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2396_AWL_Bennett_Ch15/pt5 6/25/03 3:40 PM Page 495 PA RT V STELLAR ALCHEMY 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:40 PM Page 496 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? 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:40 PM Page 497 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. chapter 15 • Our Star 497 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:40 PM Page 498 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 498 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- 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:40 PM Page 499 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 chapter 15 • Our Star 499 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:40 PM Page 500 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 500 part V • Stellar Alchemy 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. 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:40 PM Page 501 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. chapter 15 • Our Star 501 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 502 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: 502 part V • 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 chapter 15 • Our Star 503 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 504 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 504 part V • Stellar Alchemy 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). 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 505 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. chapter 15 • Our Star 505 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 506 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 506 part V • Stellar Alchemy 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 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 507 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. chapter 15 • Our Star 507 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 508 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. 508 part V • Stellar Alchemy 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. 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 509 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 chapter 15 • Our Star 509 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 510 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 510 part V • Stellar Alchemy 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 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 511 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. chapter 15 X-ray • Our Star 511 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 512 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. 512 part V • Stellar Alchemy 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. 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 513 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. chapter 15 • Our Star 513 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 514 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 514 part V • Stellar Alchemy 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. 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 515 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. chapter 15 • Our Star 515 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 516 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 516 part V • Stellar Alchemy 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. 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 517 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 continued chapter 15 • Our Star 517 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 518 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. 518 part V • Stellar Alchemy 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. 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 519 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. chapter 15 • Our Star 519 2396_AWL_Bennett_Ch15/pt5 6/25/03 3:41 PM Page 520 *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? 520 part V • Stellar Alchemy 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.