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Wolf-Rayet Stars 1
Physical Properties of Wolf-Rayet Stars
Paul A. Crowther
Department of Physics & Astronomy, University of Sheffield, Hounsfield Road,
Sheffield, S3 7RH, United Kingdom, email: Paul.Crowther@sheffield.ac.uk
Key Words stars: Wolf-Rayet; stars: fundamental parameters; stars: evolu-
tion; stars: abundances
Abstract The striking broad emission line spectroscopic appearance of Wolf-Rayet (WR)
stars has long defied analysis, due to the extreme physical conditions within their line and
continuum forming regions. Recently, model atmosphere studies have advanced sufficiently to
enable the determination of stellar temperatures, luminosities, abundances, ionizing fluxes and
wind properties. The observed distributions of nitrogen (WN) and carbon (WC) sequence WR
stars in the Milky Way and in nearby star forming galaxies are discussed; these imply lower
limits to progenitor masses of ∼25, 40, 75 M⊙ for hydrogen-depleted (He-burning) WN, WC,
and H-rich (H-burning) WN stars, respectively. WR stars in massive star binaries permit studies
of wind-wind interactions and dust formation in WC systems. They also show that WR stars
have typical masses of 10–25M⊙, extending up to 80M⊙ for H-rich WN stars. Theoretical and
observational evidence that WR winds depend on metallicity is presented, with implications for
evolutionary models, ionizing fluxes, and the role of WR stars within the context of core-collapse
supernovae and long-duration gamma ray bursts.
CONTENTS
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Paul A. Crowther
Observed Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Spectral Properties and Spectral Classification . . . . . . . . . . . . . . . . . . . . . . . 5
Absolute magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Observed distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Binary statistics and masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Rotation velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Stellar wind bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Physical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Radiative Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Stellar Temperatures and Radii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Stellar Luminosities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Ionizing fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Elemental abundances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Wind Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Wind velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Mass-loss rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Clumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Metallicity dependent winds? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Line driving in WR winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Interacting Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Close binary evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Colliding winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Dust formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Evolutionary models and properties at core-collapse . . . . . . . . . . . . . . . . . 44
Rotational mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Evolutionary model predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
WR stars as SNe and GRB progenitors . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Annu. Rev. Astro. Astrophys. Sept 2007 Vol 45
Summary Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Future Issues to be Resolved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
1 Introduction
Massive stars dominate the feedback to the local interstellar medium (ISM) in
star-forming galaxies via their stellar winds and ultimate death as core-collapse
supernovae. In particular, Wolf-Rayet (WR) stars typically have wind densities
an order of magnitude higher than massive O stars. They contribute to the
chemical enrichment of galaxies, they are the prime candidates for the immediate
progenitors of long, soft Gamma Ray Bursts (GRBs, Woosley & Bloom 2006),
and they provide a signature of high-mass star formation in galaxies (Schaerer &
Vacca 1998).
Spectroscopically, WR stars are spectacular in appearance, with strong, broad
emission lines instead of the narrow absorption lines which are typical of normal
stellar populations (e.g. Beals 1940). The class are named after Wolf & Rayet
(1867) who identified three stars in Cygnus with such broad emission lines. It
was immediately apparent that their spectra came in two flavours, subsequently
identified as those with strong lines of helium and nitrogen (WN subtypes) and
those with strong helium, carbon, and oxygen (WC and WO subtypes). Gamov
(1943) first suggested that the anomalous composition of WR stars was the result
of nuclear processed material being visible on their surfaces, although this was
not universally established until the final decade of the 20th Century (Lamers
et al. 1991). Specifically, WN and WC stars show the products of the CNO
cycle (H-burning) and the triple-α (He-burning), respectively. In reality, there is
a continuity of physical and chemical properties between O supergiants and WN
3

4 Paul A. Crowther
subtypes.
Typically, WR stars have masses of 10–25 M⊙, and are descended from O-type
stars. They spend ∼10% of their ∼5Myr lifetime as WR stars (Meynet & Maeder
2005). At Solar metallicity the minimum initial mass for a star to become a WR
star is ∼25 M⊙. This corresponds closely to the Humphreys & Davidson (1979)
limit for red supergiants (RSG), according to a comparison between the current
temperature calibration of RSG and stellar models that allow for mass-loss and
rotation (e.g. Levesque et al. 2005). Consequently, some single WR stars are
post-red supergiants within a fairly limited mass range of probably 25–30M⊙.
Evolution proceeds via an intermediate Luminous Blue Variable (LBV) phase
above 30M⊙. For close binaries, the critical mass for production of a WR star
has no such robust lower limit, since Roche lobe overflow or common envelope
evolution could produce a WR star instead of an extended RSG phase.
The strong, broad emission lines seen in spectra of WR stars are due to their
powerful stellar winds. The wind is sufficiently dense that an optical depth of
unity in the continuum arises in the outflowing material. The spectral features
are formed far out in the wind and are seen primarily in emission. The line and
continuum formation regions are geometrically extended compared to the stellar
radii and their physical depths are highly wavelength dependent. The unique
spectroscopic signature of WR stars has permitted their detection individually in
Local Group galaxies (e.g. Massey & Johnson 1998; Massey 2003), collectively
within knots of local star forming galaxies (e.g. Hadfield & Crowther 2006),
and as significant contributors to the average rest-frame UV spectrum of Lyman
Break Galaxies (Shapley et al. 2003).
The present review focuses on observational properties of classical Wolf-Rayet

Wolf-Rayet Stars 5
stars in the Milky Way and beyond, plus physical and chemical properties deter-
mined from spectroscopic analysis, plus comparisons with interior evolutionary
models, and provides revisions to the topic with respect to the excellent Abbott
& Conti (1987) review. Low mass (∼ 0.6M⊙) central stars of Planetary Nebulae
displaying a Wolf-Rayet spectroscopic appearance (denoted [WR]) are not con-
sidered. Nevertheless, analysis tools discussed here are common to both types of
star (e.g. Crowther et al. 2006a).
2 Observed Properties
2.1 Spectral Properties and Spectral Classification
Visual spectral classification of WR stars is based on emission line strengths
and line ratios following Smith (1968a). WN spectral subtypes follow a scheme
involving line ratios of N iii-v and He i-ii, ranging from WN2 to WN5 for ‘early
WN’ (WNE) stars, and WN7 to WN9 for ‘late WN’ (WNL) stars, with WN6
stars either early or late-type. A ’h’ suffix may be used to indicate the presence
of emission lines due to hydrogen (Smith, Shara & Moffat 1996).
Complications arise for WN stars with intrinsically weak emission lines. For
example, WR24 (WN6ha) has a He ii λ4686 emission equivalent width that is an
order of magnitude smaller than those in some other WN6 stars; the ‘ha’ nomen-
clature indicates that hydrogen is seen both in absorption and emission. From
a standard spectroscopic viewpoint, such stars possess mid to late WN spec-
tral classifications. However, their appearance is rather more reminiscent of Of
stars than classic WN stars, since there exists a continuity of properties between
normal O stars and late-type WN stars. These stars are widely believed to be
massive O stars with relatively strong stellar winds at a rather early evolutionary

6 Paul A. Crowther
stage. They are believed not to represent the more mature, classic He-burning
WN stars.
Smith, Crowther & Prinja (1994) extended the WN sequence to very late
WN10–11 subtypes in order to include a group of emission line stars originally
classified as Ofpe/WN9 (Bohannan & Walborn 1989). WN11 subtypes closely
resemble extreme early-type B supergiants except for the presence of He ii λ4686
emission. A quantitative comparison of optical line strengths in Of and WNL
stars is presented in figure 8 of Bohannan & Crowther (1999). R127 (WN11) in
the Large Magellanic Cloud (LMC) was later identified as a LBV (Stahl et al.
1983), whilst a famous Galactic LBV, AG Car exhibited a WN11-type spectrum
at visual minimum (Walborn 1990; Smith et al. 1994).
Various multi-dimensional classification systems have been proposed for WN
stars; they generally involve line strengths or widths, such that strong/broad
lined stars have been labelled WN-B (Hiltner & Schild 1966), WN-s (Hamann,
Koesterke & Wessolowski 1993) or WNb (Smith, Shara & Moffat 1996). Of
these, none have generally been adopted. From a physical perspective, strong-
and weak-lined WN stars do form useful sub-divisions. Therefore we shall define
weak (-w) and strong (-s) WN stars as those with He ii λ5412 equivalent widths
smaller than or larger than 40 A˚. An obvious limitation of such an approach is
that intrinsically strong-lined WN stars would be diluted by binary companions
or nearby stars in spatially crowded regions and so might not be identified as
such. WNE-w stars tend to exhibit triangular line profiles rather than the more
typical Gaussian lines of WNE-s stars (Marchenko et al. 2004), since one observes
material much closer to the stellar core that is being strongly accelerated.
WC spectral subtypes depend on the line ratios of C iii and C iv lines along

Wolf-Rayet Stars 7
with the appearance of O iii-v, spanning WC4 to WC9 subtypes, for which WC4–
6 stars are ‘early’ (WCE) and WC7–9 are ‘late’ (WCL). Rare, oxygen-rich WO
stars form an extension of the WCE sequence, exhibiting strong O vi λλ3811-34
emission (Kingsburgh, Barlow & Storey 1995). The most recent scheme involves
WO1 to WO4 subtypes depending on the relative strength of Ov-vi and C iv
emission lines (Crowther, De Marco & Barlow 1998). Finally, C iv λ5801-12
appears unusually strong in an otherwise normal WN star in a few cases, leading
to an intermediate WN/C classification (Conti & Massey 1989). WN/C stars are
indeed considered to be at an intermediate evolutionary phase between the WN
and WC stages.
Representative examples of WN and WC stars are presented in Figure 1. Var-
ious X-ray to mid-IR spectroscopic datasets of Galactic Wolf-Rayet stars are
presented in Table 1, including extreme ultraviolet synthetic spectra from model
atmospheres (Smith, Norris & Crowther 2002; Hamann & Gra¨fener 2004).
2.2 Absolute magnitudes
WR stars cannot be distinguished from normal hot stars using UBV photometry.
Broad-band visual measurements overestimate the true continuum level in ex-
treme cases by up to 1 magnitude, or more typically 0.5 mag for single early-type
WR stars due to their strong emission-line spectra. Consequently, Westerlund
(1966) introduced narrow-band ubyr filters that were specifically designed to
minimize the effect of WR emission lines (although their effect cannot be entirely
eliminated). These passbands were later refined by Smith (1968b) and by Massey
(1984), such that most photometry of WR stars has used the ubvr filter system,
which is compared to Johnson UBV filters in Fig. 1.

8 Paul A. Crowther
As with normal stars, ubv photometry permits a determination of the inter-
stellar extinction, Av. Let us adopt a typical ratio of total, AV to selective,
E(B − V ) = AB − AV extinction, RV = AV /E(B − V ) = 3.1. Following Turner
(1982), the broad-band and narrow-band optical indices for WR stars are then
related by:
Av = 4.12Eb−v = 3.40EB−V = 1.11AV
A direct determination of WR distances via stellar parallax is only possible for
γ Vel (WC8+O) using Hipparcos, and even that remains controversial (Millour
et al. 2007). Otherwise, cluster or association membership is used to provide
an approximate absolute magnitude-spectral type calibration for Milky Way WR
stars. The situation is much better for WR stars in the Magellanic Clouds, al-
though not all subtypes are represented. Typical absolute magnitudes range from
Mv = –3 mag at earlier subtypes to –6 mag for late subtypes, or exceptionally
–7 mag for hydrogen-rich WN stars. The typical spread is ±0.5 mag at individual
subtypes.
2.3 Observed distribution
Conti (1976) first proposed that a massive O star may lose a significant amount of
mass via stellar winds, revealing first the H-burning products at its surface, and
subsequently the He-burning products. These evolutionary stages are spectro-
scopically identified with the WN and WC types. This general picture has since
become known as the ‘Conti scenario’. Such stars should be over-luminous for
their mass, in accord with observations of WR stars in binary systems. Massey
(2003) provides a more general overview of massive stars within Local Group
galaxies.

Wolf-Rayet Stars 9
2.3.1 WR stars in Milky Way Wolf-Rayet stars are located in or close
to massive star forming regions within the Galactic disk. A catalogue is provided
by van der Hucht (2001). A quarter of the known WR stars in the Milky Way
reside within massive clusters at the Galactic centre or in Westerlund 1 (van der
Hucht 2006). From membership of WR stars in open clusters, Schild & Maeder
(1984) and Massey, DeGioia-Eastwood & Waterhouse (2001) investigated the
initial masses of WR stars empirically. A revised compilation is provided in
Crowther et al. (2006b).
Overall, hydrogen-rich WN stars (WNha) are observed in young, massive
clusters; their main-sequence turn-off masses (based on Meynet et al. 1994
isochrones) suggest initial masses of 65 − 110M⊙, and are believed to be core-H
burning (Langer et al. 1994; Crowther et al. 1995a). Lower-mass progenitors of
40–50M⊙ are suggested for classic mid-WN, late WC, and WO stars. Progenitors
of some early WN stars appear to be less massive still, suggesting an initial-mass
cutoff for WR stars at Solar metallicity around 25M⊙.
From an evolutionary perspective, the absence of RSGs at high luminosity and
presence of H-rich WN stars in young massive clusters suggests the following
variation of the Conti scenario in the Milky Way, i.e. for stars initially more
massive than ∼ 75M⊙
O → WN(H− rich) → LBV → WN(H− poor) → WC → SN Ic,
whereas for stars of initial mass from ∼ 40− 75M⊙,
O → LBV → WN(H− poor) → WC → SN Ic,
and for stars of initial mass in the range 25–40M⊙,
O → LBV/RSG → WN(H− poor) → SN Ib.

Wolf-Rayet Stars 11
2.3.2 WR stars in the Local Group WR stars have typically been
discovered via techniques sensitive to their unusually broad emission-line spectra,
based on objective prism searches or interference filter imaging (see Massey 2003).
Narrow-band interference filter techniques have been developed (e.g. Moffat,
Seggewiss & Shara 1985; Massey, Armandroff & Conti 1986) that distinguish
strong WR emission lines at He ii λ4686 (WN stars) and C iii λ4650 (WC stars)
from the nearby continuum. Such techniques have been applied to regions of the
Milky Way disk, the Magellanic Clouds and other nearby galaxies. An example
of this approach is presented in Figure 2 for the spiral galaxy NGC 300 (d ∼
2 Mpc). A wide-field image of NGC 300 is presented, with OB complex IV-V
indicated, together with narrow-band images centred at λ4684 (He ii 4686) and
λ4781 (continuum). Several WR stars are seen in the difference (He ii-continuum)
image, including an apparently single WC4 star (Schild et al. 2003).
It is well established that the absolute number of WR stars and their sub-
type distribution are metallicity dependent. N(WR)/N(O)∼0.15 in the relatively
metal-rich Solar Neighbourhood (Conti et al. 1983; van der Hucht 2001), yet
N(WR)/N(O)∼0.01 in the metal-deficient SMC on the basis of only 12 WR stars
(Massey, Olsen & Parker 2003) versus ∼1000 O stars (Evans et al. 2004). It
is believed that the majority of Galactic WR stars are the result of single-star
evolution, yet some stars (e.g. V444 Cyg) result from close binary evolution
(Vanbeveren et al. 1998).
Similar relative numbers of WN to WC stars are observed in the Solar Neigh-
bourhood (Hadfield et al. 2007). In contrast, WN stars exceed WC stars by a
factor of ∼5 and ∼10 for the LMC and SMC, respectively (Breysacher, Azzopardi
& Testor 1999; Massey, Olsen & Parker 2001). At low metallicity the reduced WR

12 Paul A. Crowther
population and the relative dominance of WN subtypes most likely result from
the metallicity dependence of winds from their evolutionary precursors (Mokiem
et al. 2007). Consequently, only the most massive single stars reach the WR
phase in metal-poor environments. Single stars reaching the WC phase at high
metallicity may end their lives as a RSG or WN stars in a lower metallicity en-
vironment. As such, one might suspect that most WR stars at low metallicity
are formed via binary evolution. However, Foellmi, Moffat & Guerrero (2003a)
suggest a similar WR binary fraction for the SMC and Milky Way.
Not all WR subtypes are observed in all environments. Early WN and WC
subtypes are preferred in metal-poor galaxies, such as the SMC (Massey et al.
2003), while late WC stars are more common at super-Solar metallicities, such as
M83 (Hadfield et al. 2005) Line widths of early WC and WO stars are higher than
late WC stars, although width alone is not a defining criterion for each spectral
type. The correlation between WC subclass and line width is nevertheless strong
(Torres, Conti & Massey 1986). The subtype distributions of WR stars in the
Solar Neighbourhood, LMC, and SMC are presented in Figure 3. We shall address
this aspect in Sect 4.4.
2.3.3 WR galaxies Individual WR stars may, in general, be resolved in
Local Group galaxies from ground-based observations, whilst the likelihood of
contamination by nearby sources increases at larger distances. For example, a
typical slit width of 1′′ at the 2 Mpc distance of NGC 300 corresponds to a spatial
scale of ∼10 pc. Relatively isolated WR stars have been identified, albeit in the
minority (recall Figure 2). This is even more problematic for more distant galaxies
such as M 83 where the great majority of WR stars are observed in clusters or
associations (Hadfield et al. 2005). So-called ‘WR galaxies’ are typically starburst

Wolf-Rayet Stars 13
regions exhibiting spectral features from tens, hundreds, or even thousands of WR
stars (Schaerer, Contini & Pindao 1999).
Average Milky Way/LMC WN or WC line fluxes (Schaerer & Vacca 1998) are
typically used to calculate stellar populations in WR galaxies. These should be
valid provided that the line fluxes of WR templates do not vary with environment.
However, it is well known that SMC WN stars possess weak emission lines (Conti,
Garmany & Massey 1989). In spite of small statistics and a large scatter, the
mean He ii λ4686 line luminosity of WN2–4 stars in the LMC is 1035.9 erg s−1, a
factor of five times higher than the mean of equivalent stars in the SMC (Crowther
& Hadfield 2006). The signature of WN stars is most readily seen in star forming
galaxies at He ii λ1640, where the dilution from other stellar types is at its weakest
(e.g. Hadfield & Crowther 2006). The strongest UV, optical, and near-IR lines
indicate flux ratios of I(He ii 1640)/I(He ii 4686)∼10 and I(He ii 4686)/I(He ii
1.012µm)∼6 for WN stars spanning SMC to Milky Way metallicities.
Similar comparisons for WC stars are hindered because the only carbon-sequence
WR stars at the low metallicity of the SMC and IC 1613 are WO stars. Their
emission line fluxes are systematically weaker than WC stars in the LMC and
Milky Way (Kingsburgh et al. 1995; Kingsburgh & Barlow 1995; Schaerer &
Vacca 1998). The mean C iv λλ5801-2 line luminosity of WC4 stars in the LMC
is 1036.5 erg s−1 (Crowther & Hadfield 2006). Again, detection of WC stars is
favoured via ultraviolet spectroscopy of C iv λ1550. For WC stars, the strongest
UV, optical, and near-IR lines possess flux ratios of I(C iv 1548-51)/I(C iv 5801-
12)∼6 and I(C iv 5801-12)/I(C iv 2.08µm)∼15.

14 Paul A. Crowther
2.4 Binary statistics and masses
The observed binary fraction amongst Milky Way WR stars is 40% (van der Hucht
2001), either from spectroscopic or indirect techniques. Within the low metallicity
Magellanic Clouds, close binary evolution would be anticipated to play a greater
role because of the diminished role of O star mass-loss in producing single WR
stars. However, where detailed studies have been carried out (Bartzakos, Moffat
& Niemela 2001; Foellmi, Moffat & Guerrero 2003ab), a similar binary fraction
to the Milky Way has been obtained (recall Figure 3), so metallicity-independent
LBV eruptions may play a dominant role.
The most robust method of measuring stellar masses is from Kepler’s third
law of motion, particularly for eclipsing double-lined (SB2) systems, from which
the inclination may be derived. Orbital inclinations may also be derived from
linear polarization studies (e.g. St-Louis et al. 1993) or atmospheric eclipses
(Lamontagne et al. 1996). Masses for Galactic WR stars are included in the
van der Hucht (2001) compilation, a subset of which are presented in Figure 4
together with some more recent results. WC masses span a narrow range of 9–
16M⊙, whilst WN stars span a very wide range of ∼10–83M⊙, and in some cases
exceed their OB companion, i.e. q = MWR/MO > 1 (e.g. WR22: Schweickhardt
et al. 1999). WR20a (SMSP2) currently sets the record for the highest orbital-
derived mass of any star, with ∼ 83M⊙ for each WN6ha component (Rauw et
al. 2005). As discussed above, such stars are H-rich, extreme O stars with strong
winds rather than classical H-poor WN stars. They are a factor of two lower in
mass than the apparent ∼ 150M⊙ stellar mass limit (Figer 2005), such that still
more extreme cases may await discovery. Spectroscopic measurement of masses
via surface gravities using photospheric lines is not possible for WR stars due to

Wolf-Rayet Stars 15
their dense stellar winds.
2.5 Rotation velocities
Rotation is very difficult to measure in WR stars, since photospheric features –
used to estimate v sin i in normal stars – are absent. Velocities of 200–500 km s−1
have been inferred for WR138 (Massey 1980) and WR3 (Massey & Conti 1981),
although these are not believed to represent rotation velocities, since the former
has a late-O binary companion, and the absorption lines of the latter are formed
within the stellar wind (Marchenko et al. 2004). Fortunately, certain WR stars
do harbour large scale structures, from which a rotation period may be inferred
(St-Louis et al. 2007).
Alternatively, if WR stars were rapid rotators, one would expect strong de-
viations from spherical symmetry due to gravity darkening (Von Zeipel 1924;
Owocki, Cranmer & Gayley 1996). Harries, Hillier & Howarth (1998) studied
linear spectropolarimetric datasets for 29 Galactic WR stars, from which just
four single WN stars plus one WC+O binary revealed a strong line effect, sug-
gesting significant departures from spherical symmetry. They presented radiative
transfer calculations which suggest that the observed continuum polarizations for
these stars can be matched by models with equator to pole density ratios of 2–3.
Of course, the majority of Milky Way WR stars do not show a strong linear
polarization line effect (e.g. Kurosawa, Hillier & Schulte-Ladbeck (1999).
2.6 Stellar wind bubbles
Ring nebulae are observed for a subset of WR stars. These are believed to
represent material ejected during the RSG or LBV phases that is photo-ionized

Wolf-Rayet Stars 17
and populations iteratively. Second, the problem of accounting for the effect of
millions of spectral lines upon the emergent atmospheric structure and emergent
spectrum – known as line blanketing – remains challenging for stars in which
spherical, rather than plane-parallel, geometry must be assumed due to stellar
winds, since the scale height of their atmospheres is not negligible with respect to
their stellar radii. The combination of non-LTE, line blanketing (and availability
of atomic data thereof), and spherical geometry has prevented the routine analysis
of such stars until recently.
Radiative transfer is either solved in the co-moving frame, as applied by CMF-
GEN (Hillier & Miller 1998) and PoWR (Gra¨fener, Koesterke & Hamann 2002)
or via the Sobolev approximation, as used by ISA-wind (de Koter, Schmutz &
Lamers 1993). The incorporation of line blanketing necessitates one of several
approximations. Either a ‘super-level’ approach is followed, in which spectral
lines of a given ion are grouped together in the solution of the rate equations
(Anderson 1989), or alternatively, a Monte Carlo approach is followed, which
uses approximate level populations (Abbott & Lucy 1985).
3.2 Stellar Temperatures and Radii
Stellar temperatures for WR stars are difficult to characterize, because their
geometric extension is comparable with their stellar radii. Atmospheric models
for WR stars are typically parameterized by the radius of the inner boundary R∗
at high Rosseland optical depth τRoss(∼ 10). However, only the optically thin
part of the atmosphere is seen by the observer. The measurement of R∗ depends
upon the assumption that the same velocity law holds for the visible (optically
thin) and the invisible (optically thick) part of the atmosphere.

18 Paul A. Crowther
The optical continuum radiation originates from a ‘photosphere’ where τRoss ∼
2/3. Typical WN and WC winds have reached a significant fraction of their
terminal velocity before they become optically thin in the continuum. R2/3,
the radius at τRoss = 2/3 lies at highly supersonic velocities, well beyond the
hydrostatic domain. For example, Crowther et al. (2006a) obtain R∗ = 2.9R⊙
and R2/3 = 7.7R⊙ for HD 50896 (WN4b), corresponding to T∗ = 85 kK and
T2/3 = 52 kK, respectively. In some weak-lined, early-type WN stars, this is not
strictly true since their spherical extinction is modest, in which case R∗ ∼ R2/3
(e.g. HD 9974, Marchenko et al. 2004).
Stellar temperatures of WR stars are derived from lines from adjacent ion-
ization stages of helium or nitrogen for WN stars (Hillier 1987, 1988), or lines
of carbon for WC stars (Hillier 1989). High stellar wind densities require the
simultaneous determination of mass-loss rate and stellar temperature from non-
LTE model atmospheres, since their atmospheres are so highly stratified. Metals
such as C, N and O provide efficient coolants, such that the outer wind electron
temperature is typically 8 kK to 12 kK (Hillier 1989). Figure 5 compares R∗,
R2/3, and the principal optical wind line-forming region (log ne = 1011 to 1012
cm−3) for HD 66811 (ζ Pup, O4 I(n)f), HD 96548 (WR40, WN8) and HD 164270
(WR103, WC9) on the same physical scale. Some high-ionization spectral lines
(e.g. Nv and C iv lines in WN8 and WC9 stars, respectively) are formed at
higher densities of ne ≥ 1012 cm−3 in the WR winds.
Derived stellar temperatures depend sensitively upon the detailed inclusion
of line-blanketing by iron peak elements. Inferred bolometric corrections and
stellar luminosities also depend upon detailed metal line-blanketing (Schmutz
1997; Hillier & Miller 1999). Until recently, the number of stars studied with

Wolf-Rayet Stars 19
non-LTE, clumped, metal line-blanketed models has been embarrassingly small,
due to the need for detailed, tailored analysis of individual stars using a large
number of free parameters. Hamann, Gra¨fener & Liermann (2006) have applied
their grid of line-blanketed WR models to the analysis of most Galactic WN
stars, for the most part resolving previous discrepancies between alternate line
diagnostics, which were first identified by Crowther et al. (1995b). To date, only
a limited number of WC stars in the Milky Way and Magellanic Clouds have
been studied in detail (e.g. Dessart et al. 2000; Crowther et al. 2002; Barniske,
Hamann & Gra¨fener 2007). Results for Galactic and LMC WR stars are presented
in Table 2. These range from 30 kK amongst WN10 subtypes to 40 kK at WN8
and approach 100 kK for early-type WN stars. Spectroscopic temperatures are
rather higher for WC stars, i.e. 50 kK for WC9 stars, increasing to 70 kK at WC8
and ≥100 kK for early WC and WO stars
Stellar structure models predict radii Revol that are significantly smaller than
those derived from atmospheric models. For example, R∗ = 2.7R⊙ for HD 191765
(WR134, WN6b) in Table 2, versus Revol = 0.8R⊙ which follows from hydrostatic
evolutionary models, namely
log Revol
R⊙
= −1.845 + 0.338 log L
L⊙
(1)
for hydrogen-free WR stars (Schaerer & Maeder 1992). Theoretical corrections to
such radii are frequently applied, although these are based upon fairly arbitrary
assumptions which relate particularly to the velocity law. Consequently, a direct
comparison between temperatures of most WR stars from evolutionary calcula-
tions and empirical atmospheric models is not straightforward, except that one
requires R2/3 > Revol, with the difference attributed to the extension of the su-
personic region. Petrovic, Pols & Langer (2006) established that the hydrostatic

Wolf-Rayet Stars 21
since such stars positively shy away from clusters. As a consequence, their re-
sults suggest a bi-modal distribution around 300, 000 L⊙ for early WN stars, and
1–2×106 L⊙ for all late WN stars.
From stellar structure theory, there is a mass-luminosity relation for H-free
WR stars which is described by
log L
L⊙
= 3.032 + 2.695 log M
M⊙
− 0.461
(
log M
M⊙
)2
. (3)
This expression is effectively independent of the chemical composition since the
continuum opacity is purely electron scattering (Schaerer & Maeder 1992). Spec-
troscopic luminosities need to be corrected for the luminosity that powers the
stellar wind, 12M˙v2∞, in order to determine the underlying nuclear luminosity,
Lnuc. In most cases, the recent reduction in estimates of mass-loss rates due to
wind clumping (see Sect. 4.3), plus the increase in derived luminosities due to
metal line-blanketing indicate a fairly modest corrective factor. From Table 2,
one expects typical masses of 10–15 M⊙ for hydrogen-free WR stars, which agree
fairly well with binary mass estimates (recall Fig. 4). Indeed, spectroscopically
derived WR masses obtained using this relationship agree well with binary de-
rived masses (e.g. γ Vel: De Marco et al. 2000).
3.4 Ionizing fluxes
Lyman continuum ionizing fluxes, N(LyC), are typical of mid-O stars in general
(Table 2). As such, the low number of WR stars with respect to O stars would
suggest that Wolf-Rayet stars play only a minor role in the Lyman continuum
ionization budget of young star-forming regions. H-rich late-type WN stars pro-
vide a notable exception, since their ionizing output compares closely to O2 stars
(Walborn et al. 2004). Crowther & Dessart (1998) showed that the WN6ha stars

24 Paul A. Crowther
of the Magellanic Clouds, notably the SMC (Foellmi et al 2003a). Milky Way
late-type WN stars with weak emission lines – denoted as ‘ha’ due to intrin-
sic absorption lines plus the presence of hydrogen – are universally H-rich with
XH ∼50% (Crowther et al. 1995a; Crowther & Dessart 1998).
Non-LTE analyses confirm that WN abundance patterns are consistent with
material processed by the CNO cycle in which these elements are used as cata-
lysts, i.e.
12C(p, γ)13N(e−, νe)13C(p, γ)14N(p, γ)15O(e−, νe)15N(p, α)12C
in which XN ∼1% by mass is observed in Milky Way WN stars. Carbon is highly
depleted, with typically XC ∼ 0.05%. Oxygen suffers from fewer readily accessible
line diagnostics, but probably exhibits a similarly low mass fraction as carbon
(e.g. Crowther, Smith & Hillier 1995b; Herald, Hillier & Schulte-Ladbeck 2001).
Non-LTE analysis of transition WN/C stars reveals elemental abundances (e.g.
XC ∼ 5%, XN ∼ 1% by mass) that are in good agreement with the hypothesis
that these stars are in a brief transition stage between WN and WC (Langer
1991; Crowther, Smith & Willis 1995c).
3.5.2 WC and WO stars Neither hydrogen nor nitrogen are detected in
the spectra of WC stars. Recombination line studies using theoretical coefficients
for different transitions are most readily applicable to WC stars, since they show
a large number of lines in their optical spectra. Atomic data are most reliable for
hydrogenic ions, such as C iv and O vi, so early-type WC and WO stars can be
studied most readily. Smith & Hummer (1988) suggested a trend of increasing
C/He from late to early WC stars, with C/He=0.04–0.7 by number (10% ≤ XC ≤

Wolf-Rayet Stars 25
60%), revealing the products of core He burning
4He(2α, γ)12C and 12C(α, γ)16O
although significant uncertainties remain in the rate of the latter nuclear reaction.
These reactions compete during helium burning to determine the ratio of carbon
to oxygen at the onset of carbon burning.
In reality, optical depth effects come into play, so detailed abundance determi-
nations for all subtypes require non-LTE model atmosphere analyses. Koesterke
& Hamann (1995) indicated refined values of C/He=0.1–0.5 by number (20%
≤ XC ≤ 55%), with no WC subtype dependence, such that spectral types are
not dictated by carbon abundance, contrary to suggestions by Smith & Maeder
(1991). Indeed, LMC WC4 stars possess similar surface abundances to Milky
Way WC stars (Crowther et al. 2002), for which the He ii λ5412 and C iv λ5471
optical lines represent the primary diagnostics (Hillier 1989). These recombina-
tion lines are formed at high densities of 1011 to 1012 cm−3 at radii of 3–30 R∗
(recall Figure 5). Oxygen diagnostics in WC stars lie in the near-UV, such that
derived oxygen abundances are rather unreliable unless space-based spectroscopy
is available. Where they have been derived, one finds XO ∼ 5–10% for WC stars
(e.g. Crowther et al. 2002).
Core He burning in massive stars also has the effect of transforming 14N (pro-
duced in the CNO cycle) to neon and magnesium via
14N(α, γ)18F (e−, νe)18O(α, γ)22Ne(α, n)25Mg
and serves as the main neutron source for the s-process in massive stars. Neon
lines are extremely weak in the UV/optical spectrum of WC stars (Crowther
et al. 2002), but ground-state fine-structure lines at [Ne ii] 12.8µm and [Ne iii]

26 Paul A. Crowther
15.5µm may be observed via mid-IR spectroscopy, as illustrated for γ Vel in van
der Hucht et al. (1996). Fine-structure wind lines are formed at hundreds of
stellar radii since their critical densities are of order 105 cm−3. Barlow, Roche &
Aitken (1988) came to the conclusion that neon was not greatly enhanced in γ
Vel with respect to the Solar case (∼0.1% by mass primarily in the form of 20Ne)
in γ Vel from their analysis of fine-structure lines. This was a surprising result,
since the above reaction is expected to produce ∼2% by mass of 22Ne at Solar
metallicity.
Once the clumped nature of WR winds is taken into consideration, neon is
found to be enhanced in γ Vel and other WC stars (e.g. Dessart et al. 2000).
The inferred neon mass fraction is ∼1% (see also Crowther, Morris & Smith
2006a). Meynet & Maeder (2003) note that the 22Ne enrichment depends upon
nuclear reaction rates rather than stellar models, so the remaining disagreement
may suggest a problem with the relevant reaction rates. More likely, a lower metal
content is inferred from the neon abundance than Solar metallicity evolutionary
models (Z=0.020). Indeed, if the Solar oxygen abundance from Apslund et al.
(2004) is taken into account, a revised metal content of Z=0.012 for the Sun is
impled. Allowance for depletion of heavy elements due to diffusion in the 4.5 Gyr
old Sun suggests a Solar neighbourhood metallicity of Z=0.014 (Meynet, private
communication). It is likely that allowance for a reduced CNO content would
bring predicted and measured Ne22 abundances into better agreement.
WO stars are extremely C- and O-rich, as deduced from recombination anal-
yses (Kingsburgh, Barlow & Storey 1995), and supported by non-LTE models
(Crowther et al. 2000). Further nucleosynthesis reactions produce alpha ele-

Wolf-Rayet Stars 27
ments via
16O(α, γ)20Ne(α, γ)24Mg(α, γ)28Si(α, γ)32S
producing a core which is initially dominated by 16O and 20Ne. Spitzer studies are
in progress to determine neon abundances in WO stars, in order to assess whether
these stars show evidence of α–capture of oxygen (in which case enhanced 20Ne
would again dominate over 22Ne).
4 Wind Properties
The existence of winds in early-type stars has been established since the 1960’s,
when the first rocket UV observations (e.g. Morton 1967) revealed the character-
istic P Cygni signatures of mass-loss. Electron (Thompson) scattering dominates
the continuum opacity in O and WR stars, whilst the basic mechanism by which
their winds are driven is the transfer of photon momentum to the stellar atmo-
sphere through the absorption by spectral lines. The combination of a plethora
of spectral lines within the same spectral region as the photospheric radiation
allows for efficient driving of winds by radiation pressure (Milne 1926). Wind ve-
locities can be directly measured, whilst wind density estimates rely on varying
complexity of theoretical interpretation. A theoretical framework for mass-loss
in normal hot, luminous stars was developed by Castor, Abbott & Klein (1975),
known as CAK theory, via line-driven radiation pressure.
4.1 Wind velocities
The wavelength of the blue edge of saturated P Cygni absorption profiles provides
a measure of the asymptotic wind velocity. From these wavelengths, accurate
wind velocities of WR stars can readily be obtained (Prinja, Barlow & Howarth

30 Paul A. Crowther
Rayet spectrum. Recall the comparison of ζ Pup (O4 I(n)f) to HD 96548 (WR40,
WN8) in Figure 5.
4.3 Clumping
There is overwhelming evidence in favour of highly clumped winds for WR and
O stars. Line profiles show propagating small-scale structures or ‘blobs’, which
are turbulent in nature (e.g. Moffat et al. 1988; Le´pine et al. 2000). For
optically thin lines, these wind structures have been investigated using radiation
hydrodynamical simulations by Dessart & Owocki (2005).
Alternatively, individual spectral lines, formed at ∼ 10R∗, can be used to
estimate volume filling factors f in WR winds (Hillier 1991). This technique
permits an estimate of wind clumping factors from a comparison between line
electron scattering wings (which scale linearly with density) and recombination
lines (density-squared). This technique suffers from an approximate radial density
dependence and is imprecise due to severe line blending, especially in WC stars.
Nevertheless, fits to UV, optical and IR line profiles suggest f ∼ 0.05−0.25. As a
consequence, global WR mass-loss rates are reduced by a factor of ∼ 2−4 relative
to homogeneous models (dM/dt ∝ f−1/2). Representative values are included in
Table 2. Spectroscopically derived mass-loss rates of Milky Way WN stars span
a wide range of 10−5.6 to 10−4.4M⊙ yr−1. In contrast, Galactic WC stars cover a
much narrower range in mass-loss rate, from 10−5.0 to 10−4.4M⊙ yr−1.
Independent methods support clumping-corrected WR mass-loss rates. Binary
systems permit use of the variation of linear polarization with orbital phase.
The modulation of linear polarization originates from Thomson scattering of free
electrons due to the relative motion of the companion with respect to the WR

Wolf-Rayet Stars 31
star. This technique has been applied to several WR binaries including V444 Cyg
(HD 193576=WR139, WN5+O) by St-Louis et al. (1993) and has been developed
further by Kurosawa, Hillier & Pittard (2002) using a Monte Carlo approach. For
the case of V444 Cyg, polarization results suggest a clumping factor of f ∼ 0.06.
The most likely physical explanation for the structure in WR and O star winds
arises from theoretical evidence supporting an instability in radiatively-driven
winds (Lucy & Solomon 1971; Owocki, Castor & Rybicki 1988). There is a
strong potential in line scattering to drive wind material with accelerations that
greatly exceed the mean outward acceleration. Simulations demonstrate that this
instability may lead naturally to structure. Such a flow is dominated by multiple
shock compressions, producing relatively soft X-rays. Hard X-ray fluxes from
early-type stars are believed to be restricted to colliding wind binary systems
(e.g. γ Vel: Schild et al. 2004), for which 10−7 ≤ LX/Lbol ≤ 10−6.
4.4 Metallicity dependent winds?
We shall now consider empirical evidence in favour of metallicity-dependent WR
winds. Nugis, Crowther & Willis (1998) estimated mass-loss rates for Galactic
WR stars from archival radio observations, allowing for clumped winds. Nugis &
Lamers (2000) provided empirical mass-loss scaling relations by adopting physical
parameters derived from spectroscopic analysis and/or evolutionary predictions.
For a combined sample of WN and WC stars, Nugis & Lamers (2000) obtained
log M˙/(M⊙yr−1) = −11.00 + 1.29 log L/L⊙ + 1.74 log Y + 0.47 log Z (6)
where Y and Z are the mass fractions of helium and metals, respectively.
4.4.1 WN winds Smith & Willis (1983) compared the properties of WN
stars in the LMC and Milky Way, concluding there was no significant differ-

Wolf-Rayet Stars 33
1990). Since WN stars typically exhibit CNO equilibrium abundances, there
is a maximum nitrogen content available in a given environment. For oth-
erwise identical physical parameters, Crowther (2000) demonstrated that
a reduced nitrogen content at lower metallicity favours an earlier subtype.
This is regardless of metallicity dependent mass-loss rates, and results from
the abundance sensitivity of nitrogen classification lines.
2. Additionally, a metallicity dependence of WN winds would enhance the
trend to earlier spectral subtypes. Dense WN winds at high metallicities
lead to efficient recombination from high ionization stages (e.g. N5+) to
lower ions (e.g. N3+) within the optical line formation regions. This would
not occur so effectively for low density winds, enhancing the trend towards
early-type WN stars in metal-poor environments.
Consequently, both effects favour predominantly late subtypes at high metallicity,
and early subtypes at low metallicity, which is indeed generally observed (Fig. 3).
4.4.2 WC winds It is well established that WC stars in the inner Milky
Way, and indeed all metal-rich environments, possess later spectral types than
those in the outer Galaxy, LMC and other metal-poor environments (Figure 3;
Hadfield et al. 2007). This observational trend led Smith & Maeder (1991) to
suggest that early-type WC stars are richer in carbon than late-type WC stars,
on the basis of tentative results from recombination line analyses. In this sce-
nario, typical Milky Way WC5–9 stars exhibit reduced carbon abundances than
WC4 counterparts in the LMC. However, quantitative analysis of WC subtypes
allowing for radiative transfer effects do not support a subtype dependence of
elemental abundances in WC stars (Koesterke & Hamann 1995), as discussed in
Sect 3.5.

Wolf-Rayet Stars 35
4.5 Line driving in WR winds
Historically, it has not been clear whether radiation pressure alone is sufficient
to drive the high mass-loss rates of WR stars. Let us briefly review the standard
Castor, Abbott & Klein (1975, hereafter CAK) theory behind radiatively driven
winds before addressing the question of line driving for WR stars. Pulsations
have also been proposed for WR stars, as witnessed in intensive monitoring for
the most photometrically variable WN8 star with the MOST satellite by Lefe´vre
et al. (2005). Interpretation of such observations however remains ambiguous
(Townsend & MacDonald 2006; Dorfi, Gautschy & Saio 2006).
4.5.1 Single scattering limit The combination of plentiful line opacity
in the extreme UV, where the photospheric radiation originates, allows for effi-
cient driving of hot star winds by radiation pressure (Milne 1926). In a static
atmosphere, the photospheric radiation will only be efficiently absorbed or scat-
tered in the lower layers of the atmosphere, weakening the radiative acceleration,
gline, in the outer layers. In contrast, atoms within the outer layers of an ex-
panding atmosphere see the photosphere as Doppler-shifted radiation, allowing
absorption of undiminished continuum photons in their line transitions (Sobolev
1960).
The force from optically thick lines, which provide the radiative acceleration
by absorbing the photon momentum, scale with the velocity gradient. There can
be at most ≈ c/v∞ thick lines, implying a so-called single-scattering limit
M˙v∞ ≤ L/c. (7)
Castor, Abbott & Klein (1975) and Abbott (1982) developed a self-consistent

Wolf-Rayet Stars 37
Schmutz (1997) first tackled the problem of driving WR winds from radiatively-
driven winds self-consistently using a combined Monte Carlo and radiative trans-
fer approach. He also introduced a means of photon-loss from the He ii Lyα 303A˚
line via a Bowen resonance-fluorescence mechanism. This effect led to a change
in the ionization equilibrium of helium, requiring a higher stellar luminosity. The
consideration of wind clumping by Schmutz (1997) did succeed in providing a
sufficiently strong outflow in the outer wind. Photon-loss nevertheless failed to
initiate the requisite powerful acceleration in the deep atmospheric layers. Sub-
sequent studies have supported the principal behind the photon-loss mechanism
for WR stars, although the effect is modest (e.g. De Marco et al. 2000).
The next advance for the inner wind driving was by Nugis & Lamers (2002)
whose analytical study suggested that the (hot) iron opacity peak at 105.2 K is
responsible for the observed WR mass-loss in an optically thick wind (a cooler
opacity peak exists at 104.6K). Indeed, Gra¨fener & Hamann (2005) established
that highly ionized Fe ions (Fe ix-xvii) provides the necessary opacity for ini-
tiating WR winds deep in the atmosphere for WR111 (HD 165763=WR111,
WC5). The wind acceleration due to radiation and gas pressure self-consistently
matches the mechanical and gravitational acceleration in their hydrodynamical
model. Gra¨fener & Hamann (2005) achieved the observed terminal wind velocity
by adopting an extremely low outer wind filling factor of f=0.02. This degree
of clumping is unrealistic since predicted line electron scattering wings are too
weak with respect to observations. A more physical outer wind solution should
be permitted by the inclusion of more complete opacities from other elements
such as Ne and Ar. The velocity structure from the Gra¨fener & Hamann (1995)
hydrodynamical model closely matches a typical β=1 velocity law of the form in

38 Paul A. Crowther
Eqn 8 in the inner wind. A slower β=5 law is more appropriate for the outer
wind. Indeed, such a hybrid velocity structure was first proposed by Hillier &
Miller (1999).
Theoretically, both the hydrodynamical models of Gra¨fener & Hamann (2005)
and recent Monte Carlo wind models for WR stars by Vink & de Koter (2005)
argue in favour of radiation pressure through metal lines as responsible for the
observed multiple-scattering in WR winds. The critical parameter involving the
development of strong outflows is the proximity of WR stars to the Eddington
limit, according to Gra¨fener & Hamann (2007).
Vink & de Koter (2005) performed a multiple-scattering study of WR stars
at fixed stellar temperatures and Eddington parameter. A metallicity scaling of
dM/dt ∝ Zm with m=0.86 for 10−3 ≤ Z/Z⊙ ≤ 1 was obtained. This exponent is
similar to empirical WN and O star results across a more restricted metallicity
range. Gra¨fener & Hamann (2007) predict a decrease in the exponent or late-
type WN stars at higher Γe, plus reduced wind velocities at lower metallicities.
Vink & de Koter (2005) predict that the high metal content of WC stars favour
a weaker dependence with metallicity than WN stars. A mass-loss scaling with
exponent m=0.66 for 10−1 ≤ Z/Z⊙ ≤ 1 is predicted. This is consistent with the
observed WC mass-loss dependence between the LMC and Milky Way. At low
metallicity, Vink & de Koter (2005) predict a weak dependence of m=0.35 for
10−3 ≤ Z/Z⊙ ≤ 10−1 providing atmospheric carbon and oxygen abundances are
metallicity-independent.

40 Paul A. Crowther
hole remnant, in which the system remains bound as a high mass X-ray binary
(HMXB, Wellstein & Langer 1999). The OB secondary may then evolve through
to the Wolf-Rayet phase, producing a WR plus neutron star or black hole binary.
For many years, searches for such systems proved elusive, until it was discovered
that Cyg X–3, a 4.8 hour period X-ray bright system possessed the near-IR
spectrum of a He-star (van Kerkwijk et al. 1992). Nevertheless, the nature of Cyg
X–3 remains somewhat controversial. WR plus compact companion candidates
have also been identified in external galaxies, IC 10 X–1 (Bauer & Brandt 2004)
and NGC 300 X-1 (Carpano et al. 2007).
5.2 Colliding winds
The presence of two early-type stars within a binary system naturally leads to
a wind-wind interaction region. In general, details of the interaction process are
investigated by complex hydrodynamics. Nevertheless, the analytical approach
of Stevens, Blondin & Pollock (1992) provides a useful insight into the physics of
the colliding winds.
A subset of WR stars display non-thermal (synchrotron) radio emission, in
addition to the thermal radio emission produced via free-free emission from their
stellar wind. Consequently, a magnetic field must be present in the winds of such
stars, with relativistic electrons in the radio emitting region. Shocks associated
with a wind collision may act as sites for particle acceleration through the Fermi
mechanism (Eichler & Usov 1993). Free electrons would undergo acceleration to
relativistic velocities by crossing the shock front between the interacting stellar
winds. Indeed, the majority of non-thermal WR radio emitters are known bina-
ries. For example, WR140 (WC7+O) is a highly eccentric system with a 7.9 year

42 Paul A. Crowther
lies in front of the O star. When the cavity around the O star crosses our line-
of-sight, X-ray emission is significantly less absorbed (Willis, Schild & Stevens
1995).
5.3 Dust formation
The principal sources of interstellar dust are cool, high mass-losing stars, such
as red giants, asymptotic giant branch stars, plus novae and supernovae. Dust is
observed around some massive stars, particularly LBVs with ejecta nebulae, but
aside from their giant eruptions, this may be material that has been swept up by
the stellar wind. The intense radiation fields of young, massive stars would be
expected to prevent dust formation in their local environment. However, Allen,
Swings & Harvey (1972) identified excess IR emission in a subset of WC stars,
arising from ∼1000 K circumstellar dust.
Williams, van der Hucht & The´ (1987) investigated the infrared properties
of Galactic WC stars, revealing persistent dust formation in some systems, or
episodic formation in other cases. For a single star whose wind is homogeneous
and spherically symmetric, carbon is predicted to remain singly or even doubly
ionized due to high electron temperatures of ∼104K in the region where dust
formation is observed to occur. However, the formation of graphite or more
likely amorphous carbon grains requires a high density of neutral carbon close to
the WC star.
One clue to the origin of dust is provided by WR140 (HD 193793, WC7+O)
which forms dust episodically, near periastron passage. At this phase the power
in the colliding winds is at its greatest (Williams et al. 1990). Usov (1991) ana-
lytically showed that the wind conditions of WR140 at periastron favour a strong

Wolf-Rayet Stars 43
gas compression in the vicinity of the shock surface, providing an outflow of cold
gas. It is plausible that high density, low temperature, carbon-rich material asso-
ciated with the bow-shock in a colliding wind WC binary provides the necessary
environment for dust formation.
In contrast to episodic dust formers, persistent WC systems are rarely spectro-
scopic WC binaries, for which WR104 (Ve 2-45, WC9) is the prototype identified
by Allen et al. (1972). Spectroscopic evidence from Crowther (1997) suggested
the presence of an OB companion in the WR104 system when the inner WC wind
was obscured by a dust cloud, analogous to R Coronae Borealis stars. Conclusive
proof of the binary nature of WR104 has been established by Tuthill, Monnier
& Danchi (1999) from high spatial resolution near-IR imaging. Dust associated
with WR104 forms a spatially confined stream that follows a spiral trajectory
(so-called ‘pinwheel’), analogous to a garden rotary sprinker. The cocoon stars
after which the Quintuplet cluster at the Galactic Centre was named have also
been identified as dusty WC pinwheel stars by Tuthill et al. (2006).
Binarity appears to play a key role in the formation of dust in WC stars,
providing the necessary high density within the shocked wind interaction region,
plus shielding from the hard ionizing photons. The presence of hydrogen from
the OB companion may provide the necessary chemical seeding in the otherwise
hydrogen-free WC environment. Alas, this possibility does have difficulties, since
chemical mixing between the WC and OB winds may not occur in the immediate
vicinity of the shock region. Nevertheless, it is likely that all dust forming WC
stars are binaries.

46 Paul A. Crowther
O yields below 30M⊙, and higher He yields at higher initial masses.
6.2 Evolutionary model predictions
It is possible to predict the number ratio of WR to O stars for regions of constant
star formation from rotating evolutionary models, weighted over the Initial Mass
Function (IMF). For an assumed Salpeter IMF slope for massive stars, the ratios
predicted are indeed in much better agreement with the observed distribution at
Solar metallicity (Meynet & Maeder 2003). Since the O star population is rela-
tively imprecise, the predicted WR subtype distributions are often used instead
for comparisons with observations.
From Figure 3, the Solar Neighbourhood WR subtype distribution contains
similar numbers of WC and WN stars, with an equal number of early (H-free)
and late (H-rich) WN stars. From comparison with evolutionary models, the
agreement is reasonable, except for the brevity of the H-deficient WN phase in
interior models at Solar metallicity. This aspect has been quantified by Hamann,
Gra¨fener & Liermann (2006). Synthetic WR populations from the Meynet &
Maeder (2003) evolutionary tracks predict that only 20% of WN stars should
be hydrogen-free, in contrast to over 50% of the observed sample. Non-rotating
models provide better statistics, although low luminosity early-type WN stars
are absent in such synthetic populations.
Figure 8 shows that the ratio of WC to WN stars is observed to increase with
metallicity for nearby galaxies whose WR content has been studied in detail.
One notably exception is the low-metallicity Local Group galaxy IC 10 (Massey
& Holmes 2002; Crowther et al. 2003). The WR population of IC 10 remains
controversial, since high Galactic foreground extinction favours the detection of

48 Paul A. Crowther
to have hard UV ionizing flux distributions, so they may be indirectly indicated
via the presence of strong nebular He ii λ4686 emission. Indeed, strong nebular
He ii λ4686 is observed in I Zw 18, SBS 0335-052E and other very metal-poor star
forming galaxies.
Potentially large WR populations are inferred in very metal-deficient galaxies,
depending upon the exact WR wind dependence upon metallicity (Crowther &
Hadfield 2006). Potentially, single star rotating evolutionary models are unable
to reproduce the observed WR distribution in metal-poor galaxies. Close binary
evolution might represent the primary formation channel for such metal-poor WR
stars, unless LBV eruptions provide the dominant method of removing the H-rich
envelope at low metallicity.
6.3 WR stars as SNe and GRB progenitors
The end states of massive stars have been studied from a theoretical perspective
by Heger et al. (2003). In particular, WN and WC stars are the likely pro-
genitors of (at least some) Type Ib and Type Ic core-collapse SN, respectively.
This arises because, respectively hydrogen and hydrogen/helium are absent in
such SNe (Woosley & Bloom 2006). Direct empirical evidence connecting single
WR stars to Type Ib/c SN is lacking, for which lower mass interacting binaries
represent alternative progenitors. One would need observations of ≥ 104 WR
stars in order to firmly establish a connection on a time frame of a few years,
since WR lifetimes are a few 105 yr (Meynet & Maeder 2005). Hadfield et al.
(2005) identified 103 WR stars in M83. Narrow-band optical surveys of a dozen
other high star-forming spiral galaxies within ∼10 Mpc would likely provide the
necessary statistics. However, ground-based surveys would be hindered by the

50 Paul A. Crowther
et al. 2007). If WR stars are credible progenitors of ‘magnetars’, a subset of
neutron stars that are highly magnetized (∼ 1015 G), the required WR magnetic
field would be ∼ 103 G.
Initial rapid rotation of a single massive star may be capable of circumvent-
ing an extended envelope via chemically homogeneous evolution (Maeder 1987)
if mixing occurs faster than the chemical gradients from nuclear fusion. At suf-
ficiently low metallicity, mechanical mass-loss during the WR phase would be
sufficiently weak to prevent loss of significant angular momentum permitting the
necessary conditions for a GRB (Yoon & Langer 2005). Alternatively, close binary
evolution could cause the progenitor to spin-up due to tidal interactions or the
merger of a black hole and He core within a common envelope evolution (Podsi-
adlowski et al. 2004). Both single and binary scenarios may operate. At present,
the single scenario is favoured since long-soft GRBs are predominantly observed
in host galaxies which are fainter, more irregular and more metal-deficient than
hosts of typical core-collapse supernovae (e.g. Fruchter et al. 2006).
Of course, the ejecta strongly interact with the circumstellar material, probing
the immediate vicinity of the GRB itself (van Marle, Langer & Garc´ıa-Segura
2005). This provides information on the progenitor, for which one expects ρ ∝ r−2
for WR winds (Eqn 4). A metallicity-dependence of WR winds suggests that
one would potentially expect rather different environments for the afterglows of
long-duration GRBs, depending upon the metallicity of the host galaxy. Indeed,
densities of the immediate environment of many GRBs suggest values rather
lower than typical Solar metallicity WR winds (Chevalier, Li & Frasson 2004).
Fryer, Rockefeller & Young (2006) estimate half of long GRBs apparently occur in
uniform environments, favouring a post-common envelope binary merger model.

54 Paul A. Crowther
P Cygni profiles: Spectral lines showing blue-shifted absorption plus red-shifted
emission. Characteristic of stellar outflows, associated with resonance lines of
abundant ions (e.g. C iv 1548-51A˚).
Non-LTE: Solution of full rate equations is necessary due to intense radiation
field. Radiative processes dominate over collisional processes, so Local Thermo-
dynamic Equilibrium (LTE) is not valid.
Radiatively driven winds: The transfer of photon momentum in the photo-
sphere to the stellar atmosphere through absorption by (primarily) metal spectral
lines.
Monte Carlo models: A statistical approach to the radiative transfer problem,
using the concept of photon packets.
Clumped winds: Radiatively driven winds are intrinsically unstable, producing
compressions and rarefactions in their outflows.
Collapsar: Rapidly rotating WR star undergoes core-collapse to form a black
hole fed by an accretion disk, whose rotational axis collimates the gamma ray
burst jet.
Gamma Ray Burst: Brief flash of gamma rays from cosmological distances.
Either a merger of two neutron stars (short burst) or a collapsar (long burst).
Magnetar: Highly magnetized neutron star, observationally connected with Soft
Gamma Repeaters and Anomalous X-ray Pulsars.
Reference Annotations
Gra¨fener & Hamann 2005: First solution of hydrodynamics within a realistic
Wolf-Rayet model atmosphere.
Hillier 1989 Describes the extended atmospheric structure of a WC star.

56 Paul A. Crowther
Side Bar
Luminous Blue Variables, also known as Hubble-Sandage or S Doradus type vari-
ables, share many characteristics of Wolf-Rayet stars. LBVs are widely believed
to be the immediate progenitors of classic WN stars. LBVs possess powerful
stellar winds, plus hydrogen depleted atmospheres, permitting similar analysis
techniques to be used (e.g. Hillier et al. 2001). LBVs occupy a part of the
Hertzsprung-Russell diagram adjacent to Wolf-Rayet stars. Typical spectral mor-
phologies vary irregularly between A-type (at visual maximum) and B-type (at
visual minimum) supergiants. Examples include AG Car and P Cyg in the Milky
Way, and S Dor and R127 in the LMC (e.g. Humphreys & Davidson 1994). LBVs
undergo occasional giant eruptive events – signatures of which are circumstellar
nebulae – most notably undergone by η Car during two decades in the 19th Cen-
tury (≥ 10M⊙ ejected). Giant eruptions are believed to play a major role in
the evolution of very massive stars via the removal of their hydrogen-rich enve-
lope (Davidson & Humphreys 1997; Smith et al. 2003). The origin of such huge
eruptions is unclear, since line-driven radiation pressure is incapable of producing
such outflows.
Literature Cited
Abbott DC, 1982. ApJ 263:723
Abbott DC, Bieging JH, Churchwell E, Torres AV. 1986. ApJ 303:239
Abbott DC, Conti PS. 1987. ARA&A 25:113
Abbott DC, Lucy LB. 1985. ApJ 288:679
Allen DA, Swings JP, Harvey PM. 1972. A&A 20:333
Anderson LS. 1989. ApJ 339:558

Wolf-Rayet Stars 57
Asplund M, Grevesse N, Sauval AJ, Allende Prieto C, Kiselman D. 2004. A&A
417:751
Barlow MJ, Roche PF, Aitken DA. 1988. MNRAS 232:821
Barniske A, Hamann W-R, Gra¨fener G. 2007. In Stellar Evolution at Low Metal-
licity: Mass-loss, Explosions, Cosmology, ed. HJGLM Lamers, N Langer, T
Nugis, San Francisco: ASP Conf Series 353, p.243
Bartzakos P, Moffat AFJ, Niemela VS. 2001. MNRAS 324:18
Bauer FE, Brandt WN. 2004. ApJ 601:L67
Beals CS. 1940. JRASC 34:169
Bohannan B, Crowther PA. 1999. ApJ 511:374
Bohannan B, Walborn NR. 1989. PASP 101:520
Breysacher J, Azzopardi M, Testor G. 1999. A&AS 137:117
Brown TM, Heap SR, Hubeny I, Lanz T, Lindler D. 2002. ApJ 579:L75
Cantiello M, Yoon S-C, Langer N, Livio M. 2007. A&A in press
(astro-ph/0702540)
Carpano S, Pollock AMT, Wilms J, Ehle M, Schirmer M. 2007. A&A 461:L9
Castor JI, Abbott DC, Klein RI. 1975. ApJ 195:157
Chevalier RA, Li Z-Y, Fransson C. 2004. ApJ 606:369
Chu Y-H, Treffers RR, Kwitter KB. 1983. ApJS 53:937
Clark JS, Negueruela I, Crowther PA, Goodwin SP. 2005. A&A 434:949
Conti PS, 1976, In Proc. 20th Colloq. Int. Ap. Lie´ge,, Lie´ge: University of Lie´ge,
p. 193
Conti PS, Garmany CD, Massey P. 1989. ApJ 341:113
Conti PS, Garmany CD, De Loore C, Vanbeveren D. 1983. ApJ 274:302
Conti PS, Leep ME, Perry DN. 1983. ApJ 268:228

58 Paul A. Crowther
Conti PS, Massey P. 1989. ApJ 337:251
Conti PS, Massey P, Vreux J-M. 1990. ApJ 354:359
Crowther PA. 1997. MNRAS 290:L59
Crowther PA. 2000. A&A 356:191
Crowther PA. 2007. In Stellar Evolution at Low Metallicity: Mass-loss, Explo-
sions, Cosmology eds. HJGLM Lamers, N Langer, T Nugis, San Francisco:
ASP Conf Series 353, p.157
Crowther PA, De Marco O, Barlow MJ. 1998. MNRAS 296:367
Crowther PA, Dessart L. 1998. MNRAS 296:622
Crowther PA, Dessart L, Hillier DJ, Abbott JB, Fullerton AW. 2002. A&A
392:653
Crowther PA, Drissen L, Abbott JB, Royer P, Smartt SJ. 2003. A&A 404:483
Crowther PA, Fullerton AW, Hillier DJ, Brownsberger K, Dessart L, et al. 2000.
ApJ 538:L51
Crowther PA, Hadfield LJ. 2006. A&A 449:711
Crowther PA, Hadfield LJ, Clark JS, Negueruela I, Vacca WD. 2006b. MNRAS
372, 1407
Crowther PA, Morris PW, Smith JD. 2006a. ApJ 636:1033
Crowther PA, Pasquali A, De Marco O, Schmutz W, Hillier DJ, de Koter A.
1999. A&A 350:1007
Crowther PA, Smith LJ. 1997. A&A 320:500
Crowther PA, Smith LJ, Hillier DJ. 1995b. A&A 302:457
Crowther PA, Smith LJ, Hillier DJ, Schmutz W. 1995a. A&A 293:427
Crowther PA, Smith LJ, Willis AJ. 1995c. A&A 304:269
Davidson K, Humphreys RM. 1997. ARA&A 35:1

Wolf-Rayet Stars 59
de Koter A, Schmutz W, Lamers HJGLM. 1993. A&A 277:561
De Marco O, Schmutz W, Crowther PA, Hillier DJ, Dessart L, et al. 2000. A&A
358:187
de Mello DF, Schaerer D, Heldmann J, Leitherer C. 1998. ApJ 507:199
Dessart L, Crowther PA, Hillier DJ, Willis AJ, Morris PW, van der Hucht KA.
2000. MNRAS 315:407
Dessart L, Owocki SR. 2005. A&A 432:281
Dopita MA, Bell JF, Chu Y-H, Lozinskaya TA. 1994. ApJS 93:455
Dorfi EA, Gautschy A, Saio H. 2006. A&A 453:L35
Drew JE, Barlow MJ, Unruh YC, Parker QA, Wesson R, et al. 2004, MNRAS
351:206
Eenens PRJ, Williams PM. 1994. MNRAS 269:1082
Eichler D, Usov V. 1993. ApJ 402:271
Eldridge JJ, Vink JS. 2006. A&A 452:295
Esteban C, Smith LJ, Vilchez JM, Clegg RES. 1993. A&A 272:299
Evans CJ, Howarth ID, Irwin MJ, Burnley AW, Harries TJ. 2004. MNRAS
353:601
Figer DF. 2005. Nat 434:192
Foellmi C, Moffat AFJ, Guerrero MA. 2003a. MNRAS 338:360
Foellmi C, Moffat AFJ, Guerrero MA. 2003b. MNRAS 338:1025
Fruchter AS, Levan AJ, Strolger L, Vreeswijk PM, Thorsett SE, et al. 2006. Nat
441:463
Fryer CL, Rockefeller G, Young PA. 2006. ApJ. 647:1269
Galama TJ, Groot PJ, van Paradijs J, Kouveliotou C, Augusteijn T, et al. 1998.
Nat 395:670

62 Paul A. Crowther
Langer N. 1991. A&A 248:531
Langer N. 1998. A&A 329:551
Langer N, Hamann W-R, Lennon M, Najarro F, Pauldrach AWA, Puls J. 1994.
A&A 290:819
Lefe´vre L, Marchenko SV, Moffat AFJ, Chene´ AN, Smith SR, et al. 2005. ApJ
634:L109
Leitherer C, Chapman JM, Koribalski B. 1997. ApJ 481:898
Le´pine S, Moffat AFJ, St-Louis N, Marchenko SV, Dalton MJ et al. 2000, AJ
120:3201
Levesque EM, Massey P, Olsen KAG, Plez B, Josselin E, Maeder A, Meynet G.
2005. ApJ 628:973
Lucy LB, Abbott DC. 1993. ApJ 405:738
MacFadyen AI, Woosley SE. 1999. ApJ 524:262
Maeder A. 1987 A&A 178, 159
Maeder A, Meynet G. 1994. A&A 287:803
Maeder A, Meynet G. 2001. A&A 373:555
Malesani D, Tagliaferri G, Chincarini G, Della Valle M, Fugaza D, et al. 2004.
ApJ 609, L5
Marchenko SV, Moffat AFJ, Crowther PA, Chene´ A-N, De Serres M, et al. 2004.
MNRAS 353:153
Martins F, Schaerer D, Hillier DJ. 2002. A&A 382:999
Massey P. 1980. ApJ 236:526
Massey P. 1984. ApJ 281:789
Massey P. 2002. ApJS 141:81
Massey P. 2003. ARA&A 41:15

64 Paul A. Crowther
Nugis T, Lamers HJGLM. 2002. A&A 389:162
Owocki SR, Castor JI, Rybicki GB. 1988. ApJ 355:914
Owocki SR, Cranmer SR, Gayley KG. 1996. ApJ 472:L115
Papaderos P., Izotov YI, Guseva NG, Thuan TX, Fricke KJ. 2006. A&A 454:119
Pauldrach AWA, Puls J, Kudritzki RP. 1986. A&A 184:86
Petrovic J, Pols O, Langer N. 2006. A&A 450:219
Podskadlowski Ph, Langer N, Poelarends AJT, Rappaport S, Heger A, Pfahl E.
2004. ApJ 612:1044
Prinja RK, Barlow MJ, Howarth ID. 1990. ApJ 361:607
Rauw G, Crowther PA, De Becker M, Gosset E, Naze Y, et al. 2005. A&A 432:985
Repolust T, Puls J, Herrero A. 2004. A&A 415:349
Russell SC, Dopita MA. 1990. ApJS 74:93
Schaerer D, Maeder A. 1992. A&A 263:129
Schaerer D, Contini T, Pindao M. 1999. A&AS 136:35
Schaerer D, Vacca, WD. 1998. ApJ 497:618
Schild H, Crowther PA, Abbott JB, Schmutz W. 2003. A&A 397:859
Schild H, Gu¨del M, Mewe R, Schmutz W, Raassen AJJ, et al. 2004. A&A 422:177
Schild H, Maeder A. 1984. A&A 136:237
Schmutz W. 1997. A&A 321:268
Schmutz W, Hamann W-R, Wessolowski U. 1989. A&A 210:236
Schmutz W, Leitherer C, Gruenwald R. 1992. PASP 104:1164
Schweickhardt J, Schmutz W, Stahl O, Szeifert Th, Wolf B. 1999. A&A 347:127
Shapley AE, Steidel CS, Pettini M., Adelberger KL. 2003. ApJ 588:65
Skinner SL, Zhekov SA, Gu¨del M, Schmutz W. 2002. ApJ 579:764
Smith LF. 1968a. MNRAS 138:109

Wolf-Rayet Stars 65
Smith LF. 1968b. MNRAS 140:409
Smith LF, Hummer DG. 1988. MNRAS 230:511
Smith LF, Maeder A. 1991. A&A 241:77
Smith LF, Shara MM, Moffat AFJ. 1996. MNRAS 281:163
Smith LJ, Crowther PA, Prinja RK. 1994. A&A 281:833
Smith LJ, Norris RPF, Crowther PA. 2002. MNRAS 337:1309
Smith LJ, Willis AJ. 1983. A&AS 54:229
Smith N, Gehrz RD, Hinz PM, Hoffmann WF, Hora JL, et al. 2003 AJ 125:1458
Smith N, Li W, Foley RJ, Wheeler JC, Pooley D, Chornock R, et al. 2007 ApJ
submitted (astro-ph/0612617)
Smith N, Owocki SP. 2006. ApJ 645:L45
Sobolev VV. 1960. Moving Envelopes of Stars, Cambridge, Mass: Harvard Uni-
versity Press
Springmann U. 1994. A&A 289:505
Stahl O, Wolf B, Klare G. Cassatella A, Krautter J. et al. 1983. A&A 127:49
Stevens IR, Blondin JM, Pollock AMT. 1992. ApJ 386:265
St-Louis N, Moffat AFJ, Lapointe L, Efimov YS, Shakhovskoj NM, Fox GK,
Piirola V. 1993. ApJ 410:342
St-Louis N, Chene, A-N, de la Chevrotiere A, Moffat AFJ. 2007. In Mass loss
from stars and the evolution of stellar clusters, ed. A de Koter, LJ Smith, R
Waters, San Francisco: ASP Conf Ser, in press
Torres AV, Conti PS, Massey P. 1986. ApJ 300:379
Torres-Dodgen AV, Massey P. 1988. AJ 96:1076
Townsend RHD, MacDonald J. 2006. MNRAS 368:L57
Turner DG, 1982. In IAU Symp 99: Wolf-Rayet Stars: Observations, Physics,

Wolf-Rayet Stars 67
Gunawan DY. 1997. MNRAS 289:10
Williams PM, van der Hucht KA, Pollock AMT, Florkowski DR, van der Woerd
H, Wamsteker WM. 1990. MNRAS 243:662
Williams PM, van der Hucht KA, The´ PS. 1987. A&A 182:91
Willis AJ, Crowther PA, Fullerton AW, Hutchings JB, Sonneborn G, et al. 2004.
ApJS 154:651
Willis AJ, Schild H, Stevens IR. 1995. A&A 298:549
Willis AJ, van der Hucht KA, Conti PS, Garmany CD. 1986. A&AS 63:417
Wolf CJE, Rayet G. 1867. Comptes Rendues 65:292
Woosley SE, Bloom JS. 2006. ARA&A 44:507
Woosley SE, Heger A. 2006. ApJ 637, 914
Wright AE, Barlow MJ. 1975. MNRAS 170:41
Yoon S-C, Langer N. 2005. A&A 443:643
Zahn J-P. 1992. A&A 265:115

68 Paul A. Crowther
Table 1: Wavelength-specific observed and synthetic spectral atlases (X-ray to
mid-IR) of Galactic WR stars. Predicted stellar luminosities for early-type and
late-type WR stars within each spectral window are based upon the averages of
HD 96548 (WR40, WN8, Herald, Hillier & Schulte-Ladbeck 2001), HD 164270
(WR103, WC9, Crowther, Morris & Smith 2006a) and HD 50896 (WR6, WN4b,
Morris, Crowther & Houck 2004), HD 37026 (BAT52, WC4, Crowther et al.
2002), respectively.
λ Window Lλ/Lbol Sp Type Reference
Late Early
5–25A˚ X-ray 10−7 10−7 WN Skinner et al. 2002
WC Schild et al. 2004
<912A˚ Extreme UV 39% 69% WN, WC Smith, Crowther & Norris 2002
WN Hamann & Gra¨fener 2004
912–1200A˚ Far-UV 21% 12% WN, WC Willis et al. 2004
1200–3200A˚ UV, Near-UV 33% 16% WN, WC Willis et al. 1986
3200–7000A˚ Visual 5% 2% WN, WC Conti & Massey 1989
7000–1.1µm Far-red 0.9% 0.3% WN, WC Conti, Massey & Vreux 1990
WN,WC Howarth & Schmutz 1992
1–5µm Near-IR 0.4% 0.2% WN,WC Vacca et al. 2007
5–30µm Mid-IR 0.02% 0.01% WN Morris et al. 2000
WCd van der Hucht et al. 1996

Wolf-Rayet Stars 69
Table 2: Physical and wind properties of Milky Way WR stars (LMC in paren-
thesis), adapted from Herald, Hillier & Schulte-Ladbeck (2001) and Hamann,
Gra¨fener & Liermann (2006) for WN stars, plus Barniske, Hamann & Gra¨fener
(2007), Crowther et al. (2002, 2006a) and references therein for WC stars. Abun-
dances are shown by mass fraction in percent. Mass-loss rates assume a volume
filling factor of f=0.1.
Sp T∗ logL M˙ v∞ logN(LyC) Mv Example
Type kK L⊙ M⊙yr−1 km s−1 ph s−1 mag
WN stars
3-w 85 5.34 –5.3 2200 49.2 –3.1 WR3
4-s 85 5.3 –4.9 1800 49.2 –4.0 WR6
5-w 60 5.2 –5.2 1500 49.0 –4.0 WR61
6-s 70 5.2 –4.8 1800 49.1 –4.1 WR134
7 50 5.54 –4.8 1300 49.4 –5.4 WR84
8 45 5.38 –4.7 1000 49.1 –5.5 WR40
9 32 5.7 –4.8 700 48.9 –6.7 WR105
WNha stars
6ha 45 6.18 –5.0 2500 49.9 –6.8 WR24
9ha 35 5.86 –4.8 1300 49.4 –7.1 WR108
WC and WO stars
(WO) (150) (5.22) (–5.0) (4100) (49.0) (–2.8) (BAT123)
(4) (90) (5.54) (–4.6) (2750) (49.4) (–4.5) (BAT52)
5 85 5.1 –4.9 2200 48.9 –3.6 WR111
6 80 5.06 –4.9 2200 48.9 –3.6 WR154
7 75 5.34 –4.7 2200 49.1 –4.5 WR90
8 65 5.14 –5.0 1700 49.0 –4.0 WR135
9 50 4.94 –5.0 1200 48.6 –4.6 WR103

70 Paul A. Crowther
Figure 1: Montage of optical spectroscopy of Milky Way WN and WC stars
together with the Smith (1968b) ubv and Massey (1984) r narrow-band and
Johnson UBV broad-band filters

Wolf-Rayet Stars 73
Figure 4: Stellar masses for Milky Way WR stars obtained from binary orbits
(van der Hucht 2001; Rauw et al. 2005; Villar-Sbaffi et al. 2006)

Wolf-Rayet Stars 75
Figure 6: Comparison between the Lyman continuum ionizing fluxes of early WN
CMFGEN models with fixed parameters (100 kK, logL/L⊙ = 5.48), except that
the mass-loss rates and wind velocities depend upon metallicities according to
Smith, Norris & Crowther (2002). Only the low wind density models predict a
significant flux below the He+ edge at 228A˚

76 Paul A. Crowther
Figure 7: Comparison between the mass-loss rates and luminosities of WN3–6
(squares), WC5–9 (circles) and WO (triangles) stars in the Galaxy (black), LMC
(red) and SMC (blue). Eqn 6 from Nugis & Lamers (2000) for H-poor WN (solid
line) and WC stars (dotted line) is included. Open/filled symbols refer to WN
stars with/without surface hydrogen, based upon analysis of near-IR helium lines
(Crowther 2007). Mass-loss rates are universally high if hydrogen is absent.

Wolf-Rayet Stars 77
Figure 8: Comparison between observed N(WC)/N(WN) ratio and oxygen con-
tent, for nearby spiral (red) and irregular (blue) galaxies (Massey & Johnson
1998; Crowther et al. 2003; Schild et al. 2003; Hadfield et al. 2005) together
with evolutionary model predictions by Meynet & Maeder (2005, black) and El-
dridge & Vink (2006, green). Different regions of M33 are shown (inner, middle,
outer), resulting from the strong metallicity gradient in that galaxy.