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15 Our Star

LEARNING GOALS

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 thecenter 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?

• 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?

496


I say Live, Live, because of the Sun,The dream, the excitable gift.

Anne Sexton (1928–1974)

Astronomy 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 im-

portant to us in many more ways than as an object

for astronomical study. The Sun is the source of virtu-

ally 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 theirlives. Some worshiped the Sun as a god, and others createdelaborate mythologies to explain its daily rise and set. Onlyrecently, however, have we learned how the Sun provides uswith light and heat.

Most ancient thinkers viewed the Sun as some type offire, perhaps a lump of burning coal or wood. The Greekphilosopher Anaxagoras (c. 500–428 B.C.) imagined the Sunto be a very hot, glowing rock about the size of the Greekpeninsula of Peloponnesus (comparable in size to Massa-chusetts). Thus, he was one of the first people in history tobelieve that the heavens and Earth are made from the sametypes of materials.

By the mid-1800s, the size and distance of the Sunwere reasonably well known, and scientists seriously beganto address the question of how the Sun shines. Two earlyideas held either that the Sun was a cooling ember that hadonce been much hotter or that the Sun generated energy

from some type of chemical burning similar to the burningof coal or wood. Simple calculations showed that a coolingor chemically burning Sun could shine for a few thousandyears—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-ing ember, it would have been much hotter just a few hun-dred years earlier, making it too hot for civilization to haveexisted. Chemical burning was ruled out because it cannotgenerate enough energy to account for the rate of radiationobserved from the Sun’s surface.

A more plausible hypothesis of the late 1800s sug-gested that the Sun generates energy by contracting in size,a process called gravitational contraction. If the Sun wereshrinking, it would constantly be converting gravitationalpotential energy into thermal energy, thereby keeping theSun hot. Because of its large mass, the Sun would need tocontract only very slightly each year to maintain its tem-perature—so slightly that the contraction would be un-noticeable. Calculations showed that the Sun could shinefor up to about 25 million years generating energy by grav-itational contraction. However, geologists of the late 1800shad already established the age of Earth to be far older than25 million years, leaving astronomers in an embarrassingposition.

Only after Einstein published his special theory ofrelativity, which included his discovery of E � mc2, did the true energy-generation mechanism of the Sun becomeclear. We now know that the Sun generates energy by nu-clear fusion, a source so efficient that the Sun can shine forabout 10 billion years. Because the Sun is only 4.6 billionyears 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 througha balance between two competing forces: gravity pullinginward and pressure pushing outward. This balance is calledgravitational equilibrium (or hydrostatic equilibrium).It means that, at any point within the Sun, the weight ofoverlying material is supported by the underlying pressure.A stack of acrobats provides a simple example of this bal-ance (Figure 15.1). The bottom person supports the weightof 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 theSun means that the pressure increases with depth, makingthe Sun extremely hot and dense in its central core (Fig-ure 15.2).

Earth’s atmosphere is also in gravitational equilibrium, with theweight of upper layers supported by the pressure in lowerlayers. Use this idea to explain why the air gets thinner at higheraltitudes.

THINK ABOUT IT

c h a p t e r 1 5 • Our Star 497


Although the Sun today maintains its gravitationalequilibrium with energy generated by nuclear fusion, theenergy-generation mechanism of gravitational contractionwas important in the distant past and will be importantagain in the distant future. Our Sun was born from a col-lapsing cloud of interstellar gas. The contraction of thecloud released gravitational potential energy, raising theinterior temperature higher and higher—but not highenough to halt the contraction. The cloud continued toshrink because thermal radiation from the cloud’s surfacecarried away much of the energy released by contraction,even while the interior temperature was rising. When thecentral temperature and density eventually reached thevalues necessary to sustain nuclear fusion, energy genera-tion in the Sun’s interior matched the energy lost from thesurface in the form of radiation. With the onset of fusion,the Sun entered a long-lasting state of gravitational equilib-rium that has persisted for the last 4.6 billion years.

About 5 billion years from now, when the Sun finallyexhausts its nuclear fuel, the internal pressure will drop, andgravitational contraction will begin once again. As we will seelater, some of the most important and spectacular processesin astronomy hinge on this ongoing “battle” between thecrush of gravity and a star’s internal sources of pressure.

In summary, the answer to the question “Why does theSun shine?” is that about 4.6 billion years ago gravitational

contraction made the Sun hot enough to sustain nuclearfusion in its core. Ever since, energy liberated by fusion hasmaintained the Sun’s gravitational equilibrium and kept theSun shining steadily, supplying the light and heat that sus-tain life on Earth.


In the rest of this chapter, we will discuss in detail how the Sun produces energy and how that energy travels toEarth. First, to get a “big picture” view of the Sun, let’simagine you have a spaceship that can somehow with-stand the immense heat and pressure of the solar interiorand 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 awhitish 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 luminos-ity, is an incredible 3.8 � 1026 watts. That is, every second,the Sun radiates a total of 3.8 � 1026 joules of energy intospace (recall that 1 watt � 1 joule/s). If we could somehowcapture and store just 1 second’s worth of the Sun’s lumi-

498 p a r t V • Stellar Alchemy

Figure 15.2 Gravitational equilibrium in the Sun: At each pointinside, the pressure pushing outward balances the weight of theoverlying layers.

gravitypressure

Figure 15.1 An acrobat stack is in gravitational equilibrium: Thelowest person supports the most weight and feels the greatestpressure, and the overlying weight and underlying pressure decreasefor those higher up.

2396_AWL_Bennett_Ch15/pt5 6/25/03 3:40 PM 98

nosity, it would be enough to meet current human energydemands for roughly the next 500,000 years!

Of course, only a tiny fraction of the Sun’s total energyoutput reaches Earth, with the rest dispersing in all direc-tions into space. Most of this energy is radiated in the formof visible light, but once you leave the protective blanket ofEarth’s atmosphere you’ll encounter significant amounts ofother types of solar radiation, including dangerous ultra-violet and X rays. Your spaceship will require substantialshielding to protect you from serious radiation burns causedby these high-energy forms of light.

Through a telescope, you can see that the Sun seetheswith churning gases. At most times you’ll detect at least a few sunspots blotching its surface (Figure 15.3). If youfocus your telescope solely on a sunspot, you’ll find that it isblindingly bright. Sunspots appear dark only in contrast tothe even brighter solar surface that surrounds them. A typi-cal sunspot is large enough to swallow the entire Earth, dra-matically illustrating that the Sun is immense by anyearthly standard. The Sun’s radius is nearly 700,000 kilo-meters, and its mass is 2 � 1030 kilograms—about 300,000times more massive than Earth.

Sunspots appear to move from day to day along withthe Sun’s rotation. If you watch very carefully, you maynotice that sunspots near the solar equator circle the Sunfaster than those at higher solar latitudes. This observa-tion reveals that, unlike a spinning ball, the entire Sun doesnot rotate at the same rate. Instead, the solar equator com-pletes one rotation in about 25 days, and the rotation pe-riod increases with latitude to about 30 days near the solarpoles. Table 15.1 summarizes some of the basic propertiesof the Sun.

As a brief review, describe how we measure the mass of theSun using Newton’s version of Kepler’s third law. (Hint: Lookback at Chapter 5.)

THINK ABOUT IT

As you and your spaceship continue to fall toward theSun, you notice an increasingly powerful headwind exert-ing a bit of drag on your descent. This headwind, called thesolar wind, is created by ions and subatomic particles flow-ing outward from the solar surface. The solar wind helpsshape 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, youenter the solar corona, the tenuous uppermost layer of theSun’s atmosphere (Figure 15.4). Here you find the temper-ature to be astonishingly high—about 1 million Kelvin. Thisregion emits most of the Sun’s X rays. However, the densityhere is so low that your spaceship feels relatively little heatdespite the million-degree temperature [Section 4.2].

Nearer the surface, the temperature suddenly drops toabout 10,000 K in the chromosphere, the primary sourceof the Sun’s ultraviolet radiation. At last you plunge throughthe visible surface of the Sun, called the photosphere, wherethe temperature averages just under 6,000 K. Although thephotosphere 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 conditionsat a particular altitude differ from one region to another.Some regions of the chromosphere and corona are partic-ularly hot and bright, while other regions are cooler andless 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 compassgoes crazy as you descend through the solar atmosphere,indicating that solar weather is shaped by intense magneticfields. Occasionally, huge magnetic storms occur, shootinghot gases far into space.

Into the Sun

Up to this point in your journey, you may have seen Earthand the stars when you looked back, but as you slip be-neath the photosphere, blazing light engulfs you. You are


Figure 15.3 This photo of thevisible surface of the Sun showsseveral dark sunspots.

Table 15.1 Basic Properties of the Sun

Radius (RSun) 696,000 km (about 109 times theradius of Earth)

Mass (MSun) 2 � 1030 kg (about 300,000 times the mass of Earth)

Luminosity (LSun) 3.8 � 1026 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 temperature 15 million K

VIS


inside the Sun, and your spacecraft is tossed about by in-credible turbulence. If you can hold steady long enough tosee what is going on around you, you’ll notice spouts ofhot gas rising upward, surrounded by cooler gas cascadingdown from above. You are in the convection zone, whereenergy generated in the solar core travels upward, trans-ported by the rising of hot gas and falling of cool gas calledconvection [Section 10.2]. With some quick thinking, youmay realize that the photosphere above you is the top ofthe convection zone and that convection is the cause ofthe Sun’s seething, churning appearance.

As you descend through the convection zone, the sur-rounding density and pressure increase substantially, along

with the temperature. Soon you reach depths at which theSun is far denser than water. Nevertheless, it is still a gas(more specifically, a plasma of positively charged ions andfree electrons) because each particle moves independentlyof its neighbors [Section 4.3].

About a third of the way down to the center, the tur-bulence of the convection zone gives way to the calmerplasma of the radiation zone, where energy is carried out-ward primarily by photons of light. The temperature risesto almost 10 million K, and your spacecraft is bathed in X rays trillions of times more intense than the visible lightat the solar surface.


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. Risingplumes of hot gas then transport the energy through the convection zone to the photosphere, where it isradiated into space. The photosphere, at a temperature of roughly 6,000 K, is relatively cool compared tothe 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 solarwind that blows past Earth and out beyond Pluto.

coronachromosphere

radiationzone

convectionzone

core

photosphere

solar wind

solar wind


No real spacecraft could survive, but your imaginaryone keeps plunging straight down to the solar core. Thereyou finally find the source of the Sun’s energy: nuclear fusiontransforming hydrogen into helium. At the Sun’s center,the temperature is about 15 million K, the density is morethan 100 times that of water, and the pressure is 200 bil-lion times that on the surface of Earth. The energy pro-duced in the core today will take about a million years toreach the surface.

With your journey complete, it’s time to turn aroundand head back home. We’ll continue this chapter by study-ing fusion in the solar core and then tracing the flow of theenergy generated by fusion as it moves outward throughthe Sun.

15.3 The Cosmic CrucibleThe 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 vesselcalled a crucible. Other times they tried magic. Their get-rich-quick schemes never managed to work. Today weknow that there is no easy way to turn other elements intogold, but it is possible to transmute one element or isotopeinto another.

If a nucleus gains or loses protons, its atomic numberchanges and it becomes a different element. If it gains or

loses neutrons, its atomic mass changes and it becomes adifferent isotope [Section 4.3]. The process of splitting a nu-cleus into two smaller nuclei is called nuclear fission. Theprocess of combining nuclei to make a nucleus with a greaternumber 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 nuclearpower 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 (andnegatively charged electrons) whizzing about at extremelyhigh speeds. At any one time, some of these nuclei are onhigh-speed collision courses with each other. In most cases,electromagnetic forces deflect the nuclei, preventing actualcollisions, because positive charges repel one another. Ifnuclei collide with sufficient energy, however, they can sticktogether to form a heavier nucleus (Figure 15.6).

Sticking positively charged nuclei together is not easy.The strong force, which binds protons and neutrons to-gether in atomic nuclei, is the only force in nature that can

Figure 15.5 Nuclear fission splits a nucleus into smaller nuclei(not usually of equal size), while nuclear fusion combines smallernuclei into a larger nucleus.

fusionfissionCOMMON MISCONCEPTIONS

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 thesame sense as a fire burns on Earth. Fires on Earth gen-erate light through chemical changes that consume oxy-gen and produce a flame. The glow of the Sun has morein common with the glowing embers left over after theflames have burned out. Much like hot embers, the Sun’ssurface shines with the visible thermal radiation pro-duced by any object that is sufficiently hot [Section 6.4].

However, hot embers quickly stop glowing as theycool, while the Sun keeps shining because its surface iskept hot by the energy rising from the Sun’s core. Be-cause this energy is generated by nuclear fusion, wesometimes say that it is the result of “nuclear burning”—a term that suggests nuclear changes in much the sameway that “chemical burning” suggests chemical changes.Nevertheless, while it is reasonable to say that the Sunundergoes nuclear burning in its core, it is not accurateto speak of any kind of burning on the Sun’s surface,where light is produced primarily by thermal radiation.

Figure 15.6 Positively charged nuclei can fuse only if a high-speed collision brings them close enough for the strong force to come into play.

At low speeds, electromagnetic repulsion prevents the collision of nuclei.

At high speeds, nuclei come close enough for the strong force to bind them together.



overcome the electromagnetic repulsion between two posi-tively charged nuclei [Section S4.2]. In contrast to gravita-tional and electromagnetic forces, which drop off graduallyas the distances between particles increase (by an inversesquare law [Section 5.3]), the strong force is more like glueor Velcro: It overpowers the electromagnetic force oververy small distances but is insignificant when the distancesbetween particles exceed the typical sizes of atomic nuclei.The trick to nuclear fusion, therefore, is to push the posi-tively charged nuclei close enough together for the strongforce to outmuscle electromagnetic repulsion.

The high pressures and temperatures in the solar coreare just right for fusion of hydrogen nuclei into heliumnuclei. The high temperature is important because the nu-clei must collide at very high speeds if they are to comeclose enough together to fuse. (Quantum tunneling is alsoimportant to this process [Section S4.5].) The higher thetemperature, the harder the collisions, making fusion reac-tions more likely at higher temperatures. The high pressureof the overlying layers is necessary because without it thehot plasma of the solar core would simply explode into space,shutting off the nuclear reactions. In the Sun, the pressureis high and steady, allowing some 600 million tons of hy-drogen to fuse into helium every second.

Hydrogen Fusion in the Sun:The Proton–Proton Chain

Recall that hydrogen nuclei are nothing more than indi-vidual protons, while the most common form of heliumconsists of two protons and two neutrons. Thus, the overall hydrogen fusion reaction in the Sun is:

However, collisions between two nuclei are far morecommon than three- or four-way collisions, so this overallreaction proceeds through steps that involve just two nucleiat a time. The sequence of steps that occurs in the Sun iscalled the proton–proton chain because it begins with col-lisions 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 ofone proton and one neutron, which is the isotope of hy-drogen known as deuterium. Note that this step converts aproton into a neutron, reducing the total nuclear chargefrom �2 for the two fusing protons to �1 for the resultingdeuterium nucleus. The lost positive charge is carried offby a positron, the antimatter version of an electron with a positive rather than negative charge [Section S4.2]. A neu-trino—a subatomic particle with a very tiny mass—is alsoproduced in this step.* The positron won’t last long, be-cause it soon meets up with an ordinary electron, resulting

1 4He

p p

pp

4 1H

energyp

pnn

Figure 15.7 Hydrogen fuses into helium in the Sun by way of the proton–proton chain. In step 1, twoprotons fuse to create a deuterium nucleus consisting of a proton and a neutron. In step 2, the deuteriumnucleus 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.

Step 1 Step 2 Step 3

Total reaction

Key:

gammaray

gamma ray

gamma ray

gamma ray

gamma ray

gamma ray

neutron

proton

electron

neutrino

positron

p

p

p

p

pp

p

p

p

p

p

pnn p

pn

n

n

e�

e�

e�

e�

e�

e�

pn p

pn p

pn

pn

pn

p


*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 leptonnumber is zero before the reaction because there are no leptons. Amongthe reaction products, the positron (antielectron) has lepton number �1because it is antimatter, and the neutrino has lepton number �1. Thus,the total lepton number remains zero.


in the creation of two gamma-ray photons through matter–antimatter annihilation.

Step 2. A fair number of deuterium nuclei are always pres-ent along with the protons and other nuclei in the solarcore, since step 1 occurs so frequently in the Sun (about1038 times per second). Step 2 occurs when one of thesedeuterium nuclei collides and fuses with a proton. Theresult is a nucleus of helium-3, a rare form of helium withtwo protons and one neutron. This reaction also producesa gamma-ray photon.

Step 3. The third and final step of the proton–proton chainrequires the addition of another neutron to the helium-3,thereby making normal helium-4. This final step can pro-ceed in several different ways, but the most common routeinvolves a collision of two helium-3 nuclei. Each of thesehelium-3 nuclei resulted from a prior, separate occurrenceof step 2 somewhere in the solar core. The final result is anormal helium-4 nucleus and two protons.

Total reaction. Somewhere in the solar core, steps 1 and 2must each occur twice to make step 3 possible. Six protonsgo into each complete cycle of the proton–proton chain, buttwo come back out. Thus, the overall proton–proton chainconverts four protons (hydrogen nuclei) into a helium-4nucleus, two positrons, two neutrinos, and two gamma rays.

Each resulting helium-4 nucleus has a mass that isslightly less (by about 0.7%) than the combined mass ofthe four protons that created it. Overall, fusion in the Sunconverts about 600 million tons of hydrogen into 596 mil-lion tons of helium every second. The “missing” 4 milliontons of matter becomes energy in accord with Einstein’sformula E � mc2. About 98% of the energy emerges askinetic energy of the resulting helium nuclei and radia-tive energy of the gamma rays. As we will see, this energyslowly percolates to the solar surface, eventually emergingas the sunlight that bathes Earth. About 2% of the energy is carried off by the neutrinos. Neutrinos rarely interactwith matter (because they respond only to the weak force[Section S4.2]), so most of the neutrinos created by theproton–proton chain pass straight from the solar corethrough the solar surface and out into space.

The Solar Thermostat

The rate of nuclear fusion in the solar core, which deter-mines the energy output of the Sun, is very sensitive totemperature. A slight increase in temperature would mean a much higher fusion rate, and a slight decrease in tem-perature would mean a much lower fusion rate. If the Sun’s rate of fusion varied erratically, the effects on Earthmight be devastating. Fortunately, the Sun’s central tem-perature is steady thanks to gravitational equilibrium—thebalance between the pull of gravity and the push of inter-nal pressure.

Outside the solar core, the energy produced by fusiontravels toward the Sun’s surface at a slow but steady rate. In

this steady state, the amount of energy leaving the top ofeach gas layer within the Sun precisely balances the energyentering from the bottom (Figure 15.8). Suppose the coretemperature of the Sun rose very slightly. The rate of nu-clear fusion would soar, generating lots of extra energy. Be-cause energy moves so slowly through the Sun, this extraenergy would be bottled up in the core, causing an increasein the core pressure. The push of this pressure would tem-porarily exceed the pull of gravity, causing the core to ex-pand and cool. With cooling, the fusion rate would dropback down. The expansion and cooling would continue untilgravitational equilibrium was restored, at which point thefusion rate would return to its original value.

An opposite process would restore the normal fusionrate if the core temperature dropped. A decrease in coretemperature 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 theburning rate returned to normal.

The response of the core pressure to changes in thenuclear fusion rate is essentially a thermostat that keeps the Sun’s central temperature steady. Any change in the core temperature is automatically corrected by thechange in the fusion rate and the accompanying change in pressure.

While the processes involved in gravitational equilib-rium prevent erratic changes in the fusion rate, they alsoensure that the fusion rate gradually rises over billions ofyears. Because each fusion reaction converts four hydrogennuclei into one helium nucleus, the total number of inde-pendent particles in the solar core is gradually falling. Thisgradual reduction in the number of particles causes thesolar core to shrink.

The slow shrinking of the solar core means that it mustgenerate energy more rapidly to counteract the strongercompression of gravity, so the solar core gradually getshotter as it shrinks. Theoretical models indicate that theSun’s core temperature should have increased enough toraise 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 affectEarth? Geological evidence shows that Earth’s surface tem-perature has remained fairly steady since Earth finishedforming more than 4 billion years ago, despite this 30%increase in the Sun’s energy output, because Earth has itsown thermostat. This “Earth thermostat” is the carbondioxide cycle. By maintaining a fairly steady level of atmo-spheric carbon dioxide, the carbon dioxide cycle regulatesthe greenhouse effect that maintains Earth’s surface tem-perature [Section 14.4].

“Observing” the Solar Interior

We cannot see inside the Sun, so you may be wonderinghow we can know so much about what goes on underneathits surface. Astronomers can study the Sun’s interior inthree different ways: through mathematical models of the



Sun, observations of “sun quakes,” and observations ofsolar neutrinos.

Mathematical Models The primary way we learn aboutthe interior of the Sun and other stars is by creating mathe-matical models that use the laws of physics to predict theinternal conditions. A basic model uses the Sun’s observedcomposition and mass as inputs to equations that describegravitational equilibrium, the solar thermostat, and therate at which solar energy moves from the core to the photo-sphere. With the aid of a computer, we can use the modelto calculate the Sun’s temperature, pressure, and density at any depth. We can then predict the rate of nuclear fusionin the solar core by combining these calculations withknowledge about nuclear fusion gathered in laboratorieshere on Earth.

Remarkably, such models correctly “predict” the ra-dius, surface temperature, luminosity, age, and many otherproperties of the Sun. However, current models do notpredict everything about the Sun correctly. Scientists areconstantly working to discover what is missing from them.Successful prediction of so many observed characteristics

of the Sun gives us confidence that the models are on theright track and that we really do understand what is goingon inside the Sun.

Sun Quakes A second way to learn about the inside ofthe Sun is to observe “sun quakes”—vibrations of the Sunthat are similar to the vibrations of the Earth caused byearthquakes, although they are generated very differently.Earthquakes occur when Earth’s crust suddenly shifts, gen-erating seismic waves that propagate through Earth’s interior[Section 10.2]. We can learn about Earth’s interior by record-ing 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. Thesewaves 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 measuringDoppler shifts [Section 6.5]. Light from portions of the sur-face that are rising toward us is slightly blueshifted, whilelight from portions that are falling away from us is slightlyredshifted. The vibrations are relatively small but measur-able (Figure 15.9).


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 byfusion. A rise in core temperature triggers a chain of events that causes the core to expand, lowering itstemperature to its normal value. A decrease in core temperature triggers the opposite chain of events,also restoring the normal core temperature.

slight decrease incore temperature

slight rise incore temperature

Because the energysupply is diminished,gravity starts toovercome thermalpressure.

Increased energyoutput enablesthermal pressureto overcomegravity.

Gravity compressesthe core, heats it up,and restores fusionrate to normal value.

large rise inrate of fusion

large decrease inrate of fusion

Increased thermalpressure causes thecore to expand and thencool, which restores fusionrate to normal value.

SolarThermostat:GravitationalEquilibrium


In principle, we can deduce a great deal about the solar interior by carefully analyzing these vibrations. (Byanalogy to seismology on Earth, this type of study of theSun is called helioseismology—helios means “sun.”) Re-

sults to date confirm that our mathematical models of thesolar interior are on the right track (Figure 15.10). At thesame time, they provide data that can be used to improvethe models further.

Figure 15.9 Vibrations on the surface ofthe 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 illustratedhere is just one of many possible patterns.The overall vibration pattern of the Sun is acomplex combination of patterns similar tothis one.


Mathematical Insight 15.1 Mass-Energy Conversion in the Sun

We can calculate how much mass the Sun loses through nuclearfusion by comparing the input and output masses of the proton–proton chain. A single proton has a mass of 1.6726 � 10�27 kg,so four protons have a mass of 6.690 � 10�27 kg.

A helium-4 nucleus has a mass of only 6.643 � 10�27 kg,slightly less than the mass of the four protons. The difference is:

6.690 � 10�27 kg � 6.643 � 10�27 kg � 4.7 � 10�29 kg

which is 0.7%, or 0.007, of the original mass. Thus, for example,when 1 kilogram of hydrogen fuses, the resulting helium weighsonly 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 � mc2. Thetotal 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 � mc2 ⇒ m � �c

E2�

� � 4.2 � 109 kg3.8 � 1026 joules��

�3.0 � 108 �m

s��

2

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 eachsecond in the Sun?

Solution: We have already calculated that the Sun loses 4.2 � 109 kgof mass each second and that this is only 0.7% of the mass of hy-drogen that is fused:

4.2 � 109 kg � 0.007 � mass of hydrogen fused

We now solve for the mass of hydrogen fused:

mass ofhydrogen fused

� �4.2 �

0.0

1

0

0

7

9 kg�

� 6.0 � 1011 kg � �1 m

1

e

0

t3

ri

k

c

g

ton�

� 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 remaining596 million tons becomes helium.


first major solar neutrino detector, built in the 1960s, waslocated 1,500 meters underground in the Homestake goldmine in South Dakota (Figure 15.11).

The detector for this “Homestake experiment” consistedof a 400,000-liter vat of chlorine-containing dry-cleaningfluid. It turns out that, on very rare occasions, a chlorinenucleus can capture a neutrino and change into a nucleusof radioactive argon. By looking for radioactive argon inthe tank of cleaning fluid, experimenters could count thenumber of neutrinos captured in the detector.

From the many trillions of solar neutrinos that passedthrough 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 measuredproperties of chlorine nuclei and models of nuclear fu-sion in the Sun. However, over a period of more than twodecades, neutrinos were captured only about once every 3 days on average. That is, the Homestake experiment de-tected only about one-third of the predicted number ofneutrinos. This disagreement between model predictionsand actual observations came to be called the solar neu-trino problem.

The shortfall of neutrinos found with the Homestakeexperiment led to many more recent attempts to detect solarneutrinos using more sophisticated detectors (Figure 15.12).The chlorine nuclei in the Homestake experiment could


a Temperature at different radii within the Sun.

Figure 15.10 Agreement between mathematical models of solar structure and actual measurements ofsolar structure derived from “sun quakes.” The red lines show predictions of mathematical models of theSun. 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 wavesthat propagate through the Sun’s interior layers.

fraction of the Sun’s radius

tem

per

atur

e (K

)

0.2

core radiationzone

convectionzone

0 0.4 0.6 0.8 1.0

106

107

model

data

Key

b Density at different radii within the Sun. (The density of water is1 g/cm3.)

fraction of the Sun’s radius

den

sity

(g

/cm

3 )

0.2

core radiationzone

convectionzone

0 0.4 0.6 0.8 1.0

1

0.1

0.01

10

100 model

data

Key

Solar Neutrinos Another way to study the solar interioris to observe the neutrinos coming from fusion reactions inthe core. Don’t panic, but as you read this sentence about athousand trillion solar neutrinos will zip through your body.Fortunately, they won’t do any damage, because neutrinosrarely interact with anything. Neutrinos created by fusionin the solar core fly quickly through the Sun as if passingthrough empty space. In fact, while an inch of lead will stopan X ray, stopping an average neutrino would require a slabof lead more than 1 light-year thick! Clearly, counting neu-trinos is dauntingly difficult, because virtually all of themstream right through any detector built to capture them.

Is the number of solar neutrinos zipping through our bodiessignificantly lower at night? (Hint: How does the thickness ofEarth compare with the thickness of a slab of lead needed to stop an average neutrino?)

Nevertheless, neutrinos do occasionally interact withmatter, and it is possible to capture a few solar neutrinoswith a large enough detector. Neutrino detectors are usu-ally placed deep inside mines so that the overlying layers ofrock block all other kinds of particles coming from outerspace except neutrinos, which pass through rock easily. The

THINK ABOUT IT


capture only high-energy neutrinos that are produced byone of the rare pathways of step 3 in the proton–protonchain (not shown in Figure 15.7). More recent experimentscan detect lower-energy neutrinos, including those producedby step 1 of the proton–proton chain, and therefore offer abetter probe of fusion in the Sun. To date, all these experi-ments have found fewer neutrinos than current models ofthe 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 ismissing in our understanding of how neutrinos behave.

Although the observed number of neutrinos falls short of theoretical predictions, experiments like Homestake haveshown that at least some neutrinos are coming from the Sun. Explain why this provides direct evidence that nuclearfusion really is taking place in the Sun right now. (Hint: SeeFigure 15.7.)

For the moment, many physicists and astronomers are betting that we understand the Sun just fine and thatthe discrepancy has to do with the neutrinos themselves.One intriguing idea arises from the fact that neutrinos comein 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

THINK ABOUT IT

a Scientists inspecting individual detectors within Super-Kamiokande.

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 oneof the world’s premier neutrino detectors.

Figure 15.11 This tank of dry-cleaning fluid (visible underneaththe catwalk), located deep within South Dakota’s Homestake mine,was a solar neutrino detector. The chlorine nuclei in the cleaningfluid turned into argon nuclei when they captured neutrinos fromthe Sun.



electron neutrinos. However, recent experiments have shownthat some of the electron neutrinos might change into muonand 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 fromthe Sudbury Neutrino Observatory in Canada, a new de-tector designed to search for all types of neutrinos, suggestthat neutrinos changing type is indeed the solution to thesolar neutrino problem. The observations are ongoing, andit will probably be several more years before this solutioncan be definitively confirmed.

Because of their roles in detecting solar neutrinos andidentifying the solar neutrino problem, Raymond Davis,leader of the Homestake experiment, and Masatoshi Ko-shiba, leader of Super-Kamiokande, shared in the 2002 NobelPrize for physics.

15.4 From Core to CoronaEnergy liberated by nuclear fusion in the Sun’s core musteventually reach the solar surface, where it can be radi-ated into space. The path that the energy takes to the sur-face is long and complex. In this section, we follow thatlong path.

The Path Through the Solar Interior

In Chapter 6, we discussed how atoms can absorb or emitphotons. In fact, photons can also interact with any chargedparticle, and a photon that “collides” with an electron canbe deflected into a completely new direction.

Deep in the solar interior, the plasma is so dense thatthe 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 newdirection, the photon bounces around the core in a hap-hazard way, sometimes called a random walk. With eachrandom bounce, the photon drifts farther and farther,on average, from its point of origin. As a result, photonsfrom the solar core gradually work their way outward (Fig-ure 15.13). The technical term for this slow, outward mi-gration of photons is radiative diffusion (to diffuse meansto “spread out” and radiative refers to the photons of lightor radiation).

Along the way, the photons exchange energy with theirsurroundings. Because the surrounding temperature de-clines as the photons move outward through the Sun, theyare gradually transformed from gamma rays to photons of lower energy. (Because energy must be conserved, eachgamma-ray photon becomes many lower-energy photons.)By the time the energy of fusion reaches the surface, thephotons are primarily visible light. On average, the energyreleased in a fusion reaction takes about a million years to reach the solar surface.

Radiative diffusion is just one type of diffusion. Another is thediffusion of dye through a glass of water. If you place a concen-trated spot of dye at one point in the water, each individual dyemolecule begins a random walk as it bounces among the watermolecules. The result is that the dye gradually spreads throughthe entire glass. Can you think of any other examples of diffu-sion in the world around you?

Radiative diffusion is the primary way by which energymoves outward through the radiation zone, which stretchesfrom the core to about 70% of the Sun’s radius (see Fig-ure 15.4). Above this point, where the temperature hasdropped to about 2 million K, the solar plasma absorbs pho-tons 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 absorptioncauses bubbles of hot plasma to rise upward in the processknown as convection [Section 10.2]. Convection occursbecause hot gas is less dense than cool gas. Like a hot-airballoon, a hot bubble of solar plasma rises upward throughthe cooler plasma above it. Meanwhile, cooler plasma fromabove slides around the rising bubble and sinks to lowerlayers, where it is heated. The rising of hot plasma and sink-ing of cool plasma form a cycle that transports energy out-ward 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. De-fining where the surface of the Sun begins is therefore some-thing like defining the surface of a cloud: From a distance it looks quite distinct, but up close the surface is fuzzy, notsharp. We generally define the solar surface as the layer thatappears distinct from a distance. This is the layer we identi-fied as the photosphere when we took our imaginary jour-ney into the Sun. More technically, the photosphere is thelayer of the Sun from which photons finally escape intospace after the million-year journey of solar energy outwardfrom the core.

THINK ABOUT IT


Figure 15.13 A photon in the solar interior bounces randomlyamong electrons, slowly working its way outward in a processcalled radiative diffusion.


Most of the energy produced by fusion in the solarcore 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 spec-trum that peaks in the green portion of the visible spec-trum, with substantial energy coming out in all colors ofvisible 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 scattersblue light. It is this scattered light from the Sun that makesour skies blue [Section 11.3].

Although the average temperature of the photosphereis 5,800 K, actual temperatures vary significantly from placeto place. The photosphere is marked throughout by thebubbling pattern of granulation produced by the under-lying convection (Figure 15.14b). Each granule appearsbright in the center, where hot gas bubbles upward, and darkaround the edges, where cool gas descends. If we made amovie of the granulation, we’d see it bubbling rather like a pot of boiling water. Just as bubbles in a pot of boilingwater burst on the surface and are replaced by new bubbles,each granule lasts only a few minutes before being replacedby 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 plasmaof the surrounding photosphere. If you think about this fora moment, you may wonder how sunspots can be so muchcooler than their surroundings. Why doesn’t the surround-ing hot plasma heat the sunspots? Something must be

preventing hot plasma from entering the sunspots, andthat “something” turns out to be magnetic fields.

Detailed observations of the Sun’s spectral lines revealsunspots to be regions with strong magnetic fields. Thesemagnetic fields can alter the energy levels in atoms andions and therefore can alter the spectral lines they produce.More specifically, magnetic fields cause some spectral linesto split into two or more closely spaced lines (Figure 15.15b).This effect (called the Zeeman effect) enables scientists tomap magnetic fields on the Sun by studying the spectrallines in light from different parts of the solar surface.

Magnetic fields are invisible, but in principle we couldvisualize 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 oflines, called magnetic field lines, connecting the needles of these imaginary compasses (Figure 15.16a). The strengthof the magnetic field is indicated by the spacing of the lines:Closer lines mean a stronger field (Figure 15.16b). Becausethese imaginary field lines are so much easier to visualizethan the magnetic field itself, we usually discuss magneticfields by talking about how the field lines would appear.Charged particles, such as the ions and electrons in thesolar plasma, follow paths that spiral along the magneticfield lines (Figure 15.16c). Thus, the solar plasma can movefreely along magnetic field lines but cannot easily moveperpendicular to them.

The magnetic field lines act somewhat like elastic bands,being twisted into contortions and knots by turbulent mo-tions in the solar atmosphere. Sunspots occur where themost taut and tightly wound magnetic fields poke nearlystraight out from the solar interior. Sunspots tend to occurin pairs connected by a loop of magnetic field lines. These


a This schematic diagram shows how hot gas (white arrows) riseswhile cooler gas (orange/black arrows) descends around it. Bright spotsappear on the solar surface in places where hot gas is rising frombelow, creating the granulated appearance of the solar photosphere.

Figure 15.14 Convection transports energy outward in the Sun’s convection zone.

b Granulation is evident in thisphoto of the Sun’s surface. Eachbright granule is the top of a risingcolumn of gas. At the darker linesbetween the granules, cooler gas is descending below the photo-sphere. Each granule is about 1,000 kilometers across.

VIS


tight magnetic field lines suppress convection within eachsunspot and prevent surrounding plasma from sliding side-ways into the sunspot. With hot plasma unable to enter theregion, the sunspot plasma becomes cooler than that of therest of the photosphere (Figure 15.17a).

The magnetic field lines connecting two sunspots oftensoar 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 evenweeks. Some prominences rise to heights of more than100,000 kilometers above the Sun’s surface (Figure 15.18).

The most dramatic events on the solar surface aresolar flares, which emit bursts of X rays and fast-movingcharged particles into space (Figure 15.19). Flares generallyoccur in the vicinity of sunspots, leading us to suspect thatthey occur when the magnetic field lines become so twistedand knotted that they can no longer bear the tension. Themagnetic field lines suddenly snap like tangled elastic bandstwisted beyond their limits, releasing a huge amount ofenergy. This energy heats the nearby plasma to 100 millionK over the next few minutes to few hours, generating X raysand accelerating some of the charged particles to nearly thespeed of light.

The Chromosphere and Corona

The high temperatures of the chromosphere and coronaperplexed scientists for decades. After all, temperaturesgradually decline as we move outward from the core to the

top of the photosphere. Why should this decline suddenlyreverse? 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 fromthe churning solar surface to the chromosphere and corona.

More specifically, the rising and falling of gas in theconvection zone probably shakes magnetic field lines beneaththe solar surface. This shaking generates waves along themagnetic field lines that carry energy upward to the solar


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

b Spectra of sunspots can beused to measure the strengthof their magnetic fields. Thisimage shows the spectrumof a sunspot and its surround-ings. The sunspot regionshows up as dark horizontalbands because it is darkerthan the rest of the solar sur-face in its vicinity. The verti-cal bands are absorption linesthat are present both insideand outside the sunspots.The influence of strong mag-netic fields within the sunspotregion splits a single absorp-tion line into three parts.Measuring the separation between these lines tells us the strength of the magnetic field within the sunspot.

VIS


atmosphere. Precisely how the waves deposit their energyin the chromosphere and corona is not known, but thewaves agitate the low-density plasma of these layers, some-how heating them to high temperatures. Much of this heat-ing appears to happen near where the magnetic field linesemerge from the Sun’s surface.

According to this model of solar heating, the samemagnetic fields that keep sunspots cool make the overlying

plasma of the chromosphere and corona hot. We can testthis idea observationally. The gas of the chromosphere andcorona is so tenuous that we cannot see it with our eyesexcept during a total eclipse, when we can see the faint visi-ble light scattered by electrons in the corona [Section 2.5].However, the roughly 10,000 K plasma of the chromosphereemits strongly in the ultraviolet, and the million K plasmaof the corona is the source of virtually all X rays coming


a Pairs of sunspots are connected by tightly wound magnetic field lines.

Figure 15.17 Loops of magnetic field lines can arch high abovethe solar surface, reaching heights many times larger than Earth’sdiameter.

Magnetic fields of sunspots suppress convection and prevent surrounding plasma from sliding sideways into sunspot.

Magnetic fieldstrap gas.

convection cells

T � 5,800 K T � 5,800 Ksunspots

T � 4,500 K

b This X-ray photo (from NASA’s TRACE mission) shows gas trappedwithin looped magnetic field lines.

Figure 15.16 We draw magnetic fieldlines to represent invisible magnetic fields.

stronger magnetic field

weaker magnetic field

weaker magnetic field

e�

e�

e�

e�

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 needles would point. magnetic field lines.

X-ray


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, barelyshow up in X-ray images. More detailed analyses show thatthe magnetic field lines in coronal holes project out intospace 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 solarwind, which blows through the solar system at an averagespeed 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 Pioneerand Voyager spacecraft that visited the outer planets in the1970s and 1980s are still traveling outward from our solarsystem and may soon encounter this “boundary” (called theheliopause) of the realm of the Sun.

The solar wind also gives us something tangible tostudy. In the same way that meteorites provide us with sam-ples of asteroids we’ve never visited, solar wind particlescaptured by satellites provide us with a sample of materialfrom the Sun. Analysis of these solar particles has reassur-ingly verified that the Sun is made mostly of hydrogen,just as we conclude from studying the Sun’s spectrum.


Figure 15.18 A gigantic solar prominenceerupts from the solar surface at the upperright of this ultraviolet-light photo (from theSOHO mission). The gas within this promi-nence, which is over 20 times the size ofEarth, is quite hot but still cooler than themillion-degree gas of the surrounding corona.

UV

Figure 15.19 This photo (fromTRACE) of ultraviolet light emittedby hydrogen atoms shows a solarflare erupting from the Sun’s surface.

UV


Although we’ll call it an “11-year” cycle, the intervalbetween solar maxima is sometimes as long as 15 years or as short as 7 years. The number of sunspots also variesdramatically (Figure 15.21a). In fact, sunspot activity vir-tually ceased between the years 1645 and 1715, a periodsometimes called the Maunder minimum (after E. W.Maunder, who identified it in historical sunspot records).

Another feature of the sunspot cycle is a gradualchange in the solar latitudes at which individual sunspotsform and dissolve (Figure 15.21b). As a cycle begins at solarminimum, sunspots form primarily at mid-latitudes (30°to 40°) on the Sun. The sunspots tend to form at lower lati-tudes as the cycle progresses, appearing very close to thesolar equator as the next solar minimum approaches.

A less obvious feature of the sunspot cycle is thatsomething peculiar happens to the Sun’s magnetic field at each solar minimum. The field lines connecting all pairsof sunspots (see Figure 15.17) tend to point in the samedirection throughout an 11-year solar cycle (within eachhemisphere). For example, all compass needles might pointfrom the easternmost sunspot to the westernmost sunspot in a pair. However, as the cycle ends at solar minimum, themagnetic field reverses: In the subsequent solar cycle, thefield lines connecting pairs of sunspots point in the oppositedirection. Apparently, the entire magnetic field of the Sunflip-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 theSun, called the solar cycle, really averages 22 years, since ittakes two 11-year cycles before the magnetic field is backthe way it started.


Figure 15.20 An X-ray image of the Sun reveals the million-degree gas of thecorona. Brighter regions of this image (yellow) correspond to regions of strongerX-ray emission. The darker regions are the coronal holes from which the solarwind escapes. (From the Yohkoh spaceobservatory.)

X-ray

15.5 Solar Weather and Climate

Individual sunspots, prominences, and flares are short-livedphenomena, somewhat like storms on Earth. They consti-tute what we call solar weather or solar activity. You knowfrom personal experience that the Earth’s weather is noto-riously unpredictable. The same is true for the Sun: Wecannot predict precisely when or where a particular sunspotor flare will appear. Earth’s climate, on the other hand, isquite regular from season to season. So it is with the Sun,where despite day-to-day variations the general nature andintensity of solar activity follow a predictable cycle.

The Sunspot Cycle

Long before we realized that sunspots were magnetic dis-turbances, astronomers had recognized patterns in sunspotactivity. The most notable pattern is the number of sun-spots visible on the Sun at any particular time. Thanks totelescopic observations of the Sun recorded by astrono-mers since the 1600s, we know that the number of sunspotsgradually rises and falls in a sunspot cycle with an averageperiod of about 11 years (Figure 15.21a). At the time ofsolar maximum, when sunspots are most numerous, wemay see dozens of sunspots on the Sun at one time. In con-trast, we see few if any sunspots at the time of solar mini-mum. The frequency of prominences and flares also followsthe sunspot cycle, with these events being most common at solar maximum and least common at solar minimum.


What Causes the Sunspot Cycle?

The causes of the Sun’s magnetic fields and the sunspotcycle 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 inthe solar interior, amplifying them as they rise. The Sun’srotation—faster at its equator than near its poles—thenstretches and shapes these fields.

Imagine what happens to a magnetic field line that origi-nally runs along the Sun’s surface directly from the northpole to the south pole. At the equator, the field line circlesthe Sun in 25 days, but at higher latitudes the field line lagsbehind. Gradually, this rotation pattern winds the field linemore and more tightly around the Sun (Figure 15.22). Thisprocess, operating at all times over the entire Sun, producesthe contorted field lines that generate sunspots and othersolar activity.

Investigating how the Sun’s magnetic field developsand changes in time requires sophisticated computer mod-els. Scientists are working hard on such models, but the

behavior of these fields is so complex that approximationsare necessary even with the best supercomputers. Usingthese computer models, scientists have successfully repli-cated some features of the sunspot cycle, such as changes in the number and latitude of sunspots and the magneticfield 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 differ-ent from one cycle to the next.

Solar Activity and Earth

During solar maximum, solar flares and other forms ofsolar activity send large numbers of highly energetic chargedparticles (protons and electrons) toward Earth. Sometimesthese particles travel in the smooth flow known as the solarwind. Other times they come in the form of huge magneticbubbles called coronal mass ejections. Do these forms of solarweather affect Earth? In at least some ways, the answer is a definitive yes.


a This graph shows how the number of sunspots on the Sun changes with time. The vertical axis shows thepercentage of the Sun’s surface covered by sunspots. The cycle has a period of approximately 11 years.

0.5%

0.4%

0.3%

0.2%

0.1%

0.0%1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

per

cent

age

of S

un’s

sur

face

cove

red

by

suns

pot

s

year

b This graph shows how the latitudes at which sunspot groups appear tend to shift during a single sunspotcycle. Each dot represents a group of sunspots and indicates the year (horizontal axis) and latitude (verticalaxis) at which the group appeared.

Figure 15.21 Sunspot cycle during the past century.

1900

90� N

30� N

Equator

30� S

90� S1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

year

latit

ude


The magnetic field associated with the solar wind con-stantly interacts with Earth’s magnetic field. Occasionallythese fields interconnect. When that happens, large amountsof energy are released from the magnetic field into thecharged particles near the interconnection zone. Many of these energized particles then flow down Earth’s mag-netic field lines toward the poles (Figure 15.23a). Collisionsbetween the charged particles and atoms in Earth’s upperatmosphere cause electrons in the atoms to jump to higherenergy levels [Section 4.4]. These excited atoms subsequentlyemit visible-light photons as they drop to lower energy levels,

creating the shimmering light of auroras (Figure 15.23b).Because coronal mass ejections are particularly energetic, theauroras they stimulate can be especially spectacular.

Particles streaming from the Sun after the occurrenceof solar flares, coronal mass ejections, or other major solarstorms can also have practical impacts on society. For ex-ample, these particles can hamper radio communications,disrupt electrical power delivery, and damage the electroniccomponents in orbiting satellites. During a particularlypowerful magnetic storm on the Sun in March 1989, theU.S. Air Force temporarily lost track of over 2,000 satellites,


Figure 15.22 The Sun rotates more quickly at its equator than it does near its poles. Because gas circlesthe 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 outthe directions of these stretched and distorted field lines.

N N N

S S Stime time

magneticfield line

equator

differingrotationrates

breathe in atmospheric carbon, in the form of carbon dioxide,and incorporate it year by year into each ring. We can thereforeestimate the level of solar activity in any given year by measuringthe level of carbon-14 in the corresponding ring. No clear evi-dence 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 lessen-ing solar activity. According to our theory of solar system forma-tion, the Sun must have rotated much faster when it was young[Section 9.3]. Because a combination of convection and rotationgenerates solar activity, a faster rotation rate should have meantmuch more activity. Observations of other stars that are similar to the Sun but rotate faster confirm that these stars are muchmore active. We find evidence for many more “starspots” on thesestars than on the Sun, and their relatively bright ultraviolet andX-ray emissions suggest that they have brighter chromospheresand coronas—just as we would expect if they are more active than the Sun.

Figure 15.21 shows that the sunspot cycle varies in length andintensity, and it sometimes seems to disappear altogether. Withthese facts as background, many scientists are searching for longer-term patterns in solar activity. Unfortunately, the search for longer-term variations is difficult because telescopic observations ofsunspots cover a period of only about 400 years. Some naked-eyeobservations of sunspots recorded by Chinese astronomers goback almost 2,000 years, but these records are sparse, and naked-eye observations may not be very reliable. We can also guess atpast solar activity from descriptions of solar eclipses recordedaround the world: When the Sun is more active, the corona tendsto have longer and brighter “streamers” visible to the naked eye.

Another way to gauge past solar activity is to study the amountof carbon-14 in tree rings. High-energy cosmic rays [Section 19.2]coming from beyond our own solar system produce radioactivecarbon-14 in Earth’s atmosphere. During periods of high solaractivity, the solar wind tends to grow stronger, shielding Earthfrom some of these cosmic rays. Thus, production of carbon-14drops when the Sun is more active. All the while, trees steadily

S P E C I A L TO P I C Long-Term Change in Solar Activity


and powerful currents induced in the ground circuits ofthe Quebec hydroelectric system caused it to collapse formore than 8 hours. The combined cost of the loss of powerin the United States and Canada exceeded $100 million. InJanuary 1997, AT&T lost contact with a $200-million com-munications satellite, probably because of damage causedby particles coming from another powerful solar storm.

Satellites in low-Earth orbit are particularly vulnerableduring solar maximum, when the increase in solar X raysand energetic particles heats Earth’s upper atmosphere,causing it to expand. The density of the gas surroundinglow-flying satellites therefore rises, exerting drag that sapstheir energy and angular momentum. If this drag proceedsunchecked, the satellites ultimately plummet back to Earth.Satellites in low orbits, including the Hubble Space Telescopeand the Space Station, require occasional boosts to preventthem from falling out of the sky.

Connections between solar activity and Earth’s climateare much less clear. The period from 1645 to 1715, whensolar activity seems to have virtually ceased, was a time of exceptionally low temperatures in Europe and NorthAmerica known as the Little Ice Age. Did the low solar activ-ity cause these low temperatures, or was their occurrence

a coincidence? No one knows for sure. Some researchershave claimed that certain weather phenomena, such asdrought cycles or frequencies of storms, are correlated withthe 11- or 22-year cycle of solar activity. However, the datasupporting these correlations are weak in many cases, andeven real correlations may be coincidental.

Part of the difficulty in linking solar activity with cli-mate is that no one understands how the linkage mightwork. Although emissions of ultraviolet light, X rays, andhigh-energy particles increase substantially from solar min-imum to solar maximum, the total luminosity of the Sunbarely changes at all. (The Sun becomes only about 0.1%brighter during solar maximum.) Thus, if solar activityreally is affecting Earth’s climate, it must be through somevery subtle mechanism. For example, perhaps the expan-sion of Earth’s upper atmosphere that occurs with solarmaximum somehow causes changes in weather.

The question of how solar activity is linked to Earth’sclimate is very important, because we need to know whetherglobal warming is affected by solar activity in addition tohuman activity. Unfortunately, for the time being at least,we can say little about this question.


a Interactions between Earth’s magnetic field and the magnetic field of the solar wind cansend energetic charged particles toward Earth’s poles.

Figure 15.23 Particles from the Sun cause auroras on Earth.

N

S

particles spiral around magnetic field lines

stream of solar particles from solar wind

b Aurora along the coast of Norway.


T H E B I G P I C T U R E

Putting Chapter 15 into Context

In this chapter, we have examined our Sun, the neareststar. When you look back at this chapter, make sure youunderstand these “big picture” ideas:

● The ancient riddle of why the Sun shines is now solved.The Sun shines with energy generated by fusion ofhydrogen into helium in the Sun’s core. After a million-year journey through the solar interior and an 8-minutejourney through space, a small fraction of this energyreaches Earth and supplies sunlight and heat.

● Gravitational equilibrium, the balance between pres-sure and gravity, determines the Sun’s interior struc-ture and maintains its steady nuclear burning rate.

The Sun achieved its long-lasting state of gravitationalequilibrium when energy generation by fusion in thecore came into balance with the energy lost throughthermal radiation from the surface. If the Sun were notrelatively steady, life on Earth might not have beenpossible.

● The Sun’s atmosphere displays its own version ofweather and climate, governed by solar magnetic fields.Solar weather has important influences on Earth.

● The Sun is important not only as our source of lightand heat, but also because it is the only star nearenough for us to study in great detail. In the comingchapters, we will use what we’ve learned about theSun to help us understand other stars.

SUMMARY OF KEY CONCEPTS

15.1 Why Does the Sun Shine?

• What process creates energy in the Sun? Fusion ofhydrogen into helium in the Sun’s core generates theSun’s energy.

• Why does the Sun’s size remain stable? The Sun’s sizeremains stable because it is in gravitational equilib-rium. The outward pressure of hot gas balances theinward force of gravity at every point within the Sun.

• How did the Sun become hot enough for fusion in thefirst place? As the Sun was forming, it grew hotter as it shrank in size because gravitational contractionconverted gravitational potential energy into ther-mal energy. Gravitational contraction continued toshrink the Sun and raise its central temperature untilthe core became hot and dense enough for nuclearfusion.


• What are the major layers of the Sun, from the centerout? The layers of the Sun are core, radiation zone,convection zone, photosphere, chromosphere, andcorona.

• What do we mean by the “surface” of the Sun? Weconsider the photosphere to be the surface of the Sunbecause light can pass through the photosphere butcannot escape from deeper inside the Sun. Thus,photographs of visible light from the Sun show uswhat the photosphere looks like.

• What is the Sun made of ? It is made almost entirelyof hydrogen and helium (98% of the Sun’s mass).

15.3 The Cosmic Crucible

• Why does fusion occur in the Sun’s core? The coretemperature and pressure are so high that collidingnuclei can come close enough together for the strongforce to overcome electromagnetic repulsion andbind them together.

• Why is energy produced in the Sun at such a steadyrate? The fusion rate is self-regulating like a thermo-stat. If the fusion rate increases for some reason, theadded 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 timescales, it gradually increases over billions of years,increasing the Sun’s luminosity. The increase occursbecause fusion gradually reduces the number of indi-vidual nuclei in the solar core. Four hydrogen nucleiare fused to make just one helium nucleus, causingthe core to shrink and become hotter.

• How do we know what is happening inside the Sun?We can construct theoretical models of the solarinterior using known laws of physics and then check

continued �



Sensible Statements?

Decide whether each of the following statements is sensible andexplain why it is or is not.

1. Before Einstein, gravitational contraction appeared to be aperfectly plausible mechanism for solar energy generation.

2. A sudden temperature rise in the Sun’s core is nothing toworry about, because conditions in the core will soon returnto normal.

3. If fusion in the solar core ceased today, worldwide panicwould break out tomorrow as the Sun began to grow dimmer.

4. Astronomers have recently photographed magnetic fieldschurning 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 amongprofessionals in the fields of communications and electricalpower generation.

8. By observing solar neutrinos, we can learn about nuclearfusion deep in the Sun’s core.


the models against observations of the Sun’s size,surface temperature, and energy output as well asstudies of “sun quakes” and solar neutrinos.

• What is the solar neutrino problem? Is it solved?Neutrino detectors capture fewer neutrinos comingfrom the Sun than models of fusion in the core pre-dict. This discrepancy is called the solar neutrinoproblem. The problem now appears to be solved.Apparently, neutrinos can transform themselvesamong three different types as they travel from thesolar core to Earth, while most detectors can captureonly one type. Thus, the detectors capture fewerthan the expected number of neutrinos.

15.4 From Core to Corona

• How long ago did fusion generate the energy we nowreceive as sunlight? Fusion created the energy we re-ceive today about a million years ago. It takes abouta million years for photons and then convection totransport energy through the solar interior to thephotosphere. Once sunlight emerges from the photo-sphere, it takes only about 8 minutes to reach Earth.

• How are sunspots, prominences, and flares related tomagnetic fields? Sunspots occur where strong mag-netic fields trap and isolate gas from the surround-ing plasma of the photosphere. The trapped gas cools,so the sunspots become cooler and darker than therest of the photosphere. Sunspots tend to occur inpairs connected by a loop of magnetic field, whichmay rise high above the surface as a solar promi-

nence. The magnetic fields are twisted and contortedby the Sun’s rotation, and solar flares may occurwhen the field lines suddenly snap and release theirenergy.

• What is surprising about the temperature of thechromosphere and corona, and how do we explain it?Temperature gradually decreases from the core tothe photosphere but then rises again in the chromo-sphere and corona. These high layers of the Sun areprobably heated by energy carried upward along themagnetic field lines by waves that are generated asturbulent motions in the convection zone shake themagnetic field lines.

15.5 Solar Weather and Climate

• What is the sunspot cycle? The sunspot cycle, or thevariation in the number of sunspots on the Sun’ssurface, has an average period of 11 years. The mag-netic 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 becomeincreasingly more common near the Sun’s equatoras the next minimum approaches.

• What effect does solar activity have on Earth and itsinhabitants? Particles ejected from the Sun by solarflares and other types of solar activity can affectcommunications, electrical power delivery, and theelectronic circuits in space vehicles. The connectionsbetween solar activity and Earth’s climate are notclear.


Problems

9. Gravitational Contraction. Briefly describe how gravita-tional contraction generates energy and when it was impor-tant 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 inpictures of the Sun?

12. Solar Fusion. What is the overall nuclear fusion reaction inthe Sun? Briefly describe the proton–proton chain.

13. Models of the Sun. Explain how mathematical models allowus to predict conditions inside the Sun. How can we beconfident 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 themand how they help us learn about the solar interior.

15. Energy Transport. Why does the energy produced by fusionin the solar core take so long to reach the solar surface?Describe the processes of radiative diffusion and convectionin the solar interior.

16. The Photosphere. Describe the appearance and temperatureof the Sun’s photosphere. What is granulation? How wouldgranulation appear in a movie?

17. Observing the Sun’s Atmosphere. Why is the chromospherebest viewed with ultraviolet telescopes? Why is the coronabest viewed with X-ray telescopes?

18. An Angry Sun. A Time magazine cover once suggested thatan “angry Sun” was becoming more active as human activ-ity changed Earth’s climate through global warming. It’scertainly possible for the Sun to become more active at thesame time that humans are affecting Earth, but is it possiblethat the Sun could be responding to human activity? Canhumans affect the Sun in any significant way? Explain.

*19. Number of Fusion Reactions in the Sun. Use the fact that eachcycle of the proton–proton chain converts 4.7 � 10�29 kgof mass into energy (see Mathematical Insight 15.1), alongwith the fact that the Sun loses a total of about 4.2 � 109 kgof mass each second, to calculate the total number of timesthe 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 theSun formed. However, only about 13% of this hydrogenever becomes available for fusion in the core. The rest re-mains in layers of the Sun where the temperature is too lowfor fusion.

a. Based on the given information, calculate the total mass of hydrogen available for fusion over the lifetimeof the Sun.

b. Combine your results from part (a) and the fact that theSun fuses about 600 billion kg of hydrogen each secondto calculate how long the Sun’s initial supply of hydro-gen can last. Give your answer in both seconds and years.

c. Given that our solar system is now about 4.6 billion yearsold, when will we need to worry about the Sun runningout of hydrogen for fusion?

*21. Solar Power Collectors. This problem leads you through thecalculation and discussion of how much solar power can becollected by solar cells on Earth.

a. Imagine a giant sphere surrounding the Sun with aradius of 1 AU. What is the surface area of this sphere,in square meters? (Hint: The formula for the surfacearea of a sphere is 4pr2.)

b. Because this imaginary giant sphere surrounds the Sun,the Sun’s entire luminosity of 3.8 � 1026 watts mustpass through it. Calculate the power passing througheach square meter of this imaginary sphere in watts persquare meter. Explain why this number represents themaximum power per square meter that can be collectedby a solar collector in Earth orbit.

c. List several reasons why the average power per squaremeter collected by a solar collector on the ground willalways 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 cancollect, how should you orient the collector? (Hint: Theoptimum orientation depends on both your latitudeand the time of year and day.)

*22. Solar Power for the United States. The total annual U.S. en-ergy consumption is about 2 � 1020 joules.

a. What is the average power requirement for the UnitedStates, in watts? (Hint: 1 watt � 1 joule/s.)

b. With current technologies and solar collectors on theground, the best we can hope is that solar cells willgenerate an average (day and night) power of about 200 watts/m2. (You might compare this to the maximumpower per square meter you found in problem 22b.)What total area would we need to cover with solar cellsto supply all the power needed for the United States?Give your answer in both square meters and squarekilometers.

c. The total surface area of the United States is about 2 � 107 km2. What fraction of the U.S. area would haveto be covered by solar collectors to generate all of theU.S. power needs? In one page or less, describe potentialenvironmental impacts of covering so much area withsolar collectors. Also discuss whether you think theseenvironmental impacts would be greater or less than the impacts of using current energy sources such as coal,oil, nuclear power, and hydroelectric power.



*23. The Color of the Sun. The Sun’s average surface temperatureis about 5,800 K. Use Wien’s law (see Mathematical Insight6.2) to calculate the wavelength of peak thermal emissionfrom the Sun. What color does this wavelength correspondto in the visible-light spectrum? In light of your answer, whydo 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 ushere on Earth. Be sure to consider not only factors such asits light and warmth, but also how the study of the Sun hasled us to new understanding in science and to technologi-cal developments. Overall, how important has solar re-search been to our lives?

25. The Solar Neutrino Problem. Discuss the solar neutrino prob-lem and its potential solutions. How serious do you con-sider this problem? Do you think current theoretical mod-els of the Sun could be wrong in any fundamental way?Why or why not?

26. The Sun and Global Warming. One of the most pressingenvironmental issues on Earth concerns the extent to whichhuman emissions of greenhouse gases are warming ourplanet. Some people claim that part or all of the observedwarming over the past century may be due to changes onthe Sun, rather than to anything humans have done. Dis-cuss how a better understanding of the Sun might help usunderstand the threat posed by greenhouse gas emissions.Why is it so difficult to develop a clear understanding ofhow the Sun affects Earth’s climate?


MEDIA EXPLORATIONS

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 solaractivity 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 ex-pected? Have there been any major solar storms inthe past few months? If so, did they have any signifi-cant effects on Earth? Summarize your findings in a one- to two-page report.

2. Solar Observatories in Space. Visit NASA’s Web sitefor the Sun–Earth connection and explore some of the current and planned space missions designedto observe the Sun. Choose one mission to study ingreater depth, and write a one- to two-page reporton the mission status and goals and what it hastaught or will teach us about the Sun.

3. Sudbury Neutrino Observatory. Visit the Web site forthe Sudbury Neutrino Observatory (SNO) and learnhow it has helped to solve the solar neutrino prob-lem. Write a one- to two-page report describing theobservatory, any recent results, and what we canexpect from it in the future.


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