|Annu. Rev. Astron. Astrophys. 1994. 32:
Copyright © 1994 by . All rights reserved
Recent general reviews on Wolf-Rayet stars have been made by Abbott & Conti (1987), Willis (1987, 1991), Conti & Underhill (1988), Smith (1991a), van der Hucht (1991, 1992), Maeder (1991c), and Massey & Armandroff (1991). W-R stars are nowadays considered as "bare cores" resulting mainly from stellar winds peeling off of single stars initially more massive than about 25 to 40 M. Close binaries might also lose their outer layers from Roche lobe overflow (RLOF). The main evidence for the bare core model as reviewed by Lamers et al (1991) are the following:
With their bright emission lines and their high luminosities, W-R stars are observable at large distances and are thus the stars for which we have the best sampling in other galaxies. Their emission lines also can become visible in the integrated spectrum of galaxies with active star formation, which enables us to extend the studies of young massive stars even farther out in the Universe. The discovery of the differences in W-R populations in galaxies has a long history starting with Roberts (1962) in the Milky Way and later Smith (1968a, b, c) for the Magellanic Clouds. Further studies in the LMC and SMC (Azzopardi & Breysacher 1979, 1985; Breysacher 1981) confirmed the variations of W-R populations. These were also noticed (e.g. Kunth & Sargent 1981) in a sample of blue compact galaxies, which are dwarf galaxies with very active star formation, and in the so-called H II or W-R galaxies (Conti 1991a). The observed variations concern mostly the statistics, and in particular, ratios such as W-R/O or WC/WN.
The existence and origin of the variations of W-R populations in galaxies has been extensively debated over the past decade (see Section 4.6). Indeed, properties and statistics of W-R stars depend on many parameters: metallicity Z, star formation rate (SFR), initial mass function (IMF), age and duration of the bursts, binary frequency, etc. It is essential to distinguish between (a) regions in galaxies where the assumption of an average constant star formation rate over, say, the past 20 Myr is valid, and (b) regions or galaxies where a strong recent burst has recently occurred so that the assumption of a constant SFR does not apply. The first case concerns selected volumes in the Milky Way and in other galaxies (where individual W-R stars may be counted), where a stationary situation for star formation can be assumed. Within these regions, the effects of metallicity intrinsic to stellar evolution can be assumed to be the dominant factor responsible for the differences in W-R populations. This case is examined here first, as its proper understanding is a prerequisite for the studies of the second case (Section 5), which concerns distant GH II regions. W-R galaxies, and other starbursts.
4.2 Subtypes and Chemical Abundances
The basic physical parameters of W-R stars, i.e. their masses M, luminosities L, mass loss rates , radii R, and temperatures Teff, have been discussed by Conti (1988), Abbott & Conti (1987), and van der Hucht (1992). The M are in the range of 5 to 50 M with an average of about 10 M: the L are between 104.5 and 106 L; the between 10-5 and 10-4 M / yr with an average of 4 × 10-5 M / yr; and the observed Teff are between 30,000 K and 90,000 K, There are two main groups of Wolf-Rayet stars: subtypes WN and WC; a small additional subset is labeled WO (Barlow & Hummer 1982).
4.2.1 WN STARS The WN types are nitrogen-rich helium stars (Smith 1973) showing the "equilibrium" products of the CNO hydrogen burning cycle. The late WN stars of types WN6-WN9, abbreviated WNL (Vanbeveren & Conti 1980, Conti & Massey 1989), generally still contain some hydrogen with H/He ratios between 5 and 1 by number (Conti et al 1983a; Willis 1991; Hamann et al 1991, 1993; Crowther et al 1991). The early WN stars of types WN2-WN6, or WNE, generally show no evidence of hydrogen in their spectra. (There are a few exceptions to this general abundance relation with spectral subtype.) In a smaller sample of objects, Hamann et al (1993) found a correlation of the hydrogen content with the Teff of WN stars, rather than with their subtypes; the coolest WN stars showed hydrogen and the hottest ones had none. The presence or absence of hydrogen certainly should be a determining factor influencing the opacity, temperature, and the structure of the outer layers.
The observed abundance ratios in mass fraction are C/He = (0.21-8) × 10-2; N/He = (0.035-1.4) × 10-2; and C/N (0.6-6.0) × 10-2 (cf Willis 1991, Nugis 1991). The corresponding solar ratios are respectively 1.1 × 10-2, 3.3 × 10-3, and 3.25 (Grevesse 1991 and references therein). The well-studied WN5 star HD 50896 gives similar results (cf Hillier 1987a, b, 1988). Not much is known concerning the oxygen content of WN stars. Studies of ring nebulae around some WN stars also show strong overabundances of N and He with respect to the Sun (Parker 1978; Esteban & Vilchez 1991, 1992; Esteban et a1 1992, 1993). These authors suggest that the ring nebulae have been ejected at the end of the red supergiant phase. In our opinion, it is more likely that a large part of the shell ejection, or even most of it, occurs during the first thousand years after the entry in the WNE and WC stages, which are marked by extreme mass loss, as predicted by the M vs M relation for W-R stars (cf Langer 1989b). Among WN stars, eight have inordinately strong CIV lines (Conti & Massey 1989). Labeled WN/WC stars, these are suggested to be transition objects between WN and WC stars (Section 4.5).
The observed abundance ratios span the range of equilibrium values of the CNO cycle (Maeder 1983, 1991b), with C/N and O/N ratios two orders of magnitude smaller than solar. Interestingly enough, such values are essentially independent of the various model assumptions and mainly reflect the nuclear cross sections and initial composition. The good agreement between the observed and predicted values of CNO equilibrium indicates the general correctness of our understanding of the CNO cycle and of the relevant nuclear data.
The initial CNO content, which depends of the initial Z, determines the amount of nitrogen in WN stars (Maeder 1990, Schaller et al 1992). The N abundance is thus lower for lower initial Z, but equilibrium ratios such as C/N are predicted to be independent of the initial Z. In this connection, one can understand the result by Smith (1991a) who noticed that the ratio of the 4686 He II line to the 4640 N III line is stronger for WNL stars in the LMC compared to the Galaxy.
4.2.2 WC STARS WC stars contain no hydrogen and, as a result of mass loss, are mainly He, C, and O cores as a result of mass loss (Smith & Hummer 1988, Torres 1988, de Freitas-Pacheco & Machado 1988, Hillier 1989, Willis 1991, Nugis 1991, Eenens & Williams 1992, de Freitas Pacheco et al 1993). These stars represent objects in which we see at the surface the result of triple- and other helium burning reactions. A most interesting finding is the one by Smith & Hummer, who showed that the C/He ratio is increasing for earlier WC subtypes. Smith & Maeder (1991) emphasize that a measured (C+0) / He ratio is to be preferred to the C/He and C/O ratios which go up and down during helium processing. They propose the following calibration in (C+O) / He number ratios: WC9, 0.03-0.06; WC8, 0.1; WC7, 0.2; WC6, 0.3; WC5, 0.55; WC4, 0.7-1.0; WO, > 1.
The sequence of types WC9 to WO appears as a progression in the exposure of the products of He burning. The rare WO stars (Barlow & Hummer 1982, Kingsburgh & Barlow 1991, Polcaro et al 1992, Kingsburgh et al 1994) simply appear to be the most extreme type in this sequence. Comparisons of observations and model predictions show a generally good agreement (Willis 1991, 1994): however, closer comparisons (Schaerer & Maeder 1992) suggest that in previous evolutionary phases could be higher by a factor of 2 with respect to current values by de Jager et al (1988). The above connection between WC sub-types and the (C+O) / He ratios is the key to understanding the Z-dependence of the distribution of WC stars in galaxies of different metallicities (Section 4.6).
A present uncertainty concerns neon in WC stars. Models predict a substantial abundance of neon (larger than 0.03 in mass fraction) - essentially Ne22 at high initial Z and Ne20 at low Z (Maeder 1991a). However, the only available data, which come from IRAS observation of Ne II at 15.5 microns, indicate an abundance of 0.005 in the WC8 star Vel (Barlow et al 1988). Some of the nuclear cross sections in the chain leading to Ne22 are still very uncertain and the ashes of N14 could possibly be stocked in the form of O18 (indistinguishable from O16 in W-R stars) rather than in the form of Ne22. The problem is of importance for explaining the role of WC stars as a possible site for s-elements (Prantzos et al 1990), since these elements should be formed by Ne22 (, n)Mg25. The role of W-R stars as producers of radioactive Al26, detectable through y ray observations, does not seem important according to Signore & Dupraz (1990), but according to Meynet (1994a) their role could be as important as that of supernovae.
4.3 Physical Properties
In addition to the usual model ingredients, the W-R star models specifically require special attention on a number of points. Concerning microphysics, the W-R models demand Rosseland opacities for the appropriate He-C-O mixtures (Iglesias & Rogers 1993) and detailed calculations of the ionization balance for heavy elements (Langer et al 1986, Schaller et al 1992). The Ms in stages previous to the W-R phases and their dependence on Z are very critical. Also, the adopted definitions (based on surface abundances) for the transitions from LBV to WNL, WNL to WNE, and WNE to WC are of importance for the comparison of models and observations.
For in the W-R stage, the average observed rates (Abbott et al 1986, Conti 1988) have often been used. However, these rates have led to masses and luminosities that are too high with respect to the observations (Schmutz et al 1989). A number of convergent suggestions have been provided recently in favor of a mass dependence of in WNE and WC stars. In particular, models by Langer (1989b) suggest a relation of the form: (W-R) = (0.6-1.0) × 10-7 (M / M)2.5 M / yr, where the first coefficient applies to WNE and the second to WC stars. Similar mass-dependent s have been provided from binaries (Abbott et al 1986, St Louis et al 1988), and from modeling the wind properties (Turolla et al 1988, Bandiera & Turolla 1990, Schaerer & Maeder 1992). The vs M relation generally leads to an enormous mass loss at the entry in the WNE stage, which results in very low final W-R masses. This has a considerable impact on the chemical yields of massive stars (Maeder 1992a), also resulting in an increase of the W-R lifetimes. A question remains as to whether the WN luminosities predicted from models with standard (de Jager et al 1988) are not too high with respect to the observed ones (Howarth & Schmutz 1992). Indeed, the relatively low observed luminosities of some WN stars support larger in previous stages. There are at present no indications of a mass dependence of for WNL stars, although such a relation would not be too surprising.
The maximum mass for the vibrational stability of a He star is about 16 M (Noels & Maserel 1982, Noels & Magain 1984). Thus, if a star enters the helium configuration with a mass larger than critical (which occurs in current models), it may be expected to be vibrationally unstable with high mass loss as a consequence (Maeder 1985). The fact that regular pulsations have been recently observed in the WN8 star WR 40 (Blecha et al 1992) might give some support to this claim. However, the nature of these pulsations is still under discussion (Kirbiyik 1987) and different pulsation modes have been proposed by Glatzel et al (1993) and Kiriakidis et al (1993). Attempts are also being made to explain the strong W-R winds by multi-scattering and purely radiative processes (Pauldrach et al 1988, Cassinelli 1991), by radiation and turbulence (Blomme et al 1991), or by radiation and Alfven waves (Dos Santos et al 1993). The main difficulty, which is not satisfactorily resolved, is to explain why the wind momentum of W-R stats may be up to 30 times the photon momentum (Barlow et al 1981, Cassinelli 1991; but see Lucy & Abbott 1993).
The problems of the atmospheres of hot stars have been reviewed by Kudritzki & Hummer (1990) and the different definitions of the radii and Teff in extended atmospheres by Bascheck et al (1991). Values of hit have been given recently by Conti (1988), Schmutz et al (1989, 1992), and Koesterke et al (1992): They range between about 3 × 104 and 105 K. In order to compare the observed Teff with data from interior models, a simple correction scheme has been proposed to roughly account for the optically thick winds of W-R stars (de Loore et al 1982, Langer 1989a). More refined procedures have been established by Kato & Iben (1992), by Schaller et al (1992), and in particular by Schaerer & Schmutz (1994). The net result is that from a surface temperature of 1-1.5 × 105 K (without the wind), the W-R stars are shifted down to Teff 3-10 × 104 K according to their rates, and thus also according to their masses and luminosities since there is a M-L- relation.
Since W-R stars of types WNE and WC are He-C-O cores, they have a rather simple internal structure with little compositional difference between center and surface. W-R properties and the relations between the subtypes are mostly independent of their formation. Evolutionary models predict M-L--Teff relations (Schaerer & Maeder 1992) for W-R stars without hydrogen. The mass-luminosity M-L relation is (Maeder 1983, Langer 1989a, Beech and Mitalas 1992, Schaerer & Maeder 1992):
For M > 10 M, a linear relation may be appropriate. On the observational side, the M-L relation has been confirmed (Smith & Maeder 1989, Smith et al 1994). The vs M relation is supported by binary observations as discussed above. The M-L--Teff relations also indicate that WNE stars and WC stars should follow well-defined tracks in the HR. diagrams. Such alignments seem to be present in the data of Hamann et al (1991, 1993; but see also Maeder & Meynet 1994).
For WNL stars, the luminosities are generally higher than for WNE stars (Conti 1988). Models indi1cate that WNL luminosities are mainly related to the initial masses. The reason is that the luminosity depends on the size of the He cores, which is determined mainly by the initial mass rather than by the actual mass, as long as the He cores are not themselves peeled off. Models also suggest, in agreement with observations (cf Hamann et al 1993), that the WNL Teff are mainly determined by the remaining hydrogen content.
4.4 Initial Masses, Lifetimes, Formation
Observationally, most W-R stars appear to originate from stars initially more massive than about 40 M (Conti et al 1983b, Conti 1984, Humphreys et al 1985, Tutukov & Yungelson 1985). From the presence of W-R stars in clusters down to type BO, it is clear that a few W-R stars may originate from initial masses down to 20-25 M (Firmani 1982, The et al 1982, Schild & Maeder 1984). The modeling of W-R ring nebulae (Esteban et al 1992) also supports the above values of initial masses. The minimum mass for forming WC stars does not seem significantly higher than that for WN stars.
Maeder & Meynet (1994) have obtained the lifetimes in the W-R stage for two different cases: 1. the standard case with mass loss rates by de Jager et al (1988) in pre-W-R stages and the scaling with Z0.5 at other metallicities; and 2. the case with M arbitrarily twice as large as in pre-W-R stages. Indeed, several observations, in particular the chemical abundances in WC stars (Section 4.2), the W-R luminosities (Section 4.3), and the number ratios of W-R stats (Section 4.5) clearly support the case of enhanced mass loss, for which the W-R lifetimes are shown in Figure 1. From this figure we note that:
Figure 1. Durations of the W-R phase as a function of initial stellar masses for different Z in the case of enhanced mass loss rates (from Maeder & Meynet 1994).
The formation of W-R stars is largely dominated by the overwhelming effects of mass loss, as first proposed in the "Conti" scenario (Conti 1976). Mixing processes due to rotation or tidal distortion in binaries may favor in some cases the formation of W-R stars and increase their lifetimes (Maeder 1981, 1987b). Semiconvection or some mild mixing at the edge of the He core seems necessary to account for the existence of intermediate WN/WC stars (Langer 1991b). These stars represent about 4% of the W-R stars (Conti & Massey 1989), while models without extra mixing only predict 1% or less of WN/WC stars. These stars cannot be explained by binary evolution (Vrancken et al 1991). Some additional mixing is necessary, but at the same time the small observed fraction of WN/WC stars implies that the part of the stellar mass that is actually mixed is quite small, and this puts a limit on the role of mixing at the edge of the He core.
Detailed investigations of W-R binaries have been carried out in the Galaxy by Massey (1981) and in the Magellanic Clouds by Moffat 1988 and Moffat et al 1990. Binary mass transfer by RLOF, which is an extreme case of tidal interaction, may contribute to the formation of WR+O binaries (de Loore 1982; De Greve et al 1988; Vanbeveren 1988, 1991, 1994; Schulte-Ladbeck 1989; De Greve 1991, de Loore & Vanbeveren 1994). The fraction of all stars (single + binaries) undergoing RLOF is estimated to be between 20 and 40% (Podsiadlowski et al 1992). We may note that this percentage also includes binaries that could be mixed by tidal interactions and would thus evolve homogeneously, without large increase of their radius and thus without RLOF, Indeed, the importance of RLOF in W-R+O binaries is still unclear. From the similarity of the relatively large orbital eccentricities in W-R+O and O+O binaries, Massey (1981) concluded that mass transfer probably did not play a major role in the formation of W-R+O binaries. We may conjecture that several effects contribute to the formation of W-R stars; it is likely that the relative importance of these effects changes with Z as discussed below.
4.5 W-R Statistics
4.5.1 BASIC DATA AND ITS INTERPRETATION W-R stars are observed in several galaxies of the Local Group, and provide statistical data on their relative frequencies at various metallicities. In the Milky Way, the catalogs by van der Hucht et al (1988), and by Conti & Vacca (1990) provide rather complete samples up to about 2.5 kpc. These data show that the number density of W-R stars projected onto the Galactic plane is strongly increasing with decreasing galactocentric distance. Deep surveys are extending the sampling (Shara et al 1991). The LMC and SMC catalogs are cornerstones for data at other Z (Azzopardi & Breysacher 1979, 1985; Breysacher 1981, 1986). A few additional W-R stars have also been identified (Morgan & Good 1985, Testor & Schild 1990, Schild et al 1991, Morgan et al 1991). Most (75%) of the W-R stars in the center of the 30 Dor Nebula are WNL stars of types WN6-WN7 (Moffat et al 1987), while in the surroundings the proportion is much lower. The excess of WNL stars in giant H II regions is a common feature, as evidenced by those in M33 (Drissen et al 1990, 1991). The subtype distribution of W-R stars in the Magellanic Clouds has been considered by Smith (1991b). Data on W-R stars in M31 have been obtained by Moffat & Shara (1983, 1987), Massey et al (1986, 1987a), Armandroff & Massey (1991), and Willis et al (1992). For M33, studies have been made by Wray & Corso (1972), Conti & Massey (1981), Massey & Conti (1983), Massey et al (1987a, b), Schild et al (1990), and Armandroff & Massey (1991). In both M31 and M33, the samples are still incomplete. In the two small galaxies NGC 6822 and IC 1613 of the Local Group, many W-R stars were proposed by Armandroff & Massey (1985) and Massey et al (1987a), but further analyses by Azzopardi et al (1988; see also Smith 1988) confirmed only four W-R stars in NGC 6822 and one, which was already found by Davidson & Kinman (1982), in IC 1613. The study of W-R stars in other galaxies is continuing. The galaxy IC 10 at 1.5 Mpc exhibits a very high density of W-R stars with a WC/WN number ratio of about 0.5 (Massey et al 1992). Ten individual W-R stars have been detected in the galaxy NGC 300 at a distance of 1.5 Mpc (Schild & Testor 1991, 1992).
Analyses of W-R star statistics in nearby galaxies have been made by Azzopardi et al (1988), Smith (1988), Massey & Armandroff (1991), Maeder (1991a), and Maeder & Meynet (1994). Table 2 gives the available data on the W-R/O, WC/W-R, and WC/WN ratios for galaxies of the Local Group, when an indication of the metallicity Z is available. The table is adapted from Maeder (1991a) with revisions according to recent data from Conti & Vacca (1990) for the Milky Way; for M31 the W-R/O is from Cananzi (1992); for the SMC the new W-R star found by Morgan et al (1991) is included; the WN/WC ratios are in agreement with those found by Armandroff & Massey (1991). Due to small number statistics, the ratios for NGC 6822 and IC 1613 are not significant.
Such number ratios are to be preferred to surface densities, which would depend not only on stellar evolution but also on the current SFR. For the Galaxy, the statistics for O stars is based on the survey by Garmany & Conti (1982). In other galaxies, the numbers of O stars were estimated by Azzopardi et al (1988) on the basis of UV data from Geneva and Marseille balloon experiments and on the basis of Lequeux's (1986) luminosity function. These indirect estimates lead to larger uncertainties in the numbers of O stars than in those for W-R stars.
The origin of the observed variations of the relative number of W-R stars in different environments was attributed to metallicity by Smith (1973) and Maeder et al (1980), who suggested that high Z favors mass loss, which in turn favors the formation of W-R stars. The variations of W-R subclasses in M31 were also attributed to a metallicity effect by Moffat & Shara (1983). The total dependence on Z was criticized by several authors, who attributed the differences in the W-R populations mainly to changes in the IMf and SFR (Bertelli & Chiosi 1981, 1982; Garmany et al 1982; Armandroff & Massey 1985; Massey 1985; Massey et al 1986; Massey & Armandroff 1991). As suggested by these authors, it is possible that prominent departures from the assumption of constant star formation, such as is the case in 30 Dor in the LMC (Moffat et al 1987) or in giant HII regions of M33 (Conti & Massey 1981, Drissen et at 1990) where recent bursts of SFR have occurred, may produce peculiar W-R number ratios (Section 5). However, we note that no systematic difference in the IMF slope has been found between the Galaxy, the LMC, and SMC (Humphreys & McElroy, 1984, Mateo 1988, Massey et at 1989a, Parker et al 1992, Section 2). Also, the Galactic gradient of the surface density of W-R stars is much steeper than that of their precursor O stars (Meylan & Maeder 1982, van der Hucht et al 1988) - a fact that is reflected by the changes of the W-R/O in Table 2. Thus, it is likely that the basic effect in stellar evolutionary models is Z, and that effects connected to the SFR and perhaps to the IMF are population parameters that may also influence the relative frequencies of W-R stars in G HII regions and bursts.
|ring 6-7.5 kpc||0.029||0.205||0.55||1.22|
|ring 7.5-9 kpc||0.020||0.104||0.48||0.92|
|ring 9.5-11 kpc||0.013||0.033||0.33||0.49|
4.5.2 PREDICTED W-R/O AND WC/WN VALUES As illustrated in Table 2, the W-R/O ratio increases with the metallicity of the parent galaxy (Maeder et al 1980; Azzopardi et al 1988; Smith 1988, 1991a). This general trend is also confirmed by studies of the integrated properties of H II or W-R galaxies (Arnault et al 1989; Conti 1991a, b; Smith 1991a; Vacca & Conti 1992; Mas-Hesse & Kunth 1991a, b; Mas-Hesse 1992). In stellar models a growth of the W-R/O with Z is predicted (Maeder 1991a, Maeder & Meynet 1994), resulting from the lowering of the minimum initial mass for forming W-R stars and from the increase of the lifetimes with increasing Z (and mass loss). Figure 2 compares the observations of Table 2 with theoretical values for models with enhanced as defined in Section 4.4 and for stars with a Salpeter IMF. The general agreement is quite good, confirming that metallicity is a key factor in the variations of the W-R/O ratio. Although some scatter appears, it might be due to local departures from the simple assumption of a past constant SER and to the averaging over some range of Z in large galaxies (Smith 1991a). No satisfactory agreement between observed and predicted W-R/O can be achieved for models with standard (de Jager et al 1988). The differences would be especially large at high Z, while at Z = 0.002, the W-R/O values are in both cases of mass loss equal to about 0.005. Such negligible W-R/O values at low Z are in agreement with the low fraction of W-R stars observed in metal deficient galaxies. Also, the study of the integrated spectrum and He II 4686 Å feature in dwarf galaxies shows a general absence of W-R contribution for galaxies with very low oxygen content, corresponding to about Z = 0.002 (Arnault et al 1989, Smith 1991a).
The observed WC/WN and WC/W-R numbers in Table 2 show a general growth with increasing Z, but it is not monotonic and shows an appreciable scatter. This was noted by Armandroff & Massey (1991) and Massey & Armandroff (1991) as an argument supporting the fact that metallicity is not the only determining factor for explaining the W-R statistics. From models, the change in WC/WN results from the higher which leads to an earlier visibility of the products of He burning (Maeder 1991a, Maeder & Meynet 1994). Interestingly enough, for larger M the predicted WC/WN ratios, instead of further increasing as expected, go down again as Z becomes greater than 0.01. This occurs because the WN phase of the most massive stars has already been entered during the main sequence phase and is therefore much longer. This model result accounts for the nonmonotonic behavior of WC/WN found by Armandroff & Massey (1991).
Figure 2. W-R/O as a function of Z in nearby galaxies compared to model predictions by Maeder & Meynet (1994). The solid line represents the predictions of single star models with enhanced mass loss rates (Section 4.4) and Salpeter's IMF. The dotted lines show the same for different values , the fraction of O stars undergoing mass transfer in binaries.
The comparison between observed and theoretical WC/WN or WC/W-R shows, as for the W-R/O, that a better fit is obtained for models with enhanced in previous phases. Nevertheless, the scatter is still there, and reflects departures from the assumption of a constant SFR. Such departures are prominent in some giant H II regions, such as 30 Dor in the LMC, or NGC 592, 595, and 604 in M33, which show evidence of intense star formation (Conti & Massey 1981; Drissen et al 1990, 1991). Armandroff & Massey (1985) and Massey & Armandroff (1991) noticed that regions with metallicity similar to that of the LMC and SMC have different W-R numbers. Smith & Maeder (1991) suggested that in large spirals the W-R populations will he heavily weighted toward properties of high Z values. Thus both the effects of bursts of star formation (Section 5) and of the averaging over Z may contribute to increases in the W-R/O and WC/WN ratios, a situation which may apply particularly to M33.
Close comparisons between models and observations must also account for the various channels of W-R formation and in particular the Roche lobe overflow (RLOF) in close binaries (Vanbeveren 1991, 1994; Vanbeveren & de Loore 1993). The fraction of O stars becoming W-R stars as a result of RLOF was estimated by the latter authors to be about 35% (see also Podsiadlowski et al 1992). A new analysis quoted above (Maeder & Meynet 1994) suggests that the fraction of W-R stars owing their existence to RLOF is highly variable with the metallicity of the parent galaxy; it is nearly 100% at low Z, like in the SMC (Smith 1991b), and lower than 10% in the inner regions of the Milky Way.
The above results are compatible as shown in Figure 2 with a relatively low fraction , at most 10%, of the ensemble of the O stars that become W-R as a result of binary mass transfer. Such a low fraction is consistent with by Massey's (1981) result on the distribution of the eccentricities of WR+O binaries. A close investigation of the young cluster Tr 14 (Penny et al 1993) reveals a general absence of close binaries among the brightest O stars. In further support of a low fraction of O stars undergoing RLOF, we remark that at the low Z in the SMC, the W-R/O ratio is about 0.017, while it is 0.21 in inner Galactic regions. Thus, if the fraction of O stars becoming W-R as a result of RLOF is the same in both areas, this fraction would be at most 0.017/0.21 = 8%, assuming that all W-R stars in the SMC are formed by RLOF. This fixes the upper limit of the fraction of O stars undergoing RLOF under the mentioned assumption.
Stellar winds produce fewer W-R stars at low Z, and only the binary channel seems efficient in forming WR stars. As an example, in the SMC, eight of the nine observed W-R stars may be binaries; five are confirmed (Moffat 1988, Smith 1991a). These binaries were likely formed by mass transfer (De Greve et al 1988). They are of type WNE, which suggests that the binary channel may mainly lead to WNE stars. Consistent with the SMC observations, the proportion of W-R binaries has been found to be larger toward the anticenter in the Milky Way (van der Hucht et al 1988). The hypothesis that a small fraction of the W-R stars is formed by RLOF also gives a better fit to the observed behavior of the WNE/W-R and WNL/W-R ratios with Z (Maeder & Meynet 1994). We may also note that the average ages of WNL and WNE stars are probably not the same; Moffat et al (1991) suggest that the former are relatively younger than the latter; WNL stars are also more luminous than WNE stars (Conti 1988). These facts are consistent with the result (Section 4.5) that WNL stars mainly originate from the most massive stars.
4.5.3 WC SUBTYPE STATISTICS The distributions of WC and WO stars in galaxies exhibit a number of distinct properties.
These various facts can be easily understood on the basis of recent models and of the relation between WC subtypes and the (C+O)/He ratios as shown by Smith & Maeder (1991). The entry points and lifetimes in the WC9 to WO sequence are very dependent on M and Z. At high Z and high M, due to high mass loss the WC stage is entered very early during the He burning phase, so that the surface (C+O)/He ratio is very low, which implies a type WC9 or WC8. As evolution continues, mass and luminosity decline and (C+O)/He decreases and thus the sequence of types WC9 -> WO is described. The entry point in that sequence occurs at lower L and earlier WC types for lower masses. At lower Z, as in the LMC, the entry in the WC phase occurs at a later stage of central He-burning, i.e. with higher O/C ratios (Smith et al 1990) and also with higher (C+O)/He ratios at the surface, which means earlier WC types, typically WC5-WC4 (Smith & Maeder 1991). Then, the further evolutionary sequence described is short. This behavior also explains the two above-mentioned points concerning the luminosity of WC stars at different Z. That the luminosity for a WC subtype depends on the initial Z may have consequences for the interpretation of WC lines in integrated spectra of galaxies.
From W-R stars in clusters and in galaxies, some relationships between subtypes can be understood (van der Hucht et al 1988; see also Schild & Maeder 1984, Moffat et al 1986, Moffat 1988, Schild et al 1991): For galactocentric radius R < 8.5 kpc, we have WNL -> WCL; while for R > 6.5 kpc, we find WNL -> WCE -> WO and WNE -> no WC stars.
These connections are supported by the model results (Maeder 1991a). The first connection is typical of high mass and high Z: A long WNL phase, followed by a negligible WNE phase, emerges on the late and luminous part of the WC sequence, typically at WC9 or WC8. The second connection is typical of large masses with solar or lower metallicity, while the third one corresponds to the lowest part of the mass range able to form W-R stars.
We conclude this section by underlining that the observations and understanding of W-R stars in nearby galaxies has brought the clarification of many problems, which also have far-reaching consequences for the injection of mass, momentum, and energy into the interstellar medium (Leitherer et al 1992a).