Lecture 7

Evolution of MassiveStars on the Main Sequence

and During Helium Burning - Basics

Key Physics and Issues

• Nuclear Physics

• Equation of state

• Opacity

• Mass loss

• Convection

• Rotation (magnetic fields)

• Binary membership

• Explosion physics

• Evolution in HR diagram

• Nucleosynthesis

• Surface abundances

• Presupernova structure

• Supernova properties

• Remnant properties

• Rotation and B-field of pulsars

Generalities:

Because of the general tendency of the interior temperature of stars to increase with mass, stars of just over one solar mass are chiefly powered by the CNO cycle(s) rather than the pp cycle(s). This, plus the increasing fraction of pressure due to radiation,makes their cores convective. The opacity is dominantly due to electron scattering. Despite their convective cores, the overallmain sequence structure can be crudely represented as an n = 3 polytrope.

Massive Stars

Following eq. 2- 286 through 2-289 in Clayton it is easy to show that for

Pgas ≡βPtotal =NAkTρ

μPrad =

13

aT4 = (1- β)Ptotal

that

Ptotal = NAkμ

⎛⎝⎜

⎞⎠⎟

43a

1−ββ

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

1/3

ρ4 /3

That is, a star that has β constant throughout its mass will be an n = 3 polytrope

It is further not difficult to show that a sufficient condition for β = constant in a radiative region is that

That is, if the energy generation per unit mass interior to r times the local opacity is a constant, β will be a constant and the polytrope will have index 3.

This comes from combining the equation for radiativeequilibrium with the equation for hydrostatic equilibriumand the definition of β

On the other hand, convective regions (dS = 0), will have n between 1.5 and 3 depending upon whetherideal gas dominates the entropy or radiation does.

Ideal gas (constant composition):

Radiation dominated gas:

P = const ×ρ ×T ∝ρ ×ρ2/3 = ρ5/3

since T3/2

ρ= constant

γ = n+1n

⇒ n = 32

P = 1

3aT4 ∝ρ4/3

since T3

ρ= constant

γ = n+1n

⇒ n = 3

Half way through hydrogen burning

For “normal” mass stars, ideal gas entropyalways dominates on the main sequence, butfor very massive stars Srad and Sideal can become comparable.

So massive stars are typically a hybrid polytrope with their convective cores having 3 > n > 1.5 and radiative envelopes with n approximately 3.

Overall n = 3 is not bad.

Then

1 - βμ2β 2 =

M18 Me

⎛

⎝⎜⎞

⎠⎟ Clayton 2-307

μ= (1+Zi ) Yi∑⎡⎣ ⎤⎦−1

=0.84 for 35% H, 65% He

For very large M, μβ ∝ M -1/2; for 18 Me β ≈0.80

Near the surfacethe density declinesprecipitously makingradiation pressuremore important.

1−β= fraction of the pressure from radiation

inner ~5 Msun is convective

κL

M∝(1 − β ) decreases as M(r) ↑

because L is centrally concentrated,

so β increases with M(r)

inner ~8 Msun convective

Convection plus entropy from ideal gasimplies n = 1.5

d lnρdlnP

=1γ

γ ≈5 / 3 for ideal gas at constant entropy

40% of the mass

Most of the mass and volume.

d lnρdlnP

=1γ

γ ≈4 / 3 for standard model

(with β = const) in radiative regions

For the n=3 polytrope

Tc =4.6 ×106 K μβ

MMe

⎛

⎝⎜⎞

⎠⎟

2 /3

ρc1/3

For stars on the main sequence and half way through

hydrogen burning, μ ≈ 0.84 and, unless the star is very massive,β ≈ 0.8 - 0.9. Better values are given in Fig 2-19 of Clayton. β declines slowly with mass

The density is not predicted from first principles, but detailed models

(following page) give ρc ≈1010 Me

M⎛⎝⎜

⎞⎠⎟ gm cm--3,So

Tc ≈3.9 ×107 βM

10Me

⎛

⎝⎜⎞

⎠⎟

1/3

K

9 3.27 9.16 2.8 12 3.45 6.84 7.0 15 3.58 5.58 13 20 3.74 4.40 29 25 3.85 3.73 50 40 4.07 2.72 140 60(57) 4.24 2.17 290 85(78) 4.35 1.85 510 120(99) 4.45 1.61 810

M Tc/107 ρC L/1037

All evaluated in actual models ata core H mass fraction of 0.30for stars of solarmetallicity.

ρc decreases with mass as a general consequence of the fact that

Tc3

ρ c

∝ M 2β 3μ 3 and H burning happens at a relatively constant

temperature. Until about 40 Me , the density decreases roughly

as M-1. After that it decreases more slowly. Recall β ∝ M-1/2 for

very large masses

μ ≈0.8

L ∝ M2.5

Homology

if eleectron scatteringconstκ =

n ~ 18

From homology relations on the previous page and takingκ= constant (electron scattering), an ideal gas equation of state, and n = 18, one obtains:

where μ was defined in lecture 1.

If radiation pressure dominates, as it begins to for very largevalues of mass, 1/ 42

1/ 21

2

( )

hence

(lower end) to a constant (high end)

o o o

M ML T

MM

L

κ κ ε

τ −

: :

: :

100M M> e

Overall L ~ M2.5

Competition between the p-pCompetition between the p-pchain and the CNO Cycle chain and the CNO Cycle

The slowest reaction is 14N(p,γ)15O. For temperatures near 2 x 107 K.1/3

2 2

n

14 1

14 17 1-2

T n = 4.248 60.03 0.020

n =18

nuc

τε τ

⋅

+

⎛ ⎞⎜ ⎟

∝ = =⎜ ⎟⎜ ⎟⎝ ⎠

(More on nucleosynthesis later)

The Primary CNO Cycle

In a low mass star

CNO tri-cycle

3 4 5 6 7 8 9neutron number

C(6)

N(7)

O(8)

F(9)

Ne(10)

CN cycle (99.9%)

O Extension 1 (0.1%)

O Extension 2

O Extension 3

All initial abundances within a cycle serve as catalysts and accumulate at largest τ

Extended cycles introduce outside material into CN cycle (Oxygen, …)

Mainly of interest for nucleosynthesis

In general, the rates for these reactions proceed through knownresonances whose properties are all reasonably well known.

There was a major revision of the rate for 14N(p,γ)15O in 2001 by Bertone et al., Phys. Rev. Lettr., 87, 152501.The new rate is about half as large as the old one, so the main sequence lifetime of massive stars is longer

(but definitely not linear in the reciprocal rate). Mainly affected globular cluster ages (0.7 to 1 Gy increase in lifetime due to the importance of the CNO cycle at the end of the MS life and during thick H shell burning).

Equation of state

Well defined if tedious to calculate up to the point of iron core collapse.

4

A

Electrons - the hard part - can have arbitrary relativity and degeneracy

I

on

1R

s - ideal gas - P = N

(solve

adiat

Ferm

ion P =

i integrals). At high T

3

k T

aT

ρμ

11 -3Bεyond 10 γ cμ - nεuτρino τρappinγ, nuclεaρ

μ usτ includε

foρcε, nuclεaρ εxciτεd

εlεcτρon-posiτρon

sτaτεs, coμ p

pa

lε

iρs

x coμ posiτion, ετc

Opacity

In the interior on the main sequence and within the heliumcore for later burning stages, electron capture dominates.

In its simplest form:

κ e =nes Th

ρ=ρNA Yes Th

ρ=Ye(NA s Th)

s Th=8p3

e2

mec2

⎛

⎝⎜

⎞

⎠⎟

2

κ e=0.40 Ye cm2 gm-1

Recall that for 75% H, 25% He, Ye=0.875, so κ e =0.35

For He and heavier elements κ e ≈ 0.20.

20

2

2 2

2 261 ...

Klein-Nish

10

ina

5

KN The e

h h

m c m c

h Hz

n

n

ns s⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥= − + +⎜

<<

⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

There are correction terms that must be applied to κes especially at high temperature and density

1) The electron-scattering cross section and Thomson cross section differ at high energy. The actual cross section is smaller.

2) Degeneracy – at high density the phase space for the scattered electron is less. This decreases the scattering cross section.

3) Incomplete ionization – especially as the star explodes as a supernova. Use the Saha equation.

4) Electron positron pairs may increase κ at high temperature.

Effects 1) and 2) are discussed by

Chin, ApJ, 142, 1481 (1965) Flowers & Itoh, ApJ, 206, 218, (1976) Buchler and Yueh, ApJ, 210, 440, (1976) Itoh et al, ApJ, 382, 636 (1991) and references therein

Electron conduction is not very important in massive stars but isimportant in white dwarfs and therefore the precursors to Type Iasupernovae

Itoh et al, ApJ, 285, 758, (1984) and references therein

For radiative opacities other than κes, in particular κbf and κbb,

Iglesias and Rogers, ApJ, 464, 943 (1996)

Rogers, Swenson, and Iglesias, ApJ, 456, 902 (1996)

see Clayton p 186 for a definition of terms.“f” means a continuum state is involved

During hydrogen

burning

Note centrally concentratednuclear energy generation.

convective

Convection

All stellar evolution calculations to date, except for brief snapshots,have been done in one-dimensional codes.

In these convection is universally represented using some variationof mixing length theory.

Caveats and concerns:

• The treatment must be time dependent

• Convective overshoot and undershoot

• Semiconvection (next lecture)

• Convection in parallel with other mixing processes, especially rotation

• Convection in situations where evolutionary time scales are not very much longer than the convective turnover time.

Kuhlen, Woosley, and Glatzmaier exploried the physics of stellar convectionusing 3D anelastic hydrodynamics.

The model shown is a 15 solar mass star half way through hydrogen burning. For nowthe models are not rotating, but the code includes rotation and B-fields. (Previouslyused to simulate the Earth’s dynamo).

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

from Kippenhahn and Wiegert

Convective structure

Note growth of the convective core with M

2

2

2

The adiabatic condition can be written in terms of

the temperature as

01

This defines (see Clayton p 118)

dP dT

P T

Γ+ =

−Γ

Γ

2For an ideal gas 5 / 3, but if radiation is

included the expression is more complicated

Γ =

Convective instability is favored by a large fraction of radiationpressure, i.e., a small value of β

star 2

2

2 22

2 2

32 24 3 4 5 (Clayton 2-129)

24 18 3 3 3

1 1For =1

11 convection

0.4 0.25

, 1- ; for = 0, 1-

f or

dT T dP

dr P dr

β ββ β

β β

− −Γ = < Γ <

− −

⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟Γ Γ⎝ ⎠

⎛ ⎞⎛ ⎞ ⎛ ⎞> − ⇒⎜ ⎟⎜ ⎟ ⎜ ⎟Γ⎝ ⎠ ⎝ ⎠⎝ ⎠

⎝ ⎠

2

1 = 0.8 1- 0.294 = β

⎛ ⎞⎜ ⎟Γ⎝ ⎠

So even a 20% decrease in β causes a substantial decrease in thecritical temperature gradient necessary for convection.

β decreases with increasing mass. Hence more massive stars are convective to a greater extent.

M

Me

=18.0(1−β)1/ 2

μ2β 2

⎛

⎝⎜⎞

⎠⎟ ⇒ M ↑⇒ β ↓

9 3.27 9.16 2.8 0.26 12 3.45 6.84 7.0 0.3015 3.58 5.58 13 0.3420 3.74 4.40 29 0.3925 3.85 3.73 50 0.4340 4.07 2.72 140 0.5360(57) 4.24 2.17 290 0.6085(78) 4.35 1.85 510 0.66120(99) 4.45 1.61 810 0.75

c

Several things to note:

a) Increasing size of convective core

12 - 15 M 20 - 25 M 60 - 85 M

d ln Tb) 0.17 0.1

d ln3

M

e e e

2 3

3C

4 1 Homology gives ( =1) to ( =0)

21 21c) Polytropic index varies from >1.5 to 3.0 as M increases. n = 3 not bad overall

M

d) constant, though n doe

0.19 0.

0.

T

48

10

0

C

β β

ρ β

= =

≈ 3s vary significantly; in fact, constantc

c

MTρ

≈

M Tc/107 ρC L/1037 Q

conv core

All evaluated ata core H mass fraction of 0.30for stars of solarmetallicity.

First 3 Burning Stages in the Life of a Massive Star

0

blue = energy generationpurple = energy lossgreen = convection

H-burn

He-burn

Surface convection zone

The convective core shrinks during hydrogen burning

During hydrogen burning the mean atomic weight is increasing fromnear 1 to about 4. The ideal gas entropy is thus decreasing. As the central entropy decreases compared with the outer layers of the starit is increasingly difficult to convect through most of the star’s mass.

For an ideal gas plus radiation:(see Clayton p. 123)

μ =1

2 for pure hydrogen;

4

3 for pure helium

change in entropy during Heburning is small

The convective core grows during helium burning.

During helium burning, the convective core grows largely because the mass of the helium core itself grows. This has two effects:

a) As the mass of the core grows so does its luminosity, while the radius of the convective core stays nearly the same (density goes up). For a 15 solar mass star:

10 37 -1 38 -1

He mass fraction Radius conv core Lum conv core Lum star

1 0.87 x 10 cm 3.2 x 10 erg s 2.16 x 10 erg s

0. 10 37 -1 38 -15 1.04 x 10 cm 6.8 x 10 erg s 2.44 x 10 erg s

The rest of the luminosity is coming from the H shell..

3.0 M

3.6 Me

e

blue = energy generationpurple = energy lossgreen = convection

H-burn

He-burn

Surface convection zone

b) As the mass of the helium core rises its β decreases.

3 42 3 2 31/ 3 1

A

T aTM M

N kT

ββ βρ ρ β

−: : :

The entropy during helium burning also continues to decrease,and this would have a tendency to diminish convection, but the β and L effects dominate and the helium burning convective coregrows until near the end when it shrinks both due to the decreasing central energy generation.

This decrease in β favors convection.

This growth of the helium core can have two interesting consequences:

• Addition of helium to the helium convection zone at late time increases the O/C ratio made by helium burning

• In very massive stars with low metallicity the helium convective core can grow so much that it encroaches on the hydrogen shell with major consequences for stellar structure and nucleosynthesis.

Initially the entropy is nearly flat in a zero age main sequence starso just where convection stops is a bit ambiguous. As burning proceeds though and the entropy decreases in the center, the convective extentbecomes more precisely defined. Still one expects some overshootmixing.

A widely adopted prescription is to continue arbitrarily the convective mixing beyond its mathematical boundary by some fraction,a, of the pressure scale height. Maeder uses 20%. Stothers and Chin(ApJ, 381, L67), based on the width of the main sequence, arguethat a is less than about 20%. Doom, Chiosi, and many Europeangroups use larger values. Woosley and Weaver use much less. Nomotouses none.

Convective Overshoot Mixing

Overshoot mixing:

Overshoot mixing has many effects. Among them:

• Larger helium cores

• Higher luminosities after leaving the main sequence

• Broader main sequence

• Longer lifetimes

• Decrease of critical mass for non-degenerate C-ignition. Values as low as 5 solar masses have been suggested but are considered unrealistic.

Overshoot mixing:

DeMarque et al, ApJ, 426, 165, (1994) – modeling main sequence widths in clusters suggests a = 0.23

Woo and Demarque, AJ, 122, 1602 (2001) – empirically for low mass stars, overshoot is < 15% of the core radius. Core radius a better discriminant than pressure scale height.

Brumme, Clune, and Toomre, ApJ, 570, 825, (2002) – numerical 3D simulations. Overshoot may go a significant fraction of a pressure scale height, but does not quickly establish an adiabatic gradient in the region.

Differential rotation complicates things and may have some of the same effects as overshoot.

See also http:/www.lcse.umn.edu/MOVIES

Metallicity affects the evolution in four distinct ways:

• Mass loss• Energy generation (by CNO cycle)• Opacity• Initial H/He abundance

( )

16/13 1/13o

2/1

c

5

c

decreases if Z decreases L

T

For example, 1 M at half hydrogen depletion

Z =

log T 7.

L L 2

0.02 Z = 0.00

202 7.2

1

38

o

o o

κ κ ε

κ ε

−

−

e

e

:

:

.0Le

lower main sequence:

Because of the higher luminosity, the lifetime of the lowermetallicity star is shorter (it burns about the same fraction of its mass).

METALLICITY

Upper main sequence:

The luminosities and ages are very nearly the same because theopacity is, to first order, independent of the metallicity. The central temperature is a little higher at low metallicity because of the decreased abundance of 14N to catalyze the CNO cycle. For example in a 20 solar mass star at XH = 0.3

0.02 0.001

log 7.573 7.647

log / 4.867 4.872

0.390 0.373

/ 19.60 19.92 (mass loss)

c

cc

Z Z

T

L L

Q

M M

= =

e

e

MS

MS

ln -2.9 -2.6 -2.0

1 - 2 2 - 4 4 - 9

12 - 15

ln

ln-1.4 -1.2

20 - 25

-0.3ln

85 - 120

d

d

d M

M

M

M

d

τ

τ

Schaller et al. (1992)

There is a slight difference in the lifetime onthe upper main sequence though because of the different initial helium abundances. Schaller et al.used Z = 0.001, Y = 0.243, X=0.756 and Z = 0.02,Y = 0.30, X = 0.68.

So for the higher metallicity there is less hydrogen to burn.

But there is also an opposing effect, namely mass loss.For higher metallicity the mass loss is greater and the star has a lower effective mass and lives longer.

Both effects are small unless the mass is very large.

For helium burning, there is no effect around 10 solar mases,but the higher masses have a longer lifetime with highermetallicity because mass loss decreases the mass.

For lower masses, there is a significant metallicity dependencefor the helium burning lifetime. The reason is not clear.Perhaps the more active H-burning shell in the solarmetallicity case reduces the pressure on the helium core.

For 2 solar masses half way through helium burning

Z = 0.001 Z = 0.02

log Tc 8.089 8.074

a small difference but the helium burning rate goes asas a high power of T at these temperatures. The above numbers are more than enough to explain the difference in lifetime.

Zero and low metallicity stars may end their lives as compact blue giants – depending upon semiconvectionand rotationally induced mixing

For example, Z = 0, presupernova, full semiconvection

a) 20 solar masses R = 7.8 x 1011 cm Teff = 41,000 Kb) 25 solar masses R=1.07 x 1012cm Teff = 35,000 K

Z = 0.0001 ZO

a) 25 solar masses, little semiconvection R = 2.9 x 1012 cm Teff = 20,000 Kb) 25 solar masses, full semiconvection R = 5.2 x 1013 cm Teff= 4800 K

Caveat: Primary 14N production

Caution - rotationally induced mixing changes these results

As radiation pressure becomes an increasingly dominant part ofthe pressure, β decreases in very massive stars.

This implies that the luminosity approaches Eddington.E. g. in a 100 solar mass star L = 8.1 x 1039 erg s-1, or LEdd/1.8. But β still is 0.55.

Very massive stars

In regions where the star is supported entirely by radiation pressure

and the radiation is diffusing the luminosity is the Eddington

luminosity.

The stellar structure equation for the radiative temperature gradient is

dT

dr=−

34ac

κρT 3

L(r)4pr2

implies

L(r) =cκρ

4pr2 ddr

1

3aT 4⎛

⎝⎜⎞

⎠⎟

if the pressure is givenby

Prad =(1-β)Ptot

where β = Pideal /Ptot, then

L(r)=4pr2cκρ

ddr

(1−β)Ptot

which if β is a constant gives (with hydrostatic equilibrium)

L(r)=4pr2cκρ

(1−β)GM(r)ρ

r2=(1−β)

4pGMcκ

.

If β=0, this is the Eddington luminosity

Massive stars are alwaysradiative near their surfaces,even though they can becomeconvective throughout mostof their mass.

This suggests that massive stars, as β approaches 0, willapproach the Eddington luminosity with L proportional to M.

In fact, except for a thin region near their surfaces, such stars will be entirely convective and will have a total binding energythat approaches zero as β approaches zero. But the calculation appliesto those surface layers which must stay bound.

Completely convective stars with a luminosity proportionalto mass have a constant lifetime, which is in fact the shortestlifetime a (main sequence) star can have.

8

MS

3 -1

18

/ 2.1 mill

4 0.34

ion y

1.47 10 erg s

4.8 10 erg/

ea

g

rsnuc Edd

Edd

nuc

GMc ML

M

q

q M Lτ

pκ κ

⎛ ⎞⎛ ⎞= = × ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

=

=

×

=

e

(exception supermassive stars over 105 solar masses – post-Newtonian gravity renders unstable on the main sequence)

Similarly there is a lower bound for heliumburning. The argument is the same except oneuses the q-value for helium burning to carbon and oxygen.

One gets 7.3 x 1017 erg g-1 from burning 100% He to 50% each C and O.

Thus the minimum (Eddington) lifetime for helium burning is about 300,000 years.

Limit

Limit

Since Γ ~ 4/3, such stars are loosely bound (total energy muchless than gravitational or internal energy) and are subject to large amplitude pulsations. These can be driven by eitheropacity instabilities (the κ mechanism) or nuclear burning instabilities (the ε mechanism). β is less than 0.5 for suchstars on the main sequence, but ideal gas entropy still dominates.

For solar metallicity it has long been recognized that such stars(say over 100 solar masses) would pulse violently on the mainsequence and probably lose most of their mass before dying.

Ledoux, ApJ, 94, 537, (1941)Schwarzschild & Harm, ApJ, 129, 637, (1959)Appenzeller, A&A, 5, 355, (1970)Appenzeller, A&A, 9, 216, (1970)Talbot, ApJ, 163, 17, (1971)Talbot, ApJ, 165, 121, (1971)Papaloizou, MNRAS, 162, 143, (1973)Papaloizou, MNRAS, 162, 169, (1973)

100 Me (main sequence mass) star when the central hydrogen mass fraction hits 0.01.

The luminosity of the star is 6.18 × 1039 erg s-1 (about 0.1% as bright as a Type II supernova)

Mass lost~35 solarmasses

100 Me at hydrogen depletion

κ

L

Eddington luminosity for 65 solar masses

LEdd

=4pGMc

κ=9.6 ×1039 erg s-1

0.34κ

⎛

⎝⎜⎞

⎠⎟

So about model is ~2/3 Eddington luminosity for electronscattering opacity near the surface.

As the star contracts and ignites helium burning its luminosity rises to 8 x 1039 erg s-1 and the mass continues to decreaseby mass loss. Super-Eddington mass ejection?

&M :ΔL excess R

GM: 0.001Me y−1 ΔL 38 R13 M100

-1

ΔL excess depends on κ which is at least as large

as electron scattering.

Luminous bluevariable stars?

Structural adiabatic exponent is nearly 4/3

Radial pulsations and an upper limit

1941, ApJ, 94, 537

Also see Eddington (1927, MNRAS, 87, 539)

(1941)

Upper mass limit: theoretical predictions

Stothers & Simon (1970)

Upper mass limit: theoretical predictions

Ledoux (1941)radial pulsation, e- opacity,

H100 M

Schwarzchild & Härm (1959)radial pulsation, e- opacity,

H and He, evolution65-95 M

Stothers & Simon (1970) radial pulsation, e- and atomic 80-120 M

Larson & Starrfield (1971) pressure in HII region 50-60 M

Cox & Tabor (1976)e- and atomic opacity

Los Alamos80-100 M

Klapp et al. (1987)e- and atomic opacity

Los Alamos440 M

Stothers (1992)e- and atomic opacity

Rogers-Iglesias120-150 M

Upper mass limit: observation

R136 Feitzinger et al. (1980) 250-1000 M

Eta Car various 120-150 M

R136a1 Massey & Hunter (1998) 136-155 M

Pistol Star Figer et al. (1998) 140-180 M

Eta Car Damineli et al. (2000) ~70+? M

LBV 1806-20 Eikenberry et al. (2004) 150-1000 M

LBV 1806-20 Figer et al. (2004) 130 (binary?) M

HDE 269810 Walborn et al. (2004) 150 M

WR20aBonanos et al. (2004)

Rauw et al. (2004) 82+83 M

R122 in LMC

Calculations suggested that strong non-linear pulsations would grow, steepening into shock in the outer layers and driving copious mass loss until the star became lowenough in mass that the instability would be relieved.

But what about at low metallicity?

Ezer and Cameron, Ap&SS, 14, 399 (1971) pointed out that Z = 0stars would not burn by the pp-cycle but by a high temperatureCNO cycle using catalysts produced in the star itself,Z ~ 10-9 to 10-7.

Maeder, A&A, 92, 101, (1980) suggested that low metallicity might raise Mupper to 200 solar masses.

Surprisingly though the first stability analysis was not performed formassive Pop III stars until Baraffe, Heger, and Woosley, ApJ, 550, 890,(2001).

Baraffe et al found that a) above Z ~ 10-4 solar, the κ instability dominated and below that it was negligible and b) that the ε-instabilitywas also suppressed for metallicities as low as 10-7 solar.

Reasons No heavy elements to make lines and grains High temperature of H-burning made the reactions less temperature sensitive.

They concluded that stars up to about 500 solar masses would live their (main sequence) lives without much mass loss.

In the same time frame, several studies suggested that the IMF forPop III may have been significantly skewed to heavier masses.

Abel, Bryan, and Norman, ApJ, 540, 39, (2000)Larson, astroph 9912539Nakamura and Umemura, ApJ, 569, 549,(2002)

So - very massive stars might have formed quite early in the universe, might have lived their lives in only a few million years and might have died while still in possession of nearly their initial mass.

Or given the discussion of the Eddington limit, they might not

As we shall see later the supernovae resulting from such large stars and their nucleosynthesis is special.

These stars may also play an important role in reionizing the universe (even if only 0.01% of the matter forms into such stars).

68Mev/nucleon10

13eV/nucleon:

There are really three important distinct issues: What masses were the early stars born with, what were there typical masses on the main sequence, and with what mass did they die?

CAVEAT!