Chapter 10 The 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.
General Properties Internal Structure Solar Atmosphere
Luninosity Solar Energy Internal Structure Solar Atmosphere Surface Features Magnetic Fields Solar Activities Solar Cycle
Luminosity, Watts, Joules, and Calories
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 3.81026 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 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
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…[ 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
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 Solar Atmosphere
Source of Solar Energy How do we study the interior of the Sun Solar Atmosphere Surface Features Magnetic Fields Solar Activities Solar Cycle
The Energy Source of the Sun
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 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.
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?
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
Nuclear Fission and Fusion
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 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… Helioseismology. Solar Neutrino Observations.
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
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!
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.
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
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
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
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