Evolution of Massive

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Lecture 7 Evolution of Massive Stars on the Main
Sequence Basics and Convection
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Massive Stars
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 . The overall main
sequence structure is reasonably well
represented as an n 3 polytrope.
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Competition between the p-pchain and the CNO
Cycle
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Key Physics and Issues

• Evolution in HR diagram
• Nucleosynthesis
• Surface abundances
• Presupernova structure
• Remnant properties
• Rotation and B-field
• of pulsars

• Equation of state
• Opacity
• Mass loss
• Convection
• Rotation
• Binary membership
• Magnetic fields
• Nuclear physics
• Explosion Physics

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Humphreys-Davidson Limit
blue loops during helium burning are
discussed by Kippenhahn and Weigert p.
301ff Envelope solution depends on R, M(R),
L(R), and hydrogen concentration at the base of
the hydrogen envelope. Multi-valued. Solution
depends on semi-convection, overshoot, rotation,
convection criterion. Complicated.
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• The three greatest
• uncertainties in modeling
• the presupernova evolution
• of single massive stars are
• Convection and convective boundaries
• Rotation
• Mass loss (especially the metallicity
  dependence)

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Nuclear Physics
In a low mass star
The slowest reaction is 14N(p,g)15O. For
temperatures near 2 x 107 K.
(More on nucleosynthesis later)
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The 4 CNO cycles
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CNO tri-cycle
Ne(10)
F(9)
O(8)
N(7)
C(6)
3
4
5
6
7
8
9
neutron number
All initial abundances within a cycle serve as
catalysts and accumulate at largest t
Extended cycles introduce outside material into
CN cycle (Oxygen, )
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• From homology relations on the following page
  and taking
• constant (electron scattering), an ideal gas
  equation of state,
• and n 18, one obtains

where m was defined in lecture 1.
If radiation pressure dominates, as it begins to
for very large values of mass,
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Homology
n 18
15
Equation of state
Well defined if tedious to calculate up to
the point of iron core collapse.
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Opacity
In the interior on the main sequence and within
the helium core for later burning stages,
electron capture dominates. In its simplest form
17

• There are correction terms that must be applied
  to kes especially at
• high temperature and density
• 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 k at high temperature.
18
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 is important in white dwarfs
and therefore the precursors to Type
Ia supernovae Itoh et al,
ApJ, 285, 758, (1984) and references therein
19
For radiative opacities other than kes, in
particular kbf and kbb,
Iglesias and Rogers, ApJ, 464, 943 (1996)
Rogers, Swenson, and Iglesias, ApJ,
456, 902 (1996)
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Note centrally concentrated nuclear energy
generation.
convective
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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 variation of
mixing length theory. Caveats and concerns

• The treatment must be time dependent
• Convective overshoot and undershoot
• Semiconvection
• 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.

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Kuhlen, Woosley, and Glatzmaier are exploring
the physics of stellar convection using 3D
anelastic hydrodynamics. The model shown is a 15
solar mass star half way through hydrogen
burning. For now the models are not rotating, but
the code includes rotation and B-fields.
(Previously used to simulate the Earths dynamo).
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Michael Kuhlen rotating 15 solar mass
star burning hydrogen
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Convective structure
from Kippenhahn and Wiegert
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Convective instability is favored by a large
fraction of radiation pressure, i.e., a small
value of b.
So even a 20 decrease in b causes a substantial
decrease in the critical temperature gradient
necessary for convection. See also Kippenhahn
and Weigert 13.21.
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b decreases with increasing mass. Hence more
massive stars are convective to a greater extent.
Eddingtons standard model n 3 polytrope
(Clayton, 161) with constant b and m.
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M Tc/107 rC
L/1037 Qconv core
9 3.27 9.16
2.8 0.26 12 3.45
6.84 7.0 0.30 15
3.58 5.58 13
0.34 20 3.74 4.40
29 0.39 25
3.85 3.73 50
0.43 40 4.07 2.72
140 0.53 60(57) 4.24
2.17 290 0.60 85(78)
4.35 1.85 510
0.66 120(99) 4.45 1.61
810 0.75
All evaluated at a core H mass fraction of
0.30 for stars of solar metallicity.
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Burning Stages in the Life of a Massive Star
0
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Convection plus entropy from ideal gas implies n
1.5
34 of the mass
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Most of the mass and volume.
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blue energy generation purple energy
loss green convection
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The convective core shrinks during hydrogen
burning
During hydrogen burning the mean atomic weight is
increasing from near 1 to about 4. The ideal gas
entropy is thus decreasing. As the central
entropy decreases compared with the outer layers
of the star it is increasingly difficult to
convect through most of the stars mass.
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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).
The rest of the luminosity is coming from the H
shell..
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blue energy generation purple energy
loss green convection
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b) As the mass of the helium core rises its b
decreases.
This decrease in b favors convection.
The entropy during helium burning also continues
to decrease, and this would have a tendency to
diminish convection, but the b and L effects
dominate and the helium burning convective
core grows.
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Convective Overshoot Mixing
Initially the entropy is nearly flat in a zero
age main sequence star so just where convection
stops is a bit ambiguous. As burning proceeds
though and the entropy decreases in the center,
the convective extent becomes more precisely
defined. Still one expects some
overshoot mixing. 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,
argue that a is less than about 20. Doom,
Chiosi, and many European groups use larger
values. Woosley and Weaver use much less.
Nomoto uses none.
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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.

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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 (2000) empirically for low mass
stars, overshoot is 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
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Metallicity affects the evolution in four
distinct ways

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

lower main sequence
Because of the higher luminosity, the lifetime of
the lower metallicity star is shorter (it burns
about the same fraction of its mass).
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Upper main sequence The luminosities and ages
are very nearly the same because the opacity 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
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Schaller et al. (1992)
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There is a slight difference in the lifetime
on the upper main sequence though because of the
different initial helium abundances. Schaller et
al. used Z 0.001, Y 0.243, X0.756 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.
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For helium burning, there is no effect around 10
solar mases, but the higher masses have a longer
lifetime with lower metallicity because mass loss
decreases the mass.
For lower masses, there is a significant
metallicity dependence for the helium burning
lifetime. The reason is not clear. Perhaps the
more active H-burning shell in the
solar metallicity 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
as T39 at these temperatures. The above numbers
are more than enough to explain the difference
in lifetime.
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• Zero and low metallicity stars may end their
  lives as
• compact blue giants depending upon
  semiconvection
• For example, Z 0, presupernova, full
  semiconvection
• 20 solar masses
• R 7.8 x 1011 cm Teff 41,000
  K
• 25 solar masses
• R1.07 x 1012cm Teff 35,000
  K
• Z 0.0001 ZO
• 25 solar masses, little semiconvecion
• R 2.9 x 1012 cm Teff
  20,000 K
• b) 25 solar masses, full semiconvection
• R 5.2 x 1013 cm Teff 4800 K

Caveat Primary 14N production
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Very massive stars
As radiation pressure becomes an increasingly
dominant part of the pressure, b approaches zero
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 b still is 0.55. The properties of
such massive stars, which might have comprised
Pop III are worth discussing.
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This suggests that massive stars, as b approaches
0, will approach 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
energy that approaches zero as b approaches zero.
But the calculation applies to those surface
layers which must stay bound. Completely
convective stars with a luminosity
proportional to mass have a constant lifetime,
which is in fact the shortest lifetime a (main
sequence) star can have.
(exception supermassive stars over 105 solar
masses post-Newtonian gravity renders unstable
on the main sequence)
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Limit
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Since these stars are fully convective with
radiation entropy dominant, they also have r
proportional to T3 throughout and are well
represented as n 3 polytropes. Since G 4/3,
such stars are loosely bound (total energy
much less than gravitational or internal energy)
and are subject to large amplitude pulsations.
These can be driven by either opacity
instabilities (the k mechanism) or nuclear
burning instabilities (the e mechanism). For
solar metallicity it has long been recognized
that such stars (say over 100 solar masses) would
pulse violently on the main sequence and probably
lose most of their mass before dying.
Ledoux, ApJ, 94, 537, (1941) Schwarzschild
Harm, ApJ, 129, 637, (1959) Appenzeller, AA, 5,
355, (1970) Appenzeller, AA, 9, 216,
(1970) Talbot, ApJ, 163, 17, (1971) Talbot, ApJ,
165, 121, (1971) Papaloizou, MNRAS, 162, 143,
(1973) Papaloizou, MNRAS, 162, 169, (1973)
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Radial pulsations and an upper limit
Also see Eddington (1927, MNRAS, 87, 539)
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Upper mass limit theoretical predictions
Stothers Simon (1970)
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Upper mass limit theoretical predictions
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Upper mass limit observation
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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 low enough in mass that the
instability would be relieved.
But what about at low metallicity? Ezer and
Cameron, ApSS, 14, 399 (1971) pointed out that Z
0 stars would not burn by the pp-cycle but by a
high temperature CNO cycle using catalysts
produced in the star itself, Z 10-9 to 10-7.
Maeder, AA, 92, 101, (1980) suggested that low
metallicity might raise Mupper to 200 solar
masses. Surprisingly though the first stability
analysis was not performed for massive Pop III
stars until Baraffe, Heger, and Woosley, ApJ,
550, 890, (2001).
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Baraffe et al found that a) above Z 10-4 solar,
the k instability dominsted and below that it
was negligible and b) that the e-instability was
also supressed 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 for Pop III may have been
significantly skewed to heavier masses.
Abel, Bryan, and Norman, ApJ, 540, 39,
(2000) Larson, astroph 9912539 Nakamura and
Umemura, ApJ, 569, 549,(2002)
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The next slide shows snapshots of a 3D
hydrodynamical simulation of the formation of the
first stars. Dark matter first condenses and
then forms potential wells into which
pre-galactic objects accumulate. The gas cools
through vibration and rotational bands of the H-2
molecule. The bottom two rows show slices
through the last simulation shown on the top row.
The lower right panel shows a molecular cloud (T
about 200 K) with a dense core a few hundred K
hotter. This core is gravitationally bound.
Within this core a dense knot of about 1 Msun has
formed (yellow region of the red spot in the
right panel of the second row). Recent
calculations reported by Omukai and Palla (ApJ,
561, L55, (2001)) suggest that the fragments in
the calculations of Abel et al will grow to
about 300 solar masses before accretion is shut
off by the stellar luminosity.
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Abel, Bryan, and Norman, (2002), Science, 295,
5552
600 pc
density
shock
molecular cloud analog (200 K)
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In summary it seems that very massive stars may
have formed quite early in the universe, lived
their lives in only a few million years and died
while still in possession of nearly their
initial mass. 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).