The Sun: A
February 7, 2006 Astronomy 2010 1
February 7, 2006 Astronomy 2010 2
Why Does the Sun Shine?
The Sun gives off energy (duh)!
The energy must come from somewhere -
there’s no free lunch.
Conservation of energy is a fundamental tenet of
Where does the energy come from?
Until the 20th century only 2 possibilities were
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The Sun’s Energy Output
How bright is the Sun?
The Sun produces 4x1026 watts
• Watt is the unit for the rate of
energy use, commonly seen on light
bulbs and appliances.
Our largest power plants produce
around 5 x 109 watts of power
(5,000 megawatts or 5
Sun = 8 x 1016 of these power
plants (80,000 trillion)
Anyway you look at it, the Sun
gives off a lot of energy.
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Is the Sun Powered by Chemical
What are chemical reactions?
Rearrange the atoms in molecules, as in 2H2 + O2
2H2O + energy. This reaction combines
hydrogen and oxygen gas to produce water plus
Reverse the process: 2H2O + energy 2H2 + O2.
By adding energy we can dissociate water into
hydrogen and oxygen.
The energy factor is often left out of chemical
reaction formulas, for convenience.
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Is the Sun Powered by Chemical
If the Sun is powered by burning coal or oil,
how long could its fuel last?
Only a few thousand years!
A process that uses fuel more efficiently is
needed - something that gets more energy out
of every kilogram of material.
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Gravitational contraction: falling layers of the Sun's
material compress the Sun heat energy
drop a book noise! Gravitational potential energy.
A contraction of 40m per day would account for the Sun’s
Efficiency ~ 1/10000 %
Gravity could power the Sun for about 100 million
years but the Sun is at least 4 billion years old!
Gravity can't be the Sun's main energy source
But it did help ignite the Sun when it formed
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15.2 Mass, Energy, and the Special
Theory of Relativity
To understand the way the Sun produces
energy, we need to learn a little about nuclear
physics and the special theory of relativity.
Nuclear physics deals with the structure of the
nuclei of atoms.
The special theory of relativity deals with the
behavior of things moving at close to the speed
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15.2.1 Converting Mass to Energy
Out of the special theory of relativity comes the
most famous equation in science:
This equation tells us that mass (m) is just
another form of energy (E)!
The c2 is the square of the speed of light.
1 gram of matter is equivalent to the energy
obtained by burning 15,000 barrels of oil.
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…but there are rules
We can’t simply convert atoms into energy.
We rearrange the protons and neutrons in
nuclei to get a lower-mass configuration.
The difference between initial mass and final
mass is converted to energy.
Chemical energy comes from rearranging atoms to
configurations of lower energy (mass).
Nuclear energy comes from rearranging nuclei to
configurations of lower mass (energy).
In each case, we get out the energy difference.
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Elementary Particles (condensed)
Particle Mass Charge 5 particles play a
name (MeV/c2) (e) fundamental role in
Proton 938.272 +1 the Sun.
Protons and neutrons
Neutron 939.565 0 make atomic nuclei
Electrons orbit nuclei
Electron 0.511 -1 of atoms
Photons are emitted
Neutrino <10-6 0 by the Sun
Neutrinos are also
Photon 0 0 emitted
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15.2.3 The Atomic Nucleus
Two ways to rearrange nuclei and get energy:
• produces energy by breaking up massive nuclei like
Uranium into less massive nuclei like Barium and Krypton
• A-bombs, nuclear reactors
• needs Uranium 235, Plutonium 238
• Problem: no Uranium or Plutonium on the Sun
• produces energy by combining light nuclei like Hydrogen
to make more massive nuclei like Helium.
• H-bomb, tokamak, internal confinement fusion
• Sun has lots of Hydrogen!!
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How Does Fusion Work?
a process by which two light nuclei combine to form a single
However: nuclei are positively charged
Like charges repel
Two nuclei naturally repel each other and thus cannot fuse
For fusion, electrical repulsion must be “overcome”
When two nuclei are very close the strong nuclear
force takes over and holds them together.
How do two nuclei get close enough?
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Fusion needs fast moving nuclei
Fast moving nuclei can
overcome the repulsion -
they get a running start.
Lots of fast moving
nuclei means high
The core of the Sun has
a temperature of 15
million degrees Kelvin.
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Fusion Power on Earth
Fusion is the source of
energy for hydrogen
We are trying to harness
fusion to generate
tokamak - magnetic
confinement machine as
envisioned for ITER
shown to the right
inertial confinement fusion
- Lawrence Livermore
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Fusion Powers the Sun
Temperatures in the cores of stars are above
the approximately 8 million K needed to fuse
hydrogen nuclei together.
Calculations: observed power output of the
Sun consistent with fusion of hydrogen nuclei.
Observation: neutrinos from Sun produced by
Hypothesis: all stars produce energy by
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1. fuse two hydrogen, H (1
proton-proton chain proton) to make
deuterium, 2H (1 proton,
1 neutron), neutrino
2. fuse one deuterium and
one hydrogen to make
helium-3 3He (1 proton,
2 neutrons), gamma ray
3. fuse two helium-3 to
make helium 4He plus
H H 2H e
H H 3He 3
He3He4He H H
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Why a complicated chain?
Fusion would be simpler if four protons would collide
simultaneously to make one helium nucleus
Simpler, but less likely
rare for four objects to collide simultaneously with high
chance of this happening are very, very small
rate too slow to power the Sun
proton-proton chain: each step involves collision of two
chance of two particles colliding and fusing is much higher,
so nature slowly builds up the helium nucleus.
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Fusion and Solar Structure
fusion only in
only place its
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Heat from Core determines Sun's Size
Hydrostatic equilibrium: balance between
thermal pressure from the hot core pushing
gravity squeezes the star collapse to the very
Nuclear fusion rate is very sensitive to
A slight increase/decrease in T causes
fusion rate to increase/decrease by a
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Gravity and Pressure pressure
force equilibrium table
Newton's second law: F = ma
static equilibrium: no acceleration if
forces on object balance
gravity tries to pull 1/4 pounder to
center of the Earth
pressure from table opposes gravity weight
hydrostatic equilibrium on Sun gravity
"cloud of gas" (like 1/4 pounder)
gravity pulls cloud to the center
pressure from gas below opposes
heat from fusion in the hot core
increases pressure cloud
energy output controls size of sun!
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Temperature and Pressure
motion of atoms in a
pressure: amount of
force per unit area on
piston from gas
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Balancing Fusion, Gravity and
If the rate of fusion increases, then:
1. thermal pressure increases causing the star to expand.
2. star expands to a new point where gravity would balance the
3. the expansion would reduce compression of the core
4. the temperature in the core would drop
5. the nuclear fusion rate would subsequently slow down
6. the thermal pressure would then drop
7. the star would shrink
8. the temperature would rise again and the nuclear fusion rate
9. Stability would be re-established between the nuclear reaction
rates and the gravity compression
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balance between pressure, heat from fusion and gravity
determines Sun's size
big stars have cooler cores, small stars have hotter cores –
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Helium is not the only product in the
fusion of hydrogen.
Two other particles produced
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Gamma Ray Propagation in the Sun
Positrons quickly annihilate with electrons.
Photons produced in core of the Sun take
about a million years to move to the surface.
Slow migration because they scatter off the
dense gas particles
move about only a centimeter between collisions.
In each collision, they transfer some of their energy
to the gas particles.
As they reach the photosphere, gamma rays
have become visible photons.
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Nearly massless particles with no charge.
Rarely interact with ordinary matter.
Neutrinos travel extremely fast
Almost at the speed of light if small mass.
Neutrinos pass from the core of the Sun
to the surface in only two seconds.
They take less than 8.5 minutes to travel
the distance from the Sun to the Earth.
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Use neutrino count at Earth as indicator of
the Sun’s energy output
Neutrinos have a very low probability of
interacting with matter.
Could pass through a light year of lead and
not be stopped by any of the lead atoms!
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The Sun produces A LOT of neutrinos.
In one second several million billion
neutrinos pass through your body.
Do you feel them?
Not to worry!
• The neutrinos do not damage anything.
• The great majority of neutrinos pass right
through the entire Earth as if it wasn’t there.
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Increase the odds of detecting neutrinos by
using a LARGE amount of a material that
reacts with neutrinos in a measurable way.
A chlorine isotope changes to a radioactive isotope
of argon when hit by a neutrino.
A gallium isotope changes to a radioactive isotope
Neutrinos can interact with protons and neutrons
and produce an electron. The electron can be
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Neutrino detectors use hundreds
of thousands of liters of these
materials in a container buried
under many tens of meters of
rock to shield the detectors from
other energetic particles from Nobel Prize in 2003
space called cosmic rays.
Even the largest detectors detect
only a few neutrinos per day.
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Solar Neutrino Production
Number of neutrinos produced in the Sun
is directly proportional to the number of
nuclear reactions taking place in the
Same principle with neutrinos produced
via the Carbon-Nitrogen-Oxygen chain.
The more reactions there are, the more
neutrinos are produced and the more
that should be detected here on the
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Solar Neutrino Production (cont’d)
Physicists find that the number of neutrinos
coming from the Sun is smaller than expected.
Early experiments detected only 1/3 of the
expected number of neutrinos.
These experiments used hundreds of
thousands of liters of cleaning fluid (composed
of chlorine compounds) or very pure water.
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Solar Neutrino Production (cont’d)
Later experiments using many tons of gallium
were able to detect the more abundant low-
However, those experiments also found the
same problem: too few neutrinos (the gallium
experiments found about 2/3 the expected
The puzzling lack of neutrinos from the Sun is
called the solar neutrino problem.
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Nuclear fusion is not the Sun's power source.
Not supported by observations, not likely to be the correct
The experiments were not calibrated correctly.
Unlikely that all carefully-tuned experiments were tuned in
the same wrong way. Experiments independently verified
by many other scientists; astronomers think that the results
The nuclear reaction rate in the Sun is lower than
what our calculations say.
Possible but many people have checked and re-checked
the physics of the reaction rates.
Strong constraints in how much one can lower the
temperature in the core of the Sun to slow down the
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Solar Neutrino Solution
Three types of neutrinos exist.
The Sun produces only one type, called
The experiments detect only electron-type.
On their way from the Sun, neutrinos can
transform from one type to another we only
detect 1/3 of the mix at Earth.
This also implies that neutrinos have mass,
very small, but not zero.
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The Sun produces only
e neutrinos (green).
This becomes one of the
types 1, 2, or 3 on its
way to Earth.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
These 3 mix on their way
When we look at the
neutrinos on Earth, some
of the original green is
now blue or yellow.
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