Lecture Notes
Arny Chapter 13
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Chapter 13 Stellar Evolution
Section 13.1 The Evolution of a Star
By the "evolution of a star"
we mean how a star changes in the course of its life.
Not all stars evolve (age) in the same way.
We will divide stars into two groups:
low-mass stars (<10 solar masses, this includes the Sun)
high-mass stars (>10 solar masses)
The main theme for all stars is that their whole life is spent fighting against the relentless crushing of gravity.
How do stars fight off gravity?
For most of their lives, stars use nuclear fusion in their core to
generate heat and pressure, the outward push of pressure counters
the inward pull of gravity.
See figure 13.1 on page 387.
But stars consume themselves with nuclear fusion, it is not something they
can do forever, stars must change.
Figures 13.2 and 13.3 (pages 388 and 389)
do an excellent job of summarizing the lives of stars.
My own summary is given in the Stellar
evolution handout.
This is packed with information, all of which you need to know.
Section 13.2 Star Formation
We won't cover this section in the detail that the text does.
There are clouds of gas and dust here and
there throughout the universe.
Interstellar (between stars) clouds, also called nebulas (or nebulae).
71% H, 27% He, and 2% dust ("metals").
Occasionally these clouds collapse to form stars.
Gravity pulls the material together.
Most falls into the center to become the star.
Star formation is going on even today.
About 10 new stars are born every year in our Milky Way galaxy.
The nearby Orion Nebula is a region of active star formation.
Protostar Stage
Gravitational contraction of an interstellar cloud.
As the gas falls inward, it gains energy.
The gas heats up and starts to glow.
The "star" is huge, it's still contracting.
Because of the huge surface area, it emits a lot of light.
At first, the energy for this light is supplied by gravity only, no nuclear
fusion.
Later the core gets hot and dense enough for nuclear fusion to start.
The star gets energy from both gravitational collapse and nuclear fusion
for a while.
When gravitational collapse ends (due to rising temperatures and pressures
inside), the protostar stage of the star's life has come to an end.
Protostars emit a lot of light (mainly infrared), they will out-shine normal
stars.
A protostar is like a car going down a steep hill.
It'll go really fast . . . for a little while.
A normal star is like a car with a full tank of gas, it might not go as
fast but it will go and go and go.
This protostar stage lasts a few million years (another text: about 50 million
years).
It is now a Main-Sequence Star.
More on Protostars:
We can diagram this evolution using an H-R (Hertzsprung-Russell) diagram:
One Solar Mass clouds:
This would be a nebula that develops into a star like our Sun.
Note: This diagram illustrates how the properties of the star change with
the passing of time, the star isn't "going" anywhere.
The cloud starts as a huge, cold thing.
The luminosity (total light output - mainly in infrared and radio) is fairly
large because of the huge surface area.
As the cloud collapses, the temperature goes up (the point moves left on
the diagram).
During most of its development, the star has a luminosity greater than it
will have when it reaches the main-sequence (the line is higher on the H-R
diagram), up to 100 times brighter.
The last downward part is when nuclear fusion has started and gravitational
collapse is slowing down.
Now the evolutionary paths for other stars.
.1 solar mass nebula
This small cloud evolves into a Red Dwarf star.
Into a star at the bottom of the H-R diagram.
This is a star that just barely achieved nuclear fusion.
Stars with mass between .1 and 1 will evolve along in-between paths.
.01 solar mass nebula
Any cloud with mass less than .1 solar masses will fail to
become a star.
[More accurate lower limit is about .08 solar masses.]
These glow briefly due to the gravitational energy of collapse.
But never get hot and dense enough for nuclear fusion.
They settle into small, dark objects.
These are called Brown Dwarfs.
Basically just an oversized planet.
Are there a lot of Brown Dwarfs out there?
Maybe! We just don't know yet (they are too small and dim).
10 solar mass nebula
Extra bright protostar stage as usual.
Evolves into a B0 type star.
Stars with mass >100 solar masses probably cannot form, the core gets
too hot and pressure pushes away surrounding gases limiting the star's size.
Section 13.3 Main-Sequence Stars
Main-sequence stars are boring.
This is very good news for people living on a planet orbiting a main-sequence
star, we want our star to be constant and unchanging, boring is good.
They fuse hydrogen into helium in their core to provide temperature and
pressure sufficient to hold off gravity. "Hydrostatic equilibrium"
Stars are huge things, they have plenty of fuel to burn.
Eventually all stars run out of hydrogen fuel in their core.
The core fills up with helium.
Surprisingly, large stars run out of fuel much sooner than small stars.
See Appendix Table 10 on page 550.
The values in this table are all highly approximate.
| Spectral Class | Mass (solar masses) |
Main-Sequence Lifetime (years) |
| O6 | 50 | 1 million |
| B1 | 15 | 10 million |
| B9 | 3 | 100 million |
| A7 | 1.9 | 1 billion |
| G2 | 1 | 10 billion |
| K1 | .75 | 100 billion |
| M3 | .25 | 1 trillion |
CNO stands for Carbon, Nitrogen, and Oxygen,
these elements can act as catalysts speeding the rate of hydrogen fusion
in the most massive stars.
Very high temperatures are needed to initiate the CNO cycle, which is why
it occurs only in the larger stars.
The details of the CNO cycle are not important.
Having larger, hotter cores also causes the proton-proton chain reactions
to go faster.
Together, this explains why larger stars have so much shorter main-sequence
lifetimes.
All main-sequence stars get their energy from conversion of hydrogen
into helium (which converts a little mass into energy).
Our Sun is a type G2 star with a main-sequence
lifetime of about 10 billion years.
[Calculated in the text on pages 395-6 in a very simple way.]
Our Sun is currently about 4.5 billion years old, half-way through its main-sequence
lifetime.
The next three sections refer to low-mass stars (<10 MS), like the Sun.
Section 13.4 Giant Stars
What happens to stars when they run low of their hydrogen fuel?
Hydrogen is only in short supply in the core, hydrogen fusion continues
in a shell around the core.
But less energy is being produced.
Less pressure.
The core contracts . . . and heats up!
Strange!
The core runs low of fuel which results in its heating up.
That's because gravitational collapse always releases large amounts of energy
(that was why Protostars are so luminous).
The gravitational contraction adds energy making it hotter turning up the
rate of fusion of what hydrogen still remains.
While this is happening in the core of
the star, other events occur elsewhere.
The core of the star has become hotter, this increases the pressure exerted
on the outer layers of the star.
The outer surface of the star expands.
The star becomes much greater in size.
The outer surface cools (opposite of
heating due to contraction) and the light
emitted by the star is more red in color.
The star has become a Red Giant.
These events will occur to our Sun in
about 5 billion years.
Our Sun will expand, it will swallow up
Mercury and Venus.
Yes, it will become that large!
But far less dense.
Probably any life still on the Earth at
this time will be destroyed.
Eventually, the core heats up to the point where a new nuclear reaction
can take place.
The triple-alpha process, 3 He => C + 2 g
Three heliums combining to form a carbon and two photons.
(Helium nuclei are often called "alpha" particles.)
Mass is converted to energy in this process, energy released.
This helium fusion first starts in a burst called Helium Flash.
Remember that these events are only for the low-mass stars.
The reason that the helium fusion starts
in a sudden flash is because something strange starts to happen in the core
of these stars.
The core has been contracting, getting very small and dense.
At these temperatures, the hydrogen and helium atoms have been ionized,
so the core has H and He nuclei and electrons flying around separately.
At these densities though, the electrons don't fly around.
There is a limit to which some particles
can be squeezed together.
This packing limit has been reached for the electrons.
The electrons are said to have reached their degenerate limit or
to have formed a degenerate gas.
"Degenerate" has a special meaning in physics, it means particles
all pushed to their lower limit.
"Gas" is also misleading, the electrons act more like an inflexible
crystal.
Anyway, this change in behavior of the
electrons explains why the core can erupt in a sudden helium flash.
Note that the degenerate state here only applies to the electrons, the helium
nuclei can still be flying around and having fusion in normal ways.
Section 13.5 Yellow Giants and Pulsating
Stars
Once helium fusion begins in the core, it causes changes in the rest of
the star.
The star becomes more yellow in color (which is hotter than the previous
red) and usually starts to pulsate (it starts to puff in and out).
The text does a good job of describing
this behavior, I like its analogy of the boiling water in the lidded pan.
Core produces energy.
Outer layers opaque, trap radiation.
Outer layers heat and expand.
Layer becomes transparent and cools.
Gases fall back inwards, become denser and opaque again.
Cycle repeats.
Stars that behave in this pulsating manner
are called either RR Lyrae stars ("lie-ree") or Cepheid
variable stars ("sef-ee-id").
Named for the first studied stars of these types.
Virtually all stars are "low-mass".
All low mass stars will become RR Lyrae or Cepheid variables stars during
their life.
(Lower mass stars become RR Lyrae, larger Cepheids. Our Sun will be an RR
Lyrae, I think.)
So these star types are very common.
Really low-mass stars will bypass the Red
Giant and Yellow Giant stages altogether.
Section 13.6 Death of Stars like the Sun
For a star like our Sun:
10 billion years as a main-sequence star (H fusion in core)
1 billion years as a Red Giant (contracting core, H fusion)
a few hundred million years on the "horizontal branch", a Yellow Giant (He fusion in core with shell of H fusion)
The last stage may involve pulsations, variable-star behavior.
But now the core fills with carbon, created
from the fusion of helium.
Fusion slows in the core, but energy production doesn't because the star
makes up for less fusion by again contracting, releasing gravitational energy.
Energy production in the core increases, pushing outward on the star's outer
layers.
This pulse of energy causes the outer layers of the star to be blown out
into space.
This is called a Planetary Nebula.
A central star surrounded by a pretty shell of gas.
See figure 13.16 on page 403.
When first seen, it was thought the nebula might be related to planet formation
and hence the name.
There is no connection to planet formation.
After a while, the nebula (shell) spreads out so much that it is too thin
to be seen (in 100,000 years?).
The changes occurring in a star as it becomes a red giant and planetary
nebula cause it to `change position' on the H-R diagram.
Cooler surface temperature => moves right.
Higher overall luminosity => moves up.
Figure 13.17 on page 404 is an excellent
summary of our Sun's future.
(Many of the times given in this
figure are incorrect, most important is that our Sun will spend about 10
billion years as a main-sequence star and about 1 billion years as a Red
Giant.)
(Some astronomers do not consider the Sun to become a "Red Supergiant",
instead just a "Red Giant" still.)
My version of the same figure:
After the Planetary Nebula phase, a star
like our Sun has lost almost half of its mass, blown off into space, never
to return.
The remaining core settles into a small dense object called a white dwarf.
We'll talk more about this in the next chapter.
Now we consider the high-mass stars (>10 solar masses).
Section 13.7 Old Age of Massive Stars
Even big stars spend time on the main-sequence fusing hydrogen into helium.
Core starts to fill with helium, core contracts increasing temperature to
maintain fusion rate.
Hotter core, outer layers of star pushed outwards.
Star may evolve from a blue supergiant to a red supergiant.
Helium fusion occurs, but not a sudden Helium Flash.
Helium fusion gets harder due to carbon build-up, core contracts to maintain
the high (even higher now) temperature.
Core temperature rises to the point where carbon fusion (into Ne, O, N)
can occur releasing energy. [neon, oxygen, nitrogen]
With this new energy source, gravitational collapse is temporarily halted.
But soon Ne, O, N clog up the core slowing carbon fusion.
Core contracts and heats up.
New fusion reactions (producing Si, Fe) occur producing energy. [silicon,
iron]
The creation of heavier elements from lighter ones in stars like this is
called nucleosynthesis.
Does this pattern ever stop?
Yes, the process stops with iron (Fe).
Iron is the most stable of all elements
- most stable nucleus - no energy can
be produced by fusion of iron.
When iron accumulates, the star no
longer has an energy source with
which to fight off gravity.
On the H-R diagram, the star may
drift left and right (hotter and cooler
surface) as shown in figure 13.21 page 408.
Remember that stars don't fuse just one fuel at a time.
While one element is "burned" in the core,
others are fusing in surrounding layers.
An onion skin type structure.
[The text doesn't use this term.]
Inner core Fe, surrounded by Si, O,
C, He, H all still fusing.
See figure 13.18 on page 405.
What happens after the build-up of iron?
Type II Supernova Explosion
Remember, we are talking only about very massive stars, those with at least
10 solar masses.
The star's core has filled up with iron.
The iron nuclei may be flying around and crashing violently, even undergoing
fusion or fission reactions, but not generating any new energy.
Without an energy source, the material cannot maintain the pressure needed
to halt the relentless crush of gravity.
The star is furiously fusing everything it can, but the fuel in the core
is vanishing, and then there just isn't any more fuel.
The iron core shrinks and becomes hotter.
The electron's step up and announce, "we will hold off gravity".
Recall "electron degeneracy", a fundamental limit on how
tightly electrons can be squeezed together.
It is a valiant effort but it fails.
In the violent and compact core, a reaction occurs that merges protons and
electrons together into neutrons.
p + e- => n + v [proton, electron, neutron, neutrino]
This is the reverse of "neutron decay", neutron decay happens
naturally.
The reverse process will be forced to occur in the extreme conditions in
the star.
The process happens quickly throughout
the core, the core material - previously a mixture of protons, neutrons,
and electrons - now becomes all neutrons.
With no electrons, electron degeneracy is irrelevant and the core collapse
continues.
The collapse is usually stopped, because
of a limit on the packing of neutrons called "neutron degeneracy".
What will be left is called a neutron star, but that we'll save for the
next chapter.
In less than a second, maybe as much mass
as two of our Sun has collapsed down into a ball just 10 kilometers across.
And even more of the star's mass is following, to crash down upon that core.
All the energy from the collapse blasts
the outer layers of the star back into space.
This is a supernova explosion.
The energy generated is phenomenal, the star is generating energy at a rate
greater than that of entire galaxies with hundreds of billions of stars!
Past supernovae in our galaxy have been bright enought to be seen during
daytime!
Famous Supernovas:
July 1054
Supernova explosion 7000 light-years away, bright enough to be seen in daytime.
Remnant = Crab Nebula (see figure 13.20B on page 407)
1572 Tycho's Supernova, 23,000 LY away, named for Tycho not because he was the first to see it (he wasn't) but because he made a famous study of it.
1604 Kepler's Supernova, 33,000 LY away.
Last supernova seen in our galaxy: 1680.
Supernova 1987A
Occurred in the Large Magellanic Cloud (a satellite galaxy of our Milky
Way galaxy).
170,000 light-years away (so explosion actually occurred 170,000 years ago).
Neutrino burst detected (by detectors built to measure solar neutrinos).
This was considered validation of many of the key ideas about supernovas.
Original star had a mass of 20 solar masses.
All of the above supernovae were type II,
explosions of supergiant stars.
Table 13.2 (page 412) is a good summary of the chapter.
End chapter 13.
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