The structure and evolution of stars

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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
• Main-sequence
• The Subgiant phase
• The red giant branch
• The horizontal branch and red clump
• The AGB (asymptotic giant branch)
• 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,C12NE22 surface abundance of H,He,
12C 22Ne (these are mass fractions) 2nd line
QCC MDOT mass loss rate RHOCcentral
density LOGTC log Tc X,Y,C12NE22 central
abundances

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Schemactic picture of convective regions

• 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 Tc13.62x106
current estimate Tc15.6x107 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 stars luminosity increases.
Tables show that since the Suns arrival on the
main-sequence, 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

The Sun on the main-sequence Figures from
Böhm-Vitense Ch. 13.

• 2 of mass is in heavy elements
• CNO cycle operates very slowly in central regions
• After 4.5x109yr there is enough time to reach
  equilibrium abundances. N enriched by factor 7, C
  depleted by factor 200

• 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

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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 gt10
  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.

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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 lt5000 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 T108K,
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
non-degenerate 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
  dont 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

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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 CO, 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.
• 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
• 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 gt10. Hence a process prevents them completing
their movement up the AGB, while losing mass at
the Reimers rate. This is a superwind which
removes the envelope mass before the core has
grown to its 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
? (yrs) Main-sequence 9
x109 Subgiant 3 x109 Redgiant
Branch 1 x109 Red clump 1 x 108 AGB
evolution 5x106 PNe
1x105 WD cooling gt8x109

Full AGB models Vassiliadis Wood 1993, ApJ,
413, 641
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Summary of 1 M? evolution