8||4.0||O4 V||7,100||6.1||0.2||F5 I|
|40||5.7||43,000||5.3||4.2||O4 V||31,500||5.7||3.2||O9 I||6,400||5.9||0.2||F8 I|
|25||7.9||38,000||4.9||4.2||O6 V||27,300||5.3||3.2||B0.2 I||7,900||5.4||0.9||F0 I|
|20||9.5||35,000||4.6||4.3||O7.5 V||25,800||5.0||3.3||B0.5 I||12,300||5.1||1.9||B6 I|
|15||13.5||31,000||4.3||4.3||O9.5 V||24,300||4.7||3.4||B0.5 I||9,500||4.8||1.6||A0 I|
|12||18.4||27,900||4.0||4.3||B0.5 V||22,300||4.4||3.5||B0.5 I||8,200||4.5||1.7||A8 I|
|9||31.2||24,000||3.6||4.3||B1 V||19,600||4.0||3.5||B1.5 III||3,800||4.1||0.6||M0 I|
|a Based on Ekström et al. (2012), Massey et al. (2005b), and Levesque et al. (2007).|
There are a few other caveats that need to be kept in mind when talking about the main-sequence evolution of massive stars. First, the luminosity class ("I" vs "V", say) of O-type stars depends primarily on lines that are not so much sensitive to surface gravity but rather to stellar wind strengths. The higher the bolometric luminosity at a given metallicity, the stronger the stellar wind will be ( ~ L2.1, according to Vink et al. 2000, for Teff > 27,500 K), as there is only a weak dependence upon the effective temperature in the mass-loss rates for stars this hot 1. So, stars in the high mass and luminosity range will have the strongest mass-loss rates. The luminosity class is primarily based upon the morphology of the He II 4686 line. This line is both sensitive to mass-loss rates and effective temperatures, and (for a given spectral subtype) a He II 4686 line that is strongly in absorption leads to a luminosity class "V", while one in emission leads to a luminosity class "I". When He II 4686 is in emission, along with the neighboring N III 4634, 42 line, we call the O star an "Of-type", with the implication that the star is of luminosity class "I". (The actual system is a bit more complicated than this; see, e.g., Sota et al. 2011.) The NIII emission behavior has finally been demonstrated to be dependent on stellar wind strengths, although nitrogen abundance also plays an important role (Rivero Gonzáez et al. 2011). Of course, a significant problem occurs when one looks at O stars in other galaxies that are more metal-poor than the Milky Way where the various spectral standards have been defined. Even a high-luminosity O star in the SMC may fail to show He II 4686 and be labeled a "giant" or even a "dwarf", when its absolute visual magnitude demonstrates it's a supergiant; see discussion in Massey et al. (2005b).
The other thing to keep in mind about the evolutionary models is that they are static, not hydrodynamic. Note that in Table 2 I assigned a spectral type of B0 I to the 120 M star at the start of He-burning, but the situation may be a little more complicated than that. These stars will have such high mass-loss rates that it is possible, even likely, that the 120 M star will not be identified as an O3-4 V or B0 I, but rather as a hydrogen-rich, WN Wolf-Rayet star, similar to the highest mass (but unevolved) stars seen in the R136 cluster in the LMC and NGC 3603 in the Milky Way: "Of-type stars on steroids" (Crowther et al. 1995, Massey & Hunter 1998).
Stellar Winds One of the areas of active research is the issue of what the mass-loss rates are during the hot main-sequence stage. Historically, there have been three methods for measuring the mass-loss rates in O-type stars:
Both the H and IR/radio continua methods rely upon the interaction of two particles, and they are therefore referred to as "density-squared" (2) processes. In contrast, P Cygni lines are due to scattering; i.e., a photon is absorbed and immediately re-emitted. In general, the results from the two 2 processes agreed, but with the occasional pathological cases (Lamers & Leitherer 1993, Puls et al. 1996). This happy state of affairs was changed when Fullerton et al. (2006) used the FUSE satellite to measure the mass-loss rates from the P V 118, 28 resonance doublet. This side stepped the saturation problem with the P Cygni profiles: since phosphorus is rare, the line isn't saturated. They found mass-loss rates which were, at first blush, a factor of 10 lower than what had been assumed previously with the assumption of homogeneous, spherically symmetric winds. Instead, it now accepted that stellar winds are "clumped", and not as homogeneous as had been assumed for convenience. As Fullerton et al. (2008) wrote, "Thus, a fundamental consequence of clumping in hot-star winds is that the values of (2) must be reduced. The only question is: by how much?" Naively, all other things being equal, the answer would be a factor of ten but current thinking now is that generally the value is more likely a factor of 2 or 3 (Hirschi 2008, Puls et al. 2008). But this remains one of the great uncertainties that motivates observational comparisons of the relative number of massive stars in various stages versus what is predicted by the evolutionary models with some assumed mass-loss rate.
Knowing the number of progenitor, main-sequence stars relative to the number of their evolved descendants provides a key observational test of stellar evolutionary models, but as we will see in Section 2.1, quantifying this is among the most difficult observational challenges, as the main-sequence phase is when massive stars are the visually faintest.
1.3. Luminous Blue Variables
What happens after the main-sequence, depends upon the mass of the star. For the highest mass stars, they encounter a little difficulty as they edge to cooler temperatures: the opacities of the lines increase as the temperatures decrease, and soon radiation pressure equals or exceeds the force of gravity (Lamers 1997). This point is probably associated with the phase known as the classic "Luminous Blue Variables," previously known as Hubble-Sandage variables (Hubble & Sandage 1953) or "S Doradus" variables. Of all the various phases through which a massive star passes, the details and implications of the LBV phase are probably the most poorly understood. What is generally agreed upon is that the "classic" LBVs, such as S Doradus and P Cygni, undergo giant "eruptions" every few hundred years, in which there are large photometric changes (several magnitudes) accompanied by large amounts of material coming off of the star (see, e.g., Bohannan 1997 and Conti 1997).
The star Car is often cited as the prototypical LBV. It certainly has been the most heavily studied both ground-based and space-based (e.g., HST): the SAO/NASA Astrophysics Data System reports nearly 500 refereed papers containing Car in its title, and over 1200 if conference proceedings are counted as well. Beyond question it is an interesting object in its own right, but Car is probably not much of a rosetta stone for LBVs in general, as it consists of a 5.5 year binary. The stars are in an eccentric orbit, and some have argued that the major eruptions have been triggered by mass transfer at periastron passage (see, e.g., Kashi & Soker 2010). The discovery of the binary nature of the system has been relatively recent (van Genderen et al. 1994, Damineli et al. 1997, Sonneborn et al. 2005), and has led to a series of observing campaigns at each new close passage.
Smith & Owocki (2006) suggest that, if the main-sequence mass-loss rates are actually ~ 10× lower than they the unclumped models indicate (rather than the 2-3× Puls et al. 2008 and others have argued must be the case), the mass loss during the LBV phase may be critically important to the further evolution of massive stars. Smith et al. (2004) argue for the existence of "lower mass" LBVs, as low as 10-15 M, whose winds become sufficiently strong at an effective temperature of 21,000 K to cause "pseudo-photospheres" to form, mimicking (at least) the behavior of many high luminosity LBVs. (The 21,000 K effective temperature corresponds to the "bistability jump", where a small drop in effective temperature results in a decrease in the ionization of the wind, leading to a smaller, but much denser, stellar wind. See Pauldrach & Puls 1990 and Lamers et al. 1995.) But, much of this is conjecture.
What is clear is that due to the length of time between major outbursts, it is very tough to get a good handle on the number of LBVs. The spectra of "hot" LBVs show emission of [FeII], He I, and the Balmer lines, while the latter two series usually display P Cygni profiles (see, for example, Figure 10 in Massey et al. 2007a). Their spectra can instead resemble those of P Cygni itself, with strong Balmer and He I P Cygni emission but no forbidden Fe. During their cool phase they can develop a "pseudo-photosphere", and their spectra resemble that of a late G- or F-type supergiant with strong Balmer emission. The "hot" phase is often described as their "quiescence" stage, and their "cool" phase as an "outburst" stage, but an accidental spectrum of S Dor itself in 1999 revealed the coolest spectrum in 50 years of spectroscopic monitoring; the F-type "pseudo-photosphere" was not accompanied by any major change in its photometry (Massey 2000). Of course, that may require several hundred years (see discussion in Massey 2006). We will discuss this further in Section 2.2.
1.3.1. Red and Yellow Supergiants
Stars of somewhat lower mass (< 30 M?) will evolve quickly to the red, passing first through a yellow supergiant phase. It is in this stage that a massive star will be at its visually brightest, with the peak of the flux distribution being at visible wavelengths. (Recall that stellar evolution of massive stars takes place at nearly constant bolometric luminosity, so as the star cools to temperatures similar to those of the Sun, their visual brightness will peak.) The YSG phase is so short (a few thousand to a few tens of thousands of years), that the phase has little evolutionary implications (i.e., in terms of mass loss), but as we shall see in Section 2.3 this phase acts as a very sensitive probe of the accuracy of earlier evolutionary calculations.
At the coolest temperatures, these < 30 M stars are red supergiants, the physically largest stars. Levesque (2010, 2012) has recently reviewed their physical properties. For many years, their "observed" locations in the H-R diagram (HRD) were much cooler and more luminous than stellar evolutionary theory allowed, although few researchers seemed to realize this. The basic problem was that the effective temperatures were derived primarily from lunar occultations of red giants (see discussion in Massey & Olsen 2003). The use of the new MARCS models (Gustafsson et al. 1975, Plez et al. 1992), which included sphericity and improved molecular opacities for TiO and other oxygen-rich molecules (Plez 2003, Gustafsson et al. 2003, Gustafsson et al. 2008), led to effective temperatures and luminosities that agreed well with the Geneva models over a wide range of metallicities (Levesque et al. 2005, 2006; Massey et al. 2009).
The amount of mass lost during the RSG phase is a key factor in determining what happens next to the star; it is also one of factors most poorly constrained by observation and theory (Georgy et al. 2013). High mass loss during this stage will shorten the RSG phase, and cause the star to evolve bluewards again in the HRD, going through a second YSG phase possibly becoming a Wolf-Rayet star or even an LBV (Groh et al. 2013). Otherwise, RSGs are expected to end their lives as Type II supernovae.
RSGs are "smokey": dust condenses as the star loses mass. Recently this led to the realization that RSGs suffer significant circumstellar reddening (see, e.g., Massey et al. 2005a). Little is understood about what drives this mass loss. Massey et al. (2008) quotes Stan Owocki (2007, private communication) as arguing that it doesn't take much to "drive" a RSG wind. The escape velocity from a star is just 620 km s-1 × (M / R)1/2. Although O stars have a M/R ratio that is of order unity, RSGs do not: the ratio is much smaller, more like 0.02. So, the escape velocity is down by a factor of 7, less than 100 km s-1. Owocki argues that the mass loss of a hot star is set by conditions outside the stellar interior, i.e., opacity in the atmosphere and wind, that results in the radiatively-driven mass loss (Castor et al. 1975). For RSGs, the heavy lifting has already been done by the stellar interior, as a significant fraction of the luminosity of the star has gone into making a bigger radius. "It is kind of like walking with a nearly full glass of water vs a glass that is only 1% full (O star)—even a small jiggle can lead to big changes in the mass loss for a RSG," Owocki concludes.
1.3.2. Wolf-Rayet Stars
Finally, let us introduce the Wolf-Rayet stars. These stars have strong emission-line spectra. WR stars come in basically two flavors, WN-type WRs, where the spectrum is dominated by N and He, and WC-type WRs, where the spectrum is dominated by He, C, and O. (A few WO-type WRs have been identified; these are basically WC stars with enhanced O lines.) In the "Conti scenario" (Conti 1976), a massive star peels off its H-rich outer envelope through stellar winds on the main-sequence (perhaps helped by the enhanced mass loss during the LBV phase). Once the H-burning products (N and He) are revealed, the star is spectroscopically identified as a WN-type. Further mass loss eventually peels off these layers, revealing the He-burning products (C and O)
An outstanding question is why the mass-loss rates of WRs are so high; H-poor WRs have derived mass-loss rates about 10× higher than OB stars of the same luminosity. The terminal wind velocities are similar, so it is as if the radiation pressure was somehow more efficient in these H-poor objects. Puls et al. (2008) offers several possibilities, including the speculation that this is due to WR star winds being less "leaky" because the higher core temperature and higher wind density leads to an ionization equilibrium that is stratified. Alternatively, the ionization in the outer winds may be shifted towards lower stages, leading to a more efficient acceleration. Or it could be that WR winds get an extra kick due to the hot ion peak around 160,000 K deep in the WR atmosphere.
What we do know is that the mass-loss rates on the main-sequence depend upon metallicity, as mentioned earlier, and that therefore it is easier for a massive star to become a WR at high metallicity than at low. To put this more precisely, a 20 M might be able to "peel down" all of the way to a WC star in M31 (where the metallicity is high, see Table 1), but could only evolve as far as the WN stage in M33 (where the metallicity is lower, Table 1). Or perhaps only stars of 60 M and above can become WRs in the SMC. One expectation then is that the relative number of RSGs and WRs should be a sensitive function of metallicity among the galaxies of the Local Group (Maeder et al. 1980), with relatively fewer WRs at lower metallicities. In addition, one expects that the relative number of WC and WN stars should be a strong function of metallicity, with relatively fewer WCs at lower metallicities (Massey & Johnson 1998, Meynet & Maeder 2005, Neugent et al. 2012a).
1.3.3. Supernovae (SNe)
Massive stars are expected to end their lives as core-collapse SNe, enriching the interstellar material chemically, and providing a great deal of mechanical energy. However, the only example we know of this directly in the Local Group is SN 1987A, where the progenitor star, Sk -69∘ 202, was known to be a ~ 20M B-type supergiant. At the time, evolutionary models did not include a "blue loop" for such stars; they were supposed to become supernovae as RSGs.
Core-collapse SNe are either hydrogen-rich type II SNe, or hydrogen-poor types Ib and Ic, where the latter are also helium-poor. The type II's are further classified depending upon their light curves (type II-P, whose light curves show a plateau, and II-L, where the light curve shows a magnitude-linear decline in time) or spectral features (IIn, where the spectrum shows narrow emission lines, and IIb, where the spectrum changes to become like that of a Ib).
The lack of hydrogen features in the spectra of types Ib and Ic suggest that the progenitors have been been stripped of their outer hydrogen envelopes. Two prevailing theories for how this stripping occurs are mass-loss through strong stellar winds or through binary interaction. The former naturally associates the Ib/c's with Wolf-Rayet stars, but there are no cases where an actual progenitor of a Ib or Ic has been identified. (Shara et al. 2013 argue that the identification of Wolf-Rayet stars in nearby galaxies serves the additional purpose of identifying Ib/c progenitors, so that when one of these stars explodes we'll be prepared.)
All type II-P core-collapse SNe have long been assumed to come from RSGs, although the classification of SN 1987A is that of a (peculiar) II-P and we know it didn't. Smartt et al. (2009) have identified numerous type II-P progenitors in nearby galaxies as RSGs, as well as summarizing those found by others. They argue that type II-Ps come from a mass range from 8.5 to 16.5 M. Since RSGs have masses as large as 25 M, this introduces the "red supergiant problem": why is the observed upper mass limit 16.5 M. Of course, this mass limit is not directly observed; it is inferred by making a variety of assumptions not only about the IMF slope in nearly galaxies, and it also depends upon certain reddening assumptions, etc.
One of the most remarkable recent astronomical events has been the explosion (SN 2011dh) of a YSG in M51 (distance 11 Mpc) as a Type IIb supernova (Maund et al. 2011). Two other examples of YSG progenitors for SNe explosions exist; see Georgy et al. (2013) and references therein. This fact poses some interesting, but not insurmountable, challenges to single-star massive star evolutionary theory (e.g., Georgy et al. 2013), as 15M stars (which is a typical mass for YSGs) have long been thought to end their lives in the RSG stage. But significant mass-loss during the RSG may delay the explosion (Bersten et al. 2012, Georgy et al. 2013). Alternatively, these YSGs may have been binaries, and binary evolution may have played a role in the formation of these SNe.
Of similar import has been the explosion of an LBV in NGC 7259 (distance 25 Mpc, far outside the Local Group), a Type IIn core-collapse supernova (SN); see Mauerhan et al. (2013) and references therein. The star, SN 2009ip, was a transient which had recent eruptions. (In fact, the first such eruption was mistaken for a SN explosion.) As of this writing, the result is still somewhat controversial (see, e.g., Pastorello et al. 2013), but if the discovery is confirmed, it will be remarkable in that for the first time we knew for certain what the progenitor was of a type IIn explosion, and as a demonstration that an LBV could explode as a SN.
1 The mass-loss rates change by 0.01 dex due to temperature from 40,000 to 50,000 K, according to Vink et al. (2000), equation 12. Back.