Download Lecture 9/10 Stellar evolution Ulf Torkelsson 1 Main sequence stars

Lecture 9/10
Stellar evolution
Ulf Torkelsson
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Main sequence stars
Main sequence stars derive their energy from the fusion of hydrogen into helium in the core. In
light stars, such as the Sun, the fusion is based on the proton-proton-chain. Such stars have a
convective outer shell, because the opacity is high at the low temperatures near the surface. The
lower the mass of a star the cooler it is, and consequently the deeper is the convection zone. The
entire star is convective if it is lighter than 0.3M .
In stars heavier than 1.2M the CNO-cycle starts to dominate rather than the p-p-chain. Since
the CNO-cycle has a much steeper temperature dependence the energy generation is concentrated
to a smaller part of the core. The result of this is that the heat fluxes close to the centre are so large
that the core becomes convectively unstable. The convection mixes the composition of the core,
so that it becomes chemically homogeneous. On the other hand when the surface temperature
increases the opacity in the surface layers decreases, and the outer convection zone disappears.
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The evolution of stars lighter than 8M There is a gradual increase in the helium abundance during the main-sequence phase. The increase
in molecular weight results in that the core is contracting and heating up in order to provide a
sufficient pressure to balance the gravity. As a consequence of this the surface layers are gradually
expanding. In the case of the Sun the hydrogen in the core will be exhausted after some 10 billion
years. At this time the hydrogen fusion will continue in a shell around the core. Since the shell is
actually producing more power than the core did the luminosity of the star increases. The star is
then a sub-giant. The helium that is produced will be dropped on the still hot helium core. When
the helium core has grown sufficiently big compared to the rest of the Sun, that it has reached the
Chandrasekhar-Schönberg limit, it becomes unstable and starts to contract. The hydrogen burning
shell then increases in extent, and in addition the surface layers of the star expand. Because of
the large expansion of the surface area the star is able to radiate its energy at a lower effective
temperature than before. Once the temperature in the outer layers go down its opacity will go up
and the star forms a thick outer convection zone. The star then becomes a red giant that moves
up the Hayashi track again.
The star reaches the peak of the red giant branch in the HR-diagram at the time when the
core becomes dense and hot enough to start converting helium to carbon through the triple-alphaprocess, 3 4 He→12 C. This results in that the core starts to expand again and the outer hydrogen
burning shell decreases in significance. The surface layers of the star then contract and heats up.
We get a horizontal branch star, which is less luminous than the red giant.
In case the star is lighter than 2M its core will have become degenerate before the helium
burning starts. That the core is degenerate means that its pressure is no longer determined by
the thermal motion of the particles in the gas, but rather by the quantum mechanical motion of
the electrons. In that case the pressure does not depend on temperature. The sole effect of the
temperature increase at the start of the triple-alpha-process is then that the reaction rate rapidly
increases, and thus we get a rapid increase in the luminosity of the core. The core can become
as luminous as an entire galaxy. One speaks about a core helium-flash. It is over after about 100
s, when the temperature of the core has increased so much that the core is again controlled by
ordinary thermal pressure, and at this time the core starts to expand. It is noteworthy that the
helium-flash is not observable from the outside, since all of the energy is spent on re-structuring
the interior of the star, which becomes a horizontal branch star with helium-burning in the core
and hydrogen burning in a surrounding shell.
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With time the core will also exhaust its helium, and the helium burning will then continue in a
shell. During this phase the star moves up along the asymptotic giant branch in the HR-diagram.
The star is now burning hydrogen to helium in an outer shell and helium to carbon in an inner shell.
For a large fraction of the time the helium burning is slow, and the helium-burning shell is mildly
degenerate. However the outer hydrogen-burning shell is dropping helium onto a helium shell, so
that from time to time the temperature in the helium shell increases enough that it undergoes
a helium shell flash, which expands the inner parts of the star. This expansion cools down the
hydrogen burning shell, which is producing most of the energy and thus we see the helium shell
flash as a dimming of the star. Presumably these event are also related to significant mass loss
events in the evolution of the star.
Eventually the surface layers of the star are expelled, and a degenerate carbon-oxygen core
remains at the centre of the star. This core becomes a white dwarf. On the other hand the surface
layers form a planetary nebula. The gas in the planetary nebula is expanding at a rate of 10 - 30
km s−1 , and will disolve in the interstellar medium within some 50 000 years.
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The evolution of heavy stars
Stars that are more massive than 8M can go through more stages of nuclear burning: carbon can
be converted to Na, Ne and Mg; O to S, P, Si and Mg, and so on, producing more and more shells
with different nuclear reactions. The heaviest stars will eventually burn silicon to iron in the core.
After that no further nuclear reactions are possible, since the protons and neutrons are bound the
hardest in iron. However for each step less and less energy is released. While a heavy star will
spend about 107 years on the main sequence the last stage of silicon burning will take only 2 days.
At the high temperature that the core has then reached the atomic nuclei start to be disintegrated by the energetic photons. Firstly as
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Fe + γ → 13 4 He + 4n,
(1)
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(2)
and then as
He + γ → 2p + 2n.
These reactions cost energy, so the core contracts. Under the extreme conditions in the core
(T ∼ 8 × 109 K and ρc ∼ 1013 kg m−3 ) the protons and the electrons then merge to form neutrons
p + e → n + ν.
(3)
The energy that is then lost through the newly generated neutrinos is about 10 million times as
large as the energy generated during the silicon burning. This massive energy loss results in that
core collapses down to a radius of about 50 km s−1 in a few seconds. Eventually the collapse stops
as the neutrons become degenerate and exert a quantum mechanical pressure.
The halted collapse generates a shock wave, which is propagating outwards through the star.
It is uncertain whether the shock wave on its own is able to propagate all the way out through
the star, but in the extreme conditions that are now present in the core, the stellar material
becomes opaque even to neutrinos, and these may give a push to the shock wave such that it
gains momentum and continues outward. The shock wave eventually reaches the stellar surface
after a few hours, at which time the star appears as a supernova. Typically this will be a type II
supernova, which is characterised by a spectrum with strong hydrogen lines. (There are also type
I supernovae that lack hydrogen lines.)
It is expected that a few supernovae will occur per century in the Milky Way, but in practice
only four have been observed during the last 1000 years. The reason for this is that a large part of
the Milky Way cannot be observed from the Earth since the light is blocked by dust. One of the
most interesting supernovae is the supernova that was observed by Chinese astronomers in 1054.
At the location of this one has found a nebula, the Crab Nebula, which is expanding at a speed of
more than 1 000 km s−1 . By extrapolating it backwards it is clear that this is the remnant of the
supernova that exploded in 1054. Such gas clouds are called supernova remnants, and they are
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formed from the surface layers of the star, which are thrown out by the shock wave. Furthermore
at the centre of the Crab nebula one has found a radio pulsar, a rapidly rotating neutron star. The
core of the star that forms a supernova will either become a neutron star or a black hole depending
on its mass.
In 1987 a supernova exploded in the Large Magellanic Cloud, a satellite galaxy of the Milky
Way. This is the only supernova from which we have detected the neutrinos that were formed in
the core, and as expected the neutrinos were detected a few hours ahead of that the supernova
brightened. However some other aspects of the supernova were unexpected. Since the Magellanic
Clouds are some of the best studied parts of the sky it was possible to determine which star that
had exploded, and surprisingly it turned out to be a blue supergiant, rather than a red supergiant
as expected. However this does explain why the supernova was unusually faint. A blue supergiant
is much smaller than a red supergiant, so the matter is more tightly bound to the star, thus the
supernova had to spend more of its energy on expelling the matter, which was still moving out at
30 000 km s−1 .
One of the most interesting aspects of this supernova has been its light curve after the outburst.
It took as much as 80 days for the supernova to reach its maximum light, which can be explained
by that the star was a blue supergiant. After the initial phase the light intensity has been declining
exponentially. At first the light dropped of at a rate corresponding to that most of the energy came
from the radioactive decay of 56 Co, and it is possible that it has later made a transition to being
powered by 57 Co. One important lesson to learn here is that supernovae are synthesising a wide
range of elements, and eject these to the interstellar medium. Usual fusion cannot go beyond 56 Fe,
but during the supernova explosion a large amount of neutrons are produced. The atomic nuclei
in the star may then capture these neutrons one after another and build up heavier elements. In
particular, the heaviest elements in nature are formed during the supernova explosions. On the
other hand some slightly lighter nuclei can be produced in other, slow, neutron capture processes
during the normal evolution of light stars. The nuclear reactions in the shells can serve as neutron
sources that are irradiating nuclei around the iron peak.
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Testing stellar evolution
Stellar evolution make some very important predictions. Firstly it predicts that heavy stars will
evolve more quickly than light star. Secondly it predicts that main sequence stars will evolve into
giant stars, in particular red giants. These predictions can be tested by studying stellar clusters, in
which we believe that all stars have formed at the same time. There are two kinds of stellar clusters
in the Milky Way galaxy. There are the globular clusters that are spherical clouds of 100 000 or
more stars and there are the galactic clusters that may consist of about 100 more loosely bound
stars.
If we construct an HR-diagram for a globular cluster we see that it is missing the massive
main-sequence stars, though it still has low-mass main sequence stars. In addition it has plenty
of red and asymptotic giant branch stars and horizontal branch stars. Apparently the massive
stars have already evolved off the main sequence, and many of them may even have exploded as
supernovae. The galactic clusters on the other hand have bluer main sequence stars, and fewer
giants. Thus these clusters appear to be younger.
Another interesting feature appears as we compare their metallicities. The globular clusters
have low metallicities, while the galactic clusters have high metallicities. We say that the globular
clusters are population II objects and the galactic clusters are population I objects. Population II
objects are old objects that formed early in the history of the Milky Way, when only small amounts
of metals had been synthesised in the stars. Population II objects, and in particular the globular
clusters have a more or less spherical distribution around the centre of the Milky Way, and their
density increases towards the centre. Population I objects formed later in the history of the Milky
Way, when the interstellar medium had already been enriched in metals by previous generation of
stars. These objects are concentrated to the galactic disk.
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