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Stellar Structure and evolution
Lecture 11: Evolution of massive
stars
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Learning Outcomes
The student will learn the following concepts
• Evolution of a high mass star - burning stages
and lifetimes
• The detailed model predictions and a
schematic overview
• The effect of mass-loss and stellar winds
• The Eddington luminosity
• The initial mass function and the upper mass
limit
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Example set of models - “the Geneva Group”
See handout of paper of Schaller et al.
(1992): the “standard” set of stellar
evolutionary models form the Geneva
group.
1st line in table
NB = model number (51)
AGE = age in yrs
MASS = current mass
LOGL = log L/L
LOGTE = log Teff
X,Y,C12…NE22 = surface abundance of H,He, 12C …
22Ne (these are mass fractions)
2nd line
QCC = fraction of stellar mass within convective core
MDOT. = mass loss rate:
.
log( M)
where M  mass loss rate in M solyr -1

RHOC=central density
LOGTC = log Tc
X,Y,C12…NE22 = central abundances
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Massive stars
Lets consider the upper mass region, in particular the 15M - 25M star.
What is the main-sequence lifetime of a 25M star ?
What are the timescales of its lifetime after it leaves the main-sequence ?
What is the status of star at the last point in the Geneva tracks ?
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Schematic description
The evolution of massive stars have the following general characteristics and
differences to lower mass evolution
1. The electrons in their cores do not become degenerate until the final
burning stages, when iron core is reached
2. Mass-loss plays an important role in the entire evolution (we will come
back to this)
3. The luminosity remains approximately constant in spite of internal
changes. The track on the HRD is therefore horizontal. For a 15-25M
stars we have seen a gradual redwards movement. But for higher mass (or
stars with different initial compositions) the star back and forth between low
and high effective temperatures
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From the main-sequence to He burning
1.
2.
3.
4.
5.
6.
7.
The cores of massive stars are convective, hence newly formed He is
evenly mixed in the core.
As the hydrogen is consumed, the core contracts and also shrinks in mass
(see QCC values).
The convective core becomes exhausted homogeneously, while it contracts
to a smaller volume and becomes hotter.
The star also develops a H-burning shell around the He dominated core.
The temperature at the bottom of the hydrogen envelope is too high to
sustain hydrostatic equilibrium. The envelope expands and the star
becomes cooler, moving to the red region of the HRD. It becomes a red
supergiant star.
Due to the rapid drop in temperature throughout the outer atmosphere, the
criterion for convection is reached in this region and a convection zone
develops, reaching deep into the star.
It dredges up some of the material from the original convective core. This
core material can appear at the stellar surface in the atmosphere of the red
supergiants.
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Schemactic picture of convective regions
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• “Cloudy” areas
indicate convective
regions
• Solid lines show mass
values for which
radius is 0.25 and 0.5
of total radius
• Dashed lines show
masses within which
0.5 and 0.9 of the
luminosity is produced
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From He burning to core-collapse
1.
2.
3.
4.
5.
6.
The He burning core is surrounded by a H-burning shell
The triple- process liberates less energy per unit mass than for H-burning
(~10%). Hence the lifetime is shorter, again around 10%
There is no He-flash as densities in the He-core are not high enough for
electron degeneracy.
Schematic figure below shows the structure of a star after a large fraction of
He is converted to C.
We have core of 12C and 16O, surrounded by He and H burning shells.
The core will again contract and the temperature will rise, allowing C and O
burning to Mg and Si (see Lecture 6).
7. This process continues, with increasing
Z, building up heavier and heavier
elements until the iron group elements
of Ni, Fe and Co are formed. The core
is surrounded by a series of shells at
lower T, and lower 
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Typical Timescales for later burning phases
Massive stars of course spend most of their lives on the main-sequence,
and illustrative timescales for 15M - stars given below. The Geneva
tracks only go up to the end of carbon burning, but other authors have
followed the burning through to the production of an iron core (e.g. Heger
& Langer 2000, ApJ 528, 368)
Central burning phase
Hydrogen
Helium
Carbon
Oxygen
Silicon
time (yrs)
10 x 106
1 x 106
400
1
10-2
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Mass-loss from high mass stars
Large amount of evidence now that high
mass stars loose mass through a strong
stellar wind.
• The winds are driven by radiation
pressure - UV photons from a hot, very
luminous star absorbed by the optically
thick outer atmosphere layers.
• atmosphere is optically thick at the
wavelength of many strong UV
transitions (resonance transitions) of
lines of Fe, O, Si, C (and others).
• photons absorbed, imparting
momentum to the gas and driving an
outward wind.
• measured in O and B-stars, and leads
to (terminal) wind velocities of up to
4000 km/s and mass-loss rates of up to
5 x 10-5 M yr-1
Huge effect on massive stellar
evolution - the outer layers are
effectively stripped off the star.
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Evidence for stellar winds:
“P-Cygni” lines in hot stars - resonance
transitions in optical or UV
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Wolf-Rayet Stars
H-deficient massive stars. Spectra
show either strong abundances of
He+N or C+O. These are products of
H-burning and then He burning. Likely
there is an evolutionary line, or a
relation between initial mass and final
WR star produced.
Possible evolution scenario:
O main-sequence star  blue
supergiant  red supergiant  WR
star
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The Eddington luminosity
Eddington derived the theoretical limit at which the radiation pressure of a
light-emitting body would exceed the body's gravitational attraction. That is, a
body emitting radiation at greater than the Eddington limit would break up
from its own photon pressure (see class derivation).
L
4cGM
s
Violation of this implies violation of hydrostatic equilibrium. RHS of inequality
represents the Eddington luminosity that cannot be surpassed
L Edd 
4cGM
s
 M  es 
 3.2 10 
 LSol
M Sol  s 
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If ≈es, then LEdd becomes determined uniquely by M. For massive
main-sequence stars
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L  M 
 

LSol M Sol 
Main sequence should have an upper end (M≈180M, for s=es=0.04 m2
kg-1)
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The initial mass function
How many stars are formed at each
mass in a star cluster, or star
forming region ? Is it always the
same distribution ? Is it constant
across environments and galaxies ?
Define the number of stars formed
at a given time within a given
volume, with masses in the range
(M, M+dM) as a function solely of M
(m)
This intial mass function is also sometimes defined slightly differently as
the amount of mass locked up in stars with masses in the interval (M,
M+dM) formed within a given time within a given volume:
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Total number of stars between the
masses m1 and m2:
Total mass locked up in stars between
masses m1 and m2:
Class question:
A star cluster is born from a giant molecular cloud of 10,000 M . Assuming
that all of the mass is converted into stars, estimate the mass of the gas that
goes into forming massive stars (I.e stars with M≥10 M)
How big do stars get ?
Is there an upper mass cut-off ?
What are the masses of the most massive stars ?
The most luminous stars in the galaxy have inferred masses of ~150-300M
but this value depends on estimate of logL/L and Teff. The former requires
distance, reddening, bolometric correction and the later requires reliable model
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atmosphere. Probably uncertain within a factor 2.
Upper mass limit for stars
Recent study in Nature (Figer 2005, Nat, 434, 152). The IMF was determined
for a very massive cluster, which is massive enough that there is a reasonable
probability that stars of masses >500M could exist in cluster, if they form.
Assuming a standard Salpeter IMF
holds in the Arches, how many
stars would you expect to find
above 140M if there was no
imposed upper mass cut off ?
[Note: number of stars with masses
10 < M < 140M is 296]
What is the statistical probability
that you find no stars in this region
if there is no upper mass limit ?
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The Arches cluster observed by HST
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IMF constant at different Z




Solar neighbourhood composition: H=70%, He=28% Metals=2%
LMC Z=0.5Z, and SMC Z=0.2Z
Starformation of massive stars proceeds independent of metallicity
Local Group galaxies SMC and LMC are excellent laboratories to
study massive star populations
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No evidence for environment influence



Whatever the star-formation rate, the IMF seems constant
Starburst regions, “normal” young clusters, low mass clusters in
Milky Way, LMC, SMC all similar
IMF not measured well beyond the Magellanic Clouds
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Summary
We have covered qualitative description of the evolution of star from modern
calculations
• The theoretical HRD in general, and 1M and 25M stars in detail
• Time-scales for evolutionary stages: 90% of massive star’s life is on mainsequence. Final stages of C-burning and beyond last few hundred years
• Massive stars loose mass - most massive become WR stars, with final
masses significantly less than birth mass
• Derived the Eddington luminosity - the main-sequence should have upper
mass limit
• The initial mass function implies significantly less massive stars than low
mass stars born - implications for galactic evolution.
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