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7–1
Stellar Structure and Evolution
The life of stars is a continual struggle between
gravity which tries to collapse a star and other forces
which hold the star up.
At different points in a stars life, it is different
processes which hold a star up against gravity.
In following a star’s evolution we will follow its path
in the H-R Diagram (how its temperature and
luminosity vary).
Stellar Birth
Stars form from large clouds of dust and gas called
molecular clouds.
Typically, a molecular cloud of several thousand
solar masses starts to collapse.
As it collapses, small fluctuations cause it to
subfragment into hundreds to thousands of smaller
collapsing regions—each forming an individual star.
Thus, roughly hundreds to thousands of stars are
created from each collapsing cloud creating a cluster
of stars.
In what follows, we will examine a single protostar (a
single subfragment of the cloud):
Evidence for theory of stellar birth
Each protostar begins life as a large cold (10K to
100K) cloud.
Where would it be on the HR-diagram?
As it collapses, it shrinks in size leading to a release
of gravitational energy.
Some of this energy is radiated away, but some also
goes into heating up the forming star.
As it shrinks and heats up would you expect it to
become more or less luminous or can you tell?
Evidence for interstellar material is seen from a
variety of sources.
Emission nebula:
Gas clouds near hot stars. Atoms in cloud are
excited by absorbing light from the nearby star.
Appear pinkish in color due to emission of hydrogen
balmer lines.
Reflection nebula:
Starlight reflected off dust particles in the nebula.
What path does it take on the HR diagram?
Because the dust scatters blue light most effectively,
they appear bluish in color.
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Dust clouds:
Dust in an interstellar cloud can obscure light from
stars behind it.
Often can be seen as dark patches in the milky way.
Energy Production in Stars
How is energy produced in the sun?
Earth is 4.5 billion years old so energy source for
the sun must be able to power it at least that long:
Chemical reactions (combustion)?
Young stars are often associated with nebulae
indicating that they are regions of star formation.
While most of the initial formation of stars is
obscured behind dust and gas around the star, the
last leg to the main sequence can be seen.
At its present luminosity, the sun could shine for
only about 30,000 years if its energy were produced
by chemical reactions.
Gravitational energy?
Gravitational energy could supply the sun’s
luminosity for about 30 million years.
Better but not enough.
Nuclear reactions?
Where does the excess mass go?
Nuclear reactions provide the only energy source
powerful enough to power the sun.
Nuclear fusion of hydrogen into helium in the Sun
can fuel the sun for about 10 billion years.
Nuclear Reactions
The mass of the elements per nucleon (proton or
neutron) varies slightly.
For example, 4 hydrogen nuclei (1 proton each) are
slightly more massive than one helium nucleus (2
protons and 2 neutrons).
Thus, fusing four hydrogen atoms into one helium
atom results in a loss of mass (about 0.7% of the
total mass).
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Hydrogen Fusion
Main Sequence Stars
Because nuclei are positively charged, they repel
each other.
As a protostar collapses, the gravitational energy
released heats up the star until the core becomes hot
enough for hydrogen fusion to begin.
For fusion to occur, this repulsive force must be
overcome and the nuclei brought close together.
Thus, fusion can only occur at very high
temperatures (~15,000,000K) where the nuclei are
moving fast enough to overcome the repulsion.
At this point the energy generation by fusion
counteracts gravity.
The protostar has reached the main sequence.
What if the star were compressed?
Because of this fusion depends sensitively on the
temperature:
Release of gravitational energy would heat up
interior...
What if the star were expanded?
Mass-Luminosity Relation
This sensitivity of fusion reactions to the temperature
creates a stable situation with fusion just
counteracting gravity.
Luminosity α Mass3.5
Different masses of stars will find their own stable
configuration along the main sequence:
Massive stars:
How long will a star live?
Star’s lifetime α
Fuel Available
Rate of Energy Production
A star’s available fuel goes as the mass of the star.
Its rate of energy production is the luminosity.
Low mass stars:
==> Star’s lifetime α M α M = 1
L
M3.5 M2.5
==> High mass star’s live brief lives.
Position of a star on the main sequence depends
mostly on its mass.
Why are most main sequence stars low mass red
dwarfs?
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Life on the main sequence
Eventually, stars will exhaust their fuel of hydrogen,
having fused the hydrogen into helium.
Star’s spend about 90% of their lives on the main
sequence burning hydrogen into helium.
What happens to stars at this point?
Stars are quite stable during this time maintaining
nearly the same temperature and luminosity.
The evolution of stars after life on the main sequence
follows different paths depending on the mass of the
star.
==> remain at the same point in the H-R Diagram.
This explains why most of the stars we see are main
sequence stars.
However, stars do evolve slightly during their lives
on the main sequence:
Evolution of medium mass stars
(0.4 to a few solar masses)
With no more fusion taking place one might expect
gravity to win and collapse the star into a black hole.
Helium nuclei have more charge than hydrogen, thus
it takes higher temperatures to fuse helium.
However, as the star collapses another mechanism
comes into play to counteract gravity: Electron
degeneracy pressure.
==> after hydrogen is exhausted, the core is not hot
enough to fuse helium. Thus, energy production in
the core ceases:
Recall that electrons can only have certain permitted
energies in atoms. The same is true of electrons
confined to the volume of the star.
According to the Pauli Exclusion principle, no two
electrons can occupy the same state.
In a low density gas, the Pauli Exclusion Principle is
not very important because few levels are occupied
and electrons can change energy freely.
The regions around the core still contain hydrogen.
As they are heated, hydrogen fusion begins in a shell
around the helium core.
However, as the gas is compressed to higher density,
more and more energy levels are occupied.
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If the gas is compressed enough, all of the lower
energy levels are occupied by electrons and the gas
becomes degenerate.
In a degenerate gas some electrons must occupy
higher energy levels because there are no lower
energy levels available.
Even at low temperatures (even absolute zero), these
electrons will have considerable energy, moving
about quickly.
This energy and motion creates an outward
pressure—electron degeneracy pressure.
This electron degeneracy pressure is what halts the
gravitational collapse in white dwarf stars.
Because it does not depend on the temperature or the
production of energy, electron degeneracy pressure
can hold a white dwarf star up indefinitely.
However, massive stars cannot do this. Thus, they
cannot end their lives as white dwarfs.
However, there is a limit to the size of a star which
can be supported by electron degeneracy pressure.
As mass is added to a white dwarf star, it shrinks in
size.
When a white dwarf star reaches a mass of 1.4 solar
masses it shrinks to a radius of zero.
Masses greater than 1.4 solar masses cannot be
supported by electron degeneracy pressure.
What happens to stars more massive than 1.4 solar
masses?
If the star is not too massive (perhaps up to a few
solar masses), it may shed enough mass during their
lives to get under the 1.4 solar mass limit.
Evolution of low mass stars (<0.4
solar masses)
What happens to these stars?
We’ll see later. But first we’ll take a detour to
examine the evolution of low mass stars.
As we found earlier, these stars live long lives on the
main sequence.
They also have the advantage that they are convective
throughout their interiors.
Allows it to burn all its hydrogen, not just that in the
core of the star—lives even longer than one would
otherwise expect.
In fact, their expected lifetimes are longer than the
age of the universe. Thus we would not expect to see
any which have fully evolved yet.
What is expected to happen when they run out of
hydrogen?
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As with heavier stars, the core will start to collapse
and heat up.
However, unlike heavier stars, no hydrogen left:
The star will continue to collapse.
However, being of such a low mass it never becomes
hot enough to ignite helium.
Thus, after its hydrogen burning phase, no further
fusion takes place and the star continues to cool off
Being under 1.4 solar masses, the collapse is
eventually halted by electron degeneracy pressure.
Stars will end up as white dwarf stars as well.