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					Chapter 15:
The Sun: A
  Nuclear
Powerhous
     e




 February 7, 2006   Astronomy 2010   1
                   Happy Sun




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
   physics.
Where does the energy come from?
Until the 20th century only 2 possibilities were
known:
   Chemical reactions
   Gravity


February 7, 2006        Astronomy 2010            3
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
    gigawatts)
    Sun = 8 x 1016 of these power
    plants (80,000 trillion)
 Anyway you look at it, the Sun
 gives off a lot of energy.
 February 7, 2006           Astronomy 2010    4
Is the Sun Powered by Chemical
           Reactions?
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
   energy.
   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.

February 7, 2006     Astronomy 2010              5
Is the Sun Powered by Chemical
           Reactions?
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.




February 7, 2006   Astronomy 2010          6
                   Gravity Squeeze?
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
   energy output.
   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



February 7, 2006          Astronomy 2010                  7
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
 of light.


 February 7, 2006   Astronomy 2010           8
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.


February 7, 2006    Astronomy 2010             9
                   …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.

February 7, 2006          Astronomy 2010       10
February 7, 2006   Astronomy 2010   11
 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

  February 7, 2006           Astronomy 2010                     12
       15.2.3 The Atomic Nucleus
Two ways to rearrange nuclei and get energy:
   Fission
    • 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
   Fusion
    • 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!!


February 7, 2006          Astronomy 2010                   13
           How Does Fusion Work?
Nuclear fusion:
   a process by which two light nuclei combine to form a single
   larger nucleus.
However: nuclei are positively charged
   Like charges repel
   Two nuclei naturally repel each other and thus cannot fuse
   spontaneously
   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?

February 7, 2006         Astronomy 2010                    14
         Fusion needs fast moving nuclei
Fast moving nuclei can
overcome the repulsion -
                          Low speed
they get a running start.
Lots of fast moving
nuclei means high
temperature.
The core of the Sun has
a temperature of 15
                          High speed
million degrees Kelvin.
(ouch!)



 February 7, 2006     Astronomy 2010       15
              Fusion Power on Earth
Fusion is the source of
energy for hydrogen
bombs.
We are trying to harness
fusion to generate
electricity:
   tokamak - magnetic
   confinement machine as
   envisioned for ITER
   shown to the right
   inertial confinement fusion
   - Lawrence Livermore
   National Lab
                                           ITER reactor
February 7, 2006          Astronomy 2010                  16
             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
fusion reactions.
Hypothesis: all stars produce energy by
nuclear fusion.


February 7, 2006     Astronomy 2010         17
                                                1. fuse two hydrogen, H (1
proton-proton chain                                proton) to make
                                                   deuterium, 2H (1 proton,
                                                   1 neutron), neutrino
                                                   and positron
                                                2. fuse one deuterium and
                                                   one hydrogen to make
                                                   helium-3 3He (1 proton,
                                                   2 neutrons), gamma ray
                                                   (energetic photon)
                                                3. fuse two helium-3 to
                                                   make helium 4He plus
                                                   two hydrogen
 H  H 2H  e 

                    2
                        H  H 3He              3
                                                      He3He4He  H  H
 February 7, 2006              Astronomy 2010                          18
         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
   enough energy
   chance of this happening are very, very small
   rate too slow to power the Sun
   proton-proton chain: each step involves collision of two
   particles
   chance of two particles colliding and fusing is much higher,
   so nature slowly builds up the helium nucleus.


February 7, 2006          Astronomy 2010                    19
        Fusion and Solar Structure
                                    fusion only in
                                    Sun's core
                                    only place its
                                    hot enough
                                    heat from
                                    fusion
                                    determines
                                    Sun's
                                    structure




February 7, 2006   Astronomy 2010             20
Heat from Core determines Sun's Size
Force equilibrium
Hydrostatic equilibrium: balance between
    thermal pressure from the hot core pushing
    outwards
    gravity squeezes the star collapse to the very
    center
Nuclear fusion rate is very sensitive to
temperature.
A slight increase/decrease in T causes
fusion rate to increase/decrease by a
large amount.

 February 7, 2006    Astronomy 2010           21
Gravity and Pressure                             pressure
                                                 from
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
                                                 from
hydrostatic equilibrium on Sun                   gravity
   "cloud of gas" (like 1/4 pounder)
   gravity pulls cloud to the center
                                                     pressure
   pressure from gas below opposes
                                                     from hot
   gravity
                                                     gas
   heat from fusion in the hot core
   increases pressure                        cloud
   energy output controls size of sun!
                                                     weight
                                                     from
                                                     gravity
February 7, 2006            Astronomy 2010               22
        Temperature and Pressure
 temperature: random
motion of atoms in a
gas
 pressure: amount of
force per unit area on
piston from gas
 generally pressure
increases with
increasing temperature

February 7, 2006   Astronomy 2010   23
      Balancing Fusion, Gravity and
                Pressure
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
      thermal pressure.
   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
      would increase
   9. Stability would be re-established between the nuclear reaction
      rates and the gravity compression



   February 7, 2006         Astronomy 2010                     24
             Hydrostatic Equilibrium




balance between pressure, heat from fusion and gravity
determines Sun's size
big stars have cooler cores, small stars have hotter cores –
more compressed
February 7, 2006          Astronomy 2010                   25
                   Other Particles
Helium is not the only product in the
fusion of hydrogen.
Two other particles produced
   Positron
   Neutrino




February 7, 2006        Astronomy 2010   26
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.


February 7, 2006       Astronomy 2010               27
                   Neutrinos
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.


February 7, 2006     Astronomy 2010              28
                   Neutrino Counting
In principle:
   Use neutrino count at Earth as indicator of
   the Sun’s energy output
The problem:
   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!


February 7, 2006         Astronomy 2010      29
                   Neutrino Abundance
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.



February 7, 2006         Astronomy 2010                   30
                   Detecting Neutrinos
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
   of germanium.
   Neutrinos can interact with protons and neutrons
   and produce an electron. The electron can be
   detected.


February 7, 2006          Astronomy 2010           31
Neutrino Detectors
                                 Ray Davis
 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.



                        Kamiokande

 February 7, 2006      Astronomy 2010                    32
          Solar Neutrino Production
Number of neutrinos produced in the Sun
is directly proportional to the number of
nuclear reactions taking place in the
Sun's core.
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
Earth.

February 7, 2006   Astronomy 2010     33
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.




February 7, 2006   Astronomy 2010           34
Solar Neutrino Production (cont’d)
Later experiments using many tons of gallium
were able to detect the more abundant low-
energy neutrinos.
However, those experiments also found the
same problem: too few neutrinos (the gallium
experiments found about 2/3 the expected
number).
The puzzling lack of neutrinos from the Sun is
called the solar neutrino problem.


February 7, 2006   Astronomy 2010           35
              Possible Explanations:
 Nuclear fusion is not the Sun's power source.
      Not supported by observations, not likely to be the correct
      reason.
 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
      are correct.
 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
      reactions.
February 7, 2006           Astronomy 2010                    36
             Solar Neutrino Solution
Three types of neutrinos exist.
The Sun produces only one type, called
electron neutrinos
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.

February 7, 2006     Astronomy 2010       37
                     Neutrino Oscillations
                                                      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
                                                      to Earth.
                                                      When we look at the
                                                      neutrinos on Earth, some
                                                      of the original green is
                                                      now blue or yellow.

February 7, 2006                            Astronomy 2010                  38

				
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