On the role of the WNH phase in the evolution of very massive stars: Enabling the LBV instability with feedback
aa r X i v : . [ a s t r o - ph ] F e b Draft version October 29, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
ON THE ROLE OF THE WNH PHASE IN THE EVOLUTION OF VERY MASSIVE STARS: ENABLING THELBV INSTABILITY WITH FEEDBACK
Nathan Smith
Astronomy Department, University of California, 601 Campbell Hall, Berkeley, CA 94720; nathans@astro.berkeley.edu andPeter S. Conti
JILA, University of Colorado, 389 UCB, Boulder, CO 80309
Draft version October 29, 2018
ABSTRACTWe propose the new designation “WNH” for luminous Wolf-Rayet (WR) stars of the nitrogensequence with hydrogen in their spectra. These have been commonly referred to as WNL stars (WN7h,for example), but this new shorthand avoids confusion because there are late-type WN stars withouthydrogen and early-type WN stars with hydrogen. Clearly differentiating WNH stars from H-poor/H-free WN stars is critical when discussing them as potential progenitors of Type Ib/c supernovae andgamma ray bursts — the massive WNH stars are not likely Type Ib/c supernova progenitors, andare distinct from core-He burning WR stars in several respects. We show that the stellar masses ofWNH stars are systematically higher than for bona fide
H-poor WR stars (both WN and WC), withlittle overlap. Also, the hydrogen mass fractions of the most luminous WNH stars are higher thanthose of luminous blue variables (LBVs). These two trends favor the interpretation that the mostluminous WNH stars are still core-H burning, preceding the LBV phase (at lower luminosities theWNH stars are less clearly distinguished from LBVs). While on the main sequence, a star’s massis reduced due to winds and its luminosity slowly rises, so the star increases its Eddington factor,which in turn strongly increases the mass-loss rate, pushing it even closer to the Eddington limit.Accounting for this feedback from mass loss, we show that observed masses and mass-loss rates ofWNH stars are a natural and expected outcome for very luminous stars approaching the end of core-Hburning (ages ∼ ⊙ , wefind a strong and self-consistent case that luminous WNH stars are pre-LBVs rather than post-LBVs.The steady march toward increased mass-loss rates from feedback also provides a natural explanationfor the continuity in observed spectral traits from O3 V to O3 If* to WNH noted previously. Subject headings: stars: evolution — stars: mass loss — stars: winds, outflows — stars: Wolf-Rayet INTRODUCTION
The role of mass loss in the evolution of the mostmassive stars with initial masses of ∼ ⊙ is stillpoorly understood, partly because the most luminousstars are so rare and each one seems unique at somelevel, and partly because accurate physical parametersare difficult to determine. Consequently, the connectionbetween spectral characteristics and evolutionary stateis often mangled.One persistent mystery concerns the placement of thevery luminous late-type H-rich WN stars (referred to hereas “WNH stars”, as justified below) in the evolutionarysequence of very massive stars (see Crowther et al. 1995a;Hamann et al. 2006; Langer et al. 1994). Because oftheir high mass-loss rates and consequent emission-linespectra, they are often discussed alongside or confusedwith core-He burning Wolf-Rayet (WR) stars (for reviewsof WR stars, see Abbott & Conti [1987] and Crowther[2007]), and it is sometimes suggested that their H con-tent indicates that they represent the early phases ofcore-He burning. In this interpretation, the WNH phaseoccurs immediately after – or sometimes instead of – theluminous blue varibale (LBV) phase, marking the begin-ning of the core-He burning WR stages (see for exam-ple, Schaller et al. 1993; Meynet et al. 1994; Maeder & Meynet 1994).A different suggestion has been made based on the veryhigh luminosity of some of the WNH stars and especiallybased on their membership in very young massive starclusters like R136 in 30 Doradus, NGC 3603, and theCarina Nebula (e.g., de Koter et al. 1997; Drissen et al.1995; Crowther et al. 1995a; Moffat & Seggewiss 1979).Namely, these authors suggest that it may be the caseinstead that the WNH stars are essentially core-H burn-ing stars that precede the LBV phase. This suggestionhas also been made based on the continuity in spectraltypes from O3 V to O3 If* to WNL+h as noted, for ex-ample, by Walborn (1971, 1973, 1974), Walborn et al.(2002), Lamers & Leitherer (1993), Drissen et al. (1995)and Crowther et al. (1995a).This continuity has led to the suggestion that the mostluminous stars may even skip the LBV phase altogether(Crowther et al. 1995a) – i.e. that they evolve directlyfrom O stars to WR stars (Conti 1976). However, thisdirect path is not taken in all cases because it is contra-dicted by the existence of very luminous LBVs such as η Carinae and the Pistol star. Langer et al. (1994) havediscussed the two possibilities above from the perspectiveof evolution models, and they suggest instead that bothmay be true — i.e., that a star may look like a WNH Smith & Contistar both before and after the LBV phase. Langer et al.(1994) investigated a 60 M ⊙ initial mass model, and aswe will see later, the distinction between stars of 60 and100 M ⊙ may be important in terms of their evolutionarypath.Our main conclusion in this paper is that available evi-dence strongly favors the latter interpretation above thatWNH stars are pre-LBVs, at least for the highest lumi-nosities above log(L/L ⊙ )=5.8–6.0. As discussed below,this is based on the fact that their distributions of stel-lar mass are distinct from H-poor stars and that theirhydrogen mass fractions are generally higher than LBVs(although there is a caveat to this last point depend-ing on initial mass, as discussed below). We also arguethat one might expect them to be pre-LBVs if feedbackfrom mass loss on the main-sequence is accounted for in asimple way. In § § § § THE SHORTHAND “WNH” TO DESIGNATE A DISTINCTCLASS
We propose the new designation “WNH” for lumi-nous WR-like stars of the nitrogen sequence exhibit-ing evidence for hydrogen in their spectra. In cur-rent practice, these are commonly referred to collectivelyas “WNL stars”, with individual objects classified asWN6ha, WN7h, etc. (see Smith et al. 1994; Smith etal. 1996; Crowther et al. 1995a). We do not propose tochange this more specific spectral classification schemefor individual stars. However, we do advocate that thecommon usage of “WNL stars” as a group should bechanged to “WNH stars” for two main reasons, one be-ing a practical matter and the other having to do withtheir evolutionary state and questionable relationship toother WR stars.The terms WNL, WNE, WCL, and WCE were firstused by Vanbeveren & Conti (1980) as a shorthandfor “late” and “early” type WR stars of the nitrogenand carbon sequences. Its use was quickly adopted asa convenience by other authors. Later on, the WNLterm came to mean late-type WN stars with hydro-gen as most of them have this element present. How-ever, observations have firmly established that there areboth late-type WN stars without hydrogen (the bonafide
WN stars), and, more problematic, early -type WNstars with hydrogen. A number of early-type (WN3ha,WN4ha, WN5ha) WN stars with hydrogen have beenidentified recently in the SMC (Foellmi et al. 2003a;Foellmi 2004), and some in the LMC as well (Foellmiet al. 2003b). One such WNE star with hydrogen isthe famous object HD5980, an eclipsing massive binarywhere the hydrogen-rich component had been classifiedas WN6h, WN11, LBV, or B1.5 Ia at different times dur-ing its LBV-like outburst in the 1990s (Koenigsberger2004), but had been classified as WN4h before that.WN5h is arguably on the border between early- andlate-type, and several of these have been seen in 30 Doradus and Westerlund 1 (Crowther & Dessart 1998;Crowther et al. 2006). Other Galactic examples are WR3(WN3ha), WR10 (WN5ha), WR48c (WN3h+WC4),WR49 (WN5h), WR109 (WN5h), WR128 (WN4h), andWR152 (WN3h) (Marchenko et al. 2004; Hamann et al.2006; van der Hucht 2001). Clearly, the phenomenon ofhydrogen in WN stars is not limited to late types, ren-dering “WNL” an inappropriate designation as it refersmainly to WN7/WN8 (Moffat & Seggewiss 1979). Theshorthand “WNH” would encompass both early- andlate-type WN stars with hydrogen.Second, the designation “WNH” is also useful to em-phasize the apparent fact that while they exhibit WR-like spectral features because of their strong winds (theyare sometimes referred to as “O-stars on steroids”), theWNH stars are distinct from core-He burning WR starsin several observed characteristics and most probably intheir evolutionary state. The assertion that they repre-sent a distinct evolutionary state is justified in the follow-ing sections, where we show that like LBVs, the WNHstars are consistently more massive than WN and WCstars, and that they have H mass fractions more in linewith LBVs. We argue that their observed masses, mass-loss rates, luminosities, wind speeds, and other propertiescan all be understood naturally if they represent the laterstages of core-H burning of very massive stars with ages ∼ necessary condition to push the star toward the Ed-dington limit, again arguing that WNH stars are the bestcandidates for the immediate precursors of high luminos-ity LBVs.We reiterate that we intend the term “WNH” onlyas collective shorthand for the class of WN-like starsthat show hydrogen in their spectra, because we believethem to be distinct from H-free WN stars. While thisnew terminology is arguably imperfect because one staror another might challenge categorization or blurr theboundaries, the term is needed simply to avoid confu-sion, and it makes a clear distinction that is also usefulfor purposes of discussion. Because they show a range inH mass fraction (see below), the WNH stars constitutea somewhat heterogeneous class and may even overlapwith the LBVs. In that sense, though, the term “WNH”has a usefulness similar to that of “LBV”, since the LBVclass contains stars labeled variously as S Doradus vari-ables, η Car variables, α Cygni variables, P Cygni stars,Ofpe/WN9 stars, etc., yet we still refer to them all collec-tively as “LBVs”. The term “LBV” has been useful forbroadly discussing stars that we think share a commonevolutionary phase, even though it is not always agreedwhether an individual object is a bona-fide
LBV or not.The term “WNH” is also critical to distinguish thesestars from H-free WN stars, because massive stars arethe progenitors of various types of core-collapse super-novae (SN). The single most important observable traitin classifying a SN spectrum is the presence or absenceof hydrogen, making it a Type II or a Type Ib/c, respec-tively. The “H” in “WNH” therefore serves as a clearreminder that hydrogen is present, and that these are not to be confused with the H-free Wolf-Rayet stars thatare the likely progenitors of Type Ib supernovae and pos-NH stars 3
Fig. 1.—
Masses of WNH stars compared to H-poor WN andWC stars estimated spectroscopically (top) and measured in bi-nary systems (bottom). The spectroscopic masses are taken mostlyfrom Hamann et al. (2006), except for a few in Carina and 30Dor from Crowther & Dessart (1998) and de Koter et al. (1997).Masses of WR stars in binary systems are taken from van der Hucht(2001), but are augmented or superseded in several cases as follows:WR137 (Lefevre et al. 2005), V444 Cyg (Flores et al. 2001), WR141(Grandchamps & Moffat 1991), WR151 (Villar-Sbaffi et al. 2006),HD5980A and B (Koenigsberger 2004; Foellmi et al. 2008), WR22(Rauw et al. 1996), WR20a (Rauw et al. 2005; Bonanos et al. 2004),WR25 (Gamen et al. 2006); R145/30 Dor and NGC3603/A1 (Mof-fat 2006, priv. comm.). (Note that in these histograms, numbersof different types of objects are “stacked”. For example, measuredin binary systems, there are only 4 WN stars in the 15–20 M ⊙ bin,not 5.) sibly also long-duration gamma ray bursts. The morespecific classification criteria of WN stars are not rele-vant or useful in this context as they mainly describethe temperature and ionization level of the wind. Ob-servationally, one cannot determine if the progenitor ofa SN is WNE or WNL, but in pinciple, one can tell thedifference between WN and WNH. MEASURED MASSES OF WNH STARS
Figure 1 collects mass estimates for WR stars fromthe literature, including masses measured both spectro-scopically and in binary systems. It compares presentmasses of WNH stars to H-poor WN and WC stars(spectroscopic masses are unreliable for WC stars). The There are rare objects that confuse the issue, like SN 2006jc(Foley et al. 2007; Pastorello et al. 2007; Smith et al. 2008), butthis only emphasizes the importance of highlighting the presenceof hydrogen. Also, it is worth noting that some compact binaryscenarios might produce Type Ib/c SNe with lower mass stars (e.g.,Pols & Devi 2002; De Donder & Vanbeveren 1998). spectroscopic masses are taken mostly from Hamannet al. (2006), who derived the masses using the mass-luminosity relation for helium stars from Langer (1989).They noted that this relation might not be adequate forWNH stars, but they also note that when masses mea-sured in binary systems are available for the same starsfor which they estimated a spectroscopic mass, the twomethods show no wild disagreement. For example, thespectroscopic mass they derive for the WNH star WR22in the Carina Nebula is 74 M ⊙ , compared to 72 M ⊙ de-termined from the binary orbit by Rauw et al. (1996). Thus, while the exact values for the masses in the toppanel of Figure 1 might be somewhat suspect, the maintrend of the separation between WN and WNH stars isnot. Masses measured for WR stars in binary systems aremore reliable, but there are not many of them available,shown in the bottom panel of Figure 1. The results forthe distribution of masses for different WR types mea-sured spectroscopically and in binaries show very goodgeneral agreement.The clear lesson to be learned from Figure 1 is thatWNH stars have systematically higher masses than H-poor WN and WC stars. With binaries and spectroscopicmasses, the mass distribution of H-poor WN stars clearlypeaks at 15–20 M ⊙ , while WNH stars are spread moreevenly over a large range of masses mostly above 30 M ⊙ .There are only a few cases of mass overlap between theWN stars and a small fraction of the WNH stars. Thismay be because of WN stars in binary systems whereH is present, or it may signify a real evolutionary over-lap. Note that the overlap is more prevalent in the spec-troscopic masses where unrecognized binaries are morelikely to contaminate the sample, and where the generalshape of the WNH mass distribution in the 10–25 M ⊙ range matches that for WN stars, as one might expect ifthey are not true WNH stars. All the H-poor WR starshave relatively low masses below 30 M ⊙ . The WNHstar masses peak around 50 M ⊙ (for the more numerousspectroscopic masses), and masses measured in binariesextend to very large masses – as high as more than 120M ⊙ for the WNH star R145 in 30 Doradus (Moffat 2006;private comm.).Overall, then, Figure 1 makes a strong case that WNHstars are in fact a separate and distinct group of starsfrom the H-poor WR stars. It is obviously logical to as-sume that WNH stars are more massive than WN andWC stars because they have not yet shed their H en-velopes, and that they may eventually become H-poorWR stars. In that case WNH stars must be at a sig-nificantly earlier evolutionary stage, which is consistentwith the fact that they are preferentially seen in massiveclusters within giant H ii regions like the Carina Neb-ula, NGC 3603, and 30 Doradus, whereas H-free WNstars are not. On the other hand, WNH stars may beconsistently more massive than WN or WC stars simplybecause they evolve from stars with higher initial massesand follow different evolutionary paths. Although see also Schweikhardt et al. (1999) who derive a massof 55 M ⊙ for the WNH component. Under advisement from A.F.J. Moffat (private comm.) we haveexcluded WR47, with a mass of 48 M ⊙ estimated by Moffat et al.(1990), because this system has not been studied in enough detailyet to determine if H is present or not. (See also Karteshiva 2002,who estimate its mass as only 8–12 M ⊙ .) Smith & ContiFurthermore, the wide mass discrepancy betweenWNH and H-poor WR stars and the fact that the twopopulations hardly overlap at all provides a vital clue totheir evolutionary states. It argues strongly against thenotion that WNH stars are simply the initial stages ofthe core-He burning WR phase, where they are still inthe process of shedding the last remaining layers of theirhydrogen envelopes, gradually transitioning into H-freeWN stars. (Besides, shedding the required 20–80 M ⊙ in . yr in this transition requires mass-loss rates higherthan observed for WNH stars.) Instead, the discontinu-ity in mass of 10’s of Solar masses between WNH andWN stars suggests that some other intermediate stagemust quickly remove the large mass remaining in the hy-drogen envelopes of the WNH stars before they can be-come WN stars. The obvious choice for the subsequentremoval of that mass is the violent eruptions of LBVs(Smith & Owocki 2006). In other words, based on theirmasses, WNH stars are likely to be pre-LBVs, not post-LBV stars. Interestingly, unlike the H-poor WR stars,LBVs exhibit a range of masses (with current masses ofroughly 30–100 M ⊙ ) that does overlap with that of theWNH stars, arguing that the two are closely related.We also note a systematic difference in the masses ofWC and WN stars in Figure 1. The WC star massdistribution peaks in the 5–15 M ⊙ range, whereas theWN distribution peaks at higher masses in the 15–20M ⊙ range. One might expect this if WC stars are moreevolved descendants of WN stars (Paczynski 1973), asthe products of further mass stripping by the powerfulWN stellar wind (Conti 1976) or sudden events like thatinferred for the progenitor of SN 2006jc (Smith et al.2008; Pastorello et al. 2007; Foley et al. 2007). A pre-diction of this trend is that SNe of Type Ib should resultfrom more massive progenitors than Type Ic SNe. If not,then an interesting mystery needs to be solved. In anycase, the disparity in mass between the WNH stars andall the other WR types (Fig. 1) supports the main thrustof this paper, and is obviously relevant for interpretingthe progenitors of Types Ib and Ic SNe. HYDROGEN MASS FRACTIONS
Figure 2 shows the hydrogen mass fraction, X H , as afunction of stellar luminosity for WNH stars compared toLBVs. This is obviously an important quantity for un-raveling the evolutionary relationship between these twoclasses of stars. A similar plot and its implications havealready been discussed by Langer et al. (1994), but weupdate it here with several additional values from the lit-erature. This updated information is most relevant at thehighest luminosities, as there were only a few data pointsabove log (L/L ⊙ )=6.0 in the similar plot by Langer etal. The behavior of those high-luminosity objects is thefocus here.Excluding η Car and the Pistol star, the LBVs seem tocluster around X H ≃ X H values from 0.05 to 0.5, above andbelow the values for LBVs. However, the way that thisrange of X H values for WNH stars compares to thoseof the LBVs changes with luminosity, and it depends onwhich set of WNH luminosities is adopted. In cases whenboth Crowther et al. (1995a) and Hamann et al. (2006)analyzed the same target stars, values for X H generallyagree to within a few percent if they differ at all. The disagreement is in the stellar luminosities, with the lumi-nosities from Hamann et al. (2006) being systematicallyhigher by roughly 0.5 dex for the same target stars. Thismay be due to the fact that Hamann et al. assumed thatWNH stars had relatively high luminosities. Shifting theWNH stars horizontally in Figure 2 significantly impactsour interpretation of the relative evolutionary status ofWNH stars compared to LBVs. Figures 2 a and 2 b sug-gest the following different implications, respectively:1) Figure 2 a presents a suggestive picture that therelationship between WNH stars and LBVs is depen-dent on luminosity (and hence, on initial mass). Belowlog (L/L ⊙ )=5.8 (the upper limit for RSGs and for H-free WR stars), we see that the WNH stars are generallymore evolved with lower hydrogen content than LBVs.At an intermediate luminosity range of log (L/L ⊙ )=5.8–6.0, the case is less clear; WNH stars bracket the X H values for LBVs, suggesting that they could be both pre-and post-LBVs, as in the scenario suggested by Langer etal. (1994) for a star of initial mass 60 M ⊙ correspondingto P Cygni. At high luminosities above log (L/L ⊙ )=6.0,however, no WNH stars are seen to have smaller hydro-gen mass fractions than LBVs – they generally lie abovethe LBVs, indicating that they should be pre-LBVs.2) With the higher WNH luminosites in Figure 2 b (Hamann et al. 2006), on the other hand, one would con-clude that the LBVs are intermixed with and are essen-tially indistinguishable from WNH stars in their abun-dances, except that LBVs occupy a narrower range. Thiswould imply that WNH stars can be both pre- and post-LBVs, regardless of luminosity. Given the commentsabove, this is a fair possibility at lower luminosities, butseems less likely for the high-luminosity stars above log( L / L ⊙ ) & L and X H in order to understandthe evolution of massive stars. There are a few reasonsto favor the somewhat lower luminosities of Crowther etal. (1995a) and the corresponding interpretation impliedby Figure 2 a . First, for the Carina Nebula WNH starsWR22, 24, and 25 (shown with bold triangles in Figs.2 a and 2 b ), the lower luminosities of Crowther are inmuch closer agreement with the spectroscopically simi-lar WNH stars in R136 and NGC 3603 (de Koter et al.1997; Drissen et al. 1995), shown with squares in Figure2. Also, the higher luminosity for WR25 from Hamannet al. (2006) makes this star more luminous than η Car,making it difficult to understand why η Car is so muchmore unstable and more evolved with a larger N abun-dance even though they are members of the same starcluster. Second, the implication in Figure 2 a that WNHstars precede the LBV phase at high luminosities (abovelog L/L ⊙ =5.8–6.0) is in much better agreement with theconclusions drawn from considering their current (high)masses discussed in the previous section, as well as thediscussion of the mass-loss rates to follow. In Figure 2 b ,on the other hand, the occurrence of many high luminos-ity WNH stars with X H values significantly lower thanLBVs is at odds with the impression that they typicallyhave higher stellar masses than LBVs. This argumentis admittedly somewhat circular. Therefore, we cannotconsider the measured abundances as giving any definite answer to the relative evolutionary states of WNH starsNH stars 5 Fig. 2.—
Hydrogen mass fractions, X H , as a function of stellar luminosity for WNH stars (unfilled triangles and unfilled squares)compared to those of LBVs (filled circles). The luminosity range of H-free WN stars is also shown. The two panels show X H and L forGalactic WNH stars from two different studies: (a) from Crowther et al. (1995a; or from Crowther, priv. comm.), and (b) from Hamannet al. (2006). In both studies, the typical uncertainty in X H is ± X H typicallyagree to within a few per cent, but the stellar luminosities are systematically higher in the study of Hamann et al. (2006) by roughly 0.5dex. This creates a different impression for the relationship between WNH stars and LBVs (see text), which is why we display the resultsfrom both studies. The luminosities for LBVs are the same as in Smith et al. (2004), while the values for X H are taken as follows: η Car(Hillier et al. 2001), the Pistol star (Figer et al. 1998), HD5980 (Koenigsberger 2004), AG Car, R127, and S119 (Lamers et al. 2001), Hen3-519 and P Cygni (Smith et al. 1994), HR Car (Machado et al. 2002), and R71 (Crowther et al. 1995b). The unfilled squares show thefour WNH stars in R136 with the luminosities from de Koter et al. (1997) and a rough value of X H ≃ X H ≃ X H as 0.4–0.5. and LBVs — we can only say that the scenario in Figure2 a fits together in a more consistent way with the ideathat high-luminosity WNH stars are pre-LBVs, while theimplication from Figure 2 b that WNH stars are bothpre- and post-LBVs would present an unresolved puzzle(which may nevertheless be true). One last reason to fa-vor Figure 2 a concerns the environments in which thesestars are found. The most luminous WNH stars withhigher H content than LBVs reside in massive giant H ii regions like 30 Dor, Carina, and NGC 3603. The WNHstars with lower H conent than LBVs (and at lower L )do not reside in such massive young regions (like most ofthe LBVs, incidentally). This argues for a lower initialmass and larger age for the lower- L WNH stars. In anycase, further work on the H abundances of WNH stars isneeded.Of course, factors other than initial mass may influencethe apparent values of X H as well, such as the star’s ro-tation rate and consequent level of mixing during core-Hburning phases (Maeder & Meynet 2000). This is beyondthe scope of our consideration here, but it obviously maybe important. MASS-LOSS FEEDBACK AND THE EVOLUTIONARYSTATES, MASSES, AND AGES OF WNH STARS
Our primary goal in this paper is to determine howthe WNH stars fit into the evolutionary sequence of mas-sive stars. When does the WNH phase “turn on”, howlong does it last, how much mass is lost from the star,and what are the preceding and subsequent evolutionaryphases? In the previous sections, we showed that WNHstars are considerably more massive than H-poor WR stars, arguing that they are more massive because theyhave not yet shed their H envelopes and that they there-fore represent an earlier evolutionary phase, before theheavy mass loss encountered as an LBV. We also showedthat the most luminous WNH stars tend to be more H-rich than LBVs, arguing again that they are pre-LBVs.Another way to attack the problem is to ask when inthe lifetime of a massive star we should expect the WNHphase to occur, given some initial mass, luminosity, andmass-loss rate. These expectations can then be comparedwith the measured masses, mass-loss rates, luminosities,and other properties of WNH stars.To this end, in the following discussion we considerwhat the expected properties of luminous O-type starsshould be as they reach the end of core H burning. Weare primarily interested in the rate at which the mass lossrate grows from an initial value during core-H burning.
We consider the generic effect of mass loss on the stellarproperties, and on the evolution of the mass-loss rate it-self through a “feedback” effect. The parameterizationof mass loss discussed below is quite simple, and is notclaimed to be an adequate substitute for renewed cal-culations of stellar evolution codes. Rather, it is meantonly to illustrate the principle that the effect of mass losscan account for the properties of WNH stars if they areluminous and massive stars near the end of core H burn-ing. Our results argue that renewed efforts to calculatethe evolution of massive stars with lower mass-loss ratesare essential in light of recent observational estimates oflower mass-loss rates due to wind clumping. Our argu-ments here strengthen the case that mass-loss rates ofO-type stars need to revised downward from the “stan- Smith & Conti
Fig. 3.—
Hydrogen core-burning evolution of massive stars withinitial masses of 120, 85, and 60 M ⊙ , where feedback is includedsuch that the mass-loss rate is proportional to L × Γ / (1 − Γ).Adopted quantities are the luminosity during core-H burning fromSchaller et al. (1992) for each initial mass, the initial radius forthe corresponding temperature of a main-sequence star (only rele-vant for V esc ), and the initial mass-loss rate. The initial mass-lossrates (solid dots) are those appropriate for the corresponding ini-tial luminosity and mass, with moderate clumping factors of ∼ M reduced by √ M and L . From the pre-scribed initial values, the subsequent mass-loss rate, stellar mass,Eddington factor (Γ=L/L Edd ), and escape velocity are calculatediteratively until the end of core-H burning as described in the text.The plot of stellar mass (solid lines) also shows the cumulativemass lost (dot-dashed lines). dard” observed rates (de Jager et al. 1988; Nieuwenhui-jzen & de Jager 1990) due to the observational effectsof clumping, and more in line with (but probably evenlower than) the theoretically expected values of Vink etal. (2001).In Figure 3 we consider the expected properties of starswith initial masses of 120, 85, and 60 M ⊙ as a functionof time on the core-H burning main-sequence. The pre-scribed inputs here are the initial mass, the initial valuefor the mass-loss rate, and the bolometric luminosity L ( t )throughout the core-H burning lifetime. We adopt L ( t )from the Solar metallicity models of Schaller et al. (1992),which include mass loss. Although it would be better tocalculate new stellar evolution models self-consistentlyinstead of adopting a luminosity from an existing modelwith different mass-loss rates, our approach here is ademonstrative first step. In any case, the adopted lu-minosities are sufficient to illustrate the main point ofthis paper, which is that the expected climb of the massloss with time can account for the apparent properties ofthe WNH stars.With these prescribed conditions, Figure 3 shows thetime evolution of the mass-loss rate, the stellar mass, theEddington factor Γ = L/L
Edd , where L Edd is the clas-sical Eddington limit due to electron scattering opacity,and the star’s surface escape velocity. At each time step,each quantity is calculated iteratively from the previoustime step. For instance, following the initial mass, themass at each subsequent time step is calculated by simplyreducing the mass by ˙ M × ∆ t . For reasons that will be-come obvious later, we consider only the core-H burningmain sequence lifetime and not core-He burning phases.The purpose of Figure 3 is to illustrate how these quan-tities change during the core-H burning lifetime of thestar, in response to the choice of an initial value for themass-loss rate. We are especially interested in the waythat the mass-loss rate grows due to previous mass loss– what we refer to below as mass loss “feedback”.Essentially all the observable properties of subsequentpost-MS phases and the type of supernova eventuallyseen depend critically on the adopted ˙ M ( t ). During core-H burning, stellar evolution calculations have typicallyassumed mass-loss rates adopted from observed “stan-dard” values such as those given by de Jager et al. (1988)or Nieuwenhuijzen & de Jager (1990), as was done inSchaller et al. (1992) and subsequent studies, Heger etal. (2003), Eldridge & Tout (2004), and several others. However, adopting these mass-loss rates is arguablynot the best treatment of mass loss if one is interested inasking what mass-loss rates to expect as the star evolves,since this method simply prescribes them (not to men-tion the fact that ˙ M values need to be revised downwarddue to clumping; see below). Stars at the same positionin the HR Diagram can have different masses, mass-lossrates, and other properties, arguing for a different ap-proach. This may be one of the reasons that the WNHphase is often assumed to be associated with later evolu-tionary phases; for example, following the end of core-Hburning, Schaller et al. (1992) impose a WNH phase with Newer calculations sometimes use the predicted rates of Vinket al. (2001) instead of or in combination with the de Jager et al.(1988) rates, such as Meynet & Maeder (2005) and Eldridge &Vink (2004).
NH stars 7a constant ˙ M =4 × − M ⊙ yr − until the H envelope isremoved.Here we take a different approach. Instead of pre-scribing mass-loss rates throughout the star’s evolution,we consider the effect that the mass-loss rate for a line-driven stellar wind from a hot massive star should changeduring its lifetime, responding to changes in the star’s lu-minosity with time, as well as to changes in its mass.During core-H burning, a star’s luminosity graduallyclimbs as the core contracts (Fig. 3), providing one mech-anism that will act to increase the mass-loss rate sincethe wind is radiatively driven. Simultaneously, the star’swind is removing mass from the star’s surface, loweringthe star’s mass considerably, which also acts to increasethe mass loss since the star has a shallower gravitationalpotential well. In essence, both these effects conspireto raise the star’s proximity to the classical Eddingtonlimit, since Γ = L/L
Edd is proportional to L/M. Thisincrease in mass-loss rate accelerates the growth of Γ,making the problem worse. Essentially, this behavior in-troduces a very important feedback loop that is currentlynot included in stellar evolution calculations. This feedback effect can be treated in a simple way,sufficient for our limited purposes here. The CAK theoryof radiatively driven winds (Castor et al. 1975) provides aprescription for how the mass-loss rate should vary withthe star’s luminosity L and the Eddington factor Γ (andhence, the star’s mass). Following Owocki (2003), forexample, the dependence can be written as˙ M ∝ L (cid:0) Γ1 − Γ (cid:1) − α (1)where α is the usual CAK power index. For illustra-tive purposes in Figure 2, we adopt α =0.5 as is commonin line-driven winds of O-type stars. Equation (1) thensimplifies to ˙ M ∝ L (cid:0) Γ1 − Γ (cid:1) (2)which is the mass-loss rate dependence that we adopt inFigure 3. When this feedback is included, we see that astar’s mass-loss rate will climb steadily and substantially,even during the core-H burning phase alone. Given aninitial mass-loss rate at t =0, one can then calculate themass-loss rate and the stellar mass at subsequent times,self consistently, given L ( t ), as long as it is safe to as-sume that the wind is line-driven. This assumption willbreak down as the Eddington factor climbs near Γ=1 andthe mass-loss rate skyrockets, when a continuum-drivenwind may take over (Smith & Owocki 2006; Owocki et al.2004). Given the simplistic treatment and the fact thatwe extrapolate from a single initial value, it is reassuringthat our values of ˙ M ( t ) are not too different from thepredicted values of Vink et al. (2001; dotted line in thetop panel of Fig. 3), especially at the later WNH stagesthat are the focus here.In Figure 3, the initial mass-loss rates we have adoptedare the moderately-clumped rates given by Repolustet al. (2004) appropriate for O-type dwarfs with theadopted luminosity for each of the three initial masses This usage of the term “feedback” is different from that re-ferring to the energy input and metal enrichment of the ISM bymassive stars. considered. These mass-loss rates and the degree ofclumping in stellar winds is a larger issue than we can ad-dress here (see for example, Puls et al. 2006; Fullerton etal. 2006; Bouret et al. 2005; Smith & Owocki 2006; Smith2007a; Eversberg et al. 1998; Lepine & Moffat 1999).As a result of the climbing mass-loss rate, we see thatΓ climbs significantly as well, ramping up at the end ofcore-H burning. The implications of this for triggeringthe LBV instability are discussed below in §
7. Anotherresult of the ramping-up of ˙ M is that more of the massultimately shed from the star is lost later in its life, as isalso the case if LBV eruptions are a dominant mode ofmass loss (Smith & Owocki 2006). This will significantlyimpact other properties such as the mass of the He coreproduced, as well as the angular momentum evolutionof the star and its rotational mixing. Lower mass-lossrates will cause the wind to shed less angular momentum.In turn, faster rotation will likely enhance axisymmet-ric/bipolar mass loss in later evolutionary phases (Cran-mer & Owocki 1995; Owocki et al. 1996, 1998; Owocki& Gayley 1997; Maeder & Meynet 2000). Such effectswon’t be discussed in detail below, but they need to bereinvestigated in future stellar evolution calculations. DISCUSSION
Mass-Loss Rates and Ages of WNL Stars
If Figure 3 gives the expected behavior of ˙ M ( t ) formassive stars, we can then compare it with the observedmass-loss rates of WNH stars to deduce where they mightfit in. Figure 4 is the same as Figure 3, but it includessome rough ranges of observed values corresponding toWNH stars for comparison.We see here that for these very luminous stars, themass-loss rate only climbs to values seen in WNH starsafter about 2 Myr from the beginning of the star’s life.For the luminous WNH stars, typical mass-loss rates arewell above 10 − M ⊙ yr − (Crowther et al. 1995a). Thisfavors the interpretation that the WNH stars have agesof 2–3 Myr. It is also consistent with the cohabitation of3 WNH stars in the same region alongside η Car, whoselate evolutionary stage points to an age of roughly 2.5–3Myr.An independent check on the ages of WNH stars isgiven by their observed wind speeds (bottom panel inFig. 4). We see that the observed WNH wind speedsof several hundred to 2000 km/s are not consistent withZAMS massive stars, nor with the very fast winds of H-free WN and WC stars. Instead, these values are onlyreached late in a star’s core-H burning lifetime (afterroughly 2 Myr) as a natural consequence of mass loss andthe corresponding lowered g eff as the star gets pushed tohigher values of Γ. Thus, both the observed mass-lossrates and wind speeds of WNH stars would seem to favorages above 2 Myr.Caveat: One could of course assume that WNH starsare indeed very young – that they are somehow born withsuch high mass-loss rates – but what should we expectthe star’s subsequent evolution to look like in that case?This is akin to adopting higher mass-loss rates for Ostars (homogeneous winds instead of clumped winds; seePuls et al. 2006), and this introduces severe problems asdiscussed next. Smith & Conti Fig. 4.—
Same as Figure 3, but showing some observed valuesfor WNH stars for comparison (shaded boxes). Mass-loss rates andthe range of terminal wind speeds are taken from Hamann et al.(2006). The three boxes in the top panel denote a typical rangeof mass-loss rates corresponding to WNH stars of the correspond-ing luminosities for the three different initial masses treated here.The WNH mass-loss rates from Hamann et al. include only weakclumping factors (these boxes might be lowered slightly if clump-ing is more severe, but then, so would the corresponding mass-lossrate curves). The range of WNH masses from Figure 1 (for therange of luminosities considered here) provides less of a constraint,exhibiting a wide range of values that are at least consistent withthe range of predicted masses if WNH stars are near the end ofcore-H burning.
WNH star masses, and implications for clumpedwinds and lowered mass-loss rates of O-type stars
If WNH stars do indeed reside near the end of core-Hburning with ages & Fig. 5.—
Same as Figure 3, but showing how stars run into trou-ble if feedback is included and we adopt the “standard” unclumpedmass-loss rates for the initial state, or if the standard mass-lossrates are assumed throughout. These initial standard mass-lossrates are taken from Nieuwenhuijzen & de Jager (1990), and areonly a factor of ∼ For example, if WNH stars have relatively high masseswhen they reach the ends of their core-H burning lives,then the mass-loss rates throughout core-H burning can’tbe very high. In fact, some very high masses have beenobserved for WNH stars. As shown in Figure 1, severalexamples exist of WNH stars with masses of 80–120 M ⊙ measured in binary systems.If Figures 3 and 4 are accurate representations of theNH stars 9trend of ˙ M on the main sequence, then we can see thatthe high masses of WNH stars make sense if they occurat the end of core-H burning — but only if the windsare moderately clumped . Remember that in Figure 3 weassumed that the initial mass-loss rates were those ofRepolust et al. (2004), which correspond to conservativewind clumping factors of ∼
5, reducing the mass-loss ratesby factors of ∼ derived from H α and radio observations with theassumption of homogeneous winds (de Jager et al. 1988;Nieuwenhuijzen & de Jager 1990). In this case, the earlyphases with lower mass-loss rates as an O-type star arenearly irrelevant to the star’s total mass loss. The mass-loss rate increases later as the star gradually moves intothe WNH phase and on into the LBV phase, indicatingthat most of a star’s mass is lost late in its lifetime ata quickened pace. These moderately-clumped mass-lossrates are just about as high as they can be in order forthe most massive stars to reach the Eddington limit atthe end of core-H burning.Let’s turn this question around and view the problemfrom another perspective: If we still include the feed-back effect of mass loss described earlier, as we arguablyshould, then what will happen if the stellar winds are not clumped and we adopt initial mass-loss rates that arehigher? Figure 5 shows the same type of evolution withfeedback (solid lines) as in Figure 3, with the only differ-ence being that we started with higher initial mass-lossrates. These initial rates (dots) adopt the prescription forthe “standard” values for homogeneous winds given byNieuwenhuijzen & de Jager (1990). These are the valuesthat have most commonly been used in stellar evolutioncalculations (e.g., Heger et al. 2003), although sometimesrates even a factor of 2 higher than these are used tomatch observed statistics of massive stars (Meynet et al.1994).The results of adopting the higher mass-loss rates inFigure 5 are quite dramatic (the same calculations with-out the feedback effect are shown with dashed lines inFig. 5, for comparison). Figure 5 shows that with thesehigh initial mass-loss rates, mass-loss feedback quicklydrives the star’s Eddington factor up to Γ=1 in only 1.3,2 Myr and 3 Myr for the 120, 85, and 60 M ⊙ models, re-spectively, likely triggering a very early LBV-like phasewith catastrophic mass loss. However, this is certainly inconflict with observations, at least for the 85 to 120 M ⊙ models, since — aside from the one case of η Carinae —the stars in massive young clusters like R136, NGC3603,and Carina typically do not have very massive shells ofrecently ejected material around them. Thus, we con-sider it unlikely that very luminous stars are born withmass-loss rates as high as those seen in WNH stars orwith the mass-loss rates corresponding to homogeneousstellar winds. Also, the fact that massive stars reach theend of core-H burning as WNH stars with relatively highmasses cannot be explained by models in Figure 5 with This is because of the density-squared nature of the H α andradio continuum diagnostics of the mass-loss rates. Note that when the mass-loss rates climb aggressively, thereduction in the star’s mass is likely to quell the core luminositysomewhat. Therefore, when this stage is reached it is likely thatour very simple way of treating the mass loss is invalid, and fullstellar evolution calculations will be needed. The early push towardthose higher mass-loss rates probably is valid, however. high mass-loss rates because too much mass has alreadybeen lost, whereas the high masses of WNH stars arisenaturally for moderately-clumped winds. This is the sen-sitive nature of the feedback effect – that even a smallreduction by a factor of ∼ η Car toconsider: it is the most luminous and most evolved mem-ber of a rich region containing over 65 O-type stars, aswell as the 3 well-known WNH stars (see Smith 2006 fora review, including details of the age differences amongclusters in the region). It is fair to assume that the cur-rent LBV phase of η Car is not only a post-MS phase,but probably also a post-WNH phase, since its ejecta aremore nitrogen rich than the WNH stars in Carina. It isalso safe to assume that η Car has advanced further inits evolution sooner than the WNH stars of the same agein this region simply because it is more luminous andstarted with a higher initial mass. Now, η Car is seentoday surviving as a very massive star of around 100 M ⊙ or more (allowing for a hypothetical ∼ M ⊙ companionstar), and we measure a total of something like 20-35 M ⊙ in its circumstellar material ejected in only the last fewthousand years (the Homunculus, plus more extendedouter material; see Smith et al. 2003, 2005). That means η Car began its LBV phase – and ended its MS and/orWNH phase – with more than 120 M ⊙ still bound tothe star. If there really is an upper limit of about 150M ⊙ to the mass of stars (Figer 2005), then this massbudget demands that the O-star and WNH winds wereindeed quite meager before reaching this phase. Simi-larly, there’s the Pistol star to consider as well, which isalso a post-MS object and has a present-day mass thatprobably exceeds 100 M ⊙ (Figer et al. 1998).In conclusion, then, the relatively high masses of WNHstars, the high masses of the most luminous LBVs, andthe intuition that we should include the feedback effect ofmass loss all argue that line-driven winds of massive stars must be clumped. This argument is independent of themany spectroscopic clues that these winds are clumped(e.g., Puls et al. 2006; Bouret et al. 2005; Fullerton et al.2006; Eversberg et al. 1998; Lepine & Moffat 1999). Wefind that the mass-loss rate reductions due to clumpingmust be at least a factor of 2 compared to “standard”rates for homogeneous winds, consistent with the con-servative factors adopted by Repolust et al. (2004). Itis encouraging that this amount of mass-loss reductionbrings the mass-loss rates of O stars into better agree-ment with theoretical predictions for line-driven winds ofO-type stars (e.g., Vink et al. 2001), although those maystill be to high. WNH stars as pre-LBVs, not core-He burning WRstars
Unfortunately, it is difficult to reliably determine theage of a WNH star directly from observations of its en-vironment. One can easily deduce cluster ages from ob-servations that are either too low or too high by 1 Myror more: The essential problem is that the lifetimes ofthese very massive stars are so short that they are oftencomparable to the uncertainty in the age of their parentcluster. In addition, that parent cluster or associationmay have a real age spead that makes the problem evenworse. Thus, identifying a WNH star in a young 1–2 Myr0 Smith & Conticluster like R136 or NGC3603 (if their ages are that low)does not necessarily mean that particular WNH star it-self has an age of 1–2 Myr. In any case, the validity ofascribing a single-valued age to a given cluster is highlydebatable.Since we can’t really trust direct estimates of the agesfor individual WNH stars based on their environments –at least not at the precision of ± ⊙ ,whereas WNH stars seem to be spread evenly from 20M ⊙ all the way up to the most massive stars known wellabove 100 M ⊙ . This is clearly in conflict with the no-tion that WNH stars are in the process of continuouslybecoming WN stars through their own stellar winds. In-stead, the strong discontinuity in mass distribution be-tween the WNH and WN stars argues for an interveningphase of episodic mass loss that quickly sheds 10’s of So-lar masses and removes essentially all the remaining Henvelope. This intervening rapid mass-loss phase is al-most certainly the LBV phase (regardless of what theinterpretation for the cause of the LBV phase might be;i.e. inherent instability of single stars vs. binary mergers,etc.). Unlike for H-poor WN stars, the stellar masses forLBVs overlap quite well with the WNH stars.2) At high luminosities, the hydrogen mass fractions, X H , for WNH stars tend to be higher than for LBVs(Fig. 2 a ). This requires that they are less evolved. Wenoted that this case is not definitive, since the higherWNH luminosities from Hamann et al. (2006) paint asomewhat different picture than the lower luminositiesof Crowther et al. (1995a). However, the properties ofWNH stars in the cores of NGC 3603 and 30 Doraduswould seem to favor the interpretation that they are pre-LBVs based on their abundances (de Koter et al. 1997;Drissen et al. 1995).3) We showed that if one includes feedback due tomass loss on the main sequence, then starting with amoderately-clumped initial mass-loss rate, one naturally expects the star’s mass-loss rate to climb after about 2Myr to values that would make it appear as a WNH star,near the end of core-H burning and before the LBV phase(Figs. 3 & 4). As we showed earlier, if massive stars areborn with the high mass-loss rates of WNH stars, thenthe subsequent evolution does not make sense (Fig. 5).4) Conversely, if the mass-loss rates are lower, thenthe effect of feedback is not so severe. Interestingly, therelative rate at which ˙ M (t) climbs with the lower initialmass-loss rates of clumped winds (Fig. 3) more closelymatches that of the observed mass-loss rates, even thoughthe observed rates are offset to higher values. There-fore, simply lowering the observed “standard” values ofNieuwenhuijzen & de jager (1990) by a factor of 2–3 givesa fairly accurate match to the expected mass-loss rateswith feedback and clumping. This provides a powerful,self-consistent argument that the mass-loss rates are infact lowered due to clumping in stellar winds. One of the interesting results of Figure 3 is that thissteady march toward increased mass-loss rates from feed-back on the main sequence also provides a natural expla-nation for the apparent continuity in observed spectraltraits from O3 V → O3 If* → WNH noted previously(Walborn 1971, 1973, 1974; Walborn et al. 2002; Wal-born & Blades 1997; Conti 1976; Melnick 1985; Massey& Hunter 1998; Lamers & Leitherer 1993; Drissen etal. 1995; Crowther et al. 1995a; etc.), and onward fromWNH → LBV as well. This sequence is known toshow intermediate stages, such as hot slash stars likeMelnick 42 in 30 Dor and weak-lined WNH stars likeWR25 (e.g., Walborn et al. 1992), attributed mainly tochanges in wind density during stellar evolution. Weargue that no special circumstances like pulsationally-enhanced mass loss, rapid rotation, binary mergers, orunusual abundances are needed to account for the pres-ence of WNH stars in massive young clusters with agesof around 2–3 Myr — it is a natural outcome of intiallymoderate mass loss on the main sequence that graduallygrows more severe later on (Fig. 3).
And Where are the Luminous Post-LBVs?
There are no H-free WR stars with luminosities abovelog (L/L ⊙ )=5.8 (Fig. 2), and if we favor the results shownin Figure 2 a , there are not even any WNH stars withlower hydrogen mass fractions than LBVs for luminosi-ties above log (L/L ⊙ )=6.0. One possibility is that theLBV mass loss is so extreme that giant eruptions cancompletely remove the remaining H envelope to exposethe bare He core. Thus, in Figure 2, a star would effec-tively move instantaneously from the position of an LBVlike AG Car to a lower-luminosity WR star. However, theclear absence of H-free WR stars above log (L/L ⊙ )=5.8is puzzling in that case, as is the general dearth of H-free WN stars in giant H ii regions. The sudden removalof the outer layers at the end of core-H burning shouldnot much affect the luminosity of the He core that re-mains behind, so where are these luminous H-free stars?One way out of this predicament, hinted at by Figure2 a , could be if the more massive stars explode beforeshedding their H envelopes.In fact, there is mounting evidence that some mas-sive stars may explode during the LBV phase before evermaking it all the way to the H-free WR stage (see thediscussions in Smith & Owocki 2006; Smith 2007a, andGal-Yam et al. 2007). Some examples are the recentType IIn event SN 2006gy, which may have been the ex-plosion of a very massive star like η Carinae (Smith etal. 2007), the Type IIn event SN 2006gl, whose puta-tive progenitor star identified by Gal-Yam et al. (2007)had photometric properties consistent with an LBV, thevariable radio properties of some SNe (Kotak & Vink2006; for other interpretations, however, see Soderberget al. [2006] and Ryder et al. [2006]), the SN1987A-likenebula around the LBV star HD168625 (Smith 2007b),plus many other Type IIn SNe with dense environments.There are also some He-rich stars (perhaps LBV/WNtransition stars) that appear to have suffered LBV-likemass ejections shortly before a Type Ib/c SN explosion– the clearest example being SN 2006jc (see Foley et al.2007; Pastorello et al. 2007; Smith et al. 2008), whichwas actually observed to have an LBV-like event 2 yrprior to the SN explosion. For the low-luminosity LBVsNH stars 11like HD168625 or R71, explosion as an LBV is not nec-essarily a problem – or even a surprise – because thoselower-L stars are likely to be in a post-RSG phase (seeSmith et al. 2004). For the high-luminosity LBVs abovelog (L/L ⊙ )=5.8, however, it presents a serious challengeto our current paradigms of stellar evolution. And What Have We Left Out?
Obviously, we have stopped short of a full calcula-tion of stellar evolution models that would take into ac-count the way that the core luminosity may respond tomass loss. However, in exploring the feedback effect, weadopted the core luminosities from the models of Schalleret al. (1992), which used relatively high mass-loss ratesas noted earlier. Therefore, with the lower initial mass-loss rates we argue for here (and a consequent highercore luminosity), the feedback effect we propose couldbe even more extreme. Nevertheless, we only set out todemonstrate the principle of the feedback effect and thatit can lead to high mass-loss rates of WNH stars if theyare in the latter part of core-H burning for initially verymassive O-type stars. Renewed efforts to calculate fullstellar evolution models are encouraged.Our simple analysis does not account for chemical mix-ing and possible effects of rotation on that parameter,which is still a central problem in the evolution of mas-sive stars. It is quite possible that rotationally-enhancedmixing could lead stars with identical masses to evolveon somewhat different paths, hence surface abundancescould differ. Thus, the exact time of “onset” of the WNHphase might vary from one star to another – even for starsof the same initial mass – based on the initial rotationrate and efficiency of the mixing. Therefore, our quotedage of ∼ η Car and P Cygni (see, e.g., Davidson et al.1989), where they may eject ∼ M ⊙ in a single burst(Smith et al. 2003; Smith & Owocki 2006), and theseevent are likely to repeat. There is a suspicion in the hotstar community that the most luminous objects (e.g. η Car or the Pistol star) might have fewer but more se-vere outbursts, while less luminous LBVs could repeatthese episodes many times with each individual eventless violent than for η Car (again see, e.g., contributionsin Davidson et al. 1989). The mass lost each time, thefrequency, and the total number of such outbursts as afunction of luminosity or intial mass, combined with thepotential regulating/perturbing effect of close binaries,are parameters that are badly needed for modeling thelate evolution of massive stars, but we are still far fromaccurate empirical prescriptions of this mass loss behav-ior. Therefore, we must remain skeptical of the predic-tions of stellar evolution codes beyond the end of core-Hburning for very massive stars.How do the WNH stars fit into this scenario? Coulda WNH become an LBV and thence return to the WNHstage again? This is thought to be the case, specifically, for some Ofpe/WN9 stars, since the LBVs AG Car andR127 both look like Ofpe/WN9 stars in their quiescentstate (Stahl 1986; Stahl et al. 1983). Perhaps somethingsimilar is happening for HD5980 in the SMC. Can wedetermine if such LBV/WNH transition stars are occur-ring relatively early or late in a broader LBV phase? Howdoes the initial stellar composition affect the WNH/LBVscenario we propose here? Does the presence of a num-ber of early WN stars in the SMC that are also WNHtell us something? SUMMARY: THE STRONG WINDS OF WNH STARSENABLE THE LBV PHASE
We have shown that the masses, mass-loss rates, andabundances of luminous WNH stars are distinct from H-free WR stars, that they can be explained naturally ifthey are in the late stages of core-H burning, and thatthis can be understood as a direct consequence of mass-loss feedback during core-H burning. We treat this feed-back very simplistically as the dependence of the mass-loss rate on the luminosity and Eddington factor asso-ciated with conventional line-driven wind theory, as ex-plained in §
5. We have ignored additional effects suchas rotationally or pulsationally enhanced mass loss, butthose effects may become necessary if O-star mass-lossrates are indeed reduced much below the values corre-sponding to moderate clumping factors (Repolust et al.2004) that we have adopted here. The feedback causes asteady climb in the star’s mass-loss rate.Just as this O-star mass loss provides a sort of feedbackthat leads to the higher mass-loss rates of WNH stars, sotoo does the higher mass-loss rate of the WNH phase en-able further instability in later phases. Namely, with in-creased mass loss, the WNH wind lowers the stellar masseven further as the luminosity continues to climb at anever faster pace. This runaway eventually pushes the starto the classical Eddington limit (Γ=1) as shown in Figure3. At some point along the way, perhaps at Γ ≃ ⊙ , for instance,it would appear that the star can linger on well into coreHe burning before actually triggering the LBV instabil-ity. Again, this is very interesting from the point of viewof LBVs being potential Type IIn SN progenitors.Another consequence of lower mass-loss rates through-out core-H burning is that the star will suffer less angularmomentum loss. This, in turn, makes rotation have aneven more important effect in the later stages as an LBV,as discussed by Langer and others (Langer 1998; Langeret al. 1994; Glatzel 1998; Maeder & Meynet 2000). Per-haps this rotation is critical for triggering the LBV in-stability for some range of LBVs, since models for initialmasses below 85 M ⊙ do not quite reach Γ & We have benefitted from numerous discussions about stellar winds and WNH stars with Paul Crowther, Gloria Koenigsberger, Tony Mof-fat, Stan Owocki, Joachim Puls, and Jorick Vink. We are particularlygrateful to P. Crowther, T. Moffat, Nolan Walborn, and an anonymousreferee for detailed comments on the manuscript. NS acknowledgessupport from NASA through STScI and JPL, and PSC appreciatessupport from the NSF.
