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CHAPTER 11
THE SUN
CHAPTER OUTLINE
11-1 Solar Properties
1. As viewed from the Earth, the Sun has an average angular diameter of 31´59° and is at an average distance from the Earth of 1.50  108 km. The diameter of the Sun can therefore be calculated as 1.39  106 km, or about 110 times Earth’s diameter and about 10 times Jupiter’s.
2. Using Kepler’s 3rd law we find that the mass of the Sun is 1.99  1030 kg, about 333,000 times
Earth’s mass. Thus, the Sun’s average density is 1.41 g/cm3, about the same as the density of Jupiter.
3. By observing sunspots, Galileo concluded that the Sun’s rotation period is more than a month.
Today we know that the Sun exhibits differential rotation (25 days at its equator and nearly 35
days near its poles).
4. Sunspots are regions of the photosphere that are temporarily cool and dark compared to surrounding regions.
11-2 Solar Energy
1. The Sun emits energy in all parts of the electromagnetic spectrum.
2. Luminosity is the rate at which electromagnetic energy is emitted; the solar luminosity is
about 3.85  1026 watts.
3. Solar energy strikes the Earth at the rate of 1,370 watts/m2.
The Source of the Sun’s Energy
1. In the mid-1800s, it was proposed by von Helmholtz and Kelvin that a slow gravitational contraction is the source of the Sun’s energy. Such a mechanism would power the Sun for only a few
hundred million years.
2. By the early 20th century, however, geologists showed that the Earth was billions of years
old—a period 10 times longer than that necessary for gravitational contraction to produce the
Sun’s energy. The theory had to be abandoned.
3. Einstein proposed in 1905 that mass and energy are interconvertible. During the 1930s, Hans
Bethe worked out the theory of solar nuclear reactions.
Solar Nuclear Reactions
1. An atom’s nucleus is composed of protons (massive, positively charged particles) and neutrons (massive nuclear particles with no electric charge).
2. Nuclear reactions involve forces between nuclear particles.
3. In nuclear fusion, two nuclei combine to form a larger nucleus, releasing energy in the process. In the Sun, 4 hydrogen nuclei are fused to form 1 helium nucleus and energy.
4. The fusion process in the Sun converts only 0.7% of the original mass into energy.
5. To produce the Sun’s energy output, nearly 5 million metric tons of matter must be converted
into energy each second. This, in turn, requires 626 billion kg of hydrogen be transformed into
622 billion kg of helium.
6. The proton-proton chain is the series of nuclear reactions that begins with 4 protons and ends
with a helium nucleus. This chain is the main fusion process in the Sun, responsible for 98.5% of
the energy production.
7. Deuterium is a hydrogen nucleus that contains one neutron and one proton.
8. A positron is a positively charged electron emitted from the nucleus in some nuclear reactions.
9. A neutrino is an elementary particle that has little mass and no charge but carries energy from
a nuclear reaction.
11-3 The Sun’s Interior
1. Because of the high temperatures on and in the Sun, most electrons are stripped away from
their nuclei. Most of the material of the Sun’s interior consists of free nuclei and free electrons.
2. The behavior of this solar material is similar to that of a simple gas. The most important properties in describing gases are: temperature, pressure, and particle density.
3. Particle density is the number of separate atomic and/or nuclear particles per unit of volume.
Pressure, Temperature, and Density
1. Pressure is the force per unit area. The two factors that determine the pressure of a gas are its
density and the speed of its constituent particles.
2. Since the temperature of a gas is a measure of the speed of its constituent particles, pressure is
related to temperature.
3. The greater the density of a gas in a container, the higher the number of collisions with the
walls of the container. Thus, pressure is related to density.
4. Under ideal conditions, gas pressure is proportional to its density times its temperature.
Hydrostatic Equilibrium
1. In a star or a planet, hydrostatic equilibrium is the balance between pressure caused by the
weight of material above a thin layer and the upward pressure exerted by material below that lay-
er.
2. Pressure at the Sun’s center is calculated to be 2.5  1011 times that on the surface of the Earth.
3. The high pressure and temperature at the Sun’s core results in fusion reactions; the solar core
extends out to about 25% of the Sun’s radius.
Energy Transport
1. Three possible methods by which energy can be transferred from the center of the Sun outward:
(a) Conduction: The transfer of energy in a solid by collisions between atoms and/or molecules.
This is not a significant factor in transporting energy within the Sun.
(b) Convection: the transfer of energy in a gas or liquid by means of the motion of the material.
In a star, convection between adjacent layers is significant only when the temperature difference
is great compared to the pressure difference. Convection occurs inside the Sun within about
200,000 km of the surface. Convection is not a factor in the Sun’s core.
(c) Radiation: the transfer of energy by electromagnetic waves. Inside the Sun and most stars,
radiation is the principal means of energy transport.
2. The material of the Sun is nearly opaque, so emitted radiation travels only a short distance
(about 1 cm) before being absorbed and then reemitted. It takes a very long time for a gamma-ray
photon produced by a fusion reaction to reach the Sun’s surface. Thus any information carried by
such photons about the Sun’s core is lost.
3. Neutrinos are produced in the solar core and they rarely interact with matter. Their very low
mass implies a speed very close to the speed of light. Thus they can tell us about the current conditions in the Sun’s core.
Solar Neutrinos and the Standard Solar Model / Tools of Astronomy: Solar Neutrino Experiments
1. The standard solar model is the generally accepted theory of solar energy production.
2. The model predicts that so many neutrinos flow from the Sun that 65 billion neutrinos pass
through every cm2 of your body per second.
3. Neutrinos react very little with ordinary matter so detecting them is difficult. Astronomers want
to measure the number of neutrinos reaching the Earth in order to check the standard solar model.
4. Several large detectors have been built that confirm the solar origin of neutrinos but report
finding only 50 to 60% of the neutrinos predicted by theory. The discrepancy between theory and
experiment is referred to as the “solar neutrino problem,” and the neutrino deficit depends on the
energy of the neutrinos captured by the experiment.
5. Neutrinos come in three types, related to the electron and (its lesser known relatives) the muon
and tau particles. But most experiments were designed to detect electron neutrinos. According to
the MSW theory, the observed neutrino deficit could be the result of neutrino oscillations (neutrinos changing from one type to another during their flight from the Sun to Earth).
6. The SNO experiment uses the properties of heavy water to detect all three types of neutrinos.
In 2002 it found that the number of electron neutrinos is about a third of the total number of neutrinos reaching the detector, showing that neutrinos oscillate. The SNO results are in excellent
agreement with the predictions of the standard solar model.
7. Support for the SNO results came in 2002 from the KamLAND project, which measures antineutrinos from all nuclear plants in Japan. An antineutrino is a mirror image of a neutrino, and in
this project we do not have to make any assumptions about the source of these particles.
8. In the MINOS experiment, a beam of muon neutrinos travel underground from Fermilab to a
detector in Soudan, MN; only 52% of them are detected, indicating neutrino disappearance and
therefore neutrino mass.
9. Neutrino oscillations imply that neutrinos have mass, albeit very small. Since they are the most
numerous particles in the universe (other than photons), they contribute to a small degree to its
overall mass and influence its evolution.
10. So far we have only measured about 0.005% of the total number of neutrinos emitted by the
Sun. Future experiments will attempt to measure the remaining neutrinos and will provide a further test for the standard solar model.
11-4 Helioseismology
1. In 1962 it was discovered that the Sun vibrates. The pulsations are caused by waves, similar to
sound waves, produced by pressure fluctuations in the turbulent convective motions inside the
Sun.
2. Helioseismology is the study of the propagation of these waves. It allows us to see “through”
the Sun and helps us predict solar activity.
11-5 The Solar Atmosphere
The Photosphere
1. The solar atmosphere is conveniently divided into three regions; the photosphere, the chromosphere, and the corona.
2. Photosphere is the visible “surface” of the Sun. It is the part of the solar atmosphere from
which light is emitted into space. The photosphere is a very thin layer—400 km thick.
3. When observing the limb of the Sun (the apparent edge of the Sun as seen in the sky), it appears darker than the center of the solar disk. That’s because when we observe the limb of the
Sun we see to a lesser depth because the line of sight is at a grazing angle.
4. The photosphere varies in temperature from about 6,500 K at its deepest to 4,400 K near its
outer edge. Overall, the light received from the photosphere is representative of an object with
temperature of about 5,800 K.
5. The pressure of the outer photosphere is 0.01 the pressure of the Earth’s surface. Knowing the
pressure and temperature we can calculate the density of particles in the outer photosphere: it is
about 0.0005 of the density of air at sea level on Earth.
6. The base of the photosphere shows granulation; the Sun’s surface is divided into small convection cells. Granules are areas where hot material (light areas) is rising from below and then
descending (dark surroundings).
7. The chemical composition of the photosphere is (by mass) 78% hydrogen and 20% helium; the
remaining 2% consisting of 60 elements found on Earth. The similarity in composition between
Earth and Sun points to their common origins.
8. From our knowledge of nuclear fusion, we know the Sun’s core must hold more helium. Overall, the Sun (by mass) is theorized to be about 73% hydrogen, 25% helium, and 2% for all other
elements.
The Chromosphere and Corona
1. The chromosphere is the region of the solar atmosphere (about 2,000 km thick) that lies between the photosphere and the corona. It is not usually observable from Earth except during a
total solar eclipse. It has a bright-line (emission) spectrum.
2. Corona is the outermost portion of the Sun’s atmosphere that can only be seen during a total
solar eclipse.
3. Narrow jets of gas (spicules) shoot upward from the chromosphere into the corona, reaching a
height of 6,000 to 10,000 km and lasting from 10 to 20 minutes.
4. The temperature increases as we move outward from the photosphere; it is as high as 30,000 K
in the outer portions of the chromosphere and 2 million K in the corona (increasing rapidly in a
transition region of about 300 km between the chromosphere and corona).
5. The high temperatures in the chromosphere and especially the corona are not well understood.
The leading hypothesis is that the heating results from the interaction between the Sun’s magnetic
field and its differential rotation. The presence of “solar moss” shows that the field is highly organized in the transition region.
6. A prominence is an eruption of solar material beyond the disk of the Sun. Prominences may
reach as high as a million kilometers above the photosphere. Slow-moving ones can last for several days, while explosive ones can reach speeds of 1,500 km/s.
The Solar Wind
1. The solar wind is the continuous flow of nuclear particles (mostly protons and electrons) from
the Sun.
2. Coronal holes, dark areas in an X-ray image of the Sun, correspond to regions of low density
where the magnetic field lines are open; they provide a corridor for charged particles to escape
into space, generating the solar wind.
3. Due to the solar wind, the Sun loses about 6  1016 kg every year, a tiny fraction of its total
mass.
4. Near the Earth the solar wind travels at about 400 km/s and has a density of 2–10 particles/cm3.
5. Auroras form when the charged particles from the solar wind that have been trapped by Earth’s
magnetic field strike upper atmosphere molecules causing them to glow.
11-6 Sunspots and the Solar Activity Cycle
1. Dark spots on the Sun were first reported by the Chinese in the 5th century B.C. Galileo and
Thomas Harriott were the first Europeans to report sunspots in the early 17th century. Sunspots
are temporary phenomena lasting from a few hours to a few months.
2. Sunspots are about 1,500 K cooler than the surrounding photosphere. Thus they are about 3
times less bright than their surrounding region.
3. The explanation for sunspots involves the Sun’s magnetic field. The strength of this field can
be measured using the Zeeman effect (the splitting of spectral lines by a strong magnetic field).
4. Sunspots often appear in pairs, aligned in an east-west direction, and have opposite magnetic
polarities, one being north and the other south.
5. The magnetic field in a sunspot is about 1,000 times that of the surrounding photosphere.
6. In 1851, Schwabe discovered the sunspot cycle, which lasts about 11 years.
7. The Sun went through a period of inactivity during 1645–1715. This period corresponds to the
“Little Ice Age” climatic period on Earth.
Modeling the Sunspot Cycle and the Sunspots
1. At a sunspot maximum, most spots occur about 35° north or south of the equator. As the cycle
progresses, the spots are seen closer and closer to the Sun’s equator. When the spots reach the
equator, the cycle is at a minimum and begins again.
2. The plot that shows the location and relative number of sunspots is called the butterfly diagram.
3. The leading model for the sunspot cycle involves patterns of magnetic field lines, generated by
the flow of the hot, ionized gases within the Sun’s interior, close to the boundary between the radiative and convective zones. At this boundary, the shear in the Sun’s rotational velocity drives
the formation of the field.
4. The lines form tubes that gradually become twisted due to the Sun’s differential rotation.
Forced to the surface due to convection, these magnetic tubes become visible as sunspots. Breaking the surface weakens the field lines and the sunspots die out.
5. The Sun’s overall magnetic field reverses from one sunspot cycle to the other. Thus the entire
magnetic cycle of the Sun is 22 years, twice the sunspot cycle of 11 years. During each sunspot
cycle, the polarity of the leading sunspot of a pair in a given hemisphere is the same as the polari-
ty of the Sun’s magnetic pole for that hemisphere.
6. Observations show that the Sun’s magnetic poles are connected to sunspots of opposite polarity
(trailing sunspots) near its equator by giant loops of hot plasma that extend into the corona. The
field steadily weakens due to the transfer of opposite magnetic flux to the poles.
7. At the height of sunspot maximum, the field reverses and begins to grow in a new direction.
During the flip the field is weak and uneven.
8. SOHO observations give us a better understanding of a sunspot region. The strong magnetic
field there behaves like a “plug” that stops the normal upward convective flow. This cools the
region above the plug, which then becomes denser and plunges downward at high speeds, drawing the surrounding plasma and field toward the center of the sunspot. This increases the strength
of the sunspot and this cycle repeats for as long as the field is strong enough to behave like a
plug.
Solar Flares and Coronal Mass Ejections
1. The turbulent magnetic field of the Sun causes explosive flare-ups called solar flares, which
occur mostly during sunspot maxima.
2. According to the sunspot model, flares occur when a great number of twisted tubes of magnetic
field lines release their energy at once through the photosphere.
3. Flares blast out large numbers of very energetic charged particles. In the case of the largest
flares, these particles can reach Earth in less than one hour.
4. Large solar flares cause spectacular auroras and can affect earthly radio transmissions if the
ionosphere is disrupted by the high-energy particles from the flare.
5. Coronal mass ejections (CMEs) are events in which hot coronal gas is suddenly ejected into
space at speeds of hundreds of km/s.
6. CMEs, flares and prominences are related phenomena.
7. Twisted field lines are seen in CMEs. Just like twisted coils of spring metal, they contain energy that is used to blast the material in space.
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