Chapter 10
The Sun, Our Star
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The Sun support life on Earth
1. The Sun provides energy for
photosynthesis, which releases
oxygen into the atmosphere.
2. 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.
• General Properties
– Luninosity
– Solar Energy
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Internal Structure
Solar Atmosphere
Surface Features
Magnetic Fields
Solar Activities
Solar Cycle
General Properties
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.
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
Earth’s atmosphere…
• Solar Constant…1366 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 Earth’s atmosphere is measured to be 1366
joules every second. This is precisely what we predicted from StefanBoltzmann 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
Blackbody
• A blackbody is an object that absorbs all
electromagnetic radiation on it. It also irradiate a
thermal radiation according to its temperature.
Solar Energy and Your Electricity
Bill
• In 2001, 107 million US households consumed 1,140 billion kWh of
electricity…[http://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 Earth’s 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!
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 doesn’t 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 current…Albert Einstein’s theoretical work on
photoelectric effect earned him the 1921 Nobel Prize in Physics.
Coming Homework Problem
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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 Earth’s 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?
So, how does the Sun generate so
much energy?
• General Properties
• Internal Structure
– Source of Solar Energy
– How do we study the interior of the Sun
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Solar Atmosphere
Surface Features
Magnetic Fields
Solar Activities
Solar Cycle
The Energy Source of the Sun
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Before Einstein’s 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
Einstein’s mass-energy equation, E = mc2.
This is a simplified picture that’s
not exactly correct.
Electric charge is not conserved!
The Internal Structure of the Sun
Core
1. The region where nuclear fusion takes
place to generate the solar energy.
2. T ~ 15 million degrees K.
Radiation Zone
1. Energy is transported outward primarily
by photons traveling through this region.
2. T ~ 10 million degrees K and decreases
outward.
3. No nuclear fusion.
Convection Zone
1. 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.
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…
Why Does Nuclear Fusion Occurs Only at
the Center of the Sun?
Click on image to start animation
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.
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
Proton-Proton Chain
There are many different fusions that can take place…for 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
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.
The Solar Thermostat
Nuclear fusion is the source of all the energy the Sun releases into
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space. The Sun fuses hydrogen at a steady rate, because of a
natural feedback process that acts as a thermostat for the Sun’s
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 happen…the 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…
How do we Observe the Internal Structure
of the Sun?
Based on our understanding of physics…gravitation, 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 Sun…like 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…
1. Helioseismology.
2. Solar Neutrino Observations.
Helioseismology
The red and blue patches represent
regions of solar surface receding
inward (red) and bulging outward
(blue).
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.
Paths of wave
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.
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 second…if 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!
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.
Sudbury Neutrino
Observatory in Canada, 2 km
underground. The 12 meter
diameter tank contains 1,000
tons of heavy water.
Kamiokande Neutrino
Detector, Japan
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.
The Solar Neutrino Problem
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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 don’t really understand neutrinos…our 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 massless…Perhaps this model is wrong?
Resolution of The Solar Neutrino
Problem
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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/physics/articles/bahcall/