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15 Our Star

LEARNING GOALS

15.1 Why Does the Sun Shine? • Why was the Sun dimmer in the distant past? • What process creates energy in the Sun? • How do we know what is happening inside the Sun? • Why does the Sun’s size remain stable? • What is the solar neutrino problem? Is it solved ? • How did the Sun become hot enough for fusion 15.4 From Core to Corona in the first place? • How long ago did fusion generate the energy we 15.2 Plunging to the Center of the Sun: now receive as sunlight? An Imaginary Journey • How are sunspots, prominences, and flares related • What are the major layers of the Sun, from the to magnetic fields? center out? • What is surprising about the temperature of the • What do we mean by the “surface” of the Sun? chromosphere and corona, and how do we explain it? • What is the Sun made of? 15.5 Solar Weather and Climate 15.3 The Cosmic Crucible • What is the sunspot cycle? • Why does fusion occur in the Sun’s core? • What effect does solar activity have on Earth and • Why is energy produced in the Sun at such its inhabitants? a steady rate?

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I say Live, Live, because of the Sun, from some type of chemical burning similar to the burning The dream, the excitable gift. of coal or wood. Simple calculations showed that a cooling or chemically burning Sun could shine for a few thousand Anne Sexton (1928–1974) years—an age that squared well with biblically based esti- mates of Earth’s age that were popular at the time. However, these ideas suffered from fatal flaws. If the Sun were a cool- stronomy today involves the study of the ing ember, it would have been much hotter just a few hun- entire universe, but the root of the word dred years earlier, making it too hot for civilization to have existed. Chemical burning was ruled out because it cannot astronomy comes from the Greek word A generate enough energy to account for the rate of radiation for “star.” Although we have learned a lot about the observed from the Sun’s surface. universe up to this point in the book, only now do A more plausible hypothesis of the late 1800s sug- gested that the Sun generates energy by contracting in size, we turn our attention to the study of the stars, the a process called gravitational contraction.Ifthe Sun were namesakes of astronomy. shrinking, it would constantly be converting gravitational When we think of stars, we usually think of the potential energy into thermal energy, thereby keeping the Sun hot. Because of its large mass, the Sun would need to beautiful points of light visible on a clear night. The contract only very slightly each year to maintain its tem- nearest and most easily studied star is visible only perature—so slightly that the contraction would be un- in the daytime—our Sun. Of course, the Sun is im- noticeable. Calculations showed that the Sun could shine for up to about 25 million years generating energy by grav- portant to us in many more ways than as an object itational contraction. However, geologists of the late 1800s for astronomical study. The Sun is the source of virtu- had already established the age of Earth to be far older than ally all light, heat, and energy reaching Earth, and life 25 million years, leaving astronomers in an embarrassing position. on Earth’s surface could not survive without it. Only after Einstein published his special theory of In this chapter, we will study the Sun in some relativity, which included his discovery of E mc2,did depth. We will learn how the Sun makes life possible the true energy-generation mechanism of the Sun become clear. We now know that the Sun generates energy by nu- on Earth. Equally important, we will study our Sun as clear fusion, a source so efficient that the Sun can shine for a star so that in subsequent chapters we can more about 10 billion years. Because the Sun is only 4.6 billion easily understand stars throughout the universe. 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 gener- ation by nuclear fusion, the Sun maintains its size through a balance between two competing forces: gravity pulling 15.1 Why Does the Sun Shine? inward and pressure pushing outward. This balance is called Ancient peoples recognized the vital role of the Sun in their gravitational equilibrium (or hydrostatic equilibrium). lives. Some worshiped the Sun as a god, and others created It means that, at any point within the Sun, the weight of elaborate mythologies to explain its daily rise and set. Only overlying material is supported by the underlying pressure. recently, however, have we learned how the Sun provides us A stack of acrobats provides a simple example of this bal- with light and heat. ance (Figure 15.1). The bottom person supports the weight Most ancient thinkers viewed the Sun as some type of of everybody above him, so the pressure on his body is fire, perhaps a lump of burning coal or wood. The Greek very great. At each higher level, the overlying weight is less, philosopher Anaxagoras (c. 500–428 B.C.) imagined the Sun so the pressure decreases. Gravitational equilibrium in the to be a very hot, glowing rock about the size of the Greek Sun means that the pressure increases with depth, making peninsula of Peloponnesus (comparable in size to Massa- the Sun extremely hot and dense in its central core (Fig- chusetts). Thus, he was one of the first people in history to ure 15.2). 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 THINK ABOUT IT were reasonably well known, and scientists seriously began Earth’s atmosphere is also in gravitational equilibrium, with the to address the question of how the Sun shines. Two early weight of upper layers supported by the pressure in lower ideas held either that the Sun was a cooling ember that had layers. Use this idea to explain why the air gets thinner at higher once been much hotter or that the Sun generated energy 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 contraction made the Sun hot enough to sustain nuclear lowest person supports the most weight and feels the greatest fusion in its core. Ever since, energy liberated by fusion has pressure, and the overlying weight and underlying pressure decrease maintained the Sun’s gravitational equilibrium and kept the for those higher up. Sun shining steadily, supplying the light and heat that sus- tain life on Earth. 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 15.2 Plunging to the again in the distant future. Our Sun was born from a col- Center of the Sun: lapsing cloud of interstellar gas. The contraction of the cloud released gravitational potential energy, raising the An Imaginary Journey interior temperature higher and higher—but not high In the rest of this chapter, we will discuss in detail how enough to halt the contraction. The cloud continued to the Sun produces energy and how that energy travels to shrink because thermal radiation from the cloud’s surface Earth. First, to get a “big picture” view of the Sun, let’s carried away much of the energy released by contraction, imagine you have a spaceship that can somehow with- even while the interior temperature was rising. When the stand the immense heat and pressure of the solar interior central temperature and density eventually reached the and take an imaginary journey from Earth to the center values necessary to sustain nuclear fusion, energy genera- of the Sun. tion in the Sun’s interior matched the energy lost from the surface in the form of radiation. With the onset of fusion, Approaching the Surface the Sun entered a long-lasting state of gravitational equilib- rium that has persisted for the last 4.6 billion years. As you begin your voyage from Earth, the Sun appears as a About 5 billion years from now, when the Sun finally whitish ball of glowing gas. With spectroscopy [Section 7.3], exhausts its nuclear fuel, the internal pressure will drop, and you verify that the Sun’s mass is 70% hydrogen and 28% gravitational contraction will begin once again. As we will see helium. Heavier elements make up the remaining 2%. later, some of the most important and spectacular processes The total power output of the Sun, called its luminos- in astronomy hinge on this ongoing “battle” between the ity, is an incredible 3.8 1026 watts. That is, every second, crush of gravity and a star’s internal sources of pressure. the Sun radiates a total of 3.8 1026 joules of energy into In summary, the answer to the question “Why does the space (recall that 1 watt 1 joule/s). If we could somehow Sun shine?” is that about 4.6 billion years ago gravitational 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

Radius (RSun) 696,000 km (about 109 times the radius of Earth) 30 Mass (MSun)2 10 kg (about 300,000 times the mass of Earth) 26 Luminosity (LSun) 3.8 10 watts Composition (by 70% hydrogen, 28% helium, percentage of mass) 2% heavier elements Rotation rate 25 days (equator) to 30 days (poles) Surface temperature 5,800 K (average); 4,000 K (sunspots) Core temperature15 million K

Figure 15.3 This photo of the VIS visible surface of the Sun shows several dark sunspots. As you and your spaceship continue to fall toward the Sun, you notice an increasingly powerful headwind exert- ing a bit of drag on your descent. This headwind, called the nosity, it would be enough to meet current human energy solar wind, is created by ions and subatomic particles flow- demands for roughly the next 500,000 years! ing outward from the solar surface. The solar wind helps Of course, only a tiny fraction of the Sun’s total energy shape the magnetospheres of planets [Sections 11.3, 12.4] output reaches Earth, with the rest dispersing in all direc- and blows back the material that forms the tails of comets tions into space. Most of this energy is radiated in the form [Section 13.4]. of visible light, but once you leave the protective blanket of A few million kilometers above the solar surface, you Earth’s atmosphere you’ll encounter significant amounts of enter the solar corona, the tenuous uppermost layer of the other types of solar radiation, including dangerous ultra- Sun’s atmosphere (Figure 15.4). Here you find the temper- violet and X rays. Your spaceship will require substantial ature to be astonishingly high—about 1 million Kelvin. This shielding to protect you from serious radiation burns caused region emits most of the Sun’s X rays. However, the density by these high-energy forms of light. here is so low that your spaceship feels relatively little heat Through a telescope, you can see that the Sun seethes despite the million-degree temperature [Section 4.2]. with churning gases. At most times you’ll detect at least Nearer the surface, the temperature suddenly drops to a few sunspots blotching its surface (Figure 15.3). If you about 10,000 K in the chromosphere, the primary source focus your telescope solely on a sunspot, you’ll find that it is of the Sun’s ultraviolet radiation. At last you plunge through blindingly bright. Sunspots appear dark only in contrast to the visible surface of the Sun, called the photosphere,where the even brighter solar surface that surrounds them. A typi- the temperature averages just under 6,000 K. Although the cal sunspot is large enough to swallow the entire Earth, dra- photosphere looks like a well-defined surface from Earth, matically illustrating that the Sun is immense by any it consists of gas far less dense than Earth’s atmosphere. earthly standard. The Sun’s radius is nearly 700,000 kilo- Throughout the solar atmosphere, you notice that meters, and its mass is 2 1030 kilograms—about 300,000 the Sun has its own version of weather, in which conditions times more massive than Earth. at a particular altitude differ from one region to another. Sunspots appear to move from day to day along with Some regions of the chromosphere and corona are partic- the Sun’s rotation. If you watch very carefully, you may ularly hot and bright, while other regions are cooler and notice that sunspots near the solar equator circle the Sun less dense. In the photosphere, sunspots are cooler than faster than those at higher solar latitudes. This observa- the surrounding surface, though they are still quite hot tion reveals that, unlike a spinning ball, the entire Sun does and bright by earthly standards. In addition, your compass not rotate at the same rate. Instead, the solar equator com- goes crazy as you descend through the solar atmosphere, pletes one rotation in about 25 days, and the rotation pe- indicating that solar weather is shaped by intense magnetic riod increases with latitude to about 30 days near the solar fields. Occasionally, huge magnetic storms occur, shooting poles. Table 15.1 summarizes some of the basic properties hot gases far into space. of the Sun.

THINK ABOUT IT Into the Sun As a brief review, describe how we measure the mass of the Up to this point in your journey, you may have seen Earth Sun using Newton’s version of Kepler’s third law. (Hint: Look and the stars when you looked back, but as you slip be- back at Chapter 5.) neath the photosphere, blazing light engulfs you. You are

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solar wind

photosphere co ro n a c hr om o s p h e r e

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 in- with the temperature. Soon you reach depths at which the credible turbulence. If you can hold steady long enough to Sun is far denser than water. Nevertheless, it is still a gas see what is going on around you, you’ll notice spouts of (more specifically, a plasma of positively charged ions and hot gas rising upward, surrounded by cooler gas cascading free electrons) because each particle moves independently down from above. You are in the convection zone,where of its neighbors [Section 4.3]. energy generated in the solar core travels upward, trans- About a third of the way down to the center, the tur- ported by the rising of hot gas and falling of cool gas called bulence of the convection zone gives way to the calmer convection [Section 10.2].With some quick thinking, you plasma of the radiation zone,where energy is carried out- may realize that the photosphere above you is the top of ward primarily by photons of light. The temperature rises the convection zone and that convection is the cause of to almost 10 million K, and your spacecraft is bathed in the Sun’s seething, churning appearance. X rays trillions of times more intense than the visible light As you descend through the convection zone, the sur- at the solar surface. rounding density and pressure increase substantially, along

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COMMON MISCONCEPTIONS fission fusion

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 bon- fire in the sky. However, the Sun does not burn in the same sense as a fire burns on Earth. Fires on Earth gen- Figure 15.5 Nuclear fission splits a nucleus into smaller nuclei erate light through chemical changes that consume oxy- (not usually of equal size), while nuclear fusion combines smaller gen and produce a flame. The glow of the Sun has more nuclei into a larger nucleus. in common with the glowing embers left over after the flames have burned out. Much like hot embers, the Sun’s loses neutrons, its atomic mass changes and it becomes a surface shines with the visible thermal radiation pro- different isotope [Section 4.3].The process of splitting a nu- duced by any object that is sufficiently hot [Section 6.4]. cleus into two smaller nuclei is called nuclear fission.The However, hot embers quickly stop glowing as they process of combining nuclei to make a nucleus with a greater cool, while the Sun keeps shining because its surface is number of protons or neutrons is called nuclear fusion kept hot by the energy rising from the Sun’s core. Be- (Figure 15.5). Human-built nuclear power plants rely cause this energy is generated by nuclear fusion, we on nuclear fission of uranium or plutonium. The nuclear sometimes say that it is the result of “nuclear burning”— power plant at the center of the Sun relies on nuclear fusion, a term that suggests nuclear changes in much the same turning hydrogen into helium. 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 Nuclear Fusion to speak of any kind of burning on the Sun’s surface, The 15 million K plasma in the solar core is like a “soup” where light is produced primarily by thermal radiation. 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, No real spacecraft could survive, but your imaginary electromagnetic forces deflect the nuclei, preventing actual one keeps plunging straight down to the solar core.There collisions, because positive charges repel one another. If you finally find the source of the Sun’s energy: nuclear fusion nuclei collide with sufficient energy, however, they can stick transforming hydrogen into helium. At the Sun’s center, together to form a heavier nucleus (Figure 15.6). the temperature is about 15 million K, the density is more Sticking positively charged nuclei together is not easy. than 100 times that of water, and the pressure is 200 bil- The strong force,which binds protons and neutrons to- lion times that on the surface of Earth. The energy pro- gether in atomic nuclei, is the only force in nature that can duced 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 study- ing fusion in the solar core and then tracing the flow of the energy generated by fusion as it moves outward through the Sun. 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 ap- proaches, such as melting various ores together in a vessel called a crucible. Other times they tried magic. Their get- rich-quick schemes never managed to work. Today we know that there is no easy way to turn other elements into At high speeds, nuclei come close enough for the strong force to bind gold, but it is possible to transmute one element or isotope them together. into another. Figure 15.6 Positively charged nuclei can fuse only if a high- If a nucleus gains or loses protons, its atomic number speed collision brings them close enough for the strong force changes and it becomes a different element. If it gains or to come into play.

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Step 1 Step 2 Step 3 Key: e electron gamma e ray p gamma ray neutrino n neutron e e gamma ray positron p proton p p n

Total reaction

p p n gamma ray p p p p n p p gamma ray n p p p p n n p n n p p p e n p p e gamma ray

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 posi- tively charged nuclei [Section S4.2].In contrast to gravita- pp p n n energy tional and electromagnetic forces, which drop off gradually p p p as the distances between particles increase (by an inverse 4 1H 1 4He square law [Section 5.3]), the strong force is more like glue or Velcro: It overpowers the electromagnetic force over However, collisions between two nuclei are far more very small distances but is insignificant when the distances common than three- or four-way collisions, so this overall between particles exceed the typical sizes of atomic nuclei. reaction proceeds through steps that involve just two nuclei The trick to nuclear fusion, therefore, is to push the posi- at a time. The sequence of steps that occurs in the Sun is tively charged nuclei close enough together for the strong called the proton–proton chain because it begins with col- force to outmuscle electromagnetic repulsion. lisions between individual protons (hydrogen nuclei). The high pressures and temperatures in the solar core Figure 15.7 illustrates the steps in the proton–proton chain: are just right for fusion of hydrogen nuclei into helium nuclei. The high temperature is important because the nu- Step 1. Two protons fuse to form a nucleus consisting of clei must collide at very high speeds if they are to come one proton and one neutron, which is the isotope of hy- close enough together to fuse. (Quantum tunneling is also drogen known as deuterium. Note that this step converts a important to this process [Section S4.5].) The higher the proton into a neutron, reducing the total nuclear charge temperature, the harder the collisions, making fusion reac- from 2 for the two fusing protons to 1 for the resulting tions more likely at higher temperatures. The high pressure deuterium nucleus. The lost positive charge is carried off of the overlying layers is necessary because without it the by a positron, the antimatter version of an electron with hot plasma of the solar core would simply explode into space, a positive rather than negative charge [Section S4.2].A neu- shutting off the nuclear reactions. In the Sun, the pressure trino—a subatomic particle with a very tiny mass—is also is high and steady, allowing some 600 million tons of hy- produced in this step.* The positron won’t last long, be- drogen to fuse into helium every second. cause it soon meets up with an ordinary electron, resulting

Hydrogen Fusion in the Sun: *Producing a neutrino is necessary because of a law called conservation The Proton–Proton Chain of lepton number: The number of leptons (e.g., electrons or neutrinos Recall that hydrogen nuclei are nothing more than indi- [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 vidual protons, while the most common form of helium the reaction products, the positron (antielectron) has lepton number 1 consists of two protons and two neutrons. Thus, the because it is antimatter, and the neutrino has lepton number 1. Thus, overall hydrogen fusion reaction in the Sun is: the total lepton number remains zero.

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in the creation of two gamma-ray photons through matter– this steady state, the amount of energy leaving the top of antimatter annihilation. each gas layer within the Sun precisely balances the energy entering from the bottom (Figure 15.8). Suppose the core Step 2. A fair number of deuterium nuclei are always pres- temperature of the Sun rose very slightly. The rate of nu- ent along with the protons and other nuclei in the solar clear fusion would soar, generating lots of extra energy. Be- core, since step 1 occurs so frequently in the Sun (about cause energy moves so slowly through the Sun, this extra 1038 times per second). Step 2 occurs when one of these energy would be bottled up in the core, causing an increase deuterium nuclei collides and fuses with a proton. The in the core pressure. The push of this pressure would tem- result is a nucleus of helium-3, a rare form of helium with porarily exceed the pull of gravity, causing the core to ex- two protons and one neutron. This reaction also produces pand and cool. With cooling, the fusion rate would drop a gamma-ray photon. back down. The expansion and cooling would continue until Step 3. The third and final step of the proton–proton chain gravitational equilibrium was restored, at which point the requires the addition of another neutron to the helium-3, fusion rate would return to its original value. thereby making normal helium-4. This final step can pro- An opposite process would restore the normal fusion ceed in several different ways, but the most common route rate if the core temperature dropped. A decrease in core involves a collision of two helium-3 nuclei. Each of these temperature would lead to decreased nuclear burning, helium-3 nuclei resulted from a prior, separate occurrence a drop in the central pressure, and contraction of the core. of step 2 somewhere in the solar core. The final result is a As the core shrank, its temperature would rise until the normal helium-4 nucleus and two protons. burning rate returned to normal. The response of the core pressure to changes in the Total reaction. Somewhere in the solar core, steps 1 and 2 nuclear fusion rate is essentially a thermostat that keeps must each occur twice to make step 3 possible. Six protons the Sun’s central temperature steady. Any change in go into each complete cycle of the proton–proton chain, but the core temperature is automatically corrected by the two come back out. Thus, the overall proton–proton chain change in the fusion rate and the accompanying change converts four protons (hydrogen nuclei) into a helium-4 in pressure. nucleus, two positrons, two neutrinos, and two gamma rays. While the processes involved in gravitational equilib- Each resulting helium-4 nucleus has a mass that is rium prevent erratic changes in the fusion rate, they also slightly less (by about 0.7%) than the combined mass of ensure that the fusion rate gradually rises over billions of the four protons that created it. Overall, fusion in the Sun years. Because each fusion reaction converts four hydrogen converts about 600 million tons of hydrogen into 596 mil- nuclei into one helium nucleus, the total number of inde- lion tons of helium every second. The “missing” 4 million pendent particles in the solar core is gradually falling. This tons of matter becomes energy in accord with Einstein’s gradual reduction in the number of particles causes the formula E mc2.About 98% of the energy emerges as solar core to shrink. kinetic energy of the resulting helium nuclei and radia- The slow shrinking of the solar core means that it must tive energy of the gamma rays. As we will see, this energy generate energy more rapidly to counteract the stronger slowly percolates to the solar surface, eventually emerging compression of gravity, so the solar core gradually gets as the sunlight that bathes Earth. About 2% of the energy hotter as it shrinks. Theoretical models indicate that the is carried off by the neutrinos. Neutrinos rarely interact Sun’s core temperature should have increased enough to with matter (because they respond only to the weak force raise its fusion rate and the solar luminosity by about 30% [Section S4.2]), so most of the neutrinos created by the since the Sun was born 4.6 billion years ago. proton–proton chain pass straight from the solar core How did the gradual increase in solar luminosity affect through the solar surface and out into space. Earth? Geological evidence shows that Earth’s surface tem- perature has remained fairly steady since Earth finished The Solar Thermostat forming more than 4 billion years ago, despite this 30% increase in the Sun’s energy output, because Earth has its The rate of nuclear fusion in the solar core, which deter- own thermostat. This “Earth thermostat” is the carbon mines the energy output of the Sun, is very sensitive to dioxide cycle. By maintaining a fairly steady level of atmo- temperature. A slight increase in temperature would mean spheric carbon dioxide, the carbon dioxide cycle regulates a much higher fusion rate, and a slight decrease in tem- the greenhouse effect that maintains Earth’s surface tem- perature would mean a much lower fusion rate. If the perature [Section 14.4]. Sun’s rate of fusion varied erratically, the effects on Earth might be devastating. Fortunately, the Sun’s central tem- “Observing” the Solar Interior perature is steady thanks to gravitational equilibrium—the balance between the pull of gravity and the push of inter- We cannot see inside the Sun, so you may be wondering nal pressure. how we can know so much about what goes on underneath Outside the solar core, the energy produced by fusion its surface. Astronomers can study the Sun’s interior in travels toward the Sun’s surface at a slow but steady rate. In three different ways: through mathematical models of the

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large decrease in slight decrease in slight rise in large rise in rate of fusion core temperature core temperature rate of fusion

Solar Thermostat: Gravitational Equilibrium

Because the energy Increased energy supply is diminished, output enables gravity starts to thermal pressure overcome thermal to overcome pressure. gravity.

Gravity compresses Increased thermal the core, heats it up, pressure causes the and restores fusion core to expand and then rate to normal value. cool, which restores fusion rate to normal value. Figure 15.8 The solar thermostat. Gravitational equilibrium regulates the Sun’s core temperature. Every- thing 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 of the Sun gives us confidence that the models are on the solar neutrinos. 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 mathe- Sun Quakes A second way to learn about the inside of matical models that use the laws of physics to predict the the Sun is to observe “sun quakes”—vibrations of the Sun internal conditions. A basic model uses the Sun’s observed that are similar to the vibrations of the Earth caused by composition and mass as inputs to equations that describe earthquakes, although they are generated very differently. gravitational equilibrium, the solar thermostat, and the Earthquakes occur when Earth’s crust suddenly shifts, gen- rate at which solar energy moves from the core to the photo- erating seismic waves that propagate through Earth’s interior sphere. With the aid of a computer, we can use the model [Section 10.2].We can learn about Earth’s interior by record- to calculate the Sun’s temperature, pressure, and density ing seismic waves on Earth’s surface with seismographs. at any depth. We can then predict the rate of nuclear fusion Sun quakes result from waves of pressure (sound waves) in the solar core by combining these calculations with that propagate deep within the Sun at all times. These knowledge about nuclear fusion gathered in laboratories waves cause the solar surface to vibrate when they reach here on Earth. it. Although we cannot set up seismographs on the Sun, Remarkably, such models correctly “predict” the ra- we can detect the vibrations of the surface by measuring dius, surface temperature, luminosity, age, and many other Doppler shifts [Section 6.5]. Light from portions of the sur- properties of the Sun. However, current models do not face that are rising toward us is slightly blueshifted, while predict everything about the Sun correctly. Scientists are light from portions that are falling away from us is slightly constantly working to discover what is missing from them. redshifted. The vibrations are relatively small but measur- Successful prediction of so many observed characteristics able (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 indi- cates falling gas, and blue indicates rising gas. The speckled region indicates the convec- tion 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 sults to date confirm that our mathematical models of the solar interior by carefully analyzing these vibrations. (By solar interior are on the right track (Figure 15.10). At the analogy to seismology on Earth, this type of study of the same time, they provide data that can be used to improve Sun is called helioseismology—helios means “sun.”) Re- the models further.

Mathematical Insight 15.1 Mass-Energy Conversion in the Sun

We can calculate how much mass the Sun loses through nuclear The Sun loses about 4 billion kilograms of mass every second, fusion by comparing the input and output masses of the proton– which is roughly equivalent to the combined mass of nearly proton chain. A single proton has a mass of 1.6726 1027 kg, 100 million people. 27 so four protons have a mass of 6.690 10 kg. Example: How much hydrogen is converted to helium each 27 A helium-4 nucleus has a mass of only 6.643 10 kg, second in the Sun? slightly less than the mass of the four protons. The difference is: Solution: We have already calculated that the Sun loses 4.2 109 kg 6.690 1027 kg 6.643 1027 kg 4.7 1029 kg of mass each second and that this is only 0.7% of the mass of hy- drogen that is fused: which is 0.7%, or 0.007, of the original mass. Thus, for example, when 1 kilogram of hydrogen fuses, the resulting helium weighs 4.2 109 kg 0.007 mass of hydrogen fused only 993 grams, while 7 grams of mass turns into energy. We now solve for the mass of hydrogen fused: To calculate the total amount of mass converted to energy in the Sun each second, we use Einstein’s equation E mc2.The mass of 4.2 109 kg 26 total energy produced by the Sun each second is 3.8 10 joules, hydrogen fused 0.007 so we can solve for the total mass converted to energy each second: 11 1metric ton E 6.0 10 kg E mc2 ⇒ m 103 kg c2 6.0 108 metric tons 3.8 1026 joules 4.2 109 kg m 2 The Sun fuses 600 million metric tons of hydrogen each second, 3.0 108 s of which about 4 million tons becomes energy. The remaining 596 million tons becomes helium.

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Key Key model 100 model 7 10 data data

10 ) 3

core radiation convection zone zone 1 density (g/cm

temperature (K) temperature core radiation convection 106 zone zone 0.1

0.01

0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 fraction of the Sun’s radius fraction of the Sun’s radius b Density at different radii within the Sun. (The density of water is a Temperature at different radii within the Sun. 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 first major solar neutrino detector, built in the 1960s, was is to observe the neutrinos coming from fusion reactions in located 1,500 meters underground in the Homestake gold the core. Don’t panic, but as you read this sentence about a mine in South Dakota (Figure 15.11). thousand trillion solar neutrinos will zip through your body. The detector for this “Homestake experiment” consisted Fortunately, they won’t do any damage, because neutrinos of a 400,000-liter vat of chlorine-containing dry-cleaning rarely interact with anything. Neutrinos created by fusion fluid. It turns out that, on very rare occasions, a chlorine in the solar core fly quickly through the Sun as if passing nucleus can capture a neutrino and change into a nucleus through empty space. In fact, while an inch of lead will stop of radioactive argon. By looking for radioactive argon in an X ray, stopping an average neutrino would require a slab the tank of cleaning fluid, experimenters could count the of lead more than 1 light-year thick! Clearly, counting neu- number of neutrinos captured in the detector. trinos is dauntingly difficult, because virtually all of them From the many trillions of solar neutrinos that passed stream right through any detector built to capture them. through the tank of cleaning fluid each second, experiment- ers expected to capture an average of just one neutrino per day. This predicted capture rate was based on measured THINK ABOUT IT properties of chlorine nuclei and models of nuclear fu- Is the number of solar neutrinos zipping through our bodies sion in the Sun. However, over a period of more than two significantly lower at night? (Hint: How does the thickness of decades, neutrinos were captured only about once every Earth compare with the thickness of a slab of lead needed 3 days on average. That is, the Homestake experiment de- to stop an average neutrino?) tected only about one-third of the predicted number of neutrinos. This disagreement between model predictions Nevertheless, neutrinos do occasionally interact with and actual observations came to be called the solar neu- matter, and it is possible to capture a few solar neutrinos trino problem. with a large enough detector. Neutrino detectors are usu- The shortfall of neutrinos found with the Homestake ally placed deep inside mines so that the overlying layers of experiment led to many more recent attempts to detect solar rock block all other kinds of particles coming from outer neutrinos using more sophisticated detectors (Figure 15.12). space except neutrinos, which pass through rock easily. The 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 experi- ments have found fewer neutrinos than current models of the Sun predict. This discrepancy between model and ex- periment probably means one of two things: Either some- thing 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.) b An image of the Sun created by tracing the paths of neutrinos detected by Super-Kamiokande back to the Sun. For the moment, many physicists and astronomers Figure 15.12 The Super-Kamiokande experiment in Japan is one are betting that we understand the Sun just fine and that of the world’s premier neutrino detectors. 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 neu- trinos, and most solar neutrino detectors can detect only

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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 ex- pected number of electron neutrinos. Early results from the Sudbury Neutrino Observatory in Canada, a new de- tector 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 Figure 15.13 A photon in the solar interior bounces randomly can be definitively confirmed. among electrons, slowly working its way outward in a process Because of their roles in detecting solar neutrinos and called radiative diffusion. identifying the solar neutrino problem, Raymond Davis, leader of the Homestake experiment, and Masatoshi Ko- K ABOU shiba, leader of Super-Kamiokande, shared in the 2002 Nobel THIN T IT Prize for physics. Radiative diffusion is just one type of diffusion. Another is the diffusion of dye through a glass of water. If you place a concen- trated 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 15.4 From Core to Corona the entire glass. Can you think of any other examples of diffu- Energy liberated by nuclear fusion in the Sun’s core must sion in the world around you? eventually reach the solar surface, where it can be radi- ated into space. The path that the energy takes to the sur- Radiative diffusion is the primary way by which energy face is long and complex. In this section, we follow that moves outward through the radiation zone, which stretches long path. from the core to about 70% of the Sun’s radius (see Fig- ure 15.4). Above this point, where the temperature has The Path Through the Solar Interior dropped to about 2 million K, the solar plasma absorbs pho- tons more readily (rather than just bouncing them around). In Chapter 6, we discussed how atoms can absorb or emit This point is the beginning of the solar convection zone, photons. In fact, photons can also interact with any charged where the buildup of heat resulting from photon absorption particle, and a photon that “collides” with an electron can causes bubbles of hot plasma to rise upward in the process be deflected into a completely new direction. known as convection [Section 10.2].Convection occurs Deep in the solar interior, the plasma is so dense that because hot gas is less dense than cool gas. Like a hot-air the gamma-ray photons resulting from fusion travel only balloon, a hot bubble of solar plasma rises upward through a fraction of a millimeter before colliding with an electron. the cooler plasma above it. Meanwhile, cooler plasma from Because each collision sends the photon in a random new above slides around the rising bubble and sinks to lower direction, the photon bounces around the core in a hap- layers, where it is heated. The rising of hot plasma and sink- hazard way, sometimes called a random walk.With each ing of cool plasma form a cycle that transports energy out- random bounce, the photon drifts farther and farther, ward from the top of the radiation zone to the solar surface on average, from its point of origin. As a result, photons (Figure 15.14a). from the solar core gradually work their way outward (Fig- ure 15.13). The technical term for this slow, outward mi- The Solar Surface gration of photons is radiative diffusion (to diffuse means to “spread out” and radiative refers to the photons of light Earth has a solid crust, so its surface is well defined. In or radiation). contrast, the Sun is made entirely of gaseous plasma. De- Along the way, the photons exchange energy with their fining where the surface of the Sun begins is therefore some- surroundings. Because the surrounding temperature de- thing like defining the surface of a cloud: From a distance clines as the photons move outward through the Sun, they it looks quite distinct, but up close the surface is fuzzy, not are gradually transformed from gamma rays to photons sharp. We generally define the solar surface as the layer that of lower energy. (Because energy must be conserved, each appears distinct from a distance. This is the layer we identi- gamma-ray photon becomes many lower-energy photons.) fied as the photosphere when we took our imaginary jour- By the time the energy of fusion reaches the surface, the ney into the Sun. More technically, the photosphere is the photons are primarily visible light. On average, the energy layer of the Sun from which photons finally escape into released in a fusion reaction takes about a million years space after the million-year journey of solar energy outward to reach the solar surface. from the core.

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b Granulation is evident in this VIS a This schematic diagram shows how hot gas (white arrows) rises photo of the Sun’s surface. Each while cooler gas (orange/black arrows) descends around it. Bright spots bright granule is the top of a rising appear on the solar surface in places where hot gas is rising from column of gas. At the darker lines below, creating the granulated appearance of the solar photosphere. between the granules, cooler gas is descending below the photo- sphere. 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 preventing hot plasma from entering the sunspots, and core ultimately leaves the photosphere as thermal radiation that “something” turns out to be magnetic fields. [Section 6.4].The average temperature of the photosphere Detailed observations of the Sun’s spectral lines reveal is about 5,800 K, corresponding to a thermal radiation spec- sunspots to be regions with strong magnetic fields. These trum that peaks in the green portion of the visible spec- magnetic fields can alter the energy levels in atoms and trum, with substantial energy coming out in all colors of ions and therefore can alter the spectral lines they produce. visible light. The Sun appears whitish when seen from space, More specifically, magnetic fields cause some spectral lines but in our sky the Sun appears somewhat more yellow— to split into two or more closely spaced lines (Figure 15.15b). and even red at sunset—because Earth’s atmosphere scatters This effect (called the Zeeman effect) enables scientists to blue light. It is this scattered light from the Sun that makes map magnetic fields on the Sun by studying the spectral our skies blue [Section 11.3]. lines in light from different parts of the solar surface. Although the average temperature of the photosphere Magnetic fields are invisible, but in principle we could is 5,800 K, actual temperatures vary significantly from place visualize a magnetic field by laying out many compasses. to place. The photosphere is marked throughout by the Each compass needle would point to local magnetic north. bubbling pattern of granulation produced by the under- We can represent the magnetic field by drawing a series of lying convection (Figure 15.14b). Each granule appears lines, called magnetic field lines,connecting the needles bright in the center, where hot gas bubbles upward, and dark of these imaginary compasses (Figure 15.16a). The strength around the edges, where cool gas descends. If we made a of the magnetic field is indicated by the spacing of the lines: movie of the granulation, we’d see it bubbling rather like Closer lines mean a stronger field (Figure 15.16b). Because a pot of boiling water. Just as bubbles in a pot of boiling these imaginary field lines are so much easier to visualize water burst on the surface and are replaced by new bubbles, than the magnetic field itself, we usually discuss magnetic each granule lasts only a few minutes before being replaced fields by talking about how the field lines would appear. by other granules bubbling upward. Charged particles, such as the ions and electrons in the solar plasma, follow paths that spiral along the magnetic Sunspots and Magnetic Fields field lines (Figure 15.16c). Thus, the solar plasma can move freely along magnetic field lines but cannot easily move Sunspots are the most striking features on the solar surface perpendicular to them. (Figure 15.15a). The temperature of the plasma in sunspots The magnetic field lines act somewhat like elastic bands, is about 4,000 K, significantly cooler than the 5,800 K plasma being twisted into contortions and knots by turbulent mo- of the surrounding photosphere. If you think about this for tions in the solar atmosphere. Sunspots occur where the a moment, you may wonder how sunspots can be so much most taut and tightly wound magnetic fields poke nearly cooler than their surroundings. Why doesn’t the surround- straight out from the solar interior. Sunspots tend to occur ing hot plasma heat the sunspots? Something must be 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 side- b Spectra of sunspots can be ways into the sunspot. With hot plasma unable to enter the used to measure the strength region, the sunspot plasma becomes cooler than that of the of their magnetic fields. This rest of the photosphere (Figure 15.17a). image shows the spectrum of a sunspot and its surround- The magnetic field lines connecting two sunspots often ings. The sunspot region soar high above the photosphere, through the chromosphere, shows up as dark horizontal and into the corona (Figure 15.17b). These vaulted loops bands because it is darker of magnetic field sometimes appear as solar prominences, than the rest of the solar sur- in which the field traps gas that may glow for days or even face in its vicinity. The verti- cal bands are absorption lines weeks. Some prominences rise to heights of more than that are present both inside 100,000 kilometers above the Sun’s surface (Figure 15.18). and outside the sunspots. The most dramatic events on the solar surface are The influence of strong mag- solar flares,which emit bursts of X rays and fast-moving netic fields within the sunspot charged particles into space (Figure 15.19). Flares generally region splits a single absorp- tion line into three parts. occur in the vicinity of sunspots, leading us to suspect that Measuring the separation they occur when the magnetic field lines become so twisted VIS between these lines tells us and knotted that they can no longer bear the tension. The the strength of the magnetic magnetic field lines suddenly snap like tangled elastic bands field within the sunspot. 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 top of the photosphere. Why should this decline suddenly and accelerating some of the charged particles to nearly the reverse? Some aspects of this atmospheric heating remain speed of light. a mystery today, but we have at least a general explanation: The Sun’s strong magnetic fields carry energy upward from The Chromosphere and Corona the churning solar surface to the chromosphere and corona. More specifically, the rising and falling of gas in the The high temperatures of the chromosphere and corona convection zone probably shakes magnetic field lines beneath perplexed scientists for decades. After all, temperatures the solar surface. This shaking generates waves along the gradually decline as we move outward from the core to the magnetic field lines that carry energy upward to the solar

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weaker magnetic field

stronger e magnetic field e

e

e weaker magnetic field a Magnetic field lines follow b Lines closer together c Charged particles follow the directions that compass indicate a stronger field. paths that spiral along Figure 15.16 We draw magnetic field needles would point. magnetic field lines. lines to represent invisible magnetic fields.

atmosphere. Precisely how the waves deposit their energy plasma of the chromosphere and corona hot. We can test in the chromosphere and corona is not known, but the this idea observationally. The gas of the chromosphere and waves agitate the low-density plasma of these layers, some- corona is so tenuous that we cannot see it with our eyes how heating them to high temperatures. Much of this heat- except during a total eclipse, when we can see the faint visi- ing appears to happen near where the magnetic field lines ble light scattered by electrons in the corona [Section 2.5]. emerge from the Sun’s surface. However, the roughly 10,000 K plasma of the chromosphere According to this model of solar heating, the same emits strongly in the ultraviolet, and the million K plasma magnetic fields that keep sunspots cool make the overlying of the corona is the source of virtually all X rays coming

Magnetic fields trap gas.

sunspots T 5,800 KT 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 b This X-ray photo (from NASA’s X-ray the solar surface, reaching heights many times larger than Earth’s TRACE mission) shows gas trapped diameter. 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 promi- nence, 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

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 spiral- ing along them to escape the Sun altogether. These parti- cles 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 impor- tant effects on planetary surfaces, atmospheres, and mag- netospheres. Well beyond the planets, the pressure of inter- stellar 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 sam- ples 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 reassur- Figure 15.19 This photo (from UV TRACE) of ultraviolet light emitted ingly verified that the Sun is made mostly of hydrogen, by hydrogen atoms shows a solar just as we conclude from studying the Sun’s spectrum. flare erupting from the Sun’s surface.

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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

Although we’ll call it an “11-year” cycle, the interval between solar maxima is sometimes as long as 15 years 15.5 Solar Weather or as short as 7 years. The number of sunspots also varies dramatically (Figure 15.21a). In fact, sunspot activity vir- and Climate tually ceased between the years 1645 and 1715, a period Individual sunspots, prominences, and flares are short-lived sometimes called the Maunder minimum (after E. W. phenomena, somewhat like storms on Earth. They consti- Maunder, who identified it in historical sunspot records). tute what we call solar weather or solar activity.You know Another feature of the sunspot cycle is a gradual from personal experience that the Earth’s weather is noto- change in the solar latitudes at which individual sunspots riously unpredictable. The same is true for the Sun: We form and dissolve (Figure 15.21b). As a cycle begins at solar cannot predict precisely when or where a particular sunspot minimum, sunspots form primarily at mid-latitudes (30° or flare will appear. Earth’s climate, on the other hand, is to 40°) on the Sun. The sunspots tend to form at lower lati- quite regular from season to season. So it is with the Sun, tudes as the cycle progresses, appearing very close to the where despite day-to-day variations the general nature and solar equator as the next solar minimum approaches. intensity of solar activity follow a predictable cycle. A less obvious feature of the sunspot cycle is that something peculiar happens to the Sun’s magnetic field The Sunspot Cycle at each solar minimum. The field lines connecting all pairs of sunspots (see Figure 15.17) tend to point in the same Long before we realized that sunspots were magnetic dis- direction throughout an 11-year solar cycle (within each turbances, astronomers had recognized patterns in sunspot hemisphere). For example, all compass needles might point activity. The most notable pattern is the number of sun- from the easternmost sunspot to the westernmost sunspot spots visible on the Sun at any particular time. Thanks to in a pair. However, as the cycle ends at solar minimum, the telescopic observations of the Sun recorded by astrono- magnetic field reverses: In the subsequent solar cycle, the mers since the 1600s, we know that the number of sunspots field lines connecting pairs of sunspots point in the opposite gradually rises and falls in a sunspot cycle with an average direction. Apparently, the entire magnetic field of the Sun period of about 11 years (Figure 15.21a). At the time of flip-flops every 11 years. solar maximum,when sunspots are most numerous, we The magnetic reversals hint that the sunspot cycle may see dozens of sunspots on the Sun at one time. In con- is related to the generation of magnetic fields on the Sun. trast, we see few if any sunspots at the time of solar mini- They also tell us that the complete magnetic cycle of the mum.The frequency of prominences and flares also follows Sun, called the solar cycle, really averages 22 years, since it the sunspot cycle, with these events being most common takes two 11-year cycles before the magnetic field is back at solar maximum and least common at solar minimum. the way it started.

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0.5%

0.4%

0.3%

0.2%

covered by sunspots covered 0.1% percentage of Sun’s surface of Sun’s percentage

0.0% 1900 1910 1920 1930 1940 1950 1960 1970 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

30 N

Equator latitude

30 S

90 S 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 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? behavior of these fields is so complex that approximations are necessary even with the best supercomputers. Using The causes of the Sun’s magnetic fields and the sunspot these computer models, scientists have successfully repli- cycle are not well understood, but we believe we know cated some features of the sunspot cycle, such as changes the general nature of the processes involved. Convection in the number and latitude of sunspots and the magnetic is thought to dredge up weak magnetic fields generated in field reversals that occur about every 11 years. However, the solar interior, amplifying them as they rise. The Sun’s much still remains mysterious, including why the period rotation—faster at its equator than near its poles—then of the sunspot cycle varies and why solar activity is differ- stretches and shapes these fields. ent from one cycle to the next. Imagine what happens to a magnetic field line that origi- nally runs along the Sun’s surface directly from the north pole to the south pole. At the equator, the field line circles Solar Activity and Earth the Sun in 25 days, but at higher latitudes the field line lags behind. Gradually, this rotation pattern winds the field line During solar maximum, solar flares and other forms of more and more tightly around the Sun (Figure 15.22). This solar activity send large numbers of highly energetic charged process, operating at all times over the entire Sun, produces particles (protons and electrons) toward Earth. Sometimes the contorted field lines that generate sunspots and other these particles travel in the smooth flow known as the solar solar activity. wind. Other times they come in the form of huge magnetic Investigating how the Sun’s magnetic field develops bubbles called coronal mass ejections. Do these forms of solar and changes in time requires sophisticated computer mod- weather affect Earth? In at least some ways, the answer is els. Scientists are working hard on such models, but the a definitive yes.

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NNN magnetic field line

differing rotation rates

e qu ator

time time SSS

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 config- uration. 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 con- creating the shimmering light of auroras (Figure 15.23b). stantly interacts with Earth’s magnetic field. Occasionally Because coronal mass ejections are particularly energetic, the these fields interconnect. When that happens, large amounts auroras they stimulate can be especially spectacular. of energy are released from the magnetic field into the Particles streaming from the Sun after the occurrence charged particles near the interconnection zone. Many of solar flares, coronal mass ejections, or other major solar of these energized particles then flow down Earth’s mag- storms can also have practical impacts on society. For ex- netic field lines toward the poles (Figure 15.23a). Collisions ample, these particles can hamper radio communications, between the charged particles and atoms in Earth’s upper disrupt electrical power delivery, and damage the electronic atmosphere cause electrons in the atoms to jump to higher components in orbiting satellites. During a particularly energy levels [Section 4.4].These excited atoms subsequently powerful magnetic storm on the Sun in March 1989, the emit visible-light photons as they drop to lower energy levels, U.S. Air Force temporarily lost track of over 2,000 satellites,

SPECIAL TOPIC Long-Term Change in Solar Activity

Figure 15.21 shows that the sunspot cycle varies in length and breathe in atmospheric carbon, in the form of carbon dioxide, intensity, and it sometimes seems to disappear altogether. With and incorporate it year by year into each ring. We can therefore these facts as background, many scientists are searching for longer- estimate the level of solar activity in any given year by measuring term patterns in solar activity. Unfortunately, the search for longer- the level of carbon-14 in the corresponding ring. No clear evi- term variations is difficult because telescopic observations of dence has yet been found of longer-term cycles of solar activity, sunspots cover a period of only about 400 years. Some naked-eye but the search goes on. observations of sunspots recorded by Chinese astronomers go Theoretical models predict a very long term trend of lessen- back almost 2,000 years, but these records are sparse, and naked- ing solar activity. According to our theory of solar system forma- eye observations may not be very reliable. We can also guess at tion, the Sun must have rotated much faster when it was young past solar activity from descriptions of solar eclipses recorded [Section 9.3].Because a combination of convection and rotation around the world: When the Sun is more active, the corona tends generates solar activity, a faster rotation rate should have meant to have longer and brighter “streamers” visible to the naked eye. much more activity. Observations of other stars that are similar Another way to gauge past solar activity is to study the amount to the Sun but rotate faster confirm that these stars are much of carbon-14 in tree rings. High-energy cosmic rays [Section 19.2] more active. We find evidence for many more “starspots” on these coming from beyond our own solar system produce radioactive stars than on the Sun, and their relatively bright ultraviolet and carbon-14 in Earth’s atmosphere. During periods of high solar X-ray emissions suggest that they have brighter chromospheres activity, the solar wind tends to grow stronger, shielding Earth and coronas—just as we would expect if they are more active from some of these cosmic rays. Thus, production of carbon-14 than the Sun. drops when the Sun is more active. All the while, trees steadily

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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 a coincidence? No one knows for sure. Some researchers the Quebec hydroelectric system caused it to collapse for have claimed that certain weather phenomena, such as more than 8 hours. The combined cost of the loss of power drought cycles or frequencies of storms, are correlated with in the United States and Canada exceeded $100 million. In the 11- or 22-year cycle of solar activity. However, the data January 1997, AT&T lost contact with a $200-million com- supporting these correlations are weak in many cases, and munications satellite, probably because of damage caused even real correlations may be coincidental. by particles coming from another powerful solar storm. Part of the difficulty in linking solar activity with cli- Satellites in low-Earth orbit are particularly vulnerable mate is that no one understands how the linkage might during solar maximum, when the increase in solar X rays work.Although emissions of ultraviolet light, X rays, and and energetic particles heats Earth’s upper atmosphere, high-energy particles increase substantially from solar min- causing it to expand. The density of the gas surrounding imum to solar maximum, the total luminosity of the Sun low-flying satellites therefore rises, exerting drag that saps barely changes at all. (The Sun becomes only about 0.1% their energy and angular momentum. If this drag proceeds brighter during solar maximum.) Thus, if solar activity unchecked, the satellites ultimately plummet back to Earth. really is affecting Earth’s climate, it must be through some Satellites in low orbits, including the Hubble Space Telescope very subtle mechanism. For example, perhaps the expan- and the Space Station, require occasional boosts to prevent sion of Earth’s upper atmosphere that occurs with solar them from falling out of the sky. maximum somehow causes changes in weather. Connections between solar activity and Earth’s climate The question of how solar activity is linked to Earth’s are much less clear. The period from 1645 to 1715, when climate is very important, because we need to know whether solar activity seems to have virtually ceased, was a time global warming is affected by solar activity in addition to of exceptionally low temperatures in Europe and North human activity. Unfortunately, for the time being at least, America known as the Little Ice Age. Did the low solar activ- we can say little about this question. ity cause these low temperatures, or was their occurrence

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THE BIG PICTURE The Sun achieved its long-lasting state of gravitational equilibrium when energy generation by fusion in the Putting Chapter 15 into Context core came into balance with the energy lost through In this chapter, we have examined our Sun, the nearest thermal radiation from the surface. If the Sun were not star. When you look back at this chapter, make sure you relatively steady, life on Earth might not have been understand these “big picture” ideas: possible. ● ● The ancient riddle of why the Sun shines is now solved. The Sun’s atmosphere displays its own version of The Sun shines with energy generated by fusion of weather and climate, governed by solar magnetic fields. hydrogen into helium in the Sun’s core. After a million- Solar weather has important influences on Earth. year journey through the solar interior and an 8-minute ● The Sun is important not only as our source of light journey through space, a small fraction of this energy and heat, but also because it is the only star near reaches Earth and supplies sunlight and heat. enough for us to study in great detail. In the coming ● Gravitational equilibrium, the balance between pres- chapters, we will use what we’ve learned about the sure and gravity, determines the Sun’s interior struc- Sun to help us understand other stars. ture and maintains its steady nuclear burning rate.

SUMMARY OF KEY CONCEPTS

15.1 Why Does the Sun Shine? • What is the Sun made of ? It is made almost entirely • What process creates energy in the Sun? Fusion of of hydrogen and helium (98% of the Sun’s mass). hydrogen into helium in the Sun’s core generates the Sun’s energy. 15.3 The Cosmic Crucible • Why does the Sun’s size remain stable? The Sun’s size • Why does fusion occur in the Sun’s core? The core remains stable because it is in gravitational equilib- temperature and pressure are so high that colliding rium. The outward pressure of hot gas balances the nuclei can come close enough together for the strong inward force of gravity at every point within the Sun. force to overcome electromagnetic repulsion and bind them together. • How did the Sun become hot enough for fusion in the first place? As the Sun was forming, it grew hotter • Why is energy produced in the Sun at such a steady as it shrank in size because gravitational contraction rate? The fusion rate is self-regulating like a thermo- converted gravitational potential energy into ther- stat. If the fusion rate increases for some reason, the mal energy. Gravitational contraction continued to added energy production puffs up and cools the core, shrink the Sun and raise its central temperature until bringing the rate back down. Similarly, a decrease the core became hot and dense enough for nuclear in the fusion rate allows the core to shrink and heat, fusion. bringing the fusion rate back up. • Why was the Sun dimmer in the distant past? 15.2 Plunging to the Center of the Sun: Although the fusion rate is steady on short time An Imaginary Journey scales, it gradually increases over billions of years, • What are the major layers of the Sun, from the center increasing the Sun’s luminosity. The increase occurs out? The layers of the Sun are core, radiation zone, because fusion gradually reduces the number of indi- convection zone, photosphere, chromosphere, and vidual nuclei in the solar core. Four hydrogen nuclei corona. are fused to make just one helium nucleus, causing the core to shrink and become hotter. • What do we mean by the “surface” of the Sun? We consider the photosphere to be the surface of the Sun • How do we know what is happening inside the Sun? because light can pass through the photosphere but We can construct theoretical models of the solar cannot escape from deeper inside the Sun. Thus, interior using known laws of physics and then check photographs of visible light from the Sun show us what the photosphere looks like. continued

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the models against observations of the Sun’s size, nence. The magnetic fields are twisted and contorted surface temperature, and energy output as well as by the Sun’s rotation, and solar flares may occur studies of “sun quakes” and solar neutrinos. when the field lines suddenly snap and release their • What is the solar neutrino problem? Is it solved? energy. Neutrino detectors capture fewer neutrinos coming • What is surprising about the temperature of the from the Sun than models of fusion in the core pre- chromosphere and corona, and how do we explain it? dict. This discrepancy is called the solar neutrino Temperature gradually decreases from the core to problem. The problem now appears to be solved. the photosphere but then rises again in the chromo- Apparently, neutrinos can transform themselves sphere and corona. These high layers of the Sun are among three different types as they travel from the probably heated by energy carried upward along the solar core to Earth, while most detectors can capture magnetic field lines by waves that are generated as only one type. Thus, the detectors capture fewer turbulent motions in the convection zone shake the than the expected number of neutrinos. magnetic field lines.

15.4 From Core to Corona 15.5 Solar Weather and Climate • How long ago did fusion generate the energy we now • What is the sunspot cycle? The sunspot cycle, or the receive as sunlight? Fusion created the energy we re- variation in the number of sunspots on the Sun’s ceive today about a million years ago. It takes about surface, has an average period of 11 years. The mag- a million years for photons and then convection to netic field flip-flops every 11 years or so, resulting transport energy through the solar interior to the in a 22-year magnetic cycle. Sunspots first appear photosphere. Once sunlight emerges from the photo- at mid-latitudes at solar minimum, then become sphere, it takes only about 8 minutes to reach Earth. increasingly more common near the Sun’s equator • How are sunspots, prominences, and flares related to as the next minimum approaches. magnetic fields? Sunspots occur where strong mag- • What effect does solar activity have on Earth and its netic fields trap and isolate gas from the surround- inhabitants? Particles ejected from the Sun by solar ing plasma of the photosphere. The trapped gas cools, flares and other types of solar activity can affect so the sunspots become cooler and darker than the communications, electrical power delivery, and the rest of the photosphere. Sunspots tend to occur in electronic circuits in space vehicles. The connections pairs connected by a loop of magnetic field, which between solar activity and Earth’s climate are not may rise high above the surface as a solar promi- clear.

Sensible Statements? 4. Astronomers have recently photographed magnetic fields churning deep beneath the solar photosphere. Decide whether each of the following statements is sensible and explain why it is or is not. 5. Neutrinos probably can’t harm me, but just to be safe I think I’ll wear a lead vest. 1. Before Einstein, gravitational contraction appeared to be a perfectly plausible mechanism for solar energy generation. 6. If you want to see lots of sunspots, just wait for solar maximum! 2. A sudden temperature rise in the Sun’s core is nothing to worry about, because conditions in the core will soon return 7. News of a major solar flare today caused concern among to normal. professionals in the fields of communications and electrical power generation. 3. If fusion in the solar core ceased today, worldwide panic would break out tomorrow as the Sun began to grow 8. By observing solar neutrinos, we can learn about nuclear dimmer. fusion deep in the Sun’s core.

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Problems b. Combine your results from part (a) and the fact that the Sun fuses about 600 billion kg of hydrogen each second 9. Gravitational Contraction. Briefly describe how gravita- to calculate how long the Sun’s initial supply of hydro- tional contraction generates energy and when it was impor- gen can last. Give your answer in both seconds and years. tant in the Sun’s history. c. Given that our solar system is now about 4.6 billion years 10. Solar Characteristics. Briefly describe the Sun’s luminosity, old, when will we need to worry about the Sun running mass, radius, and average surface temperature. out of hydrogen for fusion? 11. Sunspots. What are sunspots? Why do they appear dark in *21. Solar Power Collectors. This problem leads you through the pictures of the Sun? calculation and discussion of how much solar power can be collected by solar cells on Earth. 12. Solar Fusion. What is the overall nuclear fusion reaction in the Sun? Briefly describe the proton–proton chain. a. Imagine a giant sphere surrounding the Sun with a radius of 1 AU. What is the surface area of this sphere, 13. Models of the Sun. Explain how mathematical models allow in square meters? (Hint: The formula for the surface us to predict conditions inside the Sun. How can we be area of a sphere is 4pr2.) confident that the models are on the right track? b. Because this imaginary giant sphere surrounds the Sun, 14. Sun Quakes. How are “sun quakes” similar to earthquakes? the Sun’s entire luminosity of 3.8 1026 watts must How are they different? Describe how we can observe them pass through it. Calculate the power passing through and how they help us learn about the solar interior. each square meter of this imaginary sphere in watts per 15. Energy Transport. Why does the energy produced by fusion square meter. Explain why this number represents the in the solar core take so long to reach the solar surface? maximum power per square meter that can be collected Describe the processes of radiative diffusion and convection by a solar collector in Earth orbit. in the solar interior. c. List several reasons why the average power per square 16. The Photosphere. Describe the appearance and temperature meter collected by a solar collector on the ground will of the Sun’s photosphere. What is granulation? How would always be less than what you found in part (b). granulation appear in a movie? d. Suppose you want to put a solar collector on your roof. 17. Observing the Sun’s Atmosphere. Why is the chromosphere If you want to optimize the amount of power you can best viewed with ultraviolet telescopes? Why is the corona collect, how should you orient the collector? (Hint: The best viewed with X-ray telescopes? optimum orientation depends on both your latitude and the time of year and day.) 18. An Angry Sun. A Time magazine cover once suggested that an “angry Sun” was becoming more active as human activ- *22. Solar Power for the United States. The total annual U.S. en- ity changed Earth’s climate through global warming. It’s ergy consumption is about 2 1020 joules. certainly possible for the Sun to become more active at the a. What is the average power requirement for the United same time that humans are affecting Earth, but is it possible States, in watts? (Hint: 1 watt 1 joule/s.) that the Sun could be responding to human activity? Can humans affect the Sun in any significant way? Explain. b. With current technologies and solar collectors on the ground, the best we can hope is that solar cells will *19. Number of Fusion Reactions in the Sun. Use the fact that each generate an average (day and night) power of about cycle of the proton–proton chain converts 4.7 1029 kg 200 watts/m2.(You might compare this to the maximum of mass into energy (see Mathematical Insight 15.1), along power per square meter you found in problem 22b.) with the fact that the Sun loses a total of about 4.2 109 kg What total area would we need to cover with solar cells of mass each second, to calculate the total number of times to supply all the power needed for the United States? the proton–proton chain occurs each second in the Sun. Give your answer in both square meters and square *20. The Lifetime of the Sun. The total mass of the Sun is about kilometers. 2 1030 kg, of which about 75% was hydrogen when the c. The total surface area of the United States is about Sun formed. However, only about 13% of this hydrogen 2 107 km2.What fraction of the U.S. area would have ever becomes available for fusion in the core. The rest re- to be covered by solar collectors to generate all of the mains in layers of the Sun where the temperature is too low U.S. power needs? In one page or less, describe potential for fusion. environmental impacts of covering so much area with a. Based on the given information, calculate the total solar collectors. Also discuss whether you think these mass of hydrogen available for fusion over the lifetime environmental impacts would be greater or less than of the Sun. 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 PLO is about 5,800 K. Use Wien’s law (see Mathematical Insight MEDIA EX RATIONS 6.2) to calculate the wavelength of peak thermal emission from the Sun. What color does this wavelength correspond Web Projects to in the visible-light spectrum? In light of your answer, why do you think the Sun appears white or yellow to our eyes? Take advantage of the useful Web links on www. astronomyplace.com to assist you with the following projects. Discussion Questions 1. Current Solar Activity. Daily information about solar 24. The Role of the Sun. Briefly discuss how the Sun affects us activity is available at NASA’s Web site sunspotcycle. here on Earth. Be sure to consider not only factors such as com. Where are we in the sunspot cycle right now? its light and warmth, but also how the study of the Sun has When is the next solar maximum or minimum ex- led us to new understanding in science and to technologi- pected? Have there been any major solar storms in cal developments. Overall, how important has solar re- the past few months? If so, did they have any signifi- search been to our lives? cant effects on Earth? Summarize your findings in a one- to two-page report. 25. The Solar Neutrino Problem. Discuss the solar neutrino prob- lem and its potential solutions. How serious do you con- 2. Solar Observatories in Space. Visit NASA’s Web site sider this problem? Do you think current theoretical mod- for the Sun–Earth connection and explore some els of the Sun could be wrong in any fundamental way? of the current and planned space missions designed Why or why not? to observe the Sun. Choose one mission to study in greater depth, and write a one- to two-page report 26. The Sun and Global Warming. One of the most pressing on the mission status and goals and what it has environmental issues on Earth concerns the extent to which taught or will teach us about the Sun. human emissions of greenhouse gases are warming our planet. Some people claim that part or all of the observed 3. Sudbury Neutrino Observatory. Visit the Web site for warming over the past century may be due to changes on the Sudbury Neutrino Observatory (SNO) and learn the Sun, rather than to anything humans have done. Dis- how it has helped to solve the solar neutrino prob- cuss how a better understanding of the Sun might help us lem. Write a one- to two-page report describing the understand the threat posed by greenhouse gas emissions. observatory, any recent results, and what we can Why is it so difficult to develop a clear understanding of expect from it in the future. how the Sun affects Earth’s climate?

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