The Sun, Our Star [Reprint 2014 ed.] 9780674429291, 9780674429284

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The Sun, Our Star

T h e Harvard Books On Astronomy Edited by George Field, Owen Gingerich, and Charles A. Whitney The Milky Way Bart J. Bok and PHscilla F. Bok Stars and Clusters Cecilia Payne-Gaposchkin Galaxies Harlow Shapley / Revised by Paul W. Hodge Orbiting the Sun: Planets and Satellites of the Solar System Fred L. Whipple

The Sun, Our Star Robert W. Noyes

Harvard University Press Cambridge, Massachusetts, and London, England 1982

Copyright © 1982 by the President and Fellows of Harvard College All rights reserved Printed in the United States of America

Library of Congress Cataloging

in Publication

Noyes, Robert W., 1934T h e Sun, our star. (The Harvard books on astronomy) Includes index. 1. Sun. I. Title. II. Series. QB521.N68 1982 523.7 82-11733 ISBN 0-674-85435-7

Data

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Preface

his book succeeds an earlier member of the series of Harvard Books on Astronomy written by Donald H. Menzel and entitled Our Sun. Professor Menzel's choice of title reflected his appreciation of the Sun's interest to everyone, not just to the professional astronomer; and his book amply demonstrated his extraordinary ability to convey the excitement of solar research to scientists and nonscientists alike. During the years that have passed since publication of Our Sun in two editions, much more has been learned about the Sun. Today we are exploring the Sun in marvelous new ways—particularly from space—which were only in their infancy at the time of Professor Menzel's book. We are also beginning the serious investigation of other suns in the sky, at a level of sophistication which previously was restricted only to our own star. In spite of the vitality and freshness of the field of solar physics today, however, solar research still builds upon many foundations originally laid by Donald Menzel. These include theoretical foundations, such as the quantitative application of atomic physics to astronomical spectroscopy. They also include foundations of concrete and steel: Many of the solar observatories that are at the forefront of research today owe their existence directly to the initiative and dedication of Professor Menzel. It is therefore entirely fitting, as well as a distinct personal pleasure, to dedicate this book to the memory of Donald H. Menzel. In the course of preparing The Sun, Our Star I have profited from numerous scientific discussions with colleagues at Harvard and elsewhere. Drs. George Field, Owen Gingerich, Charles Whitney, and John Eddy each read the manuscript and gave useful comments. The material in Chapter 11 on solar energy is based in part on an excellent report of the Union of Concerned Scientists entitled Energy Strategies: Toward a Solar Future (Cambridge, MA: Ballinger, 1980). I wish to thank especially Penelope Gregory for her tireless efforts at typing the manuscript, and my wife Harriet for her constant support and encouragement. R. W. N.

Contents

1.

T h e Sun among the Stars

1

2.

Studying the Face of the Sun

17

3.

Probing the Depths of the Sun

56

4.

Sunspots and Their Rhythm

83

5.

T h e Solar Chromosphere

120

6.

Solar Eclipses and the Corona

141

7.

Viewing the Sun from Space

164

8.

Solar Flares: Explosions in the Corona

181

9.

Holes in the Corona and Winds from the Sun

196

10.

T h e Sun and the Earth's Climate

213

11.

Solar Energy and Man's Future

231

12.

T h e Life History of the Sun

247

Index

261

1. The Sun among the Stars

Δ ^ L i bout 5 billion years ago, a huge dark cloud of dust and vapor floated in the void between the stars of our Galaxy. The cloud was extended and formless. No one knows exactly why it began to contract upon itself. Possibly it was jostled by the shock wave from a distant exploding star, or perhaps it responded to the tidal pull of one of our Galaxy's great spiral arms, as it swept past the cloud in the Galaxy's ponderous rotation. No matter what the reason—somehow the cloud was compressed to the point where the mutual gravitational tug of all its particles of dust and vapor, each for each, overcame their natural tendency to draw apart according to their random motions. From then on the cloud began to collapse, gradually but inexorably. As the collapse continued, the separation of particles lessened and their mutual gravitational attraction increased still more. Thus the collapse accelerated, feeding on itself. Near the center of the cloud the density and gravity were greatest, so as the years rolled on the collapse rate there became much faster than near the outer reaches. Eventually a dense central core formed within the cloud. As the collapse continued over centuries and millennia, the outer parts of the initially formless cloud began to take on shape. The small degree of rotation that happened to be present in the cloud at the start of its collapse was retained, and as the cloud contracted, the rotation increased proportionally, according to the law of conservation of angular momentum. Gradually the cloud began to flatten under the influence of its increased spin, and it took on first an oval and then a disklike appearance. Some of the dust and vapor near the outer edge of the collapsing disk was prevented by its spin from falling toward the now rather dense center, and instead formed smaller peripheral condensations, each spinning around its own center in the same direction as the parent cloud. These were destined to become the Earth and other planets of our solar system. The inward rush of matter in the central collapsing cloud produced

1

heat as the dust and gases collided. This heat was especially intense toward the center of the condensation, which soon reached a temperature sufficient to melt and then vaporize all the dust grains. As the temperature rose, the gases in the center began to exert outward pressure; eventually the pressure in the center of the cloud became so great that it resisted further gravitational infall. Thus a few thousands of years after the collapse began, the inward pull of gravity was just balanced by outward pressure from the cloud's hot center, and the collapse stopped. Our proto-Sun had formed. But what a strange-looking Sun it was! Had there been astronomers at the time trying to observe this protostar, they would have seen only the surrounding cloud of dust and vapors extending far beyond the present orbit of the planet Pluto. The cloud was completely opaque to visible light, hiding the proto-Sun inside. The only hint of its presence was the feeble infrared radiation emitted by the cloud as it was warmed by the hotter stellar embryo within. Like a cocoon, the cloud enveloped this embryo as it underwent its metamorphosis into a true star. For many millions of years the protostar continued to radiate away the heat that it had accumulated from the collapse. Paradoxically, however, it did not cool off, for by radiating energy, it lost the pressure that was needed to stave off further collapse. As a result the proto-Sun experienced very gradual contraction and further heating, at just the rate needed to maintain the internal pressure in balance with the weight of the outer layers pressing on the core. The temperature in the core of the proto-Sun continued to build up for about 10 million years. After this 10-million-year gestation period of contraction and heating, however, the remarkable event of true stellar birth suddenly occurred. The interior of the proto-Sun became so hot that its first nuclear reactions were ignited. At this instant the Sun began its life as a true star, whose core was heated not by the ephemeral energy of gravitational collapse but by the nearly inexhaustible nuclear fuel contained in its vast interior. Now that the energy radiated from the surface of the infant Sun could be exactly compensated by its new nuclear energy source, there was no need to supply more energy by further gravitational contraction. Immediately, the contraction stopped. From that moment onward, the Sun's nuclear furnace has maintained the Sun in a state of equilibrium, continuously producing just enough heat and pressure to counterbalance the weight of its overlying layers. At roughly the same time, the surrounding cocoon became more and more transparent to light from the new Sun; it had gradually

2

The Sun, Our Star

thinned over the millennia, with most of its matter falling into the proto-Sun, while some of it collected into smaller condensations orbiting the central body. An astronomer watching the skies near the infant Sun's location might have detected the gradual appearance of the new star from within the vanishing infrared cocoon. While the cocoon was evaporating, heat from the young Sun was also sweeping the abundant light gases hydrogen and helium from the innermost orbiting condensations and warming the rocks of the newly born Earth to a temperature suitable for liquid water, and ultimately for life. Some 4.5 billion years later, that planet is populated with humans who, in their busy lives, sometimes pause to glance at the Sun and wonder where it came from, what it is like, and what its future will be . . . Starbirth has occurred hundreds of billions of times within our own Milky Way Galaxy over its lifetime, and our own star is only one of perhaps 100 billion stars which shine in the Galaxy today. Astronomers estimate that there are at least 100 billion galaxies, similar in stellar content to our own, in the known universe. Stars in the universe are as common as grains of sand on a beach. What a grand surmise it must have been for the first stargazer who realized that the Sun and stars were the same, and that the universe was teeming with distant suns! We do not have any firm record of such a speculation until around 1600, and it seems likely that earlier thinking along such lines would have been dismissed as idle fancy. After all, the Sun appears so much brighter and larger than the stars that there would seem to be no reason to connect the two. The idea that the stars were points of light engraved on some sort of ethereal sphere, and were literally as different from the Sun as night and day, took from hold in the minds of all educated men. Even Copernicus and Kepler held this view. The widespread realization that the Sun is nothing more and nothing less than a star is only a few hundred years old. Today even schoolchildren know that the stars are similar to the Sun, appearing much fainter only because they are enormously farther away—so far away that their disks cannot be distinguished from points by the eye, or even by a telescope. Is there anything special about that particular star we call the Sun? Of course, it is special to us because it lies in our astronomical backyard. But if we compare it to other familiar stars in the nighttime sky, how does it measure up? To answer that question, we must first know the relative distance of the Sun and other stars, so that we may com-

The Sun among the Stars

3

luinmno VENUS EARTH

1.1 Two ways of measuring distances in the solar system, (a) By standard surveying techniques, for example, measuring angles A and A' to an object from either end of a known baseline Β on the extremely well-surveyed Earth. A relatively closely approaching asteroid such as Eros, which sometimes comes within 22 million kilometers of the Earth, has been used successfully for such distance determinations. (b) Timing of radar "echoes" off distant bodies, such as the surface of a planet, can yield the distance to that body with extraordinary accuracy. In either case, Kepler's laws of planetary motion allow us to scale from the measured distance between the Earth and another body orbiting the Sun, to determine the distance from Earth to the Sun itself with comparable accuracy.

pensate quantitatively for the dimming effects of their great distance. (Since apparent brightness drops off as the square of distance, compensation for the effect is easy once we know a star's distance.) T h e distance to our own star, the Sun, has been determined with great precision, first by using standard surveying techniques, and more recently, using radar (Figure 1.1; actually it is most straightforward to measure distances to asteroids or planets by these means, and from Kepler's laws of planetary motion, scale these distances to give the E a r t h - S u n distance). T h e mean distance from Earth to the Sun in its

4

The Sun, Our Star

near-circular annual orbit is 149,597,893 kilometers, accurate to better than 5 kilometers. While such accuracy is useful to space scientists bent on making a rendezvous between a spacecraft and a distant planet, for our purposes, a round number—150 million kilometers, or 93 million miles—will suffice. This distance is known as the astronomical unit (A.U.) and is the fundamental unit for measuring distances in the universe. To appreciate properly what an enormous distance by terrestrial standards one astronomical unit is, imagine setting off for the Sun in a modern jet aircraft, one that is capable of crossing the North American continent in perhaps 5 hours at a speed of 800 kilometers per hour. At that rate, our journey to the sun would require 21 years of steady flight. However, light waves from the Sun, which travel at the ultimate speed limit known to science—the speed of light, or 300,000 kilometers per second—require only 8V3 minutes to cover the same distance. Astronomers can measure the distance to the nearby stars by a straightforward extension of earthly trigonometric surveying, by measuring angles from either end of a known measured baseline. To measure the much greater distance to the stars, a long baseline is needed,

1.2 The Earth in its annual swing around the Sun moves to either end of a 2 A.17., or 3 x 10s km, baseline every 6 months. A star exactly 206265 A . U . away will appear to be displaced by exactly 2 arcsecs relative to distant stars, every six months, or 1 arcsec over a baseline of 1 A.U. Its parallax is then exactly 1 arcsecond. The distance of 206265 A.U., equal to 3.09 χ 1013 kilometers or 3.26 light years, is defined to be 1 parsec. Astronomers can with difficulty measure parallaxes as small as 0.02 arcsec, yielding distances of stars as far away as 50 parsecs (about 160 light years).

T h e S u n a m o n g t h e Stars

5

and fortunately one is at hand: the diameter of the Earth's orbit around the Sun. Every 6 months, as our Earth swings from one side of the Sun to the other, its position with respect to the Sun changes by 2 astronomical units, or 300 million kilometers. This means that successive views of a nearby star at 6-month intervals will show a very slight displacement relative to far more distant stars (Figure 1.2). The amount of displacement gives the distance to the star. In this way the distance to the nearest star, Alpha Centauri, is found to be about 275,000 A.U., or 275,000 times the distance to the Sun. (Alpha Centauri is actually the second closest known star. A very faint companion star, aptly named Proxima Centauri, is very slightly closer. Located in the southern skies, Alpha and Proxima Centauri are not visible from latitudes above 30° N.) Our jet aircraft that would require 21 years to reach the Sun would require 5.8 million years to reach Alpha Centauri. Light would require 275,000 times 8V3 minutes, or 4.4 years, to travel the same journey, thus making Alpha Centauri 4.4 light years away. By other more complicated (and increasingly less accurate) means, astronomers can measure larger distances in the Galaxy and beyond, to other galaxies and groups of galaxies in the remotest reaches of the universe. Closer to home, in surveying our own Galaxy, we have found that its size is about 100,000 light years. We, and our Sun, live near the outer edge of a vast disk-shaped population of stars, about 30,000 light years from its center. As we look toward the center of the disk, in the direction of the constellation Sagittarius, we see the band of stars which makes up the disk between ourselves and the center—a band which is familiar to all stargazers as the Milky Way. Figure 1.3 is a photograph of a galaxy similar to ours, and approximates what our own Galaxy probably looks like, seen from "outside." A location similar to the location of the Sun in our Galaxy is marked with the symbol Θ. It is apparent that our part of the Galaxy, far from the center but not at the edge, is not a particularly distinguished neighborhood. It is not as prestigious an address as the center of the Galaxy itself, or even one of the spiral arms that give spiral galaxies like our own their distinctive appearance, and their name. (We do live close enough to one, the "Orion" arm, however, that we may easily watch some of the exciting things happening there—for example, starbirth, which is occurring there at the present time.) An astronomer from a neighboring galaxy, studying the Milky Way Galaxy, would surely first examine the spiral arms and the galactic center, but even if his interest extended to the more humdrum neighborhoods between the spiral arms, there seems to be no reason to single out ours. If he did by chance

6

The Sun, Our Star

1 3 The spiral galaxy M81. This relatively nearby galaxy is about 10 million light years away from us. It is comparable in size and in its spiral structure to our own Milky Way Galaxy. If this were our own Galaxy, the position of the Sun might be as indicated by the symbol © in the lower right, about 4/s of the distance from the center to the outer edge. (Courtesy Palomar Observatory.)

single out our own neighborhood, there is no particular reason for him to give a second glance at our star. We know this because, after learning how to measure the distance to the Sun and to nearby stars, we have been able to compare the Sun and the stars quantitatively. It turns out that our Sun is very much a run-of-the-mill star. Because of its relative nearness, it appears about 10 billion times brighter than the next brightest star in the sky, but its intrinsic brightness, or luminosity, is not at all extraordinary. Place the Sun next to the 7 bright stars in Ursa Major making up the familiar Big Dipper (about 90

The Sun among the Stars

7

light years away), and it would be invisible to the naked eye; the Big Dipper stars are about 100 times as luminous as the Sun. The most luminous stars known to astronomers are more than 1 million times as bright as the Sun. If a star of this luminosity were placed at the distance of Alpha Centauri, it would appear 10 times as bright as the full moon. If placed where the Sun is, it would vaporize the Earth. At the other end of the scale, there are myriads of stars much less luminous than the Sun. These stars do not contribute a great deal to the splendor of a starry night, because most of them are so dim as to be invisible to the naked eye. Yet they are by far the most common; only 3 of the 60 stars within 16 light years of the Earth are more luminous than the Sun. Of the 56 less luminous than the Sun, most are so faint that, even in spite of their relative closeness, they cannot be seen without the aid of a large telescope. The least luminous star known, bearing the name Van Biesbroeck No. 10, is among the closest stars to Earth, being only 19 light years away. Yet it is completely invisible to the naked eye. It casts its dull red glow with a candlepower only 3 millionths that of the Sun. If Van Biesbroeck No. 10 were to replace the Sun, our Earth's temperature would fall to less than 20° above absolute zero. All water would freeze, and our atmosphere would condense into a shallow sea of liquid air. The luminosity of a star depends on two basic properties—its size, or surface area, and its surface temperature. Other things being equal, a star with surface area twice that of another will outshine the other by a factor of two. And even if two stars have the same diameter (and hence surface area) the hotter one will outshine the colder one. (The Stefan-Boltzmann law of thermodynamics says that the total radiation emitted by a perfectly efficient emitter of radiation, known as a "black body," varies as T 4 , where Τ is its surface temperature. Stars are not perfect black bodies, but the Stefan-Boltzmann law is a reasonably good approximation to their radiation.) In order to appreciate the actual size of a star, consider our own Sun. It is easy to measure its size through elementary geometry combined with our knowledge of the distance to the Sun (Figure 1.4). The diameter works out to be about 1.4 million kilometers, which is a little more than 100 times the diameter of Earth. Within the Sun's volume one could pack a million Earths. The distance from the Sun's central core out to its surface is almost twice as great as the distance from the Earth to the Moon. Measurements of the diameter of other stars show that the Sun lies in the middle of the range of stellar sizes. The very largest supergiant

8

The Sun, Our Star

stars have diameters many hundreds of times greater. If in imagination we were to wrench the supergiant star Betelgeuse from Orion's shoulder and place it where the Sun is, then the planets Mercury, Venus, Earth, Mars, and Jupiter would lie within its interior. Compared with such a supergiant star, our Sun is a dwarf. Indeed, stars like the Sun are generally classified as "dwarf' stars. O n the other end of the scale, many stars are m u c h smaller than the Sun. T h e least luminous known dwarf star, Van Biesbroeck No. 10, mentioned above, has a diameter of only about Vio that of the Sun. Other super-compact stars called white dwarfs may be as small as the Earth itself. (The faint companion to the star Sirius is an example.) Even smaller are the bizarre stellar remnants known as neutron stars, whose size may be only a few kilometers—smaller than a typical city.

"pinhole" image of the Sun. Thus its diameter is about Vios of an astronomical unit, or about 1.4 million kilometers.

The Sun among the Stars

9

O u r Sun is in the middle range of stellar surface temperatures as well as sizes. As we shall see in Chapter 2, the yellowish-white surface of the Sun has a temperature about 5800° Κ (about 10,000° F). Increasingly hotter stars appear white-hot, blue-hot, or even violet-hot; the hottest known ones have surface temperatures of about 100,000° K. Cooler stars are orange-hot or only red-hot, and the coldest, which emit most of their energy in the invisible infrared, have temperatures as low as 2000° K. T h e properties of the Sun and stars which we have described in the past few pages are conveniently summarized in Figure 1.5. This diagram, known as a Hertzsprung-Russell diagram, is the basic means by which astronomers classify stars. In the diagram, temperature in-

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1.5 A Hertsprung-Russell diagram showing how the fundamental parameters of luminosity (vertical scale) and temperature (horizontal scale) vary for stars. Each star has a specific location in the diagram depending on its measure of surface temperature and luminosity. At the time of their birth, stars lie along a nanow band known as the main sequence, and as may be seen in the diagram, most stars, including the Sun, are there still. The band of the main sequence is narrow because throughout much of their lives both temperature and luminosity of stars are dictated mainly by a single quantity—the star's mass. Less massive stars lie near the lower end of the main sequence and more massive stars near the upper end. Later, when the Sun and similar stars become old, they will become much larger and more luminous giants and ultimately they will shrink to tiny, underluminous white dwarfs. 10

The Sun, Our Star

creases from right to left, and luminosity increases from bottom to top. Stars are sorted into spectral types according to their temperature, as shown by the letters Ο, B, A, F, G, K, and M. The Sun, with surface temperature 5800° K, is a G star. Stars that (like the Sun) have not yet shown the effects of aging lie along the main sequence, as shown. Older stars evolve in bizarre ways, first becoming giants (upper right) and later white dwarfs (lower left). The Sun itself will undergo such a metamorphosis, as will be described in Chapter 12. Today, however, the Sun lies midway along the main sequence, between hotter and brighter stars to the upper left and colder and dimmer stars to the lower right. By now it is clear why we have described the Sun as a run-of-themill star, and why it might be passed over as too ordinary for special study by an astronomer from another galaxy. Of course, we know something that this hypothetical astronomer would not know. We know that the Sun is orbited by nine planets, on the third of which life has occurred, and that out of that life has evolved a most remarkable life form—humanity. We do not yet know whether life such as ours is unique or commonplace in the Galaxy, or indeed in the universe; so far we can only speculate on this perhaps most interesting of all astronomical questions. But it does seem that any impact our existence may have made on our own solar system or the information emanating from it is tiny indeed. We could not easily detect life such as ours around other stars, and there is no reason to believe that an astronomer from another galaxy would suspect our star of harboring life, unless life were already known to be commonplace around ordinary stars like ours. Notwithstanding the Sun's probable lack of interest to astronomers from other worlds, the fact that we inhabit a piece of rock orbiting this particular star makes it for us unique, and supremely interesting. Everyone has a natural curiosity about the Sun transcending that about other stars, simply because we so obviously depend on the Sun for our well-being and even our existence. Astronomers have an additional interest in the Sun, because it is in many ways our best steppingstone to the wider universe. We are destined to see most stars always as mere points of light, even in the largest telescopes. On the Sun, however, we can resolve surface details and see astrophysical processes at work— processes which occur not only on other stars but also in other astrophysical contexts. Furthermore, the nearby Sun is so bright that we can break its light up into the finest possible gradations of colors, or wavelengths, using spectrographs or other instruments, and still have

T h e Sun among the Stars

11

1.6 Because the Sun is so close, our telescopes can resolve extremely fine detail in the solar surface and its overlying atmosphere. Examples are (lower right) the intricate fibrous structure of penumbrae surrounding sunspots; (lower left) intense x-ray emission from the solar atmosphere above sunspots; or (upper right) magnetized loop structures above the solar limb produced as gases rain back down to the surface after a large flare. The smallest features visible in the images shown are no more than a few hundred kilometers across—about V4000 of the diameter of the Sun. At present there is no hope of getting data of similar quality from even the nearest star. (The leftmost image is courtesy G. S. Vaiana and NASA; the righthand images are courtesy Sacramento Peak Observatory, AURA.)

12

The Sun, Our Star

enough light left over for detailed study. Figure 1.6 demonstrates the power of spatial and spectral resolution on the Sun with three telescopic images of solar features. T h e lower right image shows the complex forms of a sunspot— a strongly magnetized dark patch in the brilliantly emitting solar surface, or photosphere (from the Greek, meaning light-sphere). T h e lower left image shows very high-temperature emission from magnetic active regions in the atmosphere overlying sunspots. T h e temperature is so high (several million degrees) that the emission is in the form of x-rays, which can be detected only by telescopes in space above the Earth's atmosphere. T h e upper right image shows coronal loops at the limb of the Sun, tracing out the arching geometry of magnetic fields high above the surface. Features like these may well exist on other stars, and in far grander scale. However, we have only the barest hint of their existence on other stars, and we could never have imagined their characteristics without the close-up view the Sun provides us. T h e images in Figure 1.6 illustrate a relatively recent insight into solar physics, the importance of which has become so clear over the past few years that it dominates m u c h of solar research today. This is the role played by magnetic fields in virtually all of the phenomena that make the Sun an interesting subject for study. O u r Sun is a magnetic star. Motions deep in its interior generate very strong magnetic fields to create sunspots and a large variety of associated phenomena known as magnetic activity, in a quasi-periodic magnetic cycle of duration about 22 years. Twice during each cycle (that is, about every 11 years) sunspots and surface magnetic fields reach a peak, and solar observers are able to study the interaction of magnetic fields and the hot gases of the Sun's atmosphere in great detail. T h e last sunspot maxim u m occurred in 1980; the next is due about 1991. Magnetic interactions in the Sun are interesting to the astrophysicist because, by presenting the best close-at-hand example of how hot gases and magnetic fields interact, they give important hints about similar behavior elsewhere in the universe. They are also of interest to other physical scientists, even if they do not specialize in the physics of the stars. T h e Sun presents to the physicist a nearby cosmic laboratory, whose dimensions and physical characteristics could never be duplicated in a terrestrial laboratory. For example, Figure 1.7 shows a solar flare erupting above a sunspot. This event is an explosive release of energy stored in twists of coronal magnetic fields. Study of solar flares gives insight into the magnetic instabilities which occur both in the Sun and, on a reduced scale, in the plasma physics laboratory. T h e

The Sun among the Stars

13

1.7 A large solar flare is seen erupting in this image of the Sun in Ha (hydrogen light). The flare is the bright emission at lower right, above a pair of large sunspots. The flare's energy, stored in solar magnetic fields, is triggered and suddenly released by still unknown processes. This flare sent a blast wave of high-energy particles, plus x-rays and other radiation, to Earth to create northern lights, upset power grids, and cause a host of other tenestrial effects. (Courtesy Sacramento Peak Observatory, AURA.)

understanding that comes from study of magnetic interactions in flares may some day prove useful in terrestrial applications, such as the magnetic confinement of very hot gases required for some approaches to energy production by controlled thermonuclear fusion. Another aspect of the Sun's magnetism is of potential importance to all of us, scientists and nonscientists alike. The Sun's magnetic activity

14

The Sun, Our Star

1.8 The aurora borealis is one of the most familiar of Sun-Earth effects. monly known as the northern lights, these glowing patterns are produced cles ejected by the Sun in a flare strike the Earth's magnetic field, which their energy to atoms in the atmosphere near the poles, causing them to sheets of pale color. This aurora was photographed in Alaska. (Courtesy Lamprecht.)

More comwhen partitransmits radiate in Gustav

T h e Sun among the Stars

15

causes, directly or indirectly, a large variety of solar- terrestrial interactions. Some are by now well-known, such as the disturbances of terrestrial communications or electrical power generation following a large flare, or the beautiful forms of the aurora borealis which also follow large flares (Figure 1.8). T h e cycle of solar magnetic activity causes these effects to vary in frequency, and in size, with an approximately 11-year period. These and certain other cycle-linked terrestrial magnetic variations are well established. Quite likely, however, there are other, more subtle linkages which cause earthly climate and weather conditions to depend upon goings on in the Sun. Because of the enormous importance of weather and climate in our daily lives, the search for such linkages is an important aspect of solar research. In later chapters we will examine the Sun as a magnetic star. We will discuss how its magnetic fields are thought to be generated, how they interact with the very hot gases of the corona, and how their influence is transmitted to Earth. But before introducing all the theatrics of magnetic activity—sunspots, prominences, flares, the hot corona, the solar wind—we will begin by looking closely at the face of the "quiet" Sun. Our investigations will then take us to the innermost core of the Sun, and eventually to the outermost reaches of the solar system, where the solar wind merges into the space between the stars and the Sun's influence finally ends.

16

The Sun, Our Star

2. Studying the Face of the Sun

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Τ Τ e all know the Sun as a hot and bright disk in the sky. Most of us have squinted at the Sun occasionally out of passing curiosity about our own star. We don't learn much except that the experience can be painful and, if we prolong it, dangerous to our eyes. Yet occasionally most of us idly wonder what the Sun is really like: What is it made of, why is it so hot, how long will it shine so steadily? A century ago such questions were often dismissed as unanswerable, fit only for the musings of philosophers. Yet today astronomers claim to know the answers to these questions, and others far more subtle. To find out how astronomers seek such answers, and to learn some answers for ourselves, we will now take a much closer look at the face of the Sun than we ever could with the naked eye. Let us spend an imaginary day visiting a modern solar observatory, to see the Sun as professional astronomers see it. While we could pick any of a dozen or more large solar observatories for our visit, we shall choose the solar facilities of Kitt Peak National Observatory, located about 50 miles west of Tucson, Arizona. We will leave Tucson for the drive up Kitt Peak well before dawn, in order to be at the solar telescope just after sunrise. Experience has shown that the best solar image quality, or "seeing," occurs in the early morning hours. Later in the morning the Sun will warm up the telescope structure and the surrounding terrain, creating atmospheric disturbances that degrade the quality of telescopic images. As we arrive at the McMath Solar Telescope at Kitt Peak, we may be surprised to discover that it looks very different from the "nighttime" telescopes scattered about the peak (Figure 2.1). The unusual design is due to the Sun's enormous brightness compared with that of other stars. Because of its closeness, the Sun is more than 10 billion times brighter than the next brightest star in the sky, and 10 billion times 10 billion times brighter than the faintest stars studied at Kitt Peak through nighttime telescopes. The primary collecting mirror of a 17

2.1 An aerial view of the summit of Kitt Peak, near Tucson, Arizona. This National Observatory has numerous medium and large stellar telescopes, including the large 4-meter (158-inch) aperture telescope at far right. Such telescopes have conventional hemispherical domes which are usually built upon raised piers to provide better "seeing." The McMath Solar Telescope, the world's largest solar telescope, is located in the lower left. Its unusual long diagonal tube is in striking contrast to the stellar telescopes. As described in the text, this unusual design derives from the enormous brightness of the Sun compared to other stars. (Courtesy Kitt Peak National Observatory, AURA.)

2.2 (Top) A close-up photo of the McMath telescope. The huge coelostat is visible at the top of the larger vertical tower. The smaller vertical tower at the right is a separate solar telescope used primarily to measure solar magnetic fields. Most of the McMath telescope structure lies underground, as indicated below. (Bottom) A sketch of the optical layout of the McMath telescope. Sunlight strikes the 80-inch heliostat at the top of the vertical tower and is reflected 450 feet diagonally downward along the polar axis to a 60-inch image-forming minor near the bottom of the tunnel. This mirror in turn reflects the light, via a third 48-inch flat mirror, into the observing room where it forms the primary solar image. (Courtesy Kitt Peak National Observatory, AURA.)

18

The Sun, Our Star

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!

4

Studying the Face of the Sun

19

m o d e m nighttime telescope has a very large diameter and a short focal length (the distance from the mirror to the principal focus) in order to concentrate as m u c h light from the faint stars into as small and bright an image as possible. If bright sunlight were focused in such a stellar telescope, it would create a very intense hot image, heating and warping the optics and tarnishing coatings on mirrors. Because the McMath telescope was built primarily for solar studies, the degree to which it concentrates the light in forming an image is m u c h less; it has a very long focal length. Furthermore, although it is the world's largest solar telescope, its primary imaging mirror, with diameter 1.5 meters, is rather small compared with those of the largest stellar telescopes, which lie in the 4-to-6-meter range. Figure 2.2 shows a closeup view and optical layout of the McMath telescope. A flat heliostat mirror at the top of a vertical tower catches sunlight and sends it down the long diagonal tube, which is aligned precisely parallel to Earth's rotation axis. T h e heliostat mirror rotates in the opposite direction from the Earth's rotation, so that its orientation is held stationary in space and is positioned so that sunlight is continuously reflected down the tube from sunrise to sunset. At the bottom of the tube, about 140 meters (450 feet) away is the 1.5 meter-diameter primary mirror, which reflects the light 90 meters (300 feet) back up the tube, where it forms an image of the Sun. A third flat mirror reflects the image vertically downward into the observing room, where it appears on a large observing table, ready for analysis by various optical instruments. Let us now walk down the long, subterranean corridor leading to the observing room. In the center of the high-ceilinged room is the large round observing table (Figure 2.3). This is actually the top of a vertical spectrograph, an instrument we shall peer into in a few moments. Now, however, let us don a pair of the dark welder's glasses that are kept ori hand for close inspection of the solar image, and look at the face of the Sun. The Solar

Granulation

T h e bright surface of the Sun, whose image is spread out before us on the observing table, is called the photosphere, or light sphere. T h e McMath telescope produces an image of the photosphere 80 centimeters in diameter—the largest solar image produced by any existing telescope. First-time viewers are struck by the wealth of detail visible in. the photosphere—especially if the air is still and the image crisp. O n e of the first things to be noted is that the photosphere is not smooth and uniform, like a white billiard ball. Rather, it appears grainy, somewhat 20

The Sun, Our Star

2.3 Two solar astronomers squint as they align the primary McMath solar image over the spectrograph prior to starting their observation. For detailed examination of the bright solar image, it is helpful to wear dark sunglasses. (Courtesy Kitt Peak National Observatory, AURA.)

as if it were covered with innumerable grains of wheat, all packed together (Figure 2.4). This pattern is known as the solar granulation. It can be seen only when the Earth's atmosphere is stable, so that the telescopic image is sharp enough that the tiny grains do not appear blurred. The individual grains, called granules, may appear tiny in the telescope image, but their actual physical dimensions are rather large by terrestrial standards. There size is typically about 1500 kilometers— larger than the length and breadth of Texas. Figure 2.5 is a highly magStudying the Face of the Sun

21

• 2.4 Seen in a telescope under conditions of good "seeing," the Sun's surface is grainy. In this image of part of the solar disk, shown with the solar limb for scale, individual grains, or granules, appear as tiny structures only the size of the period at the end of this sentence. The small square encloses a{i area equivalent to that in the highly magnified view of Figure 2.5. (Courtesy Mt. Wilson Observatory.)

22

The Sun, Our Star

nified image of the granulation, showing its detailed structure along with a silhouette of the state of Texas for size comparison. The granules appear as bright areas, separated by narrow, darker intergranular lanes. The brightness of the granules relative to the intergranular lanes suggests that they are hotter; detailed measurements show their temperature excess, relative to the intergranular lanes, to be about 400°K. Since practically everything on the Sun is large by terrestrial standards, our awe of earthly size comparisons soon fades. The really impressive aspect of the granules is their state of dynamic motion. As we look at the granulation imaged on the observing table, it is difficult to make out this motion, for each granule has a lifetime of many minutes, and the eye soon tires of trying to follow the gradually changing details. But we may look at a series of time-lapse images of the granulation, taken every 15 seconds and then projected as a high-speed motion picture. As we sit in a darkened room at the observatory and watch such a motion picture, we immediately see that granules are in a constant state of eruptive motion. The Sun's surface looks something like the surface of a giant cauldron of boiling liquid. Hot and bright granules erupt from the interior at a speed of perhaps 500 meters per second, or about 1000 miles per hour, and spew into the overlying rarified atmosphere. There they expand and cool, as they radiate away the extra heat they have brought up from the interior. Having thus cooled, the gases become heavier and sink again, running down in the intergranular lanes and appearing dark against the hotter rising granules. During each eruption of a granule, matter is flung upward a distance of perhaps 100 kilometers (60 miles), and after cooling the matter drains an equivalent distance downward again in the intergranular lane. The duration of one of these granular eruptions is perhaps 8 minutes, but no sooner has the gas drained back than new gas is flung upward again. Each outburst is accompanied by a thunderous roar (could we but hear it across the silent vacuum of space that separates us from the Sun), for which a close analogy might be the roaring of an erupting volcano. The sound waves from granule eruptions strengthen as they propagate into the overlying solar atmosphere. Soon they turn into shock waves—sonic booms that dwarf any ever heard on Earth. It is possible, by using a homely example, to gain a vivid picture of what granulation is like, and what its origins are. Put your eye close to the wall of a glass pot full of bubbling oatmeal—and then imagine that each erupting bubble is magnified 10 million times until it is larger than the size of Texas. The analogy is not a bad one. In a pot of boiling oatmeal, heat is imparted to the fluid nearest the hot bottom of the pot

Studying the Face of the Sun

23

2.5 A close-up of the solar granulation. A silhouette of the state of Texas is superimposed for size comparison. The bright granules are about 400°Κ hotter than the narrow, dark intergranule lanes. Centered in the picture is a dark pore (see Chapter 4). The very smallest bright features are known as solar filigree and are probably the site of concentrated magnetic fields. (Courtesy Sacramento Peak Observatory, AURA.)

and is carried upward by rising fluid. The hot oatmeal bubbles are more buoyant than their surroundings and rise, to liberate their heat at the top. After the heat is freed, the bubbles cool and become denser than the new hot bubbles rising from below, so the surface layer sinks to become reheated. This process, in which heat is carried from the bottom of the pot to its top by rising hot bubbles, is called convection. For the Sun, calculations indicate that convection is an extremely efficient way of transporting heat energy outward, and in fact virtually all of the energy that heats the surface to its temperature of 5800° Κ (and is in turn radiated to Earth as heat and light waves) is first brought to the surface by convection. Convection acts with great efficiency throughout the outermost 200,000 kilometers of the Sun (about 30 percent of the radius), known as the convection zone. The granulation we see at the solar photosphere is just the very top of a seething cauldron

24

The Sun, Our Star

that extends downward into the Sun a distance more than half as great as the distance from the Earth to the moon.

The Temperature

of the Solar Surface

As we mentioned in Chapter 1, the temperature of the Sun is about 5800° K. This may be measured from the light striking the McMath observing table in several ways. The most straightforward is from the brightness of the solar image, which can be directly related to the brightness of the solar surface itself (after appropriate allowance is made for the size and focal length of the telescopes, imaging mirror, and for the absorption of sunlight in the Earth's atmosphere and in the telescope optics). The surface brightness of a "black body" (that is, a perfect emitter) as hot as the Sun depends quite sensitively on its temperature (Figure 2.6). If the Sun's surface were only 10 percent hotter (6380° Κ instead of 5800°K), it would appear about 50 percent brighter in visible light. Thus simply measuring the brightness of a solar image, which can be done within a fraction of a percent, would seem to be a very accurate way to determine the solar surface temperature, provided we can adequately compensate for light losses in the Earth's atmosphere and telescope (by no means a simple task). The surface temperature measured this way is termed the brightness temperature. One problem with estimating the Sun's temperature simply from its surface brightness is that we have no a priori assurance that the Sun emits like a black body. However, support for that assumption comes from looking at the color distribution of solar radiation. The radiation from a black body has a precisely defined color-dependence (Figure 2.6) known as the Planck function. It turns out that the color distribution of solar radiation closely approximates the Planck function. Furthermore, measurement of the relative intensity of solar emission at different colors gives a color temperature in very good agreement with the brightness temperature. A close look at the brightness of the image at the McMath telescope shows that it is not uniform over the disk of the image. Apart from the small-scale fluctuations in the granulation, there is an overall decrease in brightness from the center of the disk to the limb (compare Figure 2.4). The center of the solar disk is more than 50 percent brighter than near the limb. This limb-darkening implies that the brightness temperature of the solar surface is more than 10 percent lower when measured near the limb than near disk center. If the limb-darkening represents a true decrease of temperature toward the limb, we would expect

Studying the Face of the Sun

25

WAVELENGTH

(microns)

2.6 "Blackbody" curves showing how the intensity of radiation from perfectly efficient light emitters varies with wavelength, or color of the light. While real stars are not perfect emitters, the curves give an approximation of how the intensity of their radiation varies with color. An 8000° Κ star (such as Altair) is seen to emit most of its energy in the invisible ultraviolet, while a 3500"Κ star (such as Antares) emits most of its energy in the invisible infrared. A 5800°Κ star like the Sun emits most of its energy in the visible range. Note also that the intensity emitted per unit area of the star varies enormously with temperature (vertical scale at left).

t h e color t e m p e r a t u r e to d e c r e a s e toward t h e l i m b as well, a n d this in t u r n implies t h a t t h e limb s h o u l d b e s o m e w h a t r e d d e r in color t h a n t h e disk c e n t e r . Detailed m e a s u r e m e n t s show t h a t i n d e e d t h e emission does b e c o m e noticeably r e d d e r in color toward t h e limb of t h e S u n .

26

The Sun, Our Star

T h e upshot of both brightness and color temperature measurements is that the Sun's surface temperature, while equaling 5800° Κ when averaged over the disk, is significantly hotter (about 6390° K) at the center of the disk, and significantly cooler (about 5000° K) near the extreme limb. It would seem very strange if the Earth in its orbit were always positioned directly over a hot region on the Sun, so that this region always appeared at disk center, and fortunately there is a more reasonable explanation. As we shall see below, the real reason is that when we look "straight down" at the center of the solar disk, our line of sight penetrates to deeper and hotter regions, while when we look at a large slant angle near the limb we see higher and somewhat cooler regions.

The Solar Spectrum—Coded

Messages from Sunlight

Although the view of the Sun's image through a large telescope shows us granulation and other details that are unseeable by the unaided eye, much more information is carried in the light from the Sun, and from the stars, than can ever be gleaned from an image such as the one spread out on the observing table of the M c M a t h telescope. Within the shaft of sunlight striking the table there is a wealth of coded information—on the chemical composition of the Sun, the motions of its gases, their temperature, pressure, and density, the strength of the magnetic fields that permeate the photosphere, and more. Indeed, we have already referred to some of that information in describing the violent motions of granules, without saying how it is known. But in order to go further in our exploration of the Sun, we must understand how to decode the messages within the light from the stars. T h e key to interpreting the messages carried in sunbeams is a lightanalyzing instrument called a spectrograph. Almost every large solar or stellar telescope is equipped with a spectrograph for analyzing the light which its mirrors or lenses collect. T h e M c M a t h Solar Telescope has several powerful spectrographs, including the one upon whose top surface we saw the projected image of the Sun (see Figure 2.2). A spectrograph is a device for splitting light up into its component colors. Every reader is familiar with the colored solar spectrum, for it is produced frequently in n a t u r e — i n rainbows, for example—or in man-made objects such as a cut-glass chandelier. In rainbows or chandeliers, the component colors of light are bent, or dispersed, into different directions by refraction: light rays of different colors travel at different speeds through the water or glass medium, and as a result they

Studying the F a c e of the Sun

27

EXIT PORT

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CAMERA MIRROR

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C O L L I MATING MIRROR

2.7 Schematic diagram of a spectrograph such as that at the McMath telescope. The two cross-hatched beams show the path taken by red (longer wavelength) and violet (shorter wavelength) light after having been dispersed by the diffraction grating.

emerge in slightly different directions. While some astronomical spectrographs use prisms to disperse the light into its component colors, most use diffraction gratings instead. In both cases light is sorted according to its color, but diffraction gratings spread the light over larger angles and permit the scientist to select a very narrow band of colors for study. Figure 2.7 is a schematic diagram of the large spectrograph which extends 17 meters (55 feet) below the observing table at the McMath telescope. Light from the part of the solar image to be analyzed enters the spectrograph through a narrow entrance slit located at the center of the table, and is reflected by a mirror to the large diffraction grating, which then produces a many-colored spectrum of the light from the chosen line on the solar surface. A second mirror within the spectrograph catches the light dispersed by the grating and reflects it back to the underside of the observing table. Visitors like ourselves may look down through an aperture in the table top known as the exit port, and will be rewarded by the view of a rainbow of pure color, ranging from deep violet at one end through blue, green, yellow, orange, and red to very deep red at the other end. Normally, however, a long strip of photographic film is placed at the exit port and records a picture of the entire spectrum. Figure 2.8 shows the photographic image of a portion of the visible solar spectrum as recorded by a modern grating spectrograph employing a diffraction grating. T h e color of the light which created this

28

The Sun, Our Star

Studying the Face of the Sun

29

image varied f r o m d e e p violet at t h e upper left to d e e p red at t h e lower right. Every possible color in b e t w e e n is represented by t h e intensity of t h e light at t h e appropriate position along t h e spectrum. It is i m m e d i ately apparent that t h e intensity is n o t u n i f o r m l y spread along t h e spectrum. At a great n u m b e r of places t h e intensity is very low, so that dark vertical lines cross t h e s p e c t r u m , seemingly at r a n d o m locations. T h e s e dark lines are t h e cipher that e n c o d e s t h e secrets of t h e S u n , and w e shall n o w f o c u s our attention o n cracking their code. The Fraunhofer

Spectrum

Visible light is a f o r m of energy, radiated f r o m o n e point to a n o t h e r in e l e c t r o m a g n e t i c waves. Light waves are only o n e variety of electrom a g n e t i c radiation, and are identical in their physical properties to other e l e c t r o m a g n e t i c waves s u c h as radio waves, infrared (heat) waves, ultraviolet radiation, x-rays, and g a m m a rays. T h e entire solar e l e c t r o m a g n e t i c s p e c t r u m is s h o w n in Figure 2.9, arranged according to increasing wavelength. T h e w a v e l e n g t h of t h e e l e c t r o m a g n e t i c radiation to w h i c h our e y e s are sensitive (that is, visible light) varies f r o m about 0.0004 c e n t i m e t e r s (violet light) to 0 . 0 0 0 7 centimeters (deep red). A c o m m o n unit of m e a s u r i n g s u c h small wavelengths is t h e angstrom (A), equal to 10

8

c m , or 10~ 4 m i c r o n s (ju.m). T h i s d i m e n -

sion is about V200 t h e thickness of a page of this book. By c o m p a r i s o n , standard A M broadcast radio waves h a v e a billion times greater wavelength, or several kilometers. At t h e shortest e n d of t h e scale, g a m m a rays h a v e wavelengths a million times shorter t h a n visible light waves.

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2.9 The range of the observed solar spectrum. Electromagnetic radiation from the Sun has been observed so far at wavelengths as shori as 10'3 A (gamma ray emission from solar flares) and as long as several kilometers (very low frequency radio waves from the corona). The ratio of these extreme wavelengths is a factor of 10,000,000,000,000,000. Visible light lies within a comparatively tiny range covering a factor less than 2 in wavelength. However, about half of the total energy emitted by the Sun (shaded) falls within this narrow wavelength interval (compare Figure 2.6).

30

T h e Sun, O u r Star

The spectrum shown in Figure 2.8 covers just the visible part (shown shaded in Figure 2.9) of the entire electromagnetic spectrum. The wavelength of the light that created the image on the upper left side of Figure 2.8 is about 3900 A and that on the lower right, about 6900 A. Along a vertical direction at any position of Figure 2.8, however, the wavelength and color are the same; in that direction the image simply records how the intensity of sunlight at a particular wavelength varied over the spectrograph entrance slit. We may move the Sun's image around over the entrance slit by tilting the telescope mirrors, and see slight variations of intensity along vertical lines in the spectrum as various solar features (for example, dark sunspots) pass over the entrance slit. If we do this simple experiment, however, we will find that the dark lines always remain at substantially the same position, or wavelength, in the spectrum. They seem to be a general property of sunlight. The dark lines in the solar spectrum were first discovered by the English physicist Wollaston in 1802, then rediscovered by the German physicist Joseph von Fraunhofer in 1814, using very primitive spectroscopes. Fraunhofer made a careful map of the dark lines, and labeled the strongest ones with the letters A, B, C, and so on. As a result of this study, the dark lines in the spectrum of the Sun (and later found in stars as well) have become known as Fraunhofer lines. Some of Fraunhofer's original labels are in use today, and are shown in Figure 2.7. Fraunhofer apparently had little idea of the physical mechanism giving rise to dark lines in the solar spectrum, and was content to label them and record their wavelengths. For forty-five years their explanation remained a mystery. Finally, in 1859 the German chemist Gustav Kirchhoff, after a series of experiments, discovered that lines were produced from absorption of light by chemical elements present in the Sun. There is no better way to convey the excitement of this discovery than to quote from a letter written at the time by Kirchhoff's coworker Robert Bunsen to a colleague in England: At present Kirchhoff and I are engaged in an investigation that doesn't let us sleep. Kirchhoff has made a wonderful, entirely unexpected discovery in finding the cause of the dark lines in the solar spectrum, and he can increase them artificially in the sun's spectrum or produce them in a continuous spectrum and in exactly the same position as the corresponding Fraunhofer lines. Thus a means has been found to determine the composition of the sun and fixed stars.

In one of the experiments carried out by Kirchhoff and Bunsen, they found that if different chemical compounds were placed in the flame of Bunsen's newly developed "Bunsen burner," an emission line

Studying the Face of the Sun

31

(o)

(b)

2.10 Three experiments illustrating different types of spectra. In each experiment, light is dispersed by a triangular glass prism after passing through a narrow entrance slit, used to restrict the direction of incident light to a small angle. In (a), light from a transparent hot gas like a bunsen burner flame produces an emission line spectrum. In (b), light from a glowing solid body such as the tungsten filament of an incandescent light bulb produces a continuous spectrum. In (c) the semitransparent hot gas lies in front of a continuous emitter. If (like the burner flame compared to the lamp filament) the gas is colder than the continuous

emitter, an absorption line

(c)

spectrum is produced. This resembles the solar Fraunhofer lines, produced by a colder semitransparent atmosphere overlying the hotter solar photosphere.

spectrum was produced (Figure 2.10a). T h e wavelength of the emission lines observed depended on the chemical composition of the added chemicals. (This experiment was, and remains today, a sensitive test for the presence or absence of various elements in unknown materials.) At wavelengths between the emission lines, little light is produced by the flame. This is simply because the flame is transparent at these wavelengths; our line of sight back through the spectrograph and into the flame passes right through the transparent hot gas without encountering any emitting atoms, unless we are looking at precisely the "right" wavelength for the atoms within the Bunsen burner flame. O n the other hand, when Kirchhoff and Bunsen studied the light from a hot solid body, such as the hot electrode of a carbon arc light (today one would use a tungsten filament lamp), a continuous spectrum was seen, with light emitted at all wavelengths rather than at only a few discrete ones (Figure 2.10b). There is no wavelength at which a

32

The Sun, Our Star

solid carbon electrode or tungsten filament is transparent to our line of sight; at all wavelengths our line of vision is stopped by hot emitting atoms. In a third experiment, Kirchhoff and Bunsen studied the spectrum of a burner flame placed in front of a hot solid source of continuous emission (Figure 2.10c). The discrete lines characteristic of the chemical elements in the burner flame were still present, but at wavelengths in between, where the burner flame was transparent, the line of sight passed directly through the flame to the source of continuous emission behind. If this source is colder than the burner flame (for example, if it is a tungsten lamp run at so low an electric current that it is only red hot) the intensity of the continuous emission does not reach that of the emission lines in the burner flame; these then stand out against the fainter continuum background. But if the continuum source is hotter than the burner flame, as is a modern tungsten lamp run at its rated current, the continuous emission is brighter than the discrete lines from the chemical elements in the burner flame, so that the resulting spectrum is crisscrossed by dark lines, just like the Fraunhofer spectrum of the Sun. The explanation for this result is straightforward. At the wavelength of these discrete lines, where the burner flame is opaque to the line of sight, the continuous spectrum from the background source is absorbed so that it does not reach the spectrograph. If the burner flame is not as hot as the background source, its own emission is not intense enough to replace the light it absorbs, and an absorption line spectrum results. If the flame is hotter than the background source, its emission more than compensates for what it absorbs, and an emission line spectrum results. From these experiments, and comparison with Fraunhofers observations of the Sun, Kirchhoff concluded that a gaseous region, cooler than the solar photosphere, must lie between it and ourselves, and correctly suggested that these cooler gases in fact lie directly above the hot photosphere. Today we call these overlying gases the solar "atmosphere." A comparison of the solar spectrum with laboratory spectra of vaporized chemical elements soon revealed that Fraunhofers C and F lines were due to the element hydrogen, the D line to sodium, the Ε line to iron, and the Η and Κ lines to the element calcium. The G line was actually a blend of lines of iron, calcium, and other elements that could not be separated in spectrographs of the day. The A and Β lines were eventually found to be due to oxygen molecules present in the Earth's atmosphere, rather than in the solar atmosphere.

Studying the Face of the Sun

33

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34

The Sun, Our Star

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Energy Levels and Atomic

Transitions:

Cracking

the Code

The discovery that common terrestrial elements are present in the Sun and stars is a profound one, immediately suggesting the possibility that we can determine not only the presence or absence of chemical elements in the Sun but also the relative abundance of each. It is apparent from Figure 2.8 that some Fraunhofer lines are darker, or stronger, than others, and it is natural to suppose that this is an effect of the chemical abundance of the atom in question. The greater the abundance of absorbing atoms, the darker the absorption line they should produce. However, there are many puzzles in the Fraunhofer spectrum which should be answered before we can very confidently determine the abundance of chemical elements in the Sun. Why are some lines associated with a given element very dark while others, associated with the same element, are so weak as to be nearly invisible? What about the very numerous lines that were not found to correspond to the known spectrum of any element? And why are the lines located at the observed wavelengths, with no apparent pattern? Careful study of the measured wavelengths of lines of certain elements during the late nineteenth century finally did begin to show patterns in their spectra. Most notable was the discovery by the German schoolteacher J. Balmer in 1885 of a distinctive pattern in the lines of hydrogen. In this pattern, which exhibited itself beautifully in the laboratory and in certain stars (Figure 2.11), the lines crowd closer and closer together toward shorter wavelengths, until they merge into each other at a limiting wavelength, called the Balmer limit. Although harder to see in the Sun, because of the presence of so many other lines due to different chemical elements, the pattern is repeated there also. (We now know that because of high temperature in these stars, known as A stars, Balmer's hydrogen lines are unusually strong, while lines of other common elements are weak or absent.) Balmer was able to find, by trial and error, an equation giving to great accuracy the wavelength (λ) of the lines: λ η = 911.6 AJ(l/i — 1 In2) where η = 3, 4, 5, . . . For example, placing π = 3 in the above equation, and solving for λ 3 , one calculates λ3 = 6563 A, the wavelength of Fraunhofers red C line. For π = 4, one obtains λ4 = 4861 A, the wavelength of Fraunhofer's Ε line. In modern notation, members of this series of lines, called the Balmer series, are given the designation Η (for hydrogen) followed by the letters α, β, γ, . . . of the Greek alphabet. The observed wavelengths of the Balmer series, as observed in stars (Figure 2.10) or in the Sun (Figure 2.8), were found to

Studying the Face of the Sun

35

be in precise agreement with the above equation. The wavelengths of the Balmer series are: π 3 4 5 6 7

00

Designation Ha H/3 H-y Ηδ He

Balmer Limit

Wavelength 6563 4861 4341 4102 3970

(A)

3646

The equation given above, which predicts the observed wavelength of the Balmer series very well, appears rather complicated, and when it was discovered by Balmer there seemed no justification for it other than that it matched the data so well. It was Niels Bohr who in 1913 cracked the puzzle of the Balmer series, and in so doing laid the foundations for modern-day quantum mechanics and atomic physics— foundations which underlie many of the advances in pure and applied physics that have been made in the ensuing years. Bohr introduced three new postulates into the science of atomic physics: (1) Atoms can exist only in discrete states, for which the energy bound up in the electrons within the atom has a discrete, or quantized, value. (2) Atoms can shift from one quantized electron energy state to another. When such transitions occur from a state of high energy to one of low energy, light is emitted in discrete units called photons, whose energy is equal to the difference of energy in the initial and final states. Conversely, when a photon of just the correct energy is absorbed by an atom, one of its electrons jumps to a state whose energy is greater than before by just the energy carried by the photon. (3) Finally, the wavelength (λ) of the light emitted or absorbed in a transition is inversely related to the energy (E) of the transition, according to the equation λ = hc/E, where h is a fundamental constant of nature known as Planck's constant, and c is the speed of light. Planck's constant determines a multitude of properties of matter and radiation according to the laws of quantum physics as laid down by Bohr and others. From this equation we see that if the energy difference Ε is large, the wavelength λ must be small; high energies mean

36

The Sun, Our Star

short wavelengths (for example, x-rays or gamma rays). Similarly, low energy transitions emit or absorb long wavelength radiation (for example, infrared or radio waves). With the help of his three postulates, Bohr tried to understand the spectrum of hydrogen. Hydrogen atoms, consisting of a single proton with a single electron bound to it, are the simplest of all atoms, and for this atom at least the application is relatively straightforward, although at the time it was a stroke of genius. Bohr was able to predict the allowed energies for the bound electron, and from the difference in these energies he calculated the wavelengths of light which would be emitted or absorbed when hydrogen atoms made a transition from one state to another. His equation for these wavelengths agreed precisely with the equation Balmer had derived earlier by trial and error. This remarkable theoretical confirmation for hydrogen demonstrated the correctness of quantum mechanics, which was soon extended to m u c h more complex atoms. Today almost all Fraunhofer lines have been identified, and their wavelengths explained by Bohr's theory and extensions of it. A useful way to visualize atomic energy levels and transitions between them is through an energy-level diagram. Such a diagram is shown for hydrogen in Figure 2.12. In this diagram the energy of an atomic state is proportional to its vertical distance below the level Ε = 0 (at the top of the diagram). According to Bohr's theory applied to hydrogen, the energy is proportional to 1 In2, where π is the quantum number describing each level. The situation is analogous to a bizarre staircase (Figure 2.12b), where the depth of each tread below the top of the stairs is proportional to 1 In2, η = 1, 2, 3, . . . As a ball bounces down a staircase it becomes more "tightly bound" to the Earth, and the "binding energy" becomes available, either in the form of kinetic energy associated with the ball's bounce or a small amount of heat generated as the ball strikes the step below. In the hydrogen atom "staircase" shown, electrons give rise to the Balmer series of spectral lines when they fall to the second step from the bottom (n = 2). If an electron falls from the third step to the second, it releases a photon whose energy is proportional to the difference in height of the two steps; the wavelength of that photon is 6563 A, corresponding to the H a line. Or, if it skips from the fourth to the second step, the atom releases an H/3 photon, and so on. Similarly, if a hydrogen atom in the solar atmosphere whose electron is in the π = 2 level intercepts a photon from the photosphere whose energy is just enough to lift that electron to the third level (that

Studying the Face of the Sun

37

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2.12 (a) An energy level diagram for hydrogen, the simplest of all atoms. The energy levels are labeled by the quantum number n; the Balmer series of lines connects the level η = 2 to all higher states, while the Lyman series connects the η = 1 (ground) state to all higher states. The right-hand-anow in each series connects with a continuum of energy states above the ionization limit; radiation in the Balmer continuum or Lyman continuum occurs at wavelengths shorter than the series limit, and appears over a continuous range of wavelengths, rather than as discrete lines, (b) A "staircase" analogy, where a ball bouncing down an unevenly built staircase release energy proportional to the size of the steps. Two balls are shown, releasing energy proportional to Ha and Hß photon energies.

is, a photon whose wavelength is 6563 A), t h e n the atom will absorb the photon; the energy o f the photon will be used up in raising the electron up to the third level, and the photon will disappear. A dark absorption line appears in the solar spectrum at the wavelength where those photons are lost. Similarly, the dark line at the wavelength of H/3 shows that other electrons are being raised from the second to the fourth level, and so on. Transitions are also possible that end on states other than η = 2. A particularly important set is the group ending on the state π = 1, shown dotted in Figure 2.12. T h e s e transitions also form a series, known as the Lyman series. As may be seen in the diagram, the energy of Lyman lines is considerably greater than that o f Balmer lines, and so

38

The Sun, Our Star

their wavelength is shorter. The first member of the series, Lyman a (denoted La in the diagram) corresponds to the transition from η = 2 to η = 1 and has a wavelength of 1216 A. This very short wavelength lies in the extreme ultraviolet part of the spectrum, to which the human eye is insensitive. In addition, such short wavelengths of light are totally absorbed by the Earth's atmosphere. Hence, although the Lyman lines were predicted to be observed in the solar spectrum (and also were photographed in the laboratory), it was not until the advent of space vehicles that their emission from the Sun was actually observed. The energy levels of all atomic species may be schematized by diagrams such as that of Figure 2.12. However, for all other atoms and ions the diagrams are much more complicated than that for hydrogen. Figure 2.13 shows on the left the energy level for sodium. The two dotted lines mark the transition corresponding to the solar D line, which we can now identify as due to sodium. (Fraunhofers early map of the solar spectrum did not have the spectral resolution to show what even a very modest spectrograph can detect today: the D line in the Sun is composed of the two components, labeled and D 2 , with wavelengths of 5896 and 5890 A, respectively.) On the right hand side is the even more complex energy level diagram for nickel, showing that the transition arrays can get extremely complicated. In these diagrams the letters S, P, D, and so on, and the small superscripts and subscripts, indicate subsidiary quantum numbers other than the "principal" quantum number n. These numbers enter the quantum theory when it is extended to more complex atoms.

Chemical

Composition

of the Sun and Stars

Some lines in the Fraunhofer spectrum are stronger than others. Among the very strongest are the ones first given alphabetical designation on Fraunhofers original list. Figure 2.14 shows a tracing of the variation of intensity with wavelength near the sodium (Na) D lines. The strength of absorption lines is measured by the total amount of light they remove from the spectrum, or the area enclosed between the line intensity profile and the flat continuum level which would be present if there were no spectral line. The Na D lines are about 1000 times as strong as the weakest lines in Figure 2.14. With very accurate recording, one can detect lines that are many times weaker than the weakest shown in the figure.

Studying the Face of the Sun

39

[

Wavelength 2.14 High-resolution trace of the spectrum near the Na D , and D 2 lines. This spectrum resolves, or distinguishes, spectral features whose wavelengths are as close as 1 part in 200,000. The D1 and D 2 lines are among the stronger lines in the spectrum, which is of course why they were seen and labeled in Fraunhofefs original observations. Their strength, as measured by their area (that is the total amount of light they subtract from the spectrum), is several thousand times as great as the weakest spectral feature detectable on this trace. (Courtesy McMath-Hulbert Observatoy.)

2.13 Energy-level diagrams for two common elements in the Sun. The slanted lines are labeled by the wavelength of the spectral lines produced by transition between the states which they connect. (Top) Sodium has a relatively simple energy-level diagram. Fraunhofers D line actually consists of the two transitions D , and D 2 shown at 5896 and 5890A which connect the ground state to the first excited level. (These lines may be easily seen in Figure 2.8.) (Bottom) The nickel atom has a much more complex energy-level diagram, with actually many more transitions than are shown here. The dashed lines are "intersystem" transitions between different families of atomic states; owing to the rules of quantum mechanics, these transitions tend to be weaker than transitions within the same family.

The hydrogen Η α line, or Fraunhofers C line (Figure 2.15, top), is not as deep as the Na D lines at the center, but its profile is much broader, so the total light subtracted from the spectrum by H a is therefore greater. At the extreme end of the scale is the absorption of the Κ line of Ca + (Figure 2.15, bottom), which has extremely broad "wings" on either side that contribute additional absorption. Why are some spectral lines strong, in that they subtract a large amount of energy from the spectrum, while other lines are weak? Lines tend to be strong if the corresponding chemical element is abundant in the Sun's atmosphere. Thus, other things being equal, a line due to iron will be much stronger than one due to gold, for in the Sun as on Earth, iron is much more abundant than gold. However, other things are generally not equal. For one thing, atomic transition probabilities vary in a complex way from line to line. This may be calculated or measured in the laboratory and allowed for in the abundance determination. In addition, the fraction of atoms whose electrons are in the correct energy state (that is, the correct "energy stair tread") to produce a given absorption line depends sensitively upon the temperature. If the gas is hot, many atoms will be found with their outer electrons (the ones involved in emission or absorption) in high-lying states; if the gas is cooler, there will be more atoms in low-lying energy states. The population of the various energy states of a particular type of atom is controlled by the energy of collisions with electrons and other atoms in the Sun's atmosphere; this energy in turn varies with the temperature. To complicate matters further, the outer electrons in atoms of some elements are only rather weakly bound to the atom (using the staircase analogy, the treads are not very deep), and electron collisions easily knock these electrons completely out of their atoms. In such an atom, called an ion, it is of course only the remaining electrons which can make transitions, and its energy level staircase is entirely different from that of the parent atom. Therefore an ion will produce entirely different absorption lines than does its parent atom. In determining the total chemical abundance of an element, we must calculate the abundance of atoms and ions separately, and later add them together. It all sounds extremely complicated, and so it would be, except for a fortunate circumstance. The density of atoms at the surface of the Sun is so great that the atoms collide with each other many thousands of times every second. These collisions distribute the atoms among their various energy levels, and among the various ionization states, according to their energies in a precise way that depends only on the temperature. If we know the temperature (which, as we have seen, can be mea-

42

The Sun, Our Star

Studying the Face of the Sun

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