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Transcript
2396_AWL_Bennett_Ch15/pt5 6/25/03 3:40 PM Page 495
PA RT
V
STELLAR
ALCHEMY
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15
Our Star
L E A R N I N G G OA L S
15.1
•
•
•
Why Does the Sun Shine?
What process creates energy in the Sun?
Why does the Sun’s size remain stable?
How did the Sun become hot enough for fusion
in the first place?
15.2 Plunging to the Center of the Sun:
An Imaginary Journey
• What are the major layers of the Sun, from the
center out?
• What do we mean by the “surface” of the Sun?
• What is the Sun made of?
15.3 The Cosmic Crucible
• Why does fusion occur in the Sun’s core?
• Why is energy produced in the Sun at such
a steady rate?
496
• Why was the Sun dimmer in the distant past?
• How do we know what is happening inside the Sun?
• What is the solar neutrino problem? Is it solved ?
15.4 From Core to Corona
• How long ago did fusion generate the energy we
now receive as sunlight?
• How are sunspots, prominences, and flares related
to magnetic fields?
• What is surprising about the temperature of the
chromosphere and corona, and how do we explain it?
15.5 Solar Weather and Climate
• What is the sunspot cycle?
• What effect does solar activity have on Earth and
its inhabitants?
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I say Live, Live, because of the Sun,
The dream, the excitable gift.
Anne Sexton (1928–1974)
A
stronomy today involves the study of the
entire universe, but the root of the word
astronomy comes from the Greek word
for “star.” Although we have learned a lot about the
universe up to this point in the book, only now do
we turn our attention to the study of the stars, the
namesakes of astronomy.
When we think of stars, we usually think of the
beautiful points of light visible on a clear night. The
nearest and most easily studied star is visible only
in the daytime—our Sun. Of course, the Sun is important to us in many more ways than as an object
for astronomical study. The Sun is the source of virtually all light, heat, and energy reaching Earth, and life
on Earth’s surface could not survive without it.
In this chapter, we will study the Sun in some
depth. We will learn how the Sun makes life possible
on Earth. Equally important, we will study our Sun as
a star so that in subsequent chapters we can more
easily understand stars throughout the universe.
15.1 Why Does the Sun Shine?
Ancient peoples recognized the vital role of the Sun in their
lives. Some worshiped the Sun as a god, and others created
elaborate mythologies to explain its daily rise and set. Only
recently, however, have we learned how the Sun provides us
with light and heat.
Most ancient thinkers viewed the Sun as some type of
fire, perhaps a lump of burning coal or wood. The Greek
philosopher Anaxagoras (c. 500–428 B.C.) imagined the Sun
to be a very hot, glowing rock about the size of the Greek
peninsula of Peloponnesus (comparable in size to Massachusetts). Thus, he was one of the first people in history to
believe that the heavens and Earth are made from the same
types of materials.
By the mid-1800s, the size and distance of the Sun
were reasonably well known, and scientists seriously began
to address the question of how the Sun shines. Two early
ideas held either that the Sun was a cooling ember that had
once been much hotter or that the Sun generated energy
from some type of chemical burning similar to the burning
of coal or wood. Simple calculations showed that a cooling
or chemically burning Sun could shine for a few thousand
years—an age that squared well with biblically based estimates of Earth’s age that were popular at the time. However,
these ideas suffered from fatal flaws. If the Sun were a cooling ember, it would have been much hotter just a few hundred years earlier, making it too hot for civilization to have
existed. Chemical burning was ruled out because it cannot
generate enough energy to account for the rate of radiation
observed from the Sun’s surface.
A more plausible hypothesis of the late 1800s suggested that the Sun generates energy by contracting in size,
a process called gravitational contraction. If the Sun were
shrinking, it would constantly be converting gravitational
potential energy into thermal energy, thereby keeping the
Sun hot. Because of its large mass, the Sun would need to
contract only very slightly each year to maintain its temperature—so slightly that the contraction would be unnoticeable. Calculations showed that the Sun could shine
for up to about 25 million years generating energy by gravitational contraction. However, geologists of the late 1800s
had already established the age of Earth to be far older than
25 million years, leaving astronomers in an embarrassing
position.
Only after Einstein published his special theory of
relativity, which included his discovery of E mc 2, did
the true energy-generation mechanism of the Sun become
clear. We now know that the Sun generates energy by nuclear fusion, a source so efficient that the Sun can shine for
about 10 billion years. Because the Sun is only 4.6 billion
years old today [Section 9.5], we expect it to keep shining
for some 5 billion more years.
According to our current model of solar-energy generation by nuclear fusion, the Sun maintains its size through
a balance between two competing forces: gravity pulling
inward and pressure pushing outward. This balance is called
gravitational equilibrium (or hydrostatic equilibrium).
It means that, at any point within the Sun, the weight of
overlying material is supported by the underlying pressure.
A stack of acrobats provides a simple example of this balance (Figure 15.1). The bottom person supports the weight
of everybody above him, so the pressure on his body is
very great. At each higher level, the overlying weight is less,
so the pressure decreases. Gravitational equilibrium in the
Sun means that the pressure increases with depth, making
the Sun extremely hot and dense in its central core (Figure 15.2).
THINK ABOUT IT
Earth’s atmosphere is also in gravitational equilibrium, with the
weight of upper layers supported by the pressure in lower
layers. Use this idea to explain why the air gets thinner at higher
altitudes.
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pressure
gravity
Figure 15.2 Gravitational equilibrium in the Sun: At each point
inside, the pressure pushing outward balances the weight of the
overlying layers.
Figure 15.1 An acrobat stack is in gravitational equilibrium: The
lowest person supports the most weight and feels the greatest
pressure, and the overlying weight and underlying pressure decrease
for those higher up.
Although the Sun today maintains its gravitational
equilibrium with energy generated by nuclear fusion, the
energy-generation mechanism of gravitational contraction
was important in the distant past and will be important
again in the distant future. Our Sun was born from a collapsing cloud of interstellar gas. The contraction of the
cloud released gravitational potential energy, raising the
interior temperature higher and higher—but not high
enough to halt the contraction. The cloud continued to
shrink because thermal radiation from the cloud’s surface
carried away much of the energy released by contraction,
even while the interior temperature was rising. When the
central temperature and density eventually reached the
values necessary to sustain nuclear fusion, energy generation in the Sun’s interior matched the energy lost from the
surface in the form of radiation. With the onset of fusion,
the Sun entered a long-lasting state of gravitational equilibrium that has persisted for the last 4.6 billion years.
About 5 billion years from now, when the Sun finally
exhausts its nuclear fuel, the internal pressure will drop, and
gravitational contraction will begin once again. As we will see
later, some of the most important and spectacular processes
in astronomy hinge on this ongoing “battle” between the
crush of gravity and a star’s internal sources of pressure.
In summary, the answer to the question “Why does the
Sun shine?” is that about 4.6 billion years ago gravitational
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part V
• Stellar Alchemy
contraction made the Sun hot enough to sustain nuclear
fusion in its core. Ever since, energy liberated by fusion has
maintained the Sun’s gravitational equilibrium and kept the
Sun shining steadily, supplying the light and heat that sustain life on Earth.
15.2 Plunging to the
Center of the Sun:
An Imaginary Journey
In the rest of this chapter, we will discuss in detail how
the Sun produces energy and how that energy travels to
Earth. First, to get a “big picture” view of the Sun, let’s
imagine you have a spaceship that can somehow withstand the immense heat and pressure of the solar interior
and take an imaginary journey from Earth to the center
of the Sun.
Approaching the Surface
As you begin your voyage from Earth, the Sun appears as a
whitish ball of glowing gas. With spectroscopy [Section 7.3],
you verify that the Sun’s mass is 70% hydrogen and 28%
helium. Heavier elements make up the remaining 2%.
The total power output of the Sun, called its luminosity, is an incredible 3.8 1026 watts. That is, every second,
the Sun radiates a total of 3.8 1026 joules of energy into
space (recall that 1 watt 1 joule/s). If we could somehow
capture and store just 1 second’s worth of the Sun’s lumi-
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Table 15.1 Basic Properties of the Sun
Figure 15.3 This photo of the
visible surface of the Sun shows
several dark sunspots.
Radius (RSun)
696,000 km (about 109 times the
radius of Earth)
Mass (MSun)
2 1030 kg (about 300,000 times
the mass of Earth)
Luminosity (LSun)
3.8 1026 watts
Composition (by
percentage of mass)
70% hydrogen, 28% helium,
2% heavier elements
Rotation rate
25 days (equator) to 30 days (poles)
Surface temperature
5,800 K (average); 4,000 K (sunspots)
Core temperature
15 million K
VIS
nosity, it would be enough to meet current human energy
demands for roughly the next 500,000 years!
Of course, only a tiny fraction of the Sun’s total energy
output reaches Earth, with the rest dispersing in all directions into space. Most of this energy is radiated in the form
of visible light, but once you leave the protective blanket of
Earth’s atmosphere you’ll encounter significant amounts of
other types of solar radiation, including dangerous ultraviolet and X rays. Your spaceship will require substantial
shielding to protect you from serious radiation burns caused
by these high-energy forms of light.
Through a telescope, you can see that the Sun seethes
with churning gases. At most times you’ll detect at least
a few sunspots blotching its surface (Figure 15.3). If you
focus your telescope solely on a sunspot, you’ll find that it is
blindingly bright. Sunspots appear dark only in contrast to
the even brighter solar surface that surrounds them. A typical sunspot is large enough to swallow the entire Earth, dramatically illustrating that the Sun is immense by any
earthly standard. The Sun’s radius is nearly 700,000 kilometers, and its mass is 2 1030 kilograms—about 300,000
times more massive than Earth.
Sunspots appear to move from day to day along with
the Sun’s rotation. If you watch very carefully, you may
notice that sunspots near the solar equator circle the Sun
faster than those at higher solar latitudes. This observation reveals that, unlike a spinning ball, the entire Sun does
not rotate at the same rate. Instead, the solar equator completes one rotation in about 25 days, and the rotation period increases with latitude to about 30 days near the solar
poles. Table 15.1 summarizes some of the basic properties
of the Sun.
THINK ABOUT IT
As a brief review, describe how we measure the mass of the
Sun using Newton’s version of Kepler’s third law. (Hint: Look
back at Chapter 5.)
As you and your spaceship continue to fall toward the
Sun, you notice an increasingly powerful headwind exerting a bit of drag on your descent. This headwind, called the
solar wind, is created by ions and subatomic particles flowing outward from the solar surface. The solar wind helps
shape the magnetospheres of planets [Sections 11.3, 12.4]
and blows back the material that forms the tails of comets
[Section 13.4].
A few million kilometers above the solar surface, you
enter the solar corona, the tenuous uppermost layer of the
Sun’s atmosphere (Figure 15.4). Here you find the temperature to be astonishingly high—about 1 million Kelvin. This
region emits most of the Sun’s X rays. However, the density
here is so low that your spaceship feels relatively little heat
despite the million-degree temperature [Section 4.2].
Nearer the surface, the temperature suddenly drops to
about 10,000 K in the chromosphere, the primary source
of the Sun’s ultraviolet radiation. At last you plunge through
the visible surface of the Sun, called the photosphere, where
the temperature averages just under 6,000 K. Although the
photosphere looks like a well-defined surface from Earth,
it consists of gas far less dense than Earth’s atmosphere.
Throughout the solar atmosphere, you notice that
the Sun has its own version of weather, in which conditions
at a particular altitude differ from one region to another.
Some regions of the chromosphere and corona are particularly hot and bright, while other regions are cooler and
less dense. In the photosphere, sunspots are cooler than
the surrounding surface, though they are still quite hot
and bright by earthly standards. In addition, your compass
goes crazy as you descend through the solar atmosphere,
indicating that solar weather is shaped by intense magnetic
fields. Occasionally, huge magnetic storms occur, shooting
hot gases far into space.
Into the Sun
Up to this point in your journey, you may have seen Earth
and the stars when you looked back, but as you slip beneath the photosphere, blazing light engulfs you. You are
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solar wind
co
r
photosphere
on
a
ch
ro
m
o
h
sp
ere
convection
zone
core
radiation
zone
solar wind
Figure 15.4 The basic structure of the Sun. Nuclear fusion in the solar core generates the Sun’s energy.
Photons of light carry that energy through the radiation zone to the bottom of the convection zone. Rising
plumes of hot gas then transport the energy through the convection zone to the photosphere, where it is
radiated into space. The photosphere, at a temperature of roughly 6,000 K, is relatively cool compared to
the layers that lie above it. The temperature of the chromosphere, which is directly above the photosphere,
exceeds 10,000 K. The temperature of the corona, extending outward from the chromosphere, can reach
1 million degrees. Because the coronal gas is so hot, some of it escapes the Sun’s gravity, forming a solar
wind that blows past Earth and out beyond Pluto.
inside the Sun, and your spacecraft is tossed about by incredible turbulence. If you can hold steady long enough to
see what is going on around you, you’ll notice spouts of
hot gas rising upward, surrounded by cooler gas cascading
down from above. You are in the convection zone, where
energy generated in the solar core travels upward, transported by the rising of hot gas and falling of cool gas called
convection [Section 10.2]. With some quick thinking, you
may realize that the photosphere above you is the top of
the convection zone and that convection is the cause of
the Sun’s seething, churning appearance.
As you descend through the convection zone, the surrounding density and pressure increase substantially, along
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with the temperature. Soon you reach depths at which the
Sun is far denser than water. Nevertheless, it is still a gas
(more specifically, a plasma of positively charged ions and
free electrons) because each particle moves independently
of its neighbors [Section 4.3].
About a third of the way down to the center, the turbulence of the convection zone gives way to the calmer
plasma of the radiation zone, where energy is carried outward primarily by photons of light. The temperature rises
to almost 10 million K, and your spacecraft is bathed in
X rays trillions of times more intense than the visible light
at the solar surface.
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COMMON MISCONCEPTIONS
fusion
fission
The Sun Is Not on Fire
We are accustomed to saying that the Sun is “burning,”
a way of speaking that conjures up images of a giant bonfire in the sky. However, the Sun does not burn in the
same sense as a fire burns on Earth. Fires on Earth generate light through chemical changes that consume oxygen and produce a flame. The glow of the Sun has more
in common with the glowing embers left over after the
flames have burned out. Much like hot embers, the Sun’s
surface shines with the visible thermal radiation produced by any object that is sufficiently hot [Section 6.4].
However, hot embers quickly stop glowing as they
cool, while the Sun keeps shining because its surface is
kept hot by the energy rising from the Sun’s core. Because this energy is generated by nuclear fusion, we
sometimes say that it is the result of “nuclear burning”—
a term that suggests nuclear changes in much the same
way that “chemical burning” suggests chemical changes.
Nevertheless, while it is reasonable to say that the Sun
undergoes nuclear burning in its core, it is not accurate
to speak of any kind of burning on the Sun’s surface,
where light is produced primarily by thermal radiation.
No real spacecraft could survive, but your imaginary
one keeps plunging straight down to the solar core. There
you finally find the source of the Sun’s energy: nuclear fusion
transforming hydrogen into helium. At the Sun’s center,
the temperature is about 15 million K, the density is more
than 100 times that of water, and the pressure is 200 billion times that on the surface of Earth. The energy produced in the core today will take about a million years to
reach the surface.
With your journey complete, it’s time to turn around
and head back home. We’ll continue this chapter by studying fusion in the solar core and then tracing the flow of the
energy generated by fusion as it moves outward through
the Sun.
Figure 15.5 Nuclear fission splits a nucleus into smaller nuclei
(not usually of equal size), while nuclear fusion combines smaller
nuclei into a larger nucleus.
loses neutrons, its atomic mass changes and it becomes a
different isotope [Section 4.3]. The process of splitting a nucleus into two smaller nuclei is called nuclear fission. The
process of combining nuclei to make a nucleus with a greater
number of protons or neutrons is called nuclear fusion
(Figure 15.5). Human-built nuclear power plants rely
on nuclear fission of uranium or plutonium. The nuclear
power plant at the center of the Sun relies on nuclear fusion,
turning hydrogen into helium.
Nuclear Fusion
The 15 million K plasma in the solar core is like a “soup”
of hot gas, with bare, positively charged atomic nuclei (and
negatively charged electrons) whizzing about at extremely
high speeds. At any one time, some of these nuclei are on
high-speed collision courses with each other. In most cases,
electromagnetic forces deflect the nuclei, preventing actual
collisions, because positive charges repel one another. If
nuclei collide with sufficient energy, however, they can stick
together to form a heavier nucleus (Figure 15.6).
Sticking positively charged nuclei together is not easy.
The strong force, which binds protons and neutrons together in atomic nuclei, is the only force in nature that can
At low speeds, electromagnetic
repulsion prevents the collision
of nuclei.
15.3 The Cosmic Crucible
The prospect of turning common metals like lead into
gold enthralled those who pursued the medieval practice
of alchemy. Sometimes they tried primitive scientific approaches, such as melting various ores together in a vessel
called a crucible. Other times they tried magic. Their getrich-quick schemes never managed to work. Today we
know that there is no easy way to turn other elements into
gold, but it is possible to transmute one element or isotope
into another.
If a nucleus gains or loses protons, its atomic number
changes and it becomes a different element. If it gains or
At high speeds, nuclei come close
enough for the strong force to bind
them together.
Figure 15.6 Positively charged nuclei can fuse only if a highspeed collision brings them close enough for the strong force
to come into play.
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Step 1
e
p
p
Step 2
Key:
e
electron
Step 3
y
a ra
m
gam
e
e
gam
ma
ray
p
n
p
n
y
ra
ma
m
ga
p
n p
gamma
ray
neutrino
n
neutron
positron
p
proton
Total reaction
p
p
p
n p
p
p
gamma ray
p
n
p
p
n
p
n
p
p
n
e
p
n p
p
gamma ray
e
Figure 15.7 Hydrogen fuses into helium in the Sun by way of the proton–proton chain. In step 1, two
protons fuse to create a deuterium nucleus consisting of a proton and a neutron. In step 2, the deuterium
nucleus and a proton fuse to form helium-3, a rare form of helium. In step 3, two helium-3 nuclei fuse
to form helium-4, the common form of helium.
overcome the electromagnetic repulsion between two positively charged nuclei [Section S4.2]. In contrast to gravitational and electromagnetic forces, which drop off gradually
as the distances between particles increase (by an inverse
square law [Section 5.3]), the strong force is more like glue
or Velcro: It overpowers the electromagnetic force over
very small distances but is insignificant when the distances
between particles exceed the typical sizes of atomic nuclei.
The trick to nuclear fusion, therefore, is to push the positively charged nuclei close enough together for the strong
force to outmuscle electromagnetic repulsion.
The high pressures and temperatures in the solar core
are just right for fusion of hydrogen nuclei into helium
nuclei. The high temperature is important because the nuclei must collide at very high speeds if they are to come
close enough together to fuse. (Quantum tunneling is also
important to this process [Section S4.5].) The higher the
temperature, the harder the collisions, making fusion reactions more likely at higher temperatures. The high pressure
of the overlying layers is necessary because without it the
hot plasma of the solar core would simply explode into space,
shutting off the nuclear reactions. In the Sun, the pressure
is high and steady, allowing some 600 million tons of hydrogen to fuse into helium every second.
Hydrogen Fusion in the Sun:
The Proton–Proton Chain
Recall that hydrogen nuclei are nothing more than individual protons, while the most common form of helium
consists of two protons and two neutrons. Thus, the
overall hydrogen fusion reaction in the Sun is:
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• Stellar Alchemy
p
p
p
p
4 1H
n
p
p
n
energy
1 4He
However, collisions between two nuclei are far more
common than three- or four-way collisions, so this overall
reaction proceeds through steps that involve just two nuclei
at a time. The sequence of steps that occurs in the Sun is
called the proton–proton chain because it begins with collisions between individual protons (hydrogen nuclei).
Figure 15.7 illustrates the steps in the proton–proton chain:
Step 1. Two protons fuse to form a nucleus consisting of
one proton and one neutron, which is the isotope of hydrogen known as deuterium. Note that this step converts a
proton into a neutron, reducing the total nuclear charge
from 2 for the two fusing protons to 1 for the resulting
deuterium nucleus. The lost positive charge is carried off
by a positron, the antimatter version of an electron with
a positive rather than negative charge [Section S4.2]. A neutrino—a subatomic particle with a very tiny mass—is also
produced in this step.* The positron won’t last long, because it soon meets up with an ordinary electron, resulting
*Producing a neutrino is necessary because of a law called conservation
of lepton number: The number of leptons (e.g., electrons or neutrinos
[Chapter S4]) must be the same before and after the reaction. The lepton
number is zero before the reaction because there are no leptons. Among
the reaction products, the positron (antielectron) has lepton number 1
because it is antimatter, and the neutrino has lepton number 1. Thus,
the total lepton number remains zero.
2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 503
in the creation of two gamma-ray photons through matter–
antimatter annihilation.
Step 2. A fair number of deuterium nuclei are always present along with the protons and other nuclei in the solar
core, since step 1 occurs so frequently in the Sun (about
1038 times per second). Step 2 occurs when one of these
deuterium nuclei collides and fuses with a proton. The
result is a nucleus of helium-3, a rare form of helium with
two protons and one neutron. This reaction also produces
a gamma-ray photon.
Step 3. The third and final step of the proton–proton chain
requires the addition of another neutron to the helium-3,
thereby making normal helium-4. This final step can proceed in several different ways, but the most common route
involves a collision of two helium-3 nuclei. Each of these
helium-3 nuclei resulted from a prior, separate occurrence
of step 2 somewhere in the solar core. The final result is a
normal helium-4 nucleus and two protons.
Total reaction. Somewhere in the solar core, steps 1 and 2
must each occur twice to make step 3 possible. Six protons
go into each complete cycle of the proton–proton chain, but
two come back out. Thus, the overall proton–proton chain
converts four protons (hydrogen nuclei) into a helium-4
nucleus, two positrons, two neutrinos, and two gamma rays.
Each resulting helium-4 nucleus has a mass that is
slightly less (by about 0.7%) than the combined mass of
the four protons that created it. Overall, fusion in the Sun
converts about 600 million tons of hydrogen into 596 million tons of helium every second. The “missing” 4 million
tons of matter becomes energy in accord with Einstein’s
formula E mc 2. About 98% of the energy emerges as
kinetic energy of the resulting helium nuclei and radiative energy of the gamma rays. As we will see, this energy
slowly percolates to the solar surface, eventually emerging
as the sunlight that bathes Earth. About 2% of the energy
is carried off by the neutrinos. Neutrinos rarely interact
with matter (because they respond only to the weak force
[Section S4.2]), so most of the neutrinos created by the
proton–proton chain pass straight from the solar core
through the solar surface and out into space.
The Solar Thermostat
The rate of nuclear fusion in the solar core, which determines the energy output of the Sun, is very sensitive to
temperature. A slight increase in temperature would mean
a much higher fusion rate, and a slight decrease in temperature would mean a much lower fusion rate. If the
Sun’s rate of fusion varied erratically, the effects on Earth
might be devastating. Fortunately, the Sun’s central temperature is steady thanks to gravitational equilibrium—the
balance between the pull of gravity and the push of internal pressure.
Outside the solar core, the energy produced by fusion
travels toward the Sun’s surface at a slow but steady rate. In
this steady state, the amount of energy leaving the top of
each gas layer within the Sun precisely balances the energy
entering from the bottom (Figure 15.8). Suppose the core
temperature of the Sun rose very slightly. The rate of nuclear fusion would soar, generating lots of extra energy. Because energy moves so slowly through the Sun, this extra
energy would be bottled up in the core, causing an increase
in the core pressure. The push of this pressure would temporarily exceed the pull of gravity, causing the core to expand and cool. With cooling, the fusion rate would drop
back down. The expansion and cooling would continue until
gravitational equilibrium was restored, at which point the
fusion rate would return to its original value.
An opposite process would restore the normal fusion
rate if the core temperature dropped. A decrease in core
temperature would lead to decreased nuclear burning,
a drop in the central pressure, and contraction of the core.
As the core shrank, its temperature would rise until the
burning rate returned to normal.
The response of the core pressure to changes in the
nuclear fusion rate is essentially a thermostat that keeps
the Sun’s central temperature steady. Any change in
the core temperature is automatically corrected by the
change in the fusion rate and the accompanying change
in pressure.
While the processes involved in gravitational equilibrium prevent erratic changes in the fusion rate, they also
ensure that the fusion rate gradually rises over billions of
years. Because each fusion reaction converts four hydrogen
nuclei into one helium nucleus, the total number of independent particles in the solar core is gradually falling. This
gradual reduction in the number of particles causes the
solar core to shrink.
The slow shrinking of the solar core means that it must
generate energy more rapidly to counteract the stronger
compression of gravity, so the solar core gradually gets
hotter as it shrinks. Theoretical models indicate that the
Sun’s core temperature should have increased enough to
raise its fusion rate and the solar luminosity by about 30%
since the Sun was born 4.6 billion years ago.
How did the gradual increase in solar luminosity affect
Earth? Geological evidence shows that Earth’s surface temperature has remained fairly steady since Earth finished
forming more than 4 billion years ago, despite this 30%
increase in the Sun’s energy output, because Earth has its
own thermostat. This “Earth thermostat” is the carbon
dioxide cycle. By maintaining a fairly steady level of atmospheric carbon dioxide, the carbon dioxide cycle regulates
the greenhouse effect that maintains Earth’s surface temperature [Section 14.4].
“Observing” the Solar Interior
We cannot see inside the Sun, so you may be wondering
how we can know so much about what goes on underneath
its surface. Astronomers can study the Sun’s interior in
three different ways: through mathematical models of the
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slight decrease in
core temperature
large decrease in
rate of fusion
slight rise in
core temperature
large rise in
rate of fusion
Solar
Thermostat:
Gravitational
Equilibrium
Because the energy
supply is diminished,
gravity starts to
overcome thermal
pressure.
Gravity compresses
the core, heats it up,
and restores fusion
rate to normal value.
Increased energy
output enables
thermal pressure
to overcome
gravity.
Increased thermal
pressure causes the
core to expand and then
cool, which restores fusion
rate to normal value.
Figure 15.8 The solar thermostat. Gravitational equilibrium regulates the Sun’s core temperature. Everything is in balance if the amount of energy leaving the core equals the amount of energy produced by
fusion. A rise in core temperature triggers a chain of events that causes the core to expand, lowering its
temperature to its normal value. A decrease in core temperature triggers the opposite chain of events,
also restoring the normal core temperature.
Sun, observations of “sun quakes,” and observations of
solar neutrinos.
of the Sun gives us confidence that the models are on the
right track and that we really do understand what is going
on inside the Sun.
Mathematical Models The primary way we learn about
the interior of the Sun and other stars is by creating mathematical models that use the laws of physics to predict the
internal conditions. A basic model uses the Sun’s observed
composition and mass as inputs to equations that describe
gravitational equilibrium, the solar thermostat, and the
rate at which solar energy moves from the core to the photosphere. With the aid of a computer, we can use the model
to calculate the Sun’s temperature, pressure, and density
at any depth. We can then predict the rate of nuclear fusion
in the solar core by combining these calculations with
knowledge about nuclear fusion gathered in laboratories
here on Earth.
Remarkably, such models correctly “predict” the radius, surface temperature, luminosity, age, and many other
properties of the Sun. However, current models do not
predict everything about the Sun correctly. Scientists are
constantly working to discover what is missing from them.
Successful prediction of so many observed characteristics
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Sun Quakes A second way to learn about the inside of
the Sun is to observe “sun quakes”—vibrations of the Sun
that are similar to the vibrations of the Earth caused by
earthquakes, although they are generated very differently.
Earthquakes occur when Earth’s crust suddenly shifts, generating seismic waves that propagate through Earth’s interior
[Section 10.2]. We can learn about Earth’s interior by recording seismic waves on Earth’s surface with seismographs.
Sun quakes result from waves of pressure (sound waves)
that propagate deep within the Sun at all times. These
waves cause the solar surface to vibrate when they reach
it. Although we cannot set up seismographs on the Sun,
we can detect the vibrations of the surface by measuring
Doppler shifts [Section 6.5]. Light from portions of the surface that are rising toward us is slightly blueshifted, while
light from portions that are falling away from us is slightly
redshifted. The vibrations are relatively small but measurable (Figure 15.9).
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Figure 15.9 Vibrations on the surface of
the Sun can be detected by Doppler shifts.
In this schematic representation, red indicates falling gas, and blue indicates rising gas.
The speckled region indicates the convection zone. The vibration pattern illustrated
here is just one of many possible patterns.
The overall vibration pattern of the Sun is a
complex combination of patterns similar to
this one.
In principle, we can deduce a great deal about the
solar interior by carefully analyzing these vibrations. (By
analogy to seismology on Earth, this type of study of the
Sun is called helioseismology—helios means “sun.”) Re-
Mathematical Insight
We can calculate how much mass the Sun loses through nuclear
fusion by comparing the input and output masses of the proton–
proton chain. A single proton has a mass of 1.6726 1027 kg,
so four protons have a mass of 6.690 1027 kg.
A helium-4 nucleus has a mass of only 6.643 1027 kg,
slightly less than the mass of the four protons. The difference is:
6.690 1027 kg 6.643 1027 kg 4.7 1029 kg
which is 0.7%, or 0.007, of the original mass. Thus, for example,
when 1 kilogram of hydrogen fuses, the resulting helium weighs
only 993 grams, while 7 grams of mass turns into energy.
To calculate the total amount of mass converted to energy
in the Sun each second, we use Einstein’s equation E mc 2. The
total energy produced by the Sun each second is 3.8 1026 joules,
so we can solve for the total mass converted to energy each second:
E
mc 2
E
⇒ m c2
3.8 1026 joules
4.2 109 kg
2
m
3.0 108 s
sults to date confirm that our mathematical models of the
solar interior are on the right track (Figure 15.10). At the
same time, they provide data that can be used to improve
the models further.
15.1
Mass-Energy Conversion in the Sun
The Sun loses about 4 billion kilograms of mass every second,
which is roughly equivalent to the combined mass of nearly
100 million people.
Example: How much hydrogen is converted to helium each
second in the Sun?
Solution: We have already calculated that the Sun loses 4.2 109 kg
of mass each second and that this is only 0.7% of the mass of hydrogen that is fused:
4.2 109 kg 0.007 mass of hydrogen fused
We now solve for the mass of hydrogen fused:
4.2 109 kg
mass of
hydrogen fused
0.007
1 metric ton
6.0 1011 kg 3
10 kg
6.0 108 metric tons
The Sun fuses 600 million metric tons of hydrogen each second,
of which about 4 million tons becomes energy. The remaining
596 million tons becomes helium.
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Key
Key
100
model
107
model
data
data
core
radiation
zone
convection
zone
density (g/cm3)
temperature (K)
10
1
core
radiation
zone
106
convection
zone
0.1
0.01
0
0.2
0.4
0.6
0.8
fraction of the Sun’s radius
1.0
a Temperature at different radii within the Sun.
0
0.2
0.4
0.6
0.8
fraction of the Sun’s radius
1.0
b Density at different radii within the Sun. (The density of water is
1 g/cm3.)
Figure 15.10 Agreement between mathematical models of solar structure and actual measurements of
solar structure derived from “sun quakes.” The red lines show predictions of mathematical models of the
Sun. The blue lines show the interior structure of the Sun as indicated by vibrations of the Sun’s surface.
These vibrations tell us about conditions deep within the Sun because they are produced by sound waves
that propagate through the Sun’s interior layers.
Solar Neutrinos Another way to study the solar interior
is to observe the neutrinos coming from fusion reactions in
the core. Don’t panic, but as you read this sentence about a
thousand trillion solar neutrinos will zip through your body.
Fortunately, they won’t do any damage, because neutrinos
rarely interact with anything. Neutrinos created by fusion
in the solar core fly quickly through the Sun as if passing
through empty space. In fact, while an inch of lead will stop
an X ray, stopping an average neutrino would require a slab
of lead more than 1 light-year thick! Clearly, counting neutrinos is dauntingly difficult, because virtually all of them
stream right through any detector built to capture them.
THINK ABOUT IT
Is the number of solar neutrinos zipping through our bodies
significantly lower at night? (Hint: How does the thickness of
Earth compare with the thickness of a slab of lead needed
to stop an average neutrino?)
Nevertheless, neutrinos do occasionally interact with
matter, and it is possible to capture a few solar neutrinos
with a large enough detector. Neutrino detectors are usually placed deep inside mines so that the overlying layers of
rock block all other kinds of particles coming from outer
space except neutrinos, which pass through rock easily. The
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first major solar neutrino detector, built in the 1960s, was
located 1,500 meters underground in the Homestake gold
mine in South Dakota (Figure 15.11).
The detector for this “Homestake experiment” consisted
of a 400,000-liter vat of chlorine-containing dry-cleaning
fluid. It turns out that, on very rare occasions, a chlorine
nucleus can capture a neutrino and change into a nucleus
of radioactive argon. By looking for radioactive argon in
the tank of cleaning fluid, experimenters could count the
number of neutrinos captured in the detector.
From the many trillions of solar neutrinos that passed
through the tank of cleaning fluid each second, experimenters expected to capture an average of just one neutrino
per day. This predicted capture rate was based on measured
properties of chlorine nuclei and models of nuclear fusion in the Sun. However, over a period of more than two
decades, neutrinos were captured only about once every
3 days on average. That is, the Homestake experiment detected only about one-third of the predicted number of
neutrinos. This disagreement between model predictions
and actual observations came to be called the solar neutrino problem.
The shortfall of neutrinos found with the Homestake
experiment led to many more recent attempts to detect solar
neutrinos using more sophisticated detectors (Figure 15.12).
The chlorine nuclei in the Homestake experiment could
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Figure 15.11 This tank of dry-cleaning fluid (visible underneath
the catwalk), located deep within South Dakota’s Homestake mine,
was a solar neutrino detector. The chlorine nuclei in the cleaning
fluid turned into argon nuclei when they captured neutrinos from
the Sun.
a Scientists inspecting individual detectors within Super-Kamiokande.
capture only high-energy neutrinos that are produced by
one of the rare pathways of step 3 in the proton–proton
chain (not shown in Figure 15.7). More recent experiments
can detect lower-energy neutrinos, including those produced
by step 1 of the proton–proton chain, and therefore offer a
better probe of fusion in the Sun. To date, all these experiments have found fewer neutrinos than current models of
the Sun predict. This discrepancy between model and experiment probably means one of two things: Either something is wrong with our models of the Sun, or something is
missing in our understanding of how neutrinos behave.
THINK ABOUT IT
Although the observed number of neutrinos falls short of
theoretical predictions, experiments like Homestake have
shown that at least some neutrinos are coming from the
Sun. Explain why this provides direct evidence that nuclear
fusion really is taking place in the Sun right now. (Hint: See
Figure 15.7.)
For the moment, many physicists and astronomers
are betting that we understand the Sun just fine and that
the discrepancy has to do with the neutrinos themselves.
One intriguing idea arises from the fact that neutrinos come
in three types: electron neutrinos, muon neutrinos, and
tau neutrinos [Section S4.2].
Fusion reactions in the Sun produce only electron neutrinos, and most solar neutrino detectors can detect only
b An image of the Sun created by tracing the paths of
neutrinos detected by Super-Kamiokande back to the Sun.
Figure 15.12 The Super-Kamiokande experiment in Japan is one
of the world’s premier neutrino detectors.
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electron neutrinos. However, recent experiments have shown
that some of the electron neutrinos might change into muon
and tau neutrinos as they fly out through the solar plasma.
In that case, our detectors would count fewer than the expected number of electron neutrinos. Early results from
the Sudbury Neutrino Observatory in Canada, a new detector designed to search for all types of neutrinos, suggest
that neutrinos changing type is indeed the solution to the
solar neutrino problem. The observations are ongoing, and
it will probably be several more years before this solution
can be definitively confirmed.
Because of their roles in detecting solar neutrinos and
identifying the solar neutrino problem, Raymond Davis,
leader of the Homestake experiment, and Masatoshi Koshiba, leader of Super-Kamiokande, shared in the 2002 Nobel
Prize for physics.
15.4 From Core to Corona
Energy liberated by nuclear fusion in the Sun’s core must
eventually reach the solar surface, where it can be radiated into space. The path that the energy takes to the surface is long and complex. In this section, we follow that
long path.
The Path Through the Solar Interior
In Chapter 6, we discussed how atoms can absorb or emit
photons. In fact, photons can also interact with any charged
particle, and a photon that “collides” with an electron can
be deflected into a completely new direction.
Deep in the solar interior, the plasma is so dense that
the gamma-ray photons resulting from fusion travel only
a fraction of a millimeter before colliding with an electron.
Because each collision sends the photon in a random new
direction, the photon bounces around the core in a haphazard way, sometimes called a random walk. With each
random bounce, the photon drifts farther and farther,
on average, from its point of origin. As a result, photons
from the solar core gradually work their way outward (Figure 15.13). The technical term for this slow, outward migration of photons is radiative diffusion (to diffuse means
to “spread out” and radiative refers to the photons of light
or radiation).
Along the way, the photons exchange energy with their
surroundings. Because the surrounding temperature declines as the photons move outward through the Sun, they
are gradually transformed from gamma rays to photons
of lower energy. (Because energy must be conserved, each
gamma-ray photon becomes many lower-energy photons.)
By the time the energy of fusion reaches the surface, the
photons are primarily visible light. On average, the energy
released in a fusion reaction takes about a million years
to reach the solar surface.
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Figure 15.13 A photon in the solar interior bounces randomly
among electrons, slowly working its way outward in a process
called radiative diffusion.
THINK ABOUT IT
Radiative diffusion is just one type of diffusion. Another is the
diffusion of dye through a glass of water. If you place a concentrated spot of dye at one point in the water, each individual dye
molecule begins a random walk as it bounces among the water
molecules. The result is that the dye gradually spreads through
the entire glass. Can you think of any other examples of diffusion in the world around you?
Radiative diffusion is the primary way by which energy
moves outward through the radiation zone, which stretches
from the core to about 70% of the Sun’s radius (see Figure 15.4). Above this point, where the temperature has
dropped to about 2 million K, the solar plasma absorbs photons more readily (rather than just bouncing them around).
This point is the beginning of the solar convection zone,
where the buildup of heat resulting from photon absorption
causes bubbles of hot plasma to rise upward in the process
known as convection [Section 10.2]. Convection occurs
because hot gas is less dense than cool gas. Like a hot-air
balloon, a hot bubble of solar plasma rises upward through
the cooler plasma above it. Meanwhile, cooler plasma from
above slides around the rising bubble and sinks to lower
layers, where it is heated. The rising of hot plasma and sinking of cool plasma form a cycle that transports energy outward from the top of the radiation zone to the solar surface
(Figure 15.14a).
The Solar Surface
Earth has a solid crust, so its surface is well defined. In
contrast, the Sun is made entirely of gaseous plasma. Defining where the surface of the Sun begins is therefore something like defining the surface of a cloud: From a distance
it looks quite distinct, but up close the surface is fuzzy, not
sharp. We generally define the solar surface as the layer that
appears distinct from a distance. This is the layer we identified as the photosphere when we took our imaginary journey into the Sun. More technically, the photosphere is the
layer of the Sun from which photons finally escape into
space after the million-year journey of solar energy outward
from the core.
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a This schematic diagram shows how hot gas (white arrows) rises
while cooler gas (orange/black arrows) descends around it. Bright spots
appear on the solar surface in places where hot gas is rising from
below, creating the granulated appearance of the solar photosphere.
VIS
b Granulation is evident in this
photo of the Sun’s surface. Each
bright granule is the top of a rising
column of gas. At the darker lines
between the granules, cooler gas is descending below the photosphere. Each granule is about 1,000 kilometers across.
Figure 15.14 Convection transports energy outward in the Sun’s convection zone.
Most of the energy produced by fusion in the solar
core ultimately leaves the photosphere as thermal radiation
[Section 6.4]. The average temperature of the photosphere
is about 5,800 K, corresponding to a thermal radiation spectrum that peaks in the green portion of the visible spectrum, with substantial energy coming out in all colors of
visible light. The Sun appears whitish when seen from space,
but in our sky the Sun appears somewhat more yellow—
and even red at sunset—because Earth’s atmosphere scatters
blue light. It is this scattered light from the Sun that makes
our skies blue [Section 11.3].
Although the average temperature of the photosphere
is 5,800 K, actual temperatures vary significantly from place
to place. The photosphere is marked throughout by the
bubbling pattern of granulation produced by the underlying convection (Figure 15.14b). Each granule appears
bright in the center, where hot gas bubbles upward, and dark
around the edges, where cool gas descends. If we made a
movie of the granulation, we’d see it bubbling rather like
a pot of boiling water. Just as bubbles in a pot of boiling
water burst on the surface and are replaced by new bubbles,
each granule lasts only a few minutes before being replaced
by other granules bubbling upward.
Sunspots and Magnetic Fields
Sunspots are the most striking features on the solar surface
(Figure 15.15a). The temperature of the plasma in sunspots
is about 4,000 K, significantly cooler than the 5,800 K plasma
of the surrounding photosphere. If you think about this for
a moment, you may wonder how sunspots can be so much
cooler than their surroundings. Why doesn’t the surrounding hot plasma heat the sunspots? Something must be
preventing hot plasma from entering the sunspots, and
that “something” turns out to be magnetic fields.
Detailed observations of the Sun’s spectral lines reveal
sunspots to be regions with strong magnetic fields. These
magnetic fields can alter the energy levels in atoms and
ions and therefore can alter the spectral lines they produce.
More specifically, magnetic fields cause some spectral lines
to split into two or more closely spaced lines (Figure 15.15b).
This effect (called the Zeeman effect) enables scientists to
map magnetic fields on the Sun by studying the spectral
lines in light from different parts of the solar surface.
Magnetic fields are invisible, but in principle we could
visualize a magnetic field by laying out many compasses.
Each compass needle would point to local magnetic north.
We can represent the magnetic field by drawing a series of
lines, called magnetic field lines, connecting the needles
of these imaginary compasses (Figure 15.16a). The strength
of the magnetic field is indicated by the spacing of the lines:
Closer lines mean a stronger field (Figure 15.16b). Because
these imaginary field lines are so much easier to visualize
than the magnetic field itself, we usually discuss magnetic
fields by talking about how the field lines would appear.
Charged particles, such as the ions and electrons in the
solar plasma, follow paths that spiral along the magnetic
field lines (Figure 15.16c). Thus, the solar plasma can move
freely along magnetic field lines but cannot easily move
perpendicular to them.
The magnetic field lines act somewhat like elastic bands,
being twisted into contortions and knots by turbulent motions in the solar atmosphere. Sunspots occur where the
most taut and tightly wound magnetic fields poke nearly
straight out from the solar interior. Sunspots tend to occur
in pairs connected by a loop of magnetic field lines. These
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a This close-up view of the Sun’s surface
(right) shows two large sunspots and several
smaller ones. Both of the big sunspots are
roughly as large as Earth.
Figure 15.15 Sunspots are regions of intense
magnetic activity.
VIS
tight magnetic field lines suppress convection within each
sunspot and prevent surrounding plasma from sliding sideways into the sunspot. With hot plasma unable to enter the
region, the sunspot plasma becomes cooler than that of the
rest of the photosphere (Figure 15.17a).
The magnetic field lines connecting two sunspots often
soar high above the photosphere, through the chromosphere,
and into the corona (Figure 15.17b). These vaulted loops
of magnetic field sometimes appear as solar prominences,
in which the field traps gas that may glow for days or even
weeks. Some prominences rise to heights of more than
100,000 kilometers above the Sun’s surface (Figure 15.18).
The most dramatic events on the solar surface are
solar flares, which emit bursts of X rays and fast-moving
charged particles into space (Figure 15.19). Flares generally
occur in the vicinity of sunspots, leading us to suspect that
they occur when the magnetic field lines become so twisted
and knotted that they can no longer bear the tension. The
magnetic field lines suddenly snap like tangled elastic bands
twisted beyond their limits, releasing a huge amount of
energy. This energy heats the nearby plasma to 100 million
K over the next few minutes to few hours, generating X rays
and accelerating some of the charged particles to nearly the
speed of light.
The Chromosphere and Corona
The high temperatures of the chromosphere and corona
perplexed scientists for decades. After all, temperatures
gradually decline as we move outward from the core to the
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VIS
b Spectra of sunspots can be
used to measure the strength
of their magnetic fields. This
image shows the spectrum
of a sunspot and its surroundings. The sunspot region
shows up as dark horizontal
bands because it is darker
than the rest of the solar surface in its vicinity. The vertical bands are absorption lines
that are present both inside
and outside the sunspots.
The influence of strong magnetic fields within the sunspot
region splits a single absorption line into three parts.
Measuring the separation
between these lines tells us
the strength of the magnetic
field within the sunspot.
top of the photosphere. Why should this decline suddenly
reverse? Some aspects of this atmospheric heating remain
a mystery today, but we have at least a general explanation:
The Sun’s strong magnetic fields carry energy upward from
the churning solar surface to the chromosphere and corona.
More specifically, the rising and falling of gas in the
convection zone probably shakes magnetic field lines beneath
the solar surface. This shaking generates waves along the
magnetic field lines that carry energy upward to the solar
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weaker magnetic field
e
stronger
magnetic
field
e
e
e
weaker magnetic field
a Magnetic field lines follow
the directions that compass
needles would point.
b Lines closer together
indicate a stronger field.
c Charged particles follow
paths that spiral along
magnetic field lines.
atmosphere. Precisely how the waves deposit their energy
in the chromosphere and corona is not known, but the
waves agitate the low-density plasma of these layers, somehow heating them to high temperatures. Much of this heating appears to happen near where the magnetic field lines
emerge from the Sun’s surface.
According to this model of solar heating, the same
magnetic fields that keep sunspots cool make the overlying
Figure 15.16 We draw magnetic field
lines to represent invisible magnetic fields.
plasma of the chromosphere and corona hot. We can test
this idea observationally. The gas of the chromosphere and
corona is so tenuous that we cannot see it with our eyes
except during a total eclipse, when we can see the faint visible light scattered by electrons in the corona [Section 2.5].
However, the roughly 10,000 K plasma of the chromosphere
emits strongly in the ultraviolet, and the million K plasma
of the corona is the source of virtually all X rays coming
Magnetic fields
trap gas.
T 5,800 K
sunspots
T 4,500 K
T 5,800 K
convection
cells
Magnetic fields of sunspots suppress convection
and prevent surrounding plasma from sliding
sideways into sunspot.
a Pairs of sunspots are connected by tightly wound magnetic
field lines.
Figure 15.17 Loops of magnetic field lines can arch high above
the solar surface, reaching heights many times larger than Earth’s
diameter.
b This X-ray photo (from NASA’s
TRACE mission) shows gas trapped
within looped magnetic field lines.
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Figure 15.18 A gigantic solar prominence
erupts from the solar surface at the upper
right of this ultraviolet-light photo (from the
SOHO mission). The gas within this prominence, which is over 20 times the size of
Earth, is quite hot but still cooler than the
million-degree gas of the surrounding corona.
UV
Figure 15.19 This photo (from
TRACE) of ultraviolet light emitted
by hydrogen atoms shows a solar
flare erupting from the Sun’s surface.
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UV
from the Sun. Figure 15.20 shows an X-ray image of the Sun.
As the solar heating model predicts, the brightest regions
of the corona tend to be directly above sunspot groups.
Some regions of the corona, called coronal holes, barely
show up in X-ray images. More detailed analyses show that
the magnetic field lines in coronal holes project out into
space like broken rubber bands, allowing particles spiraling along them to escape the Sun altogether. These particles streaming outward from the corona constitute the solar
wind, which blows through the solar system at an average
speed of about 500 kilometers per second and has important effects on planetary surfaces, atmospheres, and magnetospheres. Well beyond the planets, the pressure of interstellar gas must eventually halt the solar wind. The Pioneer
and Voyager spacecraft that visited the outer planets in the
1970s and 1980s are still traveling outward from our solar
system and may soon encounter this “boundary” (called the
heliopause) of the realm of the Sun.
The solar wind also gives us something tangible to
study. In the same way that meteorites provide us with samples of asteroids we’ve never visited, solar wind particles
captured by satellites provide us with a sample of material
from the Sun. Analysis of these solar particles has reassuringly verified that the Sun is made mostly of hydrogen,
just as we conclude from studying the Sun’s spectrum.
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Figure 15.20 An X-ray image of the
Sun reveals the million-degree gas of the
corona. Brighter regions of this image
(yellow) correspond to regions of stronger
X-ray emission. The darker regions are
the coronal holes from which the solar
wind escapes. (From the Yohkoh space
observatory.)
X-ray
15.5 Solar Weather
and Climate
Individual sunspots, prominences, and flares are short-lived
phenomena, somewhat like storms on Earth. They constitute what we call solar weather or solar activity. You know
from personal experience that the Earth’s weather is notoriously unpredictable. The same is true for the Sun: We
cannot predict precisely when or where a particular sunspot
or flare will appear. Earth’s climate, on the other hand, is
quite regular from season to season. So it is with the Sun,
where despite day-to-day variations the general nature and
intensity of solar activity follow a predictable cycle.
The Sunspot Cycle
Long before we realized that sunspots were magnetic disturbances, astronomers had recognized patterns in sunspot
activity. The most notable pattern is the number of sunspots visible on the Sun at any particular time. Thanks to
telescopic observations of the Sun recorded by astronomers since the 1600s, we know that the number of sunspots
gradually rises and falls in a sunspot cycle with an average
period of about 11 years (Figure 15.21a). At the time of
solar maximum, when sunspots are most numerous, we
may see dozens of sunspots on the Sun at one time. In contrast, we see few if any sunspots at the time of solar minimum. The frequency of prominences and flares also follows
the sunspot cycle, with these events being most common
at solar maximum and least common at solar minimum.
Although we’ll call it an “11-year” cycle, the interval
between solar maxima is sometimes as long as 15 years
or as short as 7 years. The number of sunspots also varies
dramatically (Figure 15.21a). In fact, sunspot activity virtually ceased between the years 1645 and 1715, a period
sometimes called the Maunder minimum (after E. W.
Maunder, who identified it in historical sunspot records).
Another feature of the sunspot cycle is a gradual
change in the solar latitudes at which individual sunspots
form and dissolve (Figure 15.21b). As a cycle begins at solar
minimum, sunspots form primarily at mid-latitudes (30°
to 40°) on the Sun. The sunspots tend to form at lower latitudes as the cycle progresses, appearing very close to the
solar equator as the next solar minimum approaches.
A less obvious feature of the sunspot cycle is that
something peculiar happens to the Sun’s magnetic field
at each solar minimum. The field lines connecting all pairs
of sunspots (see Figure 15.17) tend to point in the same
direction throughout an 11-year solar cycle (within each
hemisphere). For example, all compass needles might point
from the easternmost sunspot to the westernmost sunspot
in a pair. However, as the cycle ends at solar minimum, the
magnetic field reverses: In the subsequent solar cycle, the
field lines connecting pairs of sunspots point in the opposite
direction. Apparently, the entire magnetic field of the Sun
flip-flops every 11 years.
The magnetic reversals hint that the sunspot cycle
is related to the generation of magnetic fields on the Sun.
They also tell us that the complete magnetic cycle of the
Sun, called the solar cycle, really averages 22 years, since it
takes two 11-year cycles before the magnetic field is back
the way it started.
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percentage of Sun’s surface
covered by sunspots
0.5%
0.4%
0.3%
0.2%
0.1%
0.0%
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
1980
1990
2000
year
a This graph shows how the number of sunspots on the Sun changes with time. The vertical axis shows the
percentage of the Sun’s surface covered by sunspots. The cycle has a period of approximately 11 years.
90 N
latitude
30 N
Equator
30 S
90 S
1900
1910
1920
1930
1940
1950
1960
1970
year
b This graph shows how the latitudes at which sunspot groups appear tend to shift during a single sunspot
cycle. Each dot represents a group of sunspots and indicates the year (horizontal axis) and latitude (vertical
axis) at which the group appeared.
Figure 15.21 Sunspot cycle during the past century.
What Causes the Sunspot Cycle?
The causes of the Sun’s magnetic fields and the sunspot
cycle are not well understood, but we believe we know
the general nature of the processes involved. Convection
is thought to dredge up weak magnetic fields generated in
the solar interior, amplifying them as they rise. The Sun’s
rotation—faster at its equator than near its poles—then
stretches and shapes these fields.
Imagine what happens to a magnetic field line that originally runs along the Sun’s surface directly from the north
pole to the south pole. At the equator, the field line circles
the Sun in 25 days, but at higher latitudes the field line lags
behind. Gradually, this rotation pattern winds the field line
more and more tightly around the Sun (Figure 15.22). This
process, operating at all times over the entire Sun, produces
the contorted field lines that generate sunspots and other
solar activity.
Investigating how the Sun’s magnetic field develops
and changes in time requires sophisticated computer models. Scientists are working hard on such models, but the
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behavior of these fields is so complex that approximations
are necessary even with the best supercomputers. Using
these computer models, scientists have successfully replicated some features of the sunspot cycle, such as changes
in the number and latitude of sunspots and the magnetic
field reversals that occur about every 11 years. However,
much still remains mysterious, including why the period
of the sunspot cycle varies and why solar activity is different from one cycle to the next.
Solar Activity and Earth
During solar maximum, solar flares and other forms of
solar activity send large numbers of highly energetic charged
particles (protons and electrons) toward Earth. Sometimes
these particles travel in the smooth flow known as the solar
wind. Other times they come in the form of huge magnetic
bubbles called coronal mass ejections. Do these forms of solar
weather affect Earth? In at least some ways, the answer is
a definitive yes.
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N
N
N
magnetic
field line
differing
rotation
rates
e
qu
ator
time
S
time
S
S
Figure 15.22 The Sun rotates more quickly at its equator than it does near its poles. Because gas circles
the Sun faster at the equator, it drags the Sun’s north-south magnetic field lines into a more twisted configuration. The magnetic field lines linking pairs of sunspots, depicted here as green and black blobs, trace out
the directions of these stretched and distorted field lines.
The magnetic field associated with the solar wind constantly interacts with Earth’s magnetic field. Occasionally
these fields interconnect. When that happens, large amounts
of energy are released from the magnetic field into the
charged particles near the interconnection zone. Many
of these energized particles then flow down Earth’s magnetic field lines toward the poles (Figure 15.23a). Collisions
between the charged particles and atoms in Earth’s upper
atmosphere cause electrons in the atoms to jump to higher
energy levels [Section 4.4]. These excited atoms subsequently
emit visible-light photons as they drop to lower energy levels,
S P E C I A L TO P I C
creating the shimmering light of auroras (Figure 15.23b).
Because coronal mass ejections are particularly energetic, the
auroras they stimulate can be especially spectacular.
Particles streaming from the Sun after the occurrence
of solar flares, coronal mass ejections, or other major solar
storms can also have practical impacts on society. For example, these particles can hamper radio communications,
disrupt electrical power delivery, and damage the electronic
components in orbiting satellites. During a particularly
powerful magnetic storm on the Sun in March 1989, the
U.S. Air Force temporarily lost track of over 2,000 satellites,
Long-Term Change in Solar Activity
Figure 15.21 shows that the sunspot cycle varies in length and
intensity, and it sometimes seems to disappear altogether. With
these facts as background, many scientists are searching for longerterm patterns in solar activity. Unfortunately, the search for longerterm variations is difficult because telescopic observations of
sunspots cover a period of only about 400 years. Some naked-eye
observations of sunspots recorded by Chinese astronomers go
back almost 2,000 years, but these records are sparse, and nakedeye observations may not be very reliable. We can also guess at
past solar activity from descriptions of solar eclipses recorded
around the world: When the Sun is more active, the corona tends
to have longer and brighter “streamers” visible to the naked eye.
Another way to gauge past solar activity is to study the amount
of carbon-14 in tree rings. High-energy cosmic rays [Section 19.2]
coming from beyond our own solar system produce radioactive
carbon-14 in Earth’s atmosphere. During periods of high solar
activity, the solar wind tends to grow stronger, shielding Earth
from some of these cosmic rays. Thus, production of carbon-14
drops when the Sun is more active. All the while, trees steadily
breathe in atmospheric carbon, in the form of carbon dioxide,
and incorporate it year by year into each ring. We can therefore
estimate the level of solar activity in any given year by measuring
the level of carbon-14 in the corresponding ring. No clear evidence has yet been found of longer-term cycles of solar activity,
but the search goes on.
Theoretical models predict a very long term trend of lessening solar activity. According to our theory of solar system formation, the Sun must have rotated much faster when it was young
[Section 9.3]. Because a combination of convection and rotation
generates solar activity, a faster rotation rate should have meant
much more activity. Observations of other stars that are similar
to the Sun but rotate faster confirm that these stars are much
more active. We find evidence for many more “starspots” on these
stars than on the Sun, and their relatively bright ultraviolet and
X-ray emissions suggest that they have brighter chromospheres
and coronas—just as we would expect if they are more active
than the Sun.
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particles spiral around
magnetic field lines
stream of solar particles
from solar wind
N
S
a Interactions between Earth’s magnetic field and the magnetic field of the solar wind can
send energetic charged particles toward Earth’s poles.
Figure 15.23 Particles from the Sun cause auroras on Earth.
b Aurora along the coast of Norway.
and powerful currents induced in the ground circuits of
the Quebec hydroelectric system caused it to collapse for
more than 8 hours. The combined cost of the loss of power
in the United States and Canada exceeded $100 million. In
January 1997, AT&T lost contact with a $200-million communications satellite, probably because of damage caused
by particles coming from another powerful solar storm.
Satellites in low-Earth orbit are particularly vulnerable
during solar maximum, when the increase in solar X rays
and energetic particles heats Earth’s upper atmosphere,
causing it to expand. The density of the gas surrounding
low-flying satellites therefore rises, exerting drag that saps
their energy and angular momentum. If this drag proceeds
unchecked, the satellites ultimately plummet back to Earth.
Satellites in low orbits, including the Hubble Space Telescope
and the Space Station, require occasional boosts to prevent
them from falling out of the sky.
Connections between solar activity and Earth’s climate
are much less clear. The period from 1645 to 1715, when
solar activity seems to have virtually ceased, was a time
of exceptionally low temperatures in Europe and North
America known as the Little Ice Age. Did the low solar activity cause these low temperatures, or was their occurrence
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a coincidence? No one knows for sure. Some researchers
have claimed that certain weather phenomena, such as
drought cycles or frequencies of storms, are correlated with
the 11- or 22-year cycle of solar activity. However, the data
supporting these correlations are weak in many cases, and
even real correlations may be coincidental.
Part of the difficulty in linking solar activity with climate is that no one understands how the linkage might
work. Although emissions of ultraviolet light, X rays, and
high-energy particles increase substantially from solar minimum to solar maximum, the total luminosity of the Sun
barely changes at all. (The Sun becomes only about 0.1%
brighter during solar maximum.) Thus, if solar activity
really is affecting Earth’s climate, it must be through some
very subtle mechanism. For example, perhaps the expansion of Earth’s upper atmosphere that occurs with solar
maximum somehow causes changes in weather.
The question of how solar activity is linked to Earth’s
climate is very important, because we need to know whether
global warming is affected by solar activity in addition to
human activity. Unfortunately, for the time being at least,
we can say little about this question.
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THE BIG PICTURE
Putting Chapter 15 into Context
In this chapter, we have examined our Sun, the nearest
star. When you look back at this chapter, make sure you
understand these “big picture” ideas:
● The ancient riddle of why the Sun shines is now solved.
The Sun shines with energy generated by fusion of
hydrogen into helium in the Sun’s core. After a millionyear journey through the solar interior and an 8-minute
journey through space, a small fraction of this energy
reaches Earth and supplies sunlight and heat.
● Gravitational equilibrium, the balance between pressure and gravity, determines the Sun’s interior structure and maintains its steady nuclear burning rate.
The Sun achieved its long-lasting state of gravitational
equilibrium when energy generation by fusion in the
core came into balance with the energy lost through
thermal radiation from the surface. If the Sun were not
relatively steady, life on Earth might not have been
possible.
● The Sun’s atmosphere displays its own version of
weather and climate, governed by solar magnetic fields.
Solar weather has important influences on Earth.
● The Sun is important not only as our source of light
and heat, but also because it is the only star near
enough for us to study in great detail. In the coming
chapters, we will use what we’ve learned about the
Sun to help us understand other stars.
S U M M A RY O F K E Y C O N C E P T S
15.1 Why Does the Sun Shine?
• What process creates energy in the Sun? Fusion of
hydrogen into helium in the Sun’s core generates the
Sun’s energy.
• Why does the Sun’s size remain stable? The Sun’s size
remains stable because it is in gravitational equilibrium. The outward pressure of hot gas balances the
inward force of gravity at every point within the Sun.
• How did the Sun become hot enough for fusion in the
first place? As the Sun was forming, it grew hotter
as it shrank in size because gravitational contraction
converted gravitational potential energy into thermal energy. Gravitational contraction continued to
shrink the Sun and raise its central temperature until
the core became hot and dense enough for nuclear
fusion.
15.2 Plunging to the Center of the Sun:
An Imaginary Journey
• What are the major layers of the Sun, from the center
out? The layers of the Sun are core, radiation zone,
convection zone, photosphere, chromosphere, and
corona.
• What do we mean by the “surface” of the Sun? We
consider the photosphere to be the surface of the Sun
because light can pass through the photosphere but
cannot escape from deeper inside the Sun. Thus,
photographs of visible light from the Sun show us
what the photosphere looks like.
• What is the Sun made of ? It is made almost entirely
of hydrogen and helium (98% of the Sun’s mass).
15.3 The Cosmic Crucible
• Why does fusion occur in the Sun’s core? The core
temperature and pressure are so high that colliding
nuclei can come close enough together for the strong
force to overcome electromagnetic repulsion and
bind them together.
• Why is energy produced in the Sun at such a steady
rate? The fusion rate is self-regulating like a thermostat. If the fusion rate increases for some reason, the
added energy production puffs up and cools the core,
bringing the rate back down. Similarly, a decrease
in the fusion rate allows the core to shrink and heat,
bringing the fusion rate back up.
• Why was the Sun dimmer in the distant past?
Although the fusion rate is steady on short time
scales, it gradually increases over billions of years,
increasing the Sun’s luminosity. The increase occurs
because fusion gradually reduces the number of individual nuclei in the solar core. Four hydrogen nuclei
are fused to make just one helium nucleus, causing
the core to shrink and become hotter.
• How do we know what is happening inside the Sun?
We can construct theoretical models of the solar
interior using known laws of physics and then check
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the models against observations of the Sun’s size,
surface temperature, and energy output as well as
studies of “sun quakes” and solar neutrinos.
• What is the solar neutrino problem? Is it solved?
Neutrino detectors capture fewer neutrinos coming
from the Sun than models of fusion in the core predict. This discrepancy is called the solar neutrino
problem. The problem now appears to be solved.
Apparently, neutrinos can transform themselves
among three different types as they travel from the
solar core to Earth, while most detectors can capture
only one type. Thus, the detectors capture fewer
than the expected number of neutrinos.
15.4 From Core to Corona
• How long ago did fusion generate the energy we now
receive as sunlight? Fusion created the energy we receive today about a million years ago. It takes about
a million years for photons and then convection to
transport energy through the solar interior to the
photosphere. Once sunlight emerges from the photosphere, it takes only about 8 minutes to reach Earth.
• How are sunspots, prominences, and flares related to
magnetic fields? Sunspots occur where strong magnetic fields trap and isolate gas from the surrounding plasma of the photosphere. The trapped gas cools,
so the sunspots become cooler and darker than the
rest of the photosphere. Sunspots tend to occur in
pairs connected by a loop of magnetic field, which
may rise high above the surface as a solar promi-
Sensible Statements?
Decide whether each of the following statements is sensible and
explain why it is or is not.
1. Before Einstein, gravitational contraction appeared to be a
perfectly plausible mechanism for solar energy generation.
2. A sudden temperature rise in the Sun’s core is nothing to
worry about, because conditions in the core will soon return
to normal.
3. If fusion in the solar core ceased today, worldwide panic
would break out tomorrow as the Sun began to grow
dimmer.
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nence. The magnetic fields are twisted and contorted
by the Sun’s rotation, and solar flares may occur
when the field lines suddenly snap and release their
energy.
• What is surprising about the temperature of the
chromosphere and corona, and how do we explain it?
Temperature gradually decreases from the core to
the photosphere but then rises again in the chromosphere and corona. These high layers of the Sun are
probably heated by energy carried upward along the
magnetic field lines by waves that are generated as
turbulent motions in the convection zone shake the
magnetic field lines.
15.5 Solar Weather and Climate
• What is the sunspot cycle? The sunspot cycle, or the
variation in the number of sunspots on the Sun’s
surface, has an average period of 11 years. The magnetic field flip-flops every 11 years or so, resulting
in a 22-year magnetic cycle. Sunspots first appear
at mid-latitudes at solar minimum, then become
increasingly more common near the Sun’s equator
as the next minimum approaches.
• What effect does solar activity have on Earth and its
inhabitants? Particles ejected from the Sun by solar
flares and other types of solar activity can affect
communications, electrical power delivery, and the
electronic circuits in space vehicles. The connections
between solar activity and Earth’s climate are not
clear.
4. Astronomers have recently photographed magnetic fields
churning deep beneath the solar photosphere.
5. Neutrinos probably can’t harm me, but just to be safe
I think I’ll wear a lead vest.
6. If you want to see lots of sunspots, just wait for solar
maximum!
7. News of a major solar flare today caused concern among
professionals in the fields of communications and electrical
power generation.
8. By observing solar neutrinos, we can learn about nuclear
fusion deep in the Sun’s core.
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Problems
9. Gravitational Contraction. Briefly describe how gravitational contraction generates energy and when it was important in the Sun’s history.
10. Solar Characteristics. Briefly describe the Sun’s luminosity,
mass, radius, and average surface temperature.
11. Sunspots. What are sunspots? Why do they appear dark in
pictures of the Sun?
12. Solar Fusion. What is the overall nuclear fusion reaction in
the Sun? Briefly describe the proton–proton chain.
13. Models of the Sun. Explain how mathematical models allow
us to predict conditions inside the Sun. How can we be
confident that the models are on the right track?
14. Sun Quakes. How are “sun quakes” similar to earthquakes?
How are they different? Describe how we can observe them
and how they help us learn about the solar interior.
15. Energy Transport. Why does the energy produced by fusion
in the solar core take so long to reach the solar surface?
Describe the processes of radiative diffusion and convection
in the solar interior.
16. The Photosphere. Describe the appearance and temperature
of the Sun’s photosphere. What is granulation? How would
granulation appear in a movie?
17. Observing the Sun’s Atmosphere. Why is the chromosphere
best viewed with ultraviolet telescopes? Why is the corona
best viewed with X-ray telescopes?
18. An Angry Sun. A Time magazine cover once suggested that
an “angry Sun” was becoming more active as human activity changed Earth’s climate through global warming. It’s
certainly possible for the Sun to become more active at the
same time that humans are affecting Earth, but is it possible
that the Sun could be responding to human activity? Can
humans affect the Sun in any significant way? Explain.
*19. Number of Fusion Reactions in the Sun. Use the fact that each
cycle of the proton–proton chain converts 4.7 1029 kg
of mass into energy (see Mathematical Insight 15.1), along
with the fact that the Sun loses a total of about 4.2 109 kg
of mass each second, to calculate the total number of times
the proton–proton chain occurs each second in the Sun.
*20. The Lifetime of the Sun. The total mass of the Sun is about
2 1030 kg, of which about 75% was hydrogen when the
Sun formed. However, only about 13% of this hydrogen
ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low
for fusion.
a. Based on the given information, calculate the total
mass of hydrogen available for fusion over the lifetime
of the Sun.
b. Combine your results from part (a) and the fact that the
Sun fuses about 600 billion kg of hydrogen each second
to calculate how long the Sun’s initial supply of hydrogen can last. Give your answer in both seconds and years.
c. Given that our solar system is now about 4.6 billion years
old, when will we need to worry about the Sun running
out of hydrogen for fusion?
*21. Solar Power Collectors. This problem leads you through the
calculation and discussion of how much solar power can be
collected by solar cells on Earth.
a. Imagine a giant sphere surrounding the Sun with a
radius of 1 AU. What is the surface area of this sphere,
in square meters? (Hint: The formula for the surface
area of a sphere is 4pr2.)
b. Because this imaginary giant sphere surrounds the Sun,
the Sun’s entire luminosity of 3.8 1026 watts must
pass through it. Calculate the power passing through
each square meter of this imaginary sphere in watts per
square meter. Explain why this number represents the
maximum power per square meter that can be collected
by a solar collector in Earth orbit.
c. List several reasons why the average power per square
meter collected by a solar collector on the ground will
always be less than what you found in part (b).
d. Suppose you want to put a solar collector on your roof.
If you want to optimize the amount of power you can
collect, how should you orient the collector? (Hint: The
optimum orientation depends on both your latitude
and the time of year and day.)
*22. Solar Power for the United States. The total annual U.S. energy consumption is about 2 1020 joules.
a. What is the average power requirement for the United
States, in watts? (Hint: 1 watt 1 joule/s.)
b. With current technologies and solar collectors on the
ground, the best we can hope is that solar cells will
generate an average (day and night) power of about
200 watts/m2. (You might compare this to the maximum
power per square meter you found in problem 22b.)
What total area would we need to cover with solar cells
to supply all the power needed for the United States?
Give your answer in both square meters and square
kilometers.
c. The total surface area of the United States is about
2 107 km2. What fraction of the U.S. area would have
to be covered by solar collectors to generate all of the
U.S. power needs? In one page or less, describe potential
environmental impacts of covering so much area with
solar collectors. Also discuss whether you think these
environmental impacts would be greater or less than
the impacts of using current energy sources such as coal,
oil, nuclear power, and hydroelectric power.
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*23. The Color of the Sun. The Sun’s average surface temperature
is about 5,800 K. Use Wien’s law (see Mathematical Insight
6.2) to calculate the wavelength of peak thermal emission
from the Sun. What color does this wavelength correspond
to in the visible-light spectrum? In light of your answer, why
do you think the Sun appears white or yellow to our eyes?
Discussion Questions
24. The Role of the Sun. Briefly discuss how the Sun affects us
here on Earth. Be sure to consider not only factors such as
its light and warmth, but also how the study of the Sun has
led us to new understanding in science and to technological developments. Overall, how important has solar research been to our lives?
25. The Solar Neutrino Problem. Discuss the solar neutrino problem and its potential solutions. How serious do you consider this problem? Do you think current theoretical models of the Sun could be wrong in any fundamental way?
Why or why not?
26. The Sun and Global Warming. One of the most pressing
environmental issues on Earth concerns the extent to which
human emissions of greenhouse gases are warming our
planet. Some people claim that part or all of the observed
warming over the past century may be due to changes on
the Sun, rather than to anything humans have done. Discuss how a better understanding of the Sun might help us
understand the threat posed by greenhouse gas emissions.
Why is it so difficult to develop a clear understanding of
how the Sun affects Earth’s climate?
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M E D I A E X P L O R AT I O N S
Web Projects
Take advantage of the useful Web links on www.
astronomyplace.com to assist you with the following
projects.
1. Current Solar Activity. Daily information about solar
activity is available at NASA’s Web site sunspotcycle.
com. Where are we in the sunspot cycle right now?
When is the next solar maximum or minimum expected? Have there been any major solar storms in
the past few months? If so, did they have any significant effects on Earth? Summarize your findings in
a one- to two-page report.
2. Solar Observatories in Space. Visit NASA’s Web site
for the Sun–Earth connection and explore some
of the current and planned space missions designed
to observe the Sun. Choose one mission to study in
greater depth, and write a one- to two-page report
on the mission status and goals and what it has
taught or will teach us about the Sun.
3. Sudbury Neutrino Observatory. Visit the Web site for
the Sudbury Neutrino Observatory (SNO) and learn
how it has helped to solve the solar neutrino problem. Write a one- to two-page report describing the
observatory, any recent results, and what we can
expect from it in the future.