- We now turn to the Sun, the object which dominates in the Solar System.
The Sun is the nearest example of a star, so it provides a good introduction
to our next topic, stars.
- The Sun contains most of the mass in the Solar System. This is critical,
because only objects which are sufficiently massive get hot enough in their
centers that nuclear reactions occur there. The Sun stands apart from the
planets because it is the only object in the Solar System in which nuclear
reactions are occurring.
- What is a nuclear reaction?
- Under extreme conditions, it is possible for several atoms of one type
of element to merge together to form a different element, or for a single
atom to be broken up into several individual atoms of other elements. These
are known as nuclear reactions, and the two types are known as fusion
and fission reactions.
- Nuclear reactions can release large amounts of energy because for
some reactions, the total mass of the product atoms have slightly less
mass than the total mass of the atoms that went into the reaction. During
the nuclear reaction, this extra mass is converted into energy, where the
amount converted is given by:
E = mc2
where c is the speed of light. Since the speed of light is a very large
number, even the conversion of a small amount of mass results in a large
amount of energy.
- Generally, putting together two small atoms to make a bigger
atom releases energy for atoms up to the mass of an iron atom, but
putting together two bigger atoms actually
requires energy. The fusion of smaller atoms is what
produces energy in stars.
- Conversely, splitting apart a big atom to make two smaller
atoms releases energy for atoms more massive than iron, but requires
energy for splitting smaller atoms. The fission of large
atoms is what produces energy in nuclear power plants.
- Lower mass atoms release energy by fusion reactions, higher
mass atoms release energy by fission reactions. Iron falls in
between the two groups; no nuclear reaction involving iron releases
energy.
- However, it is very hard to get nuclear reactions to occur. To
understand why, we need to know how atoms are held together.
- Inside an atom, protons and electrons have a property called
electric charge. Electric charge can come in two different signs,
positive and negative. Protons have positive charge, and electrons
have negative charge. There is a fundamental force in nature which
acts as an attractive force between objects with opposite charge and an
repulsive force between objects with the same charge. In an atom, the
electrons are held to the nucleus by this electromagnetic force.
- Inside the nucleus, all of the protons have positive charge. They
manage to stick together despite the repulsive electromagnetic force. This
is because there is another fundamental force called the strong force
which can hold protons and neutrons together. The force is stronger than
the repulsive electromagnetic force between the protons, but only
if two protons are brought very close together.
- The only way to get protons in different atoms close enough to each
other that the strong force can overcome the electromagnetic force and allow
the two nucleii to stick together is if the two atoms collide with each
other at a high speed. Since the speed of atoms is related to their
temperature, this means that nuclear reactions can only occur in objects
which are very hot.
- In the Sun, the nuclear reaction which occurs is called the proton-proton
cycle, in which four Hydrogen atoms are combined in a series of reactions to
form one Helium atom; this chain of reactions also produces energy (in the
form of gamma rays) and some other particles called neutrinos.
These reactions only occurs in the central regions of
the Sun where it is hottest. Energy is generated in this central region and
keeps it hot.
- The energy that is generated in the central regions of the Sun
gradually works its way out through the Sun. In the inner parts of the
Sun, energy gets out by radiation, while in the outer regions it gets out
by convection. Eventually, it makes it to
the surface of the Sun, and finally is radiated out into space. The
energy which we receive from the Sun was originally generated by nuclear
reactions in the core of the Sun.
- Convection is responsible for some of the observed features on the
Sun, such as
granulation
(granulation movie)
- Magnetic fields are also important for some of the observed features
of the Sun, such as
sunspots.
The Sun has a 22 year long magnetic cycle, which affects the number and
location of sunspots and also the amount of
solar activity,
which can affect things, e.g., radio communications, on Earth.
- The basic structure of the Sun can be characterized by several
layers:
core, radiative zone, convective zone, photosphere, chromosphere, and
corona, going from inside to out. Somewhat peculiarly, the very outer
layers of the Sun, the chromosphere and the corona, are hotter than
the photosphere. They are probably heated by a process related to the
magnetic field on the Sun.
- It is only because the inner parts of the Sun are hotter that
the Sun doesn't collapse under its own gravity. The atoms in the central
regions move faster than those in outer regions and consequently they
push outwards with more force, holding the Sun up. The force which they
exert is described by the pressure; the internal pressure is higher
than the external pressure, so the Sun is held up against gravitational
collapse.
- How do we know that this is what is going on in the Sun?
- We know that the Solar System is at least several billion years old.
Nuclear reactions are the only energy source we know of that can sustain
the energy production of the Sun for such a long time.
- We can probe the internal structure of the Sun by studying solar
oscillations (movie).
It turns out that the Sun is vibrating continually, in some
respects similar to the vibrations which occur in the Earth because of
earthquakes. In the same way we used earthquakes to probe the internal
structure of the Earth, we can use these solar oscillations to probe the
internal structure of the Sun. We find that the observed structure closely
matches that of our model which has nuclear reaction in the core of the Sun.
- Nuclear reactions produce, in addition to energy, a special kind of
particle called a neutrino. Although difficult, it is possible to detect neutrinos
coming from the nuclear reactions which occur in the core of the Sun, and
this strongly supports the idea of energy generation from nuclear reactions.
In detail, the observed number of neutrinos is slightly
different from the prediction of our model; for some time, people
wondered whether this indicated that we had a few details in the solar
model wrong, but it has recently been discovered that actually the model
is very good, but that there were some properties of neutrinos that we
hadn't understood correctly!
What is the eventual fate of the Sun?
- We expect that the Sun will eventually change, because at some point,
all of the hydrogen in the core of Sun will get converted into helium, so
there won't be any left for nuclear reactions. The hydrogen in the very
center runs out first, leaving a helium core with a shell of nuclear reactions
around it. During this stage in the Sun's evolution, the pressure forces
change, and the outer regions of the Sun will expand to be very large.
- When the hydrogen is depleted, there will be nothing keeping the
center of the Sun hotter than the outside, so there will be no pressure
which balances gravity. Consequently, the central regions of the
Sun will begin to contract.
- As the core of the Sun contracts, the central regions will heat
up. Eventually it will get hot enough for another nuclear reaction
to start. This reaction changes three Helium atoms into one Carbon
atom. This nuclear reaction keeps it hotter in the center, so the Sun
stabilizes for a while.
- Eventually, the helium in the core of the Sun is all converted into
carbon. Again, the core of the Sun will contract, because nothing balances
the inward gravitational force.
- As the core of the Sun gets denser and denser, the core material
eventually changes state into a kind of matter called degenerate matter.
Degenerate matter has the property that it provides outward pressure
even when energy is not being generated. This electron pressure
will stop the collapse of our Sun. When this sets in, the core of the
the Sun will be essentially pure carbon. The outer regions of the Sun
will most likely be blown off of the Sun during the later stages of
its evolution and return to interstellar space. We observe this for
other stars that have reached the end of their life (
Planetary nebulae gallery)
- Consequently, at the end of its lifetime, our model predicts that
the Sun will be a dense, hot, carbon core which will gradually cool
off. We actually observe many stars that have the properties we expect
the Sun will eventually have: these are called white dwarfs.
Do all stars go through the same phases of evolution as the Sun?
- Next we want to consider other stars. Are they similar to or
different from our Sun? How do we learn about stars which are so far
away?
- We already learned that we can measure masses of stars which are
in binary systems using our understanding of gravity. From observations
of many different systems, we find that stars come in a wide range of
masses; there are stars both less massive and more massive than our Sun.
- The fact that stars have different masses imply that they may
have a different evolutionary history from that of the Sun. The reason
for this is that different amounts of mass imply different strengths
of gravity in the different stars, and this implies that different stars
will reach different temperatures in their cores when they initially form.
- Stars form when a parcel of gas in the interstellar matter starts
to come together under the force of gravity. The gravitational attraction
acts to accelerate the gas, thus heating it up. More massive protostars
heat up more than less massive ones because they experience more
gravitational acceleration. Consequently, the life history of a star
depends on its mass.
- Since we know that we must have a minimum temperature in order
that nuclear reactions can occur, this implies that there is a minimum
mass for stars. Models of how the physics of gas balls work suggest
that if a protostar has less than about 1/10th the mass of the Sun, that
it will never get hot enough for nuclear reactions to start. Observations
seem to confirm this, in that we do not see stars with masses much less
than this.
- For stars which are more massive than this, up to stars with
masses somewhat larger than that of the Sun, the evolution is
similar to that of the Sun.
During most of their lifetimes, these stars convert hydrogen to helium
and the pressure generated by the heat in their cores balances the
gravitational pull which tries to compress the star. As with the Sun,
the hydrogen eventually runs out, gravity acts to compress the star
until a new nuclear reaction which converts helium to carbon starts
up. Eventually, the helium runs out, the star stars to collapse again,
but the collapse is halted by electron pressure when the carbon core
takes on a degenerate form.
- Different stars take different amount of times to go through
the stages of evolution.
- The most massive stars get the hottest in the cores, so they
are the ones that use up their fuel quickest; even though they
have more fuel (since they are more massive), the rate of consumption
is much faster, so they live shorter.
- The more massive the star, the brighter it is during most
stages of evolution.
- For stars which are much more massive than the Sun, a somewhat
different evolutionary path is followed. These have the same stages
of hydrogen and helium nuclear reactions as the less massive stars.
But after the helium is converted to carbon, these stars collapse
and even the conversion of the carbon into degenerate matter does
not provide enough pressure to stop the gravitational collapse, which
is stronger in these more massive stars. The core continues to
collapse until a new series of nuclear reactions set in which convert
the carbon into successively heavier elements until the entire core
is converted into iron. Iron is a special element from the point of
view of nuclear reactions, because there are no nuclear reactions
involving iron which can produce energy. Consequently, once an iron
core is reached, the star collapses under its gravitational force and no
nuclear reactions can stop it. Several things can happen to these
very massive stars:
- If the star is not extremely massive, the collapsing core
can turn into a different state of matter called neutron degenerate
matter, in which protons and electrons fuse together to create an
incredibly dense star known as a neutron star. Neutron degenerate
matter produces a sort of pressure called neutron pressure which can
balance the gravitational force. We observe actual neutron stars when
we see a sort of object called a pulsar.
- For the most massive stars, even neutron pressure cannot hold
the star up after nuclear reactions have finished running their course.
We know of no other force which can hold up these stars, so we suspect
that these stars may collapse into an infinitely dense point which
has such strong gravity at its surface that even light cannot escape
from it. Such is object is called a black hole, and there are indications
that such objects actually exist in the Universe.
- Many, if not all, massive stars experience a massive explosion
as they near the end of their life which expels a large fraction of
their mass back into the interstellar medium. These explosions are
called supernova explosions. Different stars probably expel different
fractions of their mass back into space.
- The end stages of stellar evolution, and supernovae explosions in
particular, are very important for the existence of
life in the Universe because they are the means by which heavy elements
are distributed into the interstellar matter.
- We think that when the Universe original formed, it contained only
hydrogen and a tiny bit of other light elements. There were no heavier
atoms such as carbon, nitrogen, and oxygen which are so important for
our existence today (we are made of these!).
- The first stars converted some of the light elements into heavier
ones by the process of nuclear reactions. Some of these heavier elements
were distributed back into the interstellar matter by ejection of matter
at the end of the lives of stars (planetary nebulae for lower mass stars
and supernovae explosions for higher mass stars).
These elements mixed with the original light elements, and
a new generation of stars were born which had some heavier elements.
This process has continued up to the current time; stars are successively
formed with more and more heavier elements, which are deposited into
the interstellar matter by supernovae explosions.
- Planetary nebulae gallery
- Stingray
- NGC 7027
- M2-9
- MyCn18
- NGC 6543
- Final stages of massive star evolution:
Eta Car
- Supernovae remnant: Cygnus
- Supernovae remnant: Crab
- Some of the heavier elements form into planets around new stars,
and it is from this material that life evolved. We believe that the
heavy elements which we are made of were originally created inside
of massive stars! In a literal sense, we are all made of stardust.
- All of this description of what goes on inside of stars comes
from our stellar models, which predict what stars will look like and
how they evolve based on our understanding of the physics of gas
balls and nuclear reactions. These models, however, are quite well
verified by observations of real stars, and we now turn to the
demonstration of why we think that these models are correct.
- When we study stars, all that we get to study is the light they
emit, since they are too far away for us to go to them and study
them hands-on. Consequently, we need to understand the properties
of light and find out what we can infer about objects from the light
they emit.
- What can we observe when we look at stars, and what can we infer from
these observations?
- Color. From the color of stars, we infer the temperature - hotter
stars are bluer and cooler stars are redder.
- Brightness. The brightness of a star depends on three things: its
distance, temperature, and size. More distant stars are fainter, cooler
stars are fainter, and smaller stars are fainter.
- Spectral absorption lines. The absorption lines which are present
in the spectra of stars depend on the composition of a star and its
temperature.
- The Doppler shift allows us to measure something about the radial
velocity of a stars.
- When we make these observations of stars, we find:
- Most stars have similar compositions, namely: mostly hydrogen, some
helium, and a little bit of everything else.
- Stars come in a wide range of temperatures. The
different temperatures make the stars have different spectra, and stars
are classified by spectral type (OBAFGKM), which is a temperature
sequence. O stars have surface temperatures around 30000 degrees, M stars
around 3000 degrees. The Sun is a G star with a surface temperature
around 5500 degrees.
- Stars also come in a wide range of brightnesses. Brightnesses
are harder to interpret because they are affected by three things:
temperature, size of star, and distance. We can measure the temperature
from the spectrum but we have a problem separating the effects of size
and distance. We can pose the question: are different brightnesses a result
of different distances, or different intrinsic brightness? Alternatively,
are all stars the same size?
- We are greatly aided in our study of stars by the presence of
clusters of stars, which are groups of stars in the sky. These
clusters are real physical associations of stars, meaning that all
stars in a cluster are at about the same distance from us.
- When we observe clusters, the effect of distance is the same for
all stars. We find that stars in a cluster have different brightnesses,
and this is caused by a combination of different temperatures and different
sizes.
- When we look at a cluster, or, alternatively, when we look at
a bunch of isolated stars and correct for the effects of different
distances (by measuring distances using parallax, as we talked about
long ago), we find that there is an interesting relation between the
size of stars and their temperatures. A very useful tool for understanding
stars is a diagram
which plots the color against the luminosity. In
such a plot, stars are only found at several locations:
- Most stars are found along a line in this diagram, known as the
main sequence. The hotter stars along this sequence are brighter,
even more than expected from their temperature: they are also bigger.
- Some stars are found which are cool but bright. The only way this
can be is if such stars are very large. Consequently these stars are
known as red giants. They are red because they are cool, and bright
because they are very large.
- Some stars are found which are hot but faint. These stars are known
as white dwarfs.
- There are many more fainter stars than there are brighter stars.
- We can now pose the question: why do different stars have different
appearances? Several possibilities come to mind: do stars with different
appearances have different masses, ages, or compositions?
- We already learned that we can measure composition from the spectra
of stars and we find that most stars have similar compositions. So this is
not responsible for the different appearances.
- We can measure masses of stars in binary systems, and we find that
stars of different masses lie in different locations along the main
sequence. The hot, bright stars on the main sequence are much more massive
than the cool, faint stars. The main sequence is a mass sequence.
- Red giants are more complicated, however. We find red giants of
a variety of masses. We believe that red giants are older stars.
To understand this, we can consider what our stellar models predict for
the appearance of stars as they age.
- Our stellar models use basic physics to predict what is going on
both inside and on the surface of stars. These models predict that stars
of different masses will have different internal and external temperatures
after they are formed, depending on their mass: massive stars will be
hotter than less massive stars. Our understanding of nuclear reactions
and the balance between pressure and gravity also allows us to predict
sizes of stars, and we find that we expect more massive stars to be
larger than less massive stars. These predictions are exactly what we
observe along the main sequence.
- The stellar models predict that as hydrogen is depleted, the
outer parts of a star will expand and the star will get cooler at its
surface. This happens roughly independently of the mass of the star.
Consequently, our stellar models predict that we will observe red giants
of a range of masses, just as we see.
- The stellar models predict that when the nuclear reactions finally
convert all of the core helium to carbon, all that will remain of most stars
(all except the most massive ones) is a small, hot core. This is exactly
what is observed as white dwarfs.
- Our models also predict how long it will take for stars of different
masses to go through their evolutionary stages. We find that massive
stars will go through these stages much faster than less massive stars.
This occurs because they are so hot in their cores that nuclear reactions
proceed at a much faster pace, and the nuclear fuel runs out much faster
than in less massive stars, even though the more massive stars have more
fuel.
- This understanding leads to predictions about the appearance of
stars in star clusters of different ages which is spectacularly confirmed
by observations. It turns out that the stars in star clusters are not
only at the same distance from us, but they are also all about the same
age.
- When we look at a very young star cluster, stars of all masses are
still converting hydrogen in their cores. Consequently, all stars are still
on the main sequence.
- As a cluster gets older, the more massive stars run out of hydrogen
and become giants. At this point we no longer see the bright end of the
main sequence, because these are the stars which have evolved to become
the giants.
- As the cluster ages further, stars are depleted from the upper end
of the main sequence as they run out of hydrogen in their cores. We get
more and more giants. After a certain age, we begin to see white dwarfs
in the clusters, because these are the remnants of stars which have gone
all the way through their nuclear reactions.
- These predictions for the appearance of the color-magnitude diagram
are verified by observation. Consequently, we have a very strong feeling
that we understand the physics of stars.
- Note that our understanding of stars and our ability to match the
observations very accurately provides strong evidence that some stars must be
very old. We see some young clusters, but we also see clusters that must
be 10-20 billion years old in order for us to be able to match the observations
with our models. This provides independent evidence that the Universe is
old (the other evidence came from studying radioactive decay of specimens
within our Solar System).
Up: AY110 class notes
Previous: PART 4 - THE
Jon Holtzman
2009-11-20
