Chapter 10 The Sun, Our Star

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Chapter 10The Sun, Our Star

• The Sun support life on Earth
• The Sun provides energy for photosynthesis, which
  releases oxygen into the atmosphere.
• The greenhouse effect trap some of the solar
  energy on Earth, keeping it warm (at the right
  temperature for us).
• The Sun ultimately determines the fate of the
  life on Earth.
• The Sun is the only star that we can study in
  details.
• The Sun is the test bed for our theory of the
  stars.

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• General Properties
• Luninosity
• Solar Energy
• Internal Structure
• Solar Atmosphere
• Surface Features
• Magnetic Fields
• Solar Activities
• Solar Cycle

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General Properties
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Luminosity, Watts, Joules, and Calories

• Luminosity
• The energy an object radiates per unit time. So,
  it is a measure of power.
• Watt
• Unit of power. One watt is one Joule per second.
  
• Joule
• Unit of energy.
• Lifting a 1 kg (2.2 lb) mass up by 10 cm (4
  inches) on the surface of Earth would requires 1
  joule of energy.
• Accelerating a 2 kilograms (4.4 Pounds) mass from
  rest to a speed of 1 m/sec (2.25 miles/hour)
  requires 1 joule of energy.
• 1 Calories 4.2 Joules.
• The Sun generates 9 ? 1025 calories of energy
  every second, or
• 90,000,000,000,000,000,000,000,000 calories per
  second.

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Solar Luminosity and Solar Constant

• So, how do we measure solar luminosity?
• The total energy output of the Sun can be derived
  from Stefan-Boltzmann Law
• If we know the size of the Sun is 700,000 km,
  that its surface temperature is 5,800 K, and
  assume it is radiating like a blackbody, then we
  can calculate the total energy the Sun is
  irradiating per second (the luminosity) according
  to Stefan-Blotzmann Law.
• If we know the luminosity of the Sun is 3.8?1026
  watts, and know that the distance between the Sun
  and the Earth is 1AU, then we can predict how
  much energy we should be receiving from the Sun
  just outside the Earths atmosphere
• Solar Constant1366 w/m2, or 1.36 kW/m2
• The magnitude of energy flow from the Sun
  measured in a 1 m2 (or 10 ft ? 10 ft) area
  outside of the Earths atmosphere is measured to
  be 1366 joules every second. This is precisely
  what we predicted from Stefan-Boltzmann Law.
• The energy output of the Sun was thought to be
  constant in time (but this is not strictly
  correct), therefore, it is referred to as the
  solar constant.
• 1300 watts of electric power is enough to
• Light thirteen 100 watts light bulbs
• Run 20 laptop PCs

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Blackbody

• A blackbody is an object that absorbs all
  electromagnetic radiation on it. It also
  irradiate a thermal radiation according to its
  temperature.

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Solar Energy and Your Electricity Bill

• In 2001, 107 million US households consumed 1,140
  billion kWh of electricityhttp//www.eia.doe.gov
  /emeu/reps/enduse/er01_us.html
• hWh kilo-Watt hour
• 1 kW 1000 Watt 1000 juoles/sec
• 1 kWh 1000 joules/sec ? 1 hour
• 1000 joules/sec ? 3600 sec
• 3.6 million joules
• Each US household needs 1.2 kW of electric power
  constantly
• 1,140 ? 109 kWh ? 107 ? 106 households ? 365
  days ? 24 hour/day 1.2 kWh per hour per
  household
• 1.2 kW per household
• So, ideally, if you can build a solar energy
  collector with 100 efficiency, and that the Sun
  shines 24 hours a day, and the Earths atmosphere
  is completely transparent, and it is never
  cloudy, then you only need a solar energy
  collector with a size of 1 m2 to supply all your
  electricity need!

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Of Course, in Reality

• On the surface of the Earth, solar irradiance is
  reduced due to the reflection and absorption by
  the atmosphere, and only about 1 kW is available
  near the equator
• It is always cloudy
• The Sun doesnt shine 24 hours a day
• Solar cell efficiency is about only 10 to 30
  (very expansive material)
• Solar cells utilize an effect called
  photoelectric effect when photons with
  sufficient energy is illuminated on certain type
  of materials, the electrons in the materials can
  escape the bound of the atoms and become free
  electrons (in the material) to generate electric
  currentAlbert Einsteins theoretical work on
  photoelectric effect earned him the 1921 Nobel
  Prize in Physics.

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Coming Homework Problem

• According to the Hawaii Electric Company (HECO),
  its power generating capacity is approximately
  1,700 MW (Mega Watts), or 1.7 ? 109 Watts (1 Watt
  is 1 Joule per second), or 1.7 ? 109 Joule per
  second (1 Joule is about 4.2 Calories). The
  amount of solar energy outside the Earths
  atmosphere is 1,300 Watt/m2, meaning if we can
  collect all the solar energy falling on a 1 m2
  size solar energy collector we can extract 1,300
  Joule of energy per second. Assuming that after
  the absorption of the solar energy by the
  atmosphere, and the inefficiency of the solar
  energy collector, we can get about 500 Watt/m2 on
  the ground. How big a solar energy collector (in
  unit of m2 or km2) do we need to completely
  replace the power generating capacity of HECO?

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So, how does the Sun generate so much energy?
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• General Properties
• Internal Structure
• Source of Solar Energy
• How do we study the interior of the Sun
• Solar Atmosphere
• Surface Features
• Magnetic Fields
• Solar Activities
• Solar Cycle

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The Energy Source of the Sun

• Before Einsteins special theory of relativity,
  the most plausible theory for the generation of
  the energy in the Sun was gravitational
  contraction
• as the solar nebula collapses due to the
  gravitational pull of the denser core region,
  gravitational potential energy is converted into
  thermal energy. However, according to
  calculation, the Sun can sustain its energy
  output for only about 25 million years if
  gravitational potential energy is the source of
  the solar energy.
• Today, we understand that the energy source of
  the Sun is the nuclear fusion process which
  combines hydrogen nuclei to form helium, and at
  the same time releasing a very large amount of
  energy per reaction. The increase of temperature
  at the center of the Sun due to gravitational
  contraction eventually trigger nuclear fusion,
  which converts some of the mass into energy,
  according to Einsteins mass-energy equation, E
  mc2.

This is a simplified picture thats not exactly
correct. Electric charge is not conserved!
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The Internal Structure of the Sun

• Core
• The region where nuclear fusion takes place to
  generate the solar energy.
• T 15 million degrees K.
• Radiation Zone
• Energy is transported outward primarily by
  photons traveling through this region.
• T 10 million degrees K and decreases outward.
• No nuclear fusion.
• Convection Zone
• Energy is transported through convection hot gas
  rises, irradiates their energy, and becomes cold.
  Cold gas sink to the bottom.
• Example at home boiling water.
• Example at play glider and hang-glider.

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The Equilibrium Between Gravity and Pressure
The temperature and density inside the Sun
increase due to gravitational contraction.
Without a force to counter gravitation force, the
Sun will continue to contract. However, as the
Sun contracts, the density and temperature of the
interior also increase. This increases the
thermal pressure of the interior, pushing outward
against the gravitational force.

• Gravitational force pulls the gas inward
• Thermal pressure push the gas outward
• When inward gravitational force is equal to the
  outward push of thermal pressure, the size of the
  Sun remains constant
• If the mass of the Sun is high enough, the
  internal pressure and temperature can be high
  enough for nuclear fusion to begin

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Why Does Nuclear Fusion Occurs Only at the Center
of the Sun?

• Temperature Density
• Temperature is a measurement of the average
  kinetic energy of the particles.
• A volume of gas at very high temperature means
  that the particles of the gas move at very high
  speed.
• The very high speed is needed to overcome the
  repulsive electromagnetic force between the
  protons to get them very close to each other.
• High density is necessary so that the probability
  of fusion is high.
• Once the protons are close to each other, the
  strong nuclear force can bind them together to
  make a new and heavier element.

Click on image to start animation
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Nuclear Fission and Fusion

• Nuclear Fission
• The process of splitting an atomic nucleus is
  called nuclear fission.
• Our nuclear power plants generate power by
  splitting large nuclei such as uranium or
  plutonium into smaller ones.
• Nuclear Fusion
• The process of combining (or fusing) two small
  atoms into a larger one

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Proton-Proton Chain

• There are many different fusions that can take
  placefor example,
• The predominant fusion process in the core of the
  Sun is the proton-proton chain
• Proton-Proton chain fuses four protons into one
  helium,

Click on picture to start animation
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How does the energy generated at the center get
to the surface and to us?

• The energy generated by the nuclear fusion
  process is released in the form of photons
  (radiative energy). The photons interact with the
  solar plasma (mostly with the electrons). Each
  time a photon encounters an electron, it changes
  its direction. Thus, the photons go through a
  zigzag path to the surface. It takes about 1
  million years for a photon to travel from the
  center of the Sun to its surface.
• Because of all the interactions along the way,
  the photons lost memory about the core where they
  originate
• At the upper portion of the solar interior,
  convection is the more efficient energy transport
  mechanism to get the energy to the surface.

The random walk of photon to the surface.
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The Solar Thermostat

• Nuclear fusion is the source of all the energy
  the Sun releases into space. The Sun fuses
  hydrogen at a steady rate, because of a natural
  feedback process that acts as a thermostat for
  the Suns interior.
• Because the nuclear fusion rate is very sensitive
  to temperature, if the temperature of the core
  increases by some amount, the fusion rate would
  go up very rapidly, generating a large amount of
  energy.
• Because the energy is transported slowly to the
  surface, this extra energy will pile up in the
  interior, causing the temperature and the
  pressure to increase.
• The increased pressure pushes the envelop to
  expand and cool, reducing the fusion rate.
• If the temperature is decreased below its steady
  state value, the reverse would happenthe
  decrease core temperature would reduce the fusion
  rate, causing the core to contract. The
  contraction in turn increases the temperature and
  pressure, restoring the fusion rate

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How do we Observe the Internal Structure of the
Sun?

• Based on our understanding of
  physicsgravitation, mechanics, thermodynamics,
  electromagnetism, nuclear physics, and elementary
  particle physics, we can build a mathematical
  model of the internal structure of the Sun that
  produces the observed properties of the Sunlike
  its mass, size, surface temperature, luminosity,
  etc. This model is usually referred to as the
  Standard Solar Model. However, to verify our
  model, it is necessary to actually look under the
  surface of the Sun.
• Almost all the radiations (from X-ray to Radio
  frequency radiation) from the Sun originate from
  the outer layers of the Sun, from the visible
  surface (the photosphere) to the corona. These
  lights do not carry information about the
  interior of the Sun. To see inside the Sun, we
  need to use special observational methods.
• There are two methods that allow us to see
  inside the Sun
• Helioseismology.
• Solar Neutrino Observations.

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Helioseismology

• Helioseismology
• The study of how the surface of the Sun moves
  expands and contracts, can tell us about the
  internal structure of the Sun. This is similar to
  how we study the internal structure of the Earth
  by studying how sound waves propagate through
  Earth.
• The surface of the Sun is oscillating up and down
  due to the excitation of seismic waves.
• We observe the motion of the solar surface by
  observing the Doppler shift of light from the
  surface of the Sun.

The red and blue patches represent regions of
solar surface receding inward (red) and bulging
outward (blue).
The surface of the Sun is oscillating up and down
due to the excitation of seismic waves.
Different seismic wave travels through different
part of the solar interior. Thus, by studying the
behavior of the seismic waves, we can infer the
internal structure of the Sun.
Paths of wave
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Solar Neutrinos

• Neutrino
• A type of elementary particles (three different
  flavors, actually) with very low mass and
  interacts only through the weak (nuclear) force.
• Neutrinos are produced in the proton-proton chain
  that powers the Sun. We know how many neutrinos
  are produced by the Sun every secondif our
  standard solar model is correct.
• Neutrinos are very difficult to detect From the
  many trillions of solar neutrinos passing through
  the neutrino detectors every second, only roughly
  one neutrino a day is expected to be recorded!

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Neutrino Observatories
Homestake Neutrino Detector in South Dakota, 1.5
km underground. Neutrino detectors are placed
underground to shield them from other unwanted
interaction with other cosmic ray particles.
Kamiokande Neutrino Detector, Japan
Sudbury Neutrino Observatory in Canada, 2 km
underground. The 12 meter diameter tank contains
1,000 tons of heavy water.
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Neutrino Observatories
The Homestake neutrino detector contains 470 tons
of dry-cleaning fluid such as Tetrachloroethylene.
A neutrino converts a chlorine atom into one of
argon via the charged current interaction. The
fluid is periodically purged with helium gas
which would remove the argon. The helium is then
cooled to separate out the argon. These chemical
detection methods are useful only for counting
neutrinos no neutrino direction or energy
information is available.
Homestake Neutrino Detector in South Dakota, 1.5
km underground. Neutrino detectors are placed
underground to shield them from other unwanted
interaction with other cosmic ray particles.
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The Solar Neutrino Problem

• According to calculation based on the standard
  solar model, we should be observing about one
  solar neutrino per day in our neutrino detectors.
  But we only get about one solar neutrino every
  three days in the data obtained from Homestake
  experiment by Ray Davis in 1968.
• Three possible explanations
• The standard solar model is wrong?
• However, results derived from helioseismology
  observations in the 1990s consistantly showed
  that the internal structure of the Sun is
  consistent with the standard solar model
• The experiment was wrong?
• Homestake results were verified by the
  Kamiokande experiment by Masatoshi Koshiba in
  1989.
• We dont really understand neutrinosour
  understanding of the neutrinos is incomplete?
• In the standard model of particle physics,
  neutrinos are have zero electric charge, interact
  very weakly with matter, and are masslessPerhaps
  this model is wrong?

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Resolution of The Solar Neutrino Problem

• There are three different types of neutrinos
  (electron, muon, and tau neutrinos). The earlier
  neutrino detectors (Homestake and Kamiokande)
  were sensitive to only one of the three types
  the electron neutrinos.
• In 1969, Bruno Pontecorvo and Vladmir Gribov of
  the Soviet Union proposed that lower energy solar
  neutrinos switch from electron neutrino to
  another type as they travel in the vacuum from
  the Sun to the Earth. The process can go back and
  forth between different types. The number of
  personality changes, or oscillations, depends
  upon the neutrino energy. At higher neutrino
  energies, the process of oscillation is enhanced
  by interactions with electrons in the Sun or in
  the Earth. Stas Mikheyev, Alexei Smirnov, and
  Lincoln Wolfenstein first proposed that
  interactions with electrons in the Sun could
  exacerbate the personality disorder of neutrinos,
  i.e., the presence of matter could cause the
  neutrinos to oscillate more vigorously between
  different types.
• New neutrino detectors ( Sudbury Neutrino
  Observatory in Canada) sensitive to all three
  different types of neutrino finally resolved this
  issue.
• Sudbury results indicated that the number of
  solar neutrinos is consistent with our standard
  model of the Sun!

Solar Neutrino Experiment 2002 Nobel Price in
Physics http//nobelprize.org/nobel_prizes/physic
s/articles/bahcall/