Structure and Evolution of Stars

Lecture 15

ANRV320-AA45-05 ARI 14 July 2007 16:21

3500

NIV

OIV

U u b B v V r

CIII HeII CIII

WC5

WC6

WC8

WC9

CIV

NIV

WN

WC

Rec

tifi

ed f

lux

+ C

on

stan

tR

ecti

fied

flu

x +

Co

nst

ant

Tran

smis

sio

n

Wavelength (Å)

NIII –V HeII HeII

WN4

WN6

WN7

WN8

HeI

0

0

5

0

1

10

15

20

12

2

4

6

8

10

60005500500045004000

3500 60005500500045004000

3500 60005500500045004000

Figure 1Montage 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.

www.annualreviews.org • Physical Properties of Wolf-Rayet Stars 181

Annu. R

ev. A

stro

. A

stro

phys.

2007.4

5:1

77-2

19. D

ow

nlo

aded

fro

m a

rjourn

als.

annual

revie

ws.

org

by S

TE

WA

RD

OB

SE

RV

AT

OR

Y o

n 0

3/2

4/0

8. F

or

per

sonal

use

only

.

ANRV320-AA45-05 ARI 14 July 2007 16:21

Hell 4686

off-Hell 4686

on-off image

NGC300

Figure 2Composite ESO Wide Field Imager B, V, R, and Hα image of NGC 300 obtained at theMPG/ESO 2.2-m telescope (Press Photo 18a-h/02). A box marks the OB association iv-v(40 × 40 arcsec). Narrow-band images of the association are shown on the right, centered at λ

4684 (He ii 4686, top) and λ 4781 (off-He ii 4686, middle), plus a difference image (on-off,bottom) obtained with ESO VLT/FORS2 (Schild et al. 2003). A number of WR stars showinga He ii excess (white) can be seen in the lower right image, including a WC4 star (white circle inall FORS2 images).

Consequently, only the most massive single stars reach the WR phase in metal-poorenvironments. Single stars reaching the WC phase at high metallicity may end theirlives as RSG or WN stars in a lower metallicity environment. As such, one mightsuspect that most WR stars at low metallicity are formed via binary evolution. How-ever, Foellmi, Moffat & Guerrero (2003a) suggest a similar WR binary fraction forthe SMC and Milky Way.

Not all WR subtypes are observed in all environments. Early WN and WC sub-types are preferred in metal-poor galaxies, such as the SMC (Massey, Olsen & Parker2003), whereas late WC stars are more common at super-Solar metallicities, suchas M83 (Hadfield et al. 2005). Line widths of early WC and WO stars are higherthan late WC stars, although width alone is not a defining criterion for each spectraltype. The correlation between WC subclass and line width is nevertheless strong(Torres, Conti & Massey 1986). The subtype distributions of WR stars in the SolarNeighborhood, LMC, and SMC are presented in Figure 3. We address this aspectin Section 4.4.

www.annualreviews.org • Physical Properties of Wolf-Rayet Stars 185

An

nu

. R

ev.

Ast

ro.

Ast

rop

hy

s. 2

00

7.4

5:1

77

-21

9.

Do

wn

load

ed f

rom

arj

ou

rnal

s.an

nu

alre

vie

ws.

org

by

ST

EW

AR

D O

BS

ER

VA

TO

RY

on

03

/24

/08

. F

or

per

son

al u

se o

nly

.

ANRV320-AA45-05 ARI 14 July 2007 16:21

0.9 1.20

3.0

WNWC

WR11(WC8 + 0)

WR42(WC7 + 0)

WR30(WC6 + 0)

WR151(WN5 + 0)

WR155(WN6 + 0)

WR141(WN6 + 0)

WR22(WN7ha + 0)

WR47(WN6 + 0)

WR20a(2 x WN6ha)

0.5

1.0

1.5

2.0

2.5

1.5

log MWR (M )

q =

MW

R /

Mo

1.8

Figure 4Stellar masses for MilkyWay WR stars, MWR,obtained from binaryorbits (van der Hucht2001, Rauw et al. 2005,Villar-Sbaffi et al. 2006).

these are not believed to represent rotation velocities, because the former has a late-Obinary companion, and the absorption lines of the latter are formed within the stellarwind (Marchenko et al. 2004). Fortunately, certain WR stars do harbor large-scalestructures, from which a rotation period may be inferred (St-Louis et al. 2007).

Alternatively, if WR stars were rapid rotators, one would expect strong deviationsfrom spherical symmetry owing to gravity darkening (Von Zeipel 1924; Owocki,Cranmer & Gayley 1996). Harries, Hillier & Howarth (1998) studied linear spec-tropolarimetric data sets for 29 Galactic WR stars, from which just four single WNstars plus one WC+O binary revealed a strong line effect, suggesting significantdepartures from spherical symmetry. They presented radiative transfer calculationssuggesting that the observed continuum polarizations for these stars can be matchedby models with equator-to-pole density ratios of 2–3. Of course, the majority of MilkyWay WR stars do not show a strong linear polarization line effect [e.g., Kurosawa,Hillier & Schulte-Ladbeck (1999)].

2.6. Stellar Wind BubblesRing nebulae are observed for a subset of WR stars. These are believed to representmaterial ejected during the RSG or LBV phases that is photoionized by the WR star.The first known examples, NGC 2359 and NGC 6888, display a shell morphology, al-though many subsequently detected in the Milky Way and Magellanic Clouds exhibit

188 Crowther

Annu. R

ev. A

stro

. A

stro

phys.

2007.4

5:1

77-2

19. D

ow

nlo

aded

fro

m a

rjourn

als.

annual

revie

ws.

org

by S

TE

WA

RD

OB

SE

RV

AT

OR

Y o

n 0

3/2

4/0

8. F

or

per

sonal

use

only

.

ANRV320-AA45-05 ARI 14 July 2007 16:21

20 R(Sun)

HD 96548(WN8)

HD 66811(O4 If)

HD 164270(WC9)

Figure 5Comparisons between stellar radii at Rosseland optical depths of 20 ( = R∗, orange) and 2/3( = R2/3, red ) for HD 66811 (O4 If ), HD 96548 (WR40, WN8), and HD 164270 (WR103,WC9), shown to scale. The primary optical wind line-forming region,1011 ≤ ne ≤ 1012 cm−3, is shown in dark blue, plus higher density wind material,ne ≥ 1012 cm−3, is indicated in light blue. The figure illustrates the highly extended winds ofWR stars with respect to Of supergiants (Repolust, Puls & Herrero 2004; Herald, Hillier &Schulte-Ladbeck 2001; Crowther, Morris & Smith 2006b).

evolutionary models, namely

logRevol

R⊙= −1.845 + 0.338 log

LL⊙

(1)

for H-free WR stars (Schaerer & Maeder 1992). Theoretical corrections to suchradii are frequently applied, although these are based upon fairly arbitrary assump-tions that relate particularly to the velocity law. Consequently, a direct comparisonbetween temperatures of most WR stars from evolutionary calculations and empiricalatmospheric models is not straightforward, except that one requires R2/3 > Revol, withthe difference attributed to the extension of the supersonic region. Petrovic, Pols &Langer (2006) established that the hydrostatic cores of metal-rich WR stars above∼15 M⊙ exceed Revol in Equation 1 by significant factors if mass loss is neglected, ow-ing to their proximity to the Eddington limit, !e = 1. Here, the Eddington parameter,!e , is the ratio of radiative acceleration owing to Thomson (electron) scattering tosurface gravity and may be written as

!e = 10−4.5qeL/L⊙

M/M⊙, (2)

where the number of free electrons per atomic mass unit is qe . In reality, high em-pirical WR mass-loss rates imply that inflated radii are not expected, such that thediscrepancy in hydrostatic radii between stellar structure and atmospheric models hasnot yet been resolved.

www.annualreviews.org • Physical Properties of Wolf-Rayet Stars 191

An

nu

. R

ev.

Ast

ro.

Ast

rop

hy

s. 2

00

7.4

5:1

77

-21

9.

Do

wn

load

ed f

rom

arj

ou

rnal

s.an

nu

alre

vie

ws.

org

by

ST

EW

AR

D O

BS

ER

VA

TO

RY

on

03

/24

/08

. F

or

per

son

al u

se o

nly

.

ANRV320-AA45-05 ARI 14 July 2007 16:21

SMCa

LMCb

Milky way (d< 3kpc)c

WN WC

WN WC

32 4 5 6 7 8 9 WO 4 5 6 7 8 9

32 4 5 6 7 8 9 WO

WN WC3 4 5 6 WO

4

0

5

10

15

0

5

10

15

20

25

0

55

0

30

25

20

15

10

5

0

15

10

5

0

N

N

N

Figure 3Subtype distribution of(a) Small Magellanic Cloud,(b) Large Magellanic Cloud,(c) Milky Way (d < 3 kpc)WN (blue) and WC (green)Wolf-Rayet stars, accordingto Foellmi, Moffat &Guerrero (2003a,b),Bartzakos, Moffat &Niemela (2001), van derHucht (2001). Both visualand close WR binaries areshaded (e.g., only three ofthe LMC WC4 stars areclose binaries according toBartzakos et al. 2001). Rare,intermediate WN/C starsare included in the WNsample.

2.3.3. WR galaxies. Individual WR stars may, in general, be resolved in Local Groupgalaxies from ground-based observations, while the likelihood of contamination bynearby sources increases at larger distances. For example, a typical slit width of 1 arcsecat the 2-Mpc distance of NGC 300 corresponds to a spatial scale of ∼10 pc. Relativelyisolated WR stars have been identified, albeit in the minority (recall Figure 2). Thisis even more problematic for more distant galaxies such as M83 where the greatmajority of WR stars are observed in clusters or associations (Hadfield et al. 2005).So-called WR galaxies are typically starburst regions exhibiting spectral features fromtens, hundreds, or even thousands of WR stars (Schaerer, Contini & Pindao 1999).

Average Milky Way/LMC WN or WC line fluxes (Schaerer & Vacca 1998) aretypically used to calculate stellar populations in WR galaxies. These should be validprovided 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 λ 4686line luminosity of WN2–4 stars in the LMC is 1035.9 erg s−1, a factor of five timeshigher than the mean of equivalent stars in the SMC (Crowther & Hadfield 2006).

186 Crowther

Annu. R

ev. A

stro

. A

stro

phys.

2007.4

5:1

77-2

19. D

ow

nlo

aded

fro

m a

rjourn

als.

annual

revie

ws.

org

by S

TE

WA

RD

OB

SE

RV

AT

OR

Y o

n 0

3/2

4/0

8. F

or

per

sonal

use

only

.

Neugent & Massey 2019

Figure 12.4. Kippen-

hahn diagram of the evo-

lution of a 60M⊙ star at

Z = 0.02 with mass loss.

Cross-hatched areas indi-

cate where nuclear burn-

ing occurs, and curly sym-

bols indicate convective

regions. See text for de-

tails. Figure from Maeder

& Meynet (1987).

material that was formerly in the He-burning convective core is exposed at the surface: N, which was

consumed in He-burning reactions, disappears while the products of He-burning, C and O, appear.

The last 0.2Myr of evolution this star spends as a WC star.

In general, mass-loss rates during all evolution phases increase with stellar mass, resulting in

timescales for mass loss that are less that the nuclear timescale for M ∼> 30M⊙. As a result, there

is a convergence of the final (pre-supernova) masses to ∼ 5 − 10M⊙. However, this effect is much

diminished for metal-poor stars because the mass-loss rates are generally lower at low metallicity.

12.3 Advanced evolution of massive stars

The evolution of the surface properties described in the previous section corresponds to the hydrogen

and helium burning phases of massive stars. Once a carbon-oxygen core has formed after He burning,

which is massive enough (> 1.06M⊙) to undergo carbon ignition, the subsequent evolution of the

core is a series of alternating nuclear burning and core contraction cycles in quick succession (see

Fig. 12.5). Due to strong neutrino losses (see Sect. 12.3.1) the core evolution is sped up enormously:

∼< 103 years pass between the onset of carbon burning until the formation of an iron core. During

this time the mass of the C-O core remains fixed. Furthermore, the stellar envelope hardly has time

to respond to the rapid changes in the core, with the consequence that the evolution of the envelope

is practically disconnected from that of the core. As a result the position of a massive star in the HR

diagram remains almost unchanged during carbon burning and beyond. We can thus concentrate on

the evolution of the core of the star from this point onwards.

12.3.1 Evolution with significant neutrino losses

Neutrinos are produced as a by-product of some nuclear reactions. However, even in the absence of

nuclear reactions, weak interaction processes can result in spontaneous neutrino production at high

T and high ρ. Owing to the fundamental coupling of the electromagnetic and weak interactions, for

each electronic process that emits a photon, there is a small but finite probability (of the order of

172

Table 12.1. Properties of nuclear burning stages in a 15M⊙ star (from Woosley et al. 2002).

burning stage T (109 K) ρ (g/cm3) fuel main products timescale

hydrogen 0.035 5.8 H He 1.1 × 107 yr

helium 0.18 1.4 × 103 He C, O 2.0 × 106 yr

carbon 0.83 2.4 × 105 C O, Ne 2.0 × 103 yr

neon 1.6 7.2 × 106 Ne O, Mg 0.7 yr

oxygen 1.9 6.7 × 106 O, Mg Si, S 2.6 yr

silicon 3.3 4.3 × 107 Si, S Fe, Ni 18 d

Following carbon exhaustion in the centre, the core – which is now composed mostly of O and

Ne – contracts on its neutrino-accelerated Kelvin-Helmholtz timescale and carbon burning continues

in a convective shell around this core. Several such convective shell-burning episodes can occur in

succession, as shown in Fig. 12.7, their number depending on the mass of the star. The discrete nature

of these shell burning events can also produce a discrete (discontinuous) dependence of the final state

of the core on the initial stellar mass.

In stars with masses up to about 11M⊙ (C-O core masses less than 1.38M⊙) carbon burning

proceeds somewhat differently. The C-O core becomes partially degenerate and neutrino losses ef-

fectively cool the centre of the star, so that carbon does not ignite in the centre but in an off-centre

shell in a mildly degenerate flash (analogous to, but much less violent than the He flash in low-mass

stars). After one or more of these mild carbon flashes the burning front moves to the centre and

stable carbon burning in a convective core follows. After carbon burning, the O-Ne core becomes

degenerate and no further nuclear fuels are ignited. The structure of these stars is then very similar to

those of AGB stars with degenerate CO cores, discussed in Ch. 11, and such stars have been named

super-AGB stars. The fate of such stars is uncertain and depends on whether the O-Ne core can reach

the Chandrasekhar limit by shell burning. If this is the case the core eventually collapses, producing a

supernova explosion. On the other hand, if mass loss is strong enough to remove the envelope before

the Chandrasekhar limit is reached, the final remnant is a O-Ne white dwarf.

Neon and oxygen burning

In stars with masses ∼> 11M⊙, once the temperature in the contracting O-Ne core reaches ≈ 1.5×109 K

neon is ‘burned’ into oxygen and magnesium by a combination of photo-disintegration and α-capture

reactions (Sec. 6.4.5). Neon burning always occurs in a convective core, regardless of stellar mass. By

this time increased neutrino losses have accelerated the rate of evolution by a factor ∼ 103 compared

to the carbon-burning phase (see Fig. 12.6). The duration of the neon-burning phase is therefore very

short, of order 1 year. Neon burning then shifts to a shell, as was the case for carbon burning, but in

this case the time left until the next fuel is ignited is so short that no significant shell burning occurs.

When T9 ≈ 2.0 oxygen is ignited in the core by means of the16O+16O reaction, producing mostly

28Si and 32S with a significant admixture of other isotopes (see below). Oxygen burning also occurs in

a convective core, with a typical mass of ≈ 1.0M⊙ (see Fig. 12.7). The duration is somewhat longer

than that of neon burning, of order 1 year, despite the higher neutrino loss rate at this stage. The

reasons for this longer duration are the large oxygen mass fraction, ∼ 0.7, and the large energy gain

per gram compared to Ne burning. Similar to carbon burning, after central oxygen burning a number

of convective oxygen-burning shells appears in quick succession. By this point the remaining time

until core collapse (< 1 yr) is so short that the overlying helium- and carbon-burning shells remain

frozen into the stellar structure.

176

15

Sprin

g 20

09 Example of spectral analysis: hot starsO4 supergiant �

Puppis

Pauldrach, Puls,

Kudritzki

et al. 1994,

SSRev, 66, 105

UV spectrum

Stellar winds

Wolf-Rayet (WN11) star in NGC 300 at 2 Mpc distance

Bresolin et al. 2002

1 INTRODUCTION 10

The photon is absorbed and reemitted again

=

WIND

The principle of radiatively driven winds

Photons

STAR

OBSERVER

totally transferred momentum

electron

nucleus

Figure 2: Principle of radiative line-driving (see text).

�

r

r + dr

v + dv

v

L�

Conc

epci

on 2

007

46

complex atomic models for O-stars (Pauldrach et al., 2001)

Munich solar eclipse, 1999

4 P CYGNI PROFILES 23

Figure 14: Response of theoretical P Cygni profiles to a variation of ion density (line strength)and velocity field. See text.

In all figures it was assumed that the ion density varies proportional to the total wind density.For different assumptions on this relation, completely different line shapes can arise, as you willsee during your lab work.

NOTE: From a certain threshold on, the profiles are no longer changing when the ion density isfurther increased. This is the reason to call such profiles saturated !

Doublets: superposition of two profiles

A closer look at the observed P Cygni profiles (e.g., Sect. 3) reveals that all but the Niv λ1720line consist of two components. This is because most of the UV resonance lines from a certain ionhave two different ground states7 with very similar energies (both of which can be radiativelyexcited). This means, that these profiles consist of two superimposed P Cygni components,called doublets. This fact has to be accounted for in the simulation and analysis, of course.

Regarding the determination of v∞, this quantity still can be read off the blue edge of thecomposite profile. One just has to translate the frequency shift with respect to the transition

7due to fine-structure splitting

!"#$%%&'&#(

!!"# " !!!"#

$$!

! " !!$$!

!!"# " !!!"#

$

$!

#%&& " "!

%&&!$$!"!!! !"#$ ! ! $

$!"!!!#!!

!$ " !$!!$$!"!!!

!

)**+#,-./01

2345&#67&-"#-$%8,-./0/

93%:,-2345&#67&-"#-$%8,-.//;

7!$<

%+=-7

%+=->?7@

ABA:3>

ACA:3>

%+=-!?#@

ABA:3>

ACA:3>

%+=-##:

!max

3 Jul 2003 22:16 AR AR194-AA41-02.tex AR194-AA41-02.sgm LaTeX2e(2002/01/18) P1: GJB

MASSIVE STARS IN THE LOCAL GROUP 33

Figure 5 A comparison is shown between the observed mass-loss rates determined by Puls

et al. (1996) and that predicted by the empirical fit of de Jager et al. (1988) (open symbols)

and the theoretical formalism of Vink et al. (2001) ( filled symbols). Circles denote Galactic

stars, squares denote LMC stars, and triangles denote SMC stars.

the situation is more complicated than a simple power-law scaling, with a thresh-

old effect at low Z. However, over the metallicity range usually considered (i.e.,

SMC to solar neighborhood), a scaling with (Z/Z⇥)0.5 turns out to be a good

approximation, at least for O-type stars (see his table 2). However, Vink et al.

(2001) concludes that the mass-loss rates scale as (Z/Z⇥)0.7 when one includes

the dependence of the terminal velocity with metallicity.

Further observational checks would be useful on mass-loss rates, particularly at

higher metallicities. So far, mass-loss rates have been derived in a consistent man-

ner only for Milky Way, LMC, and SMC stars, which cover a range of metallicity

of a factor of 3.7 (Table 1). This could be pushed to a factor of �15 by studiesof massive stars throughout the Local Group, and probe regions that are higher in

metallicity than the solar neighborhood, e.g., in the Andromeda Galaxy. Fledgling

efforts in this direction have been taken by Bianchi et al. (1994, 1996), Smartt

et al. (2001), Urbaneja et al. (2002), and even beyond the Local Group by Bresolin

et al. (2002a). (See also Prinja & Crowther 1998, who reanalyze much of these

data, but stop short of deriving mass-loss rates.) The UV observations needed to

measure the terminal velocities are well within the reach of HST, and the optical

data (needed to determine the other stellar parameters) are obtainable with 8-m

class ground-based spectroscopy.

An

nu

. R

ev

. A

stro

. A

stro

ph

ys.

20

03

.41

:15

-56

. D

ow

nlo

ad

ed

fro

m w

ww

.an

nu

alr

ev

iew

s.o

rgb

y C

am

bri

dg

e U

niv

ers

ity

on

07

/18

/11

. F

or

pers

on

al

use

on

ly.

Massey 2003