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The structure and evolution of
stars
Lecture 10: The evolution of 1M
mass stars
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Learning Outcomes
The student will learn the standard ideas of the
evolution of solar type stars, including
theories and ideas of the
1. Main-sequence
2. The Subgiant phase
3. The red giant branch
4. The horizontal branch and red clump
5. The AGB (asymptotic giant branch)
6. Planetary nebula and WD
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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 =
MDOT. = mass loss rate:
.
log( M)
where M  mass loss rate in M

RHOC=central density
LOGTC = log Tc
X,Y,C12…NE22 = central abundances
sol
yr -1
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Schemactic picture of convective regions
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TIFF (Uncompressed) decompressor
are needed to see this picture.
• “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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The main-sequence phase
See handouts for the distribution of mass, temperature, pressure and density
for the young Sun at the age of 5.4 x 107 yrs (Böhm-Vitense p156, Table 13.1),
and compare with the observed estimates now.
For zero-age Sun Tc=13.62x106 ; current estimate Tc=15.6x107 K. Why ?
During H-burning, 4H4He. After 50% of H has been transformed, number of
particles has decreased by factor 0.73, if He was originally 10% (by number).
What are the implications of this ?
As core becomes hotter, slightly more energy is generated and the star’s
luminosity increases. Tables show that since the Sun’s arrival on the mainsequence, it has become ~30% more luminous. Hence stars of a given
mass but different ages populate the main-sequence with a width of ~0.5
dex.
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The main-sequence phase
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The Sun on the main-sequence: Figures from Böhm-Vitense Ch. 13.
• Pressure increases steeply in centre
• 50% of mass is within radius 0.25R
• Only 1% of total mass is in the convection zone
and above
• 2% of mass is in heavy elements
• CNO cycle operates very slowly in central
regions
• After ~4.5x109yr there is enough time to
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reach equilibrium abundances. N enriched by
factor 7, C depleted by factor 200
H-exhaustion early evolution
The cores of 1M stars become He rich. There is no convective processes required,
hence the star does not become fully mixed. Fusion is most efficient in the centre,
where T is highest.
• As He content increases, core shrinks and heats up  He rich core grows
• The T is not high enough for the triple- process
• H-burning continues in a shell around the core, and as T increases, the CNO
process can occur in the shell
• As CNO T16 energy generation is concentrated in the regions of highest T and
highest H content (in shell T ~ 20 x106 K)
• This high T causes high P outside the core and the H
envelope expands.
• This expansion becomes more pronounced when >10%
of the stellar mass in the He core.
• This early expansion terminates the main-sequence
lifetime
• Luminosity remains approximately constant, hence Teff
must decrease, star moves right along the red subgiant
branch.
Subgiant branch
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The red-giant phase
The shell source slowly burns, moving through
the star, as the He core grows. But the star
cannot expand and cool indefinitely.
When the temperature of the outer layers reach
<5000 K the envelopes become fully convective.
This enables greater luminosity to be carried by
the outer layers and hence quickly forces the star
almost vertically in the HR diagram
The star approaches the Hayashi line, and a
small increase in the He core mass causes a
relatively large expansion of the envelope.
There is no physically simple, step by step
explanation of how a star becomes a red giant.
All numerical computations obtain red giant
configurations. as solutions to the structure
equations.
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The He-flash and core He-burning
The helium core does not reach threshold T for further burning as it
ascends the RGB, and as it is not producing energy it continues to
contract until it becomes degenerate.
At tip of the RGB the e– in core are completely
degenerate. P is due to degenerate e– pressure,
which is independent of T.
T is defined mainly by the energy distribution of
the heavy particles (He nuclei). Remember
gravitational collapse is resisted by e–
degeneracy pressure.
For T~108K, triple- reactions start in the very
dense core. They generate energy, heating core,
and KE of He nuclei increases, increasing the
energy production. Energy generation and
heating under degenerate conditions leads to
runway - the He Flash
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The He-flash and core He-burning
During the He-flash, the core temperature changes within seconds. The rapid
increase in T leads the e– again following Maxwell velocity distribution and
degeneracy is removed. The pressure increases and core expands.
The star finds a new equilibrium configuration with an expanded nondegenerate core which is hot enough to burn He. The H-burning shell source
has also expanded, and has lower T and density and generates less energy
than before. The star sits in the Red Clump (metal rich stars) or the Horizontal
Branch (metal poor stars).
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Globular clusters and the horizontal branch
and
Globular clusters are old and metal poor we don’t see a red clump. We see a
horizontal branch:
• H-burning shells, He burning cores
• Mass-loss drives bluewards evolution
• Lowest mass H-envelope stars are
bluest
• More metal rich stars appear towards
red
• Clump stars  extreme red end of HB
• Why do low metallicity stars end up on
HB ?
• Why and how do they loose mass after
He-flash, and metal rich stars do not ?
• Structure equations give equilibrium
configurations on HB
47 Tuc – Globular cluster
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The AGB and thermal pulses
The triple- reaction is even more T-dependent
( T30), hence energy generation is even more
centrally condensed. Note the H-burning shell is
generating energy.
The core will soon consist only of C+O, and in a
similar way to before, the CO-core grows while a
He-burning shell source develops.
These two shell sources force expansion of the
envelop and the star evolves up the red giant
branch a second time - these is called the
asymptotic giant branch.
For high metallicity stars, the AGB coincides closely with the first RGB.
For globulars (typical heavy element composition 100 times lower than solar)
they appear separated.
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The stellar wind and planetary nebula
phase
Large radiation pressure at tip of AGB probably drives mass-loss. Particles
may absorb photons from radiation field and be accelerated out of the
gravitational potential well. Observations of red giants and supergiants
(more massive evolved stars) are in the range 10-9 to 10-4 M yr-1
Mass-loss is generally classified into two types of wind.
1. Stellar wind: described by empirical formula (Dieter Reimers), linking
mass, radius, luminosity with simple relation and a constant from
observations. Typical wind rates are of order 10-6 M yr-1

M 1013
2.
L R M0
L0 R0 M
M 0 yr -1
A superwind: a stronger wind, leading to stellar ejecta observable in shell
surrounding central star

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The existence of a superwind is suggested by two independent variables. The
high density observed within the observed shells in stellar ejecta, and relative
paucity of very bright stars on the AGB.
The latter (Prialnik P. 161) comes from the number of AGB stars expected
compared to observed is >10. Hence a process prevents them completing their
movement up the AGB, while losing mass at the Reimer’s rate.
This is a superwind which removes the envelope mass before the core has
grown to it’s maximal possible size. Direct observations of some stars indicate
mass-loss rates of order 10-6 M yr-1 . Probably this is due to pulsational
instability and thermal pulses in envelope e.g. Mira type variables.
Superwind causes envelope ejection. The
cores evolve into C-O white dwarfs (see
Lecture 12). Core mass at tip of AGB ~0.6 M
and most white dwarfs have masses close to
this.
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Summary of 1 M evolution
Approximate typical timescales
Phase
Main-sequence
Subgiant
Redgiant Branch
Red clump
AGB evolution
PNe
WD cooling
 (yrs)
9 x109
3 x109
1 x109
1 x 108
~5x106
~1x105
>8x109
Full AGB models :
Vassiliadis & Wood 1993, ApJ, 413, 641
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Summary of 1 M evolution
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