The Nature of Light Ie early 1800s, the French philosopher Auguste Comte ar-I that because the stars are so far away, humanity would iitvur know their nature and composition. But the means to learr about the stars was already there for anyone to see— s:arlig!it just 3 f«w yearS 'a^et Comte's bold pronouncement, scientist began analyzing starlight to learn the very things thai he h.ul di'emed unknowable. We now know that atoms of each chemical element emir and absorb light at a unique set of wavelengths characteristic of that cement alone. The red light in ihe accompanying image of a gas in space is of a wavelength emitted by nitrogen and no ■ lemcnt; the particular green light in this image is unique to oxygen, and the particular blue light is unique to helium. The •'■Hgiit uom nearby planers, Hisrant stars, and remote galaxies also ■-/■has characteristic ''fingerprints" that reveal the chemical composition of these celestial objects. la this chapter we learn about the basic properties of light. ' Light has a dual nature: It has the properties of both waves and .particles. The light emitted by an object depends upon the object's remperntLire; we can use this to determine the surface temperatures of stars. By studying the structure of atoms, we will Icam why each element emits and absorbs light only ar specific wavelengths and will see how astronomers determine what the atmo-' spheres of planets and stars are made of, The motion of a light source alio affects wavelengths, permitting us to deduce how fast Hnrs and other objects are approaching or receding. These are but ^» few of the reasons why understanding light is a prerequisite to ^aderstanding the universe. The Ring Nebula is a shell of glowing gases surrounding a dying star. Tne spectrum of the emitted light reveals which gases are present. (huLUe Heritage Teaii, AURA/b l bcl/NASA] Galileo Galilei and Isaac Newton were among the first to ask basic questions about light. Does light travel instantaneously from one place to another, or does it move with a measurable speed? Whatever the nature of light, it does seem to travel swiftly from a source to our eyes. We see a distant event before we hoar the accompanying sound. (For example, we see a flash of lightning before we hear the thunderclap.) In the early 1600s, Galileo tried to measure the speed of light. He and an assistant stood at night on two hilltops a known distance apart, each holding a shuttered lantern. First, Galileo opened the shutter of The speed af light in a vacuum is a universal constant: It has the same value everywhgre in the cosmos Uarmng Goals By reading the sections of this chapter, you will learn How we measure the speed of light 3*2 How we know that light is an electromagnetic wave How an object's temperature is related to the radiation it emits ^ The relationship between an object's temperature and the amumt of energy it emits The evidence that light has both particle and wave aspects 5-6 How astronomers can detect an object's chemical composition by studying the light it emits 5-7 The quantum rules that govern the structure of an atom 5-8 The relationship between atomic structure and the light emitted by objects 5-9 How an object's motion affects the light we receive from that object Chapter 5 r The Nature of Light 99 his lantern; as soon as his assistant saw the flash of light, he opened his own. Galileo used his pulse as a timer to try to measure the time between opening his lantern and seeing the light from his assistant's lantern. From the distance and time, he hoped to compute the speed at which the light had traveled to the distant hilltop and back. Calilco found that the measmed time failed to increase no-ticeahly, no matter how distant the assistant was stationed. Galileo therefore concluded that the speed of light is too high tn be measured by slow human reactions. Thus, he was unable to tell whether or not light travels instantaneously. The Speed of Light: Astronomical Measurements The first evidence that light does not travel instantaneously was presented in 1676 by Olaus Römer, a Danish astronomer. Remer had been studying the orbits of the moons of Jupiter by carefully timing the moments when they passed into or out of Jupiter's shadow. To Rimer's surprise, the timing of these eclipses of Jupiter's moons seemed to depend on the relative positions of Jupiter and Earth. When Earth was far from Jupiter (that is, near conjunction; see Figure 4-6), the eclipses occurred several minutes later than when Earth was close to Jupiter (near opposition). Reiner realized that this puzzling effect could be explained if light needs time to travel from Jupiter to Earth. When Earth is closest to Jupiter, the image of one of Jupiter's moons disappearing into Jupiter's shadow arrives at our telescopes a little sooner than it does when Jupiter and Earth ate farther apart (Figure 5-1;. The range of variation in the times at which such eclipses are observed is about 16.6 minutes, which Romer interpreted as the length of time required for light to travel across the diameter of Earth's orbit (a distance of 2 AU). The size of Earth's orbit was not accurately known in Rimer's day, and he never actually calculated the speed of light. Today, using the modern value of 150 million kilometers for the astronomical unit, Romer's method When Earrh is near Jupiter, ^ we observe edipses ^ of Jupiter's moons earlier than expected. Sun Ö lEarth When Earth is far from Jupiti we observe eclipses of Jupirer's moons later than expected. Figure 5-1 Homer's Evidence That Light Ooes Not Travel instantaneously The timing of eclipses of Jupiter's moons as seen from Earth depends on the EarthOupiter distance. Ramer correctly attributed this effect to variations in the time required ~or light to travel from Jupiter to Earth. II Stationary ! mirror i source Observer Q Figure 5-2 The Fizeau-Foucault Method of Measuring the Speed of Light Light from a ligh: source (1) is reflected off a rotating mirror to a stationary mirror (2) aid from there back to the rotating mirror (3), "he ray that reaches the observer (4] is deflected away from the path of the initial beam because the rotating mirror has moved slightly while the light was making the round trip. The speed of light is calculated from the deflection angle and the dimensions of the apparatus. yields a value for the speed of light equal to roughly 300,000 km/s (186,000 mi/s). The Speed of Light: Measurements on Earth Almost two centuries after Remer, the speed of light was measured very precisely in an experiment carried out on Earth. In 1850, the French physicists Armand-Hippolyte Fizeau and jean Foucault built the apparatus sketched in Figure 5-2. Light from a light source reflects from a rotating mirror toward a stationary mirror 20 meters away. The rotating mirror moves slightly while the light is making the round trip, so the returning light ray is deflected away from the source by a small angle. By measuring this angle and knowing the dimensions of their apparatus, Fizeau and Foucault could deduce the speed of light. Once again, the answer was very nearly 300,000 km/s. The speed of light in a vacuum is usually designated by the letter c (from the Latin celeritas, meaning "speed"). The modern value is c = 299,792.458 km/s (186,282.397 mi/s). In most calculations you can use c = 3.00 X 105 km/s = 3.00 X 10£ m/s The most convenient set of units to use for c is different in different situations. The value in kilometers per second (km/s) is often most useful when comparing c to the speeds of objects in space, while the value in meters per second (m/s) is preferred when doing calculations involving the wave nature of light (which we will discuss in Section 5-2). CAUTION! Note that the quantity c is the speed of light in a vacuum. Light travels more slowly through air, water, glass, or any other transparent substance than it does in a vacuum. In our study of astronomy, however, we will almosi always consider light traveling through the vacuum {or near-vacuum) of space. The speed of light in empty space is one of the most important numbers in modern physical science. This value appears in many equations that describe atoms, gravity, electricity, and mag- Figure 5-3 A Prism and a Spectrum When a beam of sunlight passes through a glass prism, the light is broken into a rainbow-colored band called a netism. According to Einstein's special theory of relativity, nothing can travel faster than the speed of light. 5-2 Light is electromagnetic radiation and ts characterized by its wavelength Light is energy. This fact is apparent to anyone ItlS^ who has felt the warmth of the sunshine on a summer's day. But what exactly is light? How is it produced? What is it made of: How does it move through space? Scholars have struggled with these questions throughout history. Visible tight, radio waves, and X rays are all the same type oF wave: They differ only in their wavelength First p lis I li break*, light mm iii spectrum Figure 5-4 Newton's Experiment on the Nature of Light li a crucial experiment, Newton :ook sunlight that had passed throjgh a prism and sent it through a second prism. Between the two prisms was a screen with a hole in it that allowed only one color of the spectrum to pass through. This same color emerged from the second prism. Newton's experiment spectrum- The wavelengths of different colors of light are shown on the rignt (1 nm = 1 nanometer = 10~9 m). Newton and the Nature of Color The first major breakthrough in understanding light came from a simple experiment performed by Isaac Newton around 1670. Newton was familiar with what he called the "celebrated Phenomenon of Colours," in which a beam of sunlight passing through a glass prism spreads out into the colors of the rainbow (Figure 5-3). This rainbow is called a spectrum (plural spectra). ^5MfeL^. Until Newton's time, it was thought that a prism somehow added colors to white light. To test this idea, Newton placed a second prism so that just one color of the spectrum passed through it (l;igure 5-4). According to the old theory, this should have caused a further change in the color of the light. But Newton found that each color of the spectrum was unchanged by the second prism; red remained red, blue remained Screen lets only one Second prism hends light, bur dots nut diange its colui proved that prisms do rot add color to light but merely bend different colors through cifferent angles. It also showed that white light, sich as sunlight, is actually a combination of all the ccloi b tl idl appear in its spectrum. 1Ó0 Chapter 5 The Nature of Light 101 blue, and so on. He concluded that a prism merely separates colors and does not add color. Hence, the spectrum produced by the first prism shows that sunlight is a mixture of ail the colors of the rainbow. Newton suggested that light is composed of particles too small to detect individually. In 1678, however, the Dutch physicist and astronomer Christiaan Huygens proposed a rival explanation. He suggested that light travels in the form of waves rather than particles. Young and the Wave Nature of Light Around 1801, Thomas Young in England carried out an experiment that convincingly demonstrated the wavelike aspect of light. He passed a beam of light through two thin, parallel slits in an opaque screen, as shown in Figure 5-5*7. On a white surface some distance beyond the slits, the light formed a pattern of alternating bright and dark bands. Young reasoned that if a beam of light was a stream of particles (as Newton had suggested), the two beams of light from the slits should simply form bright images of the slits on the white surface. The pattern of bright and dark bands he observed is just what would be expected, however, if light had wavelike properties. An analogy with water waves demonstrates why. AMALQiaX Imagine ocean waves pounding against a reef or ' breakwater that has two openings (Figure SSb). A pattern of ! ripples is formed on the other side of the barrier as the waves [ come through the two openings and interfere with each other, i At certain points, wave crests arrive simultaneously from the i two openings. These reinforce each other and produce high I waves. At other points, a crest from one opening meets a trough from the other opening. These cancel each other out, leaving ; areas of still water. This process of combining two waves also ! takes place in Young's double-slit experiment: The bright bands : are regions where waves from the two slits reinforce each other, . while the dark bands appear where waves from the two slits ; cancel each other. Maxwell and Light as an Electromagnetic Wave The discovery of the wave nature of light posed some obvious questions. What exactly is "waving" in light? That is, what is it about light that goes up and down like water waves on the ocean? Because we can see light from the Sun, planets, and stars, light waves must be able to travel across empty space. Hence, whatever is "waving" cannot be any material substance. What, then, is it? The answer came from a seemingly unlikely source—a comprehensive theory that described electricity and magnetism. Numerous experiments during the first half of the nineteenth century demonstrated an intimate connection between electric and magnetic forces. A central idea to emerge from these experiments is the concept of a field, an immaterial yet measurable disturbance of any region of space in which electric or magnetic forces are felt. Thus, an electric charge is surrounded by an electric field, and a magnet is surrounded by a magnetic field. Experiments in the early 1800s demonstrated that moving an electric charge produces a magnetic field; conversely, moving a magnet gives rise to an electric field. Laser light Bright bands: where light waves Írom the two slits reinforce each other Magnetic field. /Electric field Dark bands: where light waves from the two slits cancel each other (a) An experiment with light (b) An analogous experiment with water waves Figure 5-5 Young's Double-Slit Experiment (a) "Thomas Young's classic rinuhle-slit experiment can easily be repeated in the modern laboratory by shining light fom a laser onto two closely spaced pa'allel sli:s. Alternating dark and bright bands appear on a screen Deyond the slits, (b) The intensity of light on the sceen in (a) is analogous to the height of water waves that pass through a barrier with two openings (The photograph shows this experiment with water waves in a small tank) In certain locations, wave crests from both openings reinforce each other to produce extra high waves. At other locations a crest From one opening meets a trough from the other. The crest and trough cancel each other, producing still water, (trie Schrempp/Photo Hesearchers) In the 1860s, the Scottish mathematician and physicist James Clerk Maxwell succeeded in describing all the basic properties of electricity and magnetism in four equations. This mathematical achievement demonstrated that electric and magnetic forces are really two aspects of the same phenomenon, which we now call elcctromagiietism. By combining his four equations, Maxwell showed that electric and magnetic fields should travel through space in the form of waves at a speed of 3.0 X 105 km/s—a value equal to the best available value for the speed of light. Maxwell's suggestion that Figure 5-6 Electromagnetic Radiation All forms of light consist of The wave is oscillating electric and magnetic fields that move through traveling space at a speed of 3.00 x 10s km/s = 3.00 x 10s rn/s. This in this diieaion figure shows a "snapshot" of these fields at one instant. The distance between two successive crests, Called Lhe wavelength of the light, is usually designated b/ the Greek letter x (lambda). these waves do exist and are observed as light was soon confirmed by experiments. Because of its electric and magnetic properties, light is also called electromagnetic radiation. CAUTION! You may associate the term radiation with radioac-: tive materials like uranium, but this term refers to anything that 1 radiates, or spreads away, from its source. For example, scien-! tists sometimes refer to sound waves as "acoustic radiation." Radiation does not have to be related to radioactivity! Electromagnetic radiation consists of oscillating electric and magnetic fields, as shown in Figure 5-6. The distance between two successive wave crests is called the wavelength of the light, usually designated by the Greek letter A (lambda). No matter what the wavelength, electromagnetic radiation always travels at the same speed c = 3.0 X 105 km/s = 3.0 X 10s m/s in a vacuum. More than a century elapsed between Newton's experiments with a prism and the confirmation of the wave nature of light. One reason for this delay is that visible light, the light to which the human eye is sensitive, has extremely short wavelengths—less than a thousandth of a millimeter—that are not easily detectable. To express such tiny distances conveniently, scientists use a unit of length called the nanometer (abbreviated nm), where 1 nm = 10"9 m. Experiments demonstrated that visible light has wavelengths covering the range from about 400 nm for violet light: to about 700 nm for red light. Intermediate colors of the rainbow like yellow (550 nm) have intermediate wavelengths, as shown in Figure 5-7. (Some astronomers prefer to measure wavelengths in angstroms. One angstrom, abbreviated A, is one-tenth of a nanometer: 1 A = O.i nm - 10~10 m. In these units, the wavelengths of visible light extend from about 4000 A to about 7000 A. We will not use the angstrom unit in this book, however.) Visible and Nonvisible Light Maxwell's equations place no restrictions on the wavelength of electromagnetic radiation. Hence, electromagnetic waves could and should exist with wavelengths both longer and shorter than the 400-700 nm range of visible light. Consequently, researchers began to look for invisible forms of light. These are forms of electromagnetic radiation to which the cells of the human retina do not respond. The first kind of invisible radiation to be discovered actually preceded Maxwell's work by more than a half century. Around 1800 the British astronomer William Herschel passed sunlight through a prism and held a thermometer just beyond the red end of the visible spectrum. The thermometer registered a temperature increase, indicating that it was being exposed to an invisible form of energy. This invisible energy, now called infrared radiation, was later realized to be electromagnetic radiation with wavelengths somewhat longer than those of visible light. In experiments with electric sparks in 1888, the German physicist Heinrich Hertz succeeded in producing electromagnetic radiation with even longer wavelengths of a few centimeters or more. These are now known as radio waves. In 1895 another German physicist, Wilhelm Röntgen, invented a machine that produces electromagnetic radiation with wavelengths shorter rhan 8p Figure 5-7 Ttie Electromagnetic Spectrum The full array ii all types of electromagnetic radiation is called the electro nagnetLC Spectrum. It extends frnm the longest-wavelength radio waves to the sho-test-wavelength gamma rays. Visible Ugh: occupies only a tiny portion of the full electromagnetic spectrum. 66 102 Chapter 5 The Nature of Light {a} Mobile phone: radio waves (bj Microwave oven: (c) TV remote: microwaves infrared tight than centimeters: X = 0.2112 m. Then we can use the above for-niLila tu find the frequency v. Figure 5-8 Ltees of Nonviable Electromagnetic Radiation (a) A mobile phone is actually a radio transmitter and receiver The wavelengths i ispd are in the range 16 to 36 cm. (b) A microwave oven produces radiation with a wavelength near 10 cm. The water in food absorbs this radiation, thus heating the food, (c) A remote control sends commands to a television using a beam of infrared light, (d) Ultraviolet ladtation in moderation gives ynu a sunran, but in excess can cause sunburn or skin cancer. 10 nm, now known as X rays, The X-ray machines in modern medical and dental offices are direct descendants of Rontgen's invention. Over the years radiation has been discovered with many other wavelengths. Thus, visible light occupies only a tiny fraction of the full range of possible wavelengths, collectively called the electromagnetic spectrum. As Figure 5-7 shows, the electromagnetic spectrum stretches from the longest-wavelength radio waves to the shortest-wavelength gamma rays. Figure 5-8 shows some applications of nonvisihle light in modern technology. On the long-wavelength side of the visible spectrum, infrared radiation covers the range from about 700 nm to 1 mm. Astronomers interested in infrared radiation often express wavelength in micTumeters or microns, abbreviated |im, where 1 pm = 1G-3 mm = 10~6 m. Microwaves have wavelengths from roughly 1 mm to 30 cm, while radio waves have even longer wavelengths. At wavelengths shorter than those of visible light, ultraviolet radiation extends from about 400 nm down to 10 nm. Next are X rays, which have wavelengths between about 10 and 0.01 nm, and beyond them at even shorter wavelengths are gamma rays. Note that the rough boundaries between different types of radiation are simply arbitrary divisions in the electromagnetic spectrum. Frequency and Wavelength Astronomers who work with radio telescopes often prefer to speak of frequency rather than wavelength. The frequency of a wave is the number of wave crests that pass a given point in one second. Equivalently, it is the number of complete cycles of the wave that pass per second (a complete cycle is from one crest to the next). Frequency is usually denoted by the Greek letter v (nu). The unit of frequency is the cycle per second, also called the hertz (abbreviated Hz) in honor of Hernrich Hertz, the physicist who (e) X rays can penetrate through soft tissue but not through bone, which makes them useful for medical imaging, (f) Gamma rays des:roy career cells by breaking their DNA molecules, making them unable to multiply. (Ian Britton, Royalty-Free/Corbis, Michael Porsche/Corbis, Bill Lush/Taxi/Getty, Neil McAllister/Alamy, Edward Kinsman/Photo Researchers, Inc., Wilt and Deni Mclntyre/Science Photo Library) first produced radio waves. For example, if 500 crests of a wave pass you in one second, the frequency of the wave is 500 cycles per second or 500 Hz. In working with frequencies, it is often convenient to use the prefix mega- (meaning "million," or 106, and abbreviated M) or kilo- (meaning "thousand," or 103, and abbreviated k). For example, AM radio stations broadcast at frequencies between 535 and 1605 kHz (kilohertz), while FM radio stations broadcast at frequencies in the range from 88 Lo 108 MHz (megahertz). The relationship between the frequency and wavelength of an electromagnetic wave is a simple one. Because light moves at a constant speed c = 3 X 10s m/s, if the wavelength (distance from one crest to the next) is made shorter, the frequency must increase (more of those closely spaced crests pass you each second). The frequency v of light is related to its wavelength K by the equation Frequency and wavelength of an electromagnetic wave v = frequency of an electromagnetic wave (in h2) c = speed of light = 3 X 108 m/s X = wavelength of the wave (in meters) That is, the frequency of a wave equals the wave speed divided by the wavelength. For example, hydrogen atoms in space emit radio waves with a wavelength of 21.12 cm. To calculate the frequency of this radiation, we must first express the wavelength in meters rather 3 X 10s m/s 0.2112 m 1.42 X 10s Hz = 1420 MHz Visible light has a much shorter wavelength and higher frequency than radio waves. You can use the above formula to show that for yellow-orange light of wavelength 600 nm, the frequency is 5 X 1014 Hz or 500 million megahertz! While Young's experiment (Figure 5-5) showed convincingly that light has wavelike aspects, it was discovered in the early 1900s that light also has some of the characteristics of a stream of particles and waves. We will explore light's dual nature in Section 5-5. 5-3 An opaque object emits electromagnetic radiation according to its temperature To learn about objects in the heavens, astronomers study the character of the electromagnetic radiation coming from those objects. Such studies can be very revealing because different kinds of electromagnetic radiation are typically produced in different ways. As an example, on Earth the most common way to generate radio waves is to make an electric current oscillate back and forth (as is done in the broadcast antenna of a radio station). By contrast, X As an object is heated, It glows mare brightly and ' rays for medical and dental purposes its Peak color shif+s +° are usually produced by bombard- shorter wavelengths ing atoms in a piece of metal with fast-moving particles extracted from within other atoms. Our own Sun emits radio waves from near its glowing surface and X rays from its corona (see the photo that opens Chapter 3). Hence, these observations indicate the presence of electric currents near the Sun's surface and of fast-moving uarticles in the Sun's outermost regions. (We will discuss the Sun at length in Chapter 18.) Radiation from Heated Objects j£gjgjj£j' The simplest and most common way to produce elec-iflB^ tromagnetic radiation, either on or off Earth, is to heat an object. The hot filament of wire inside an ordinary lightbulb emits white light, and a neon sign has a characteristic red glow because neon gas within the tube is heated by an electric current. In like fashion, almost all the visible light that we receive from space comes from hot objects like the Sun and rhe stars. The kind and amount of light emitted by a hot object tell us not only how hot it is but also about other properties of the object. We can tell whether the hot object is made of relatively dense or relatively thin material. Consider the difference between a lightbulb and a neon sign. The dense, solid filament of a lightbulb makes white light, which is a mixture of all different visible wavelengths, while the thin, transparent neon gas produces light of a rather definite red color and, hence, a rather definite wavelength. For now we will concentrate our attention on the light produced by dense, opaque objects. (We will return to the light produced by gases in Section 5-6.) Even though the Sun and stars are gaseous, not solid, it turns out chat they emit light with many of the same properties as light emitted by a hot, glowing, solid object. Imagine a welder or blacksmith heating a har of iron. As the bar becomes hot, it begins to glow deep red, as shown in Figure 5-L>ii. (You can see this same glow from the coils of a toaster or from an electric range turned on "high.") As the temperature rises further, the bar begins to give off a brighter orange light (Figure 5-9b). At still higher temperatures, it shines with a brilliant yellow light (Figure 5-9c). If the bar could be prevented from melt- (a) Hot: glows deep red [b] Hotter: glows orange Figure 5-9 rijUuxg Heating a Bar of Iron This sequence of photographs shaws how ths appearance of a heated bar of iron changes with temperature. As the temperature increases, the bar glows Tiore brightly because t radiates (c) Even hotter: glows yellow more energy. The color of the bar also changes because as the temperature goes up, the dominant wavelength of light emitted by the bar decreases. (©1984 Richard Megna/Fundamental Photographs) 104 Chapter 5 The Nature of Light 105 Figure 5-10 An Infrared Portrait in this \mag= made with a camera sensitive to infrared radiation, the different colors represent regions cf different temperature. That this image is made from infrared radiation is indicated by the highlighted ] in the wavelength tab. Red areas (like the man's tare) are the warmest and enit the most infrared light, while blue-green areas [incljdirg the rran's hands and hair) aie at the lowest temperatures and emit the least radiation (Dr Artiur Tucker/Photo Researchers) ing and vaporizing, at extremely high temperatures it would emit a dazzling blue-white light. As this example shows, the amount of energy emitted by the hot, dense object and the dominant wavelength of the emitted ra-diaiiun both depend on the temperature of the object. The hotter the object, the more energy it emits and the shorter the wavelength at which most of the energy is emitted. Colder objects emit relatively tittle energy, and this emission is primarily at long wavelengths. These observations explain why you can't see in the dark. The temperatures of people, animals, and furniture are rather less than even that of the iron bar in Figure S-9a. So, while these objects emit radiation even in a darkened room, most of this emission is at wavelengths greater than those of ted light, in the infrared part of the spectrum (see Figure 5-7). Your eye is not sensitive to infrared, and you thus cannot see ordinary, objects in a darkened room. But you can detect this radiation by using a camera that is sensitive to infrared light (Figure 5-10). To better understand the relationship between the temperature of a dense object and the radiation it emits, it is helpful to know iust what "temperature" means. The temperature of a substance is directly related to the average speed of the tiny atoms— the building blocks that come in distinct forms for each distinct chemical element—that make up the substance. (Typical atoms are about 10~10 m = 0.1 nm in diameter, or about 1/5000 as large as a typical wavelengTh of visible light.) If something is hot, its atoms are moving at high speeds; if it is cold, its atoms are moving slowly. Scientists usually prefer to use the Kelvin temperature scale, on which temperature is measured in kelvins (K) upward from absolute zero. This is the coldest possible temperature, at which atoms move as slowly as possible (they can never quite stop completely). On the more familiar Celsius and Fahrenheit temperature scales, absolute zero (0 K) is -273°C and -460QF. Ordinary room temperaiure is 293 K, 20°C, or 68DF. Mux 5-1 discusses the relationships among the Kelvin, Celsius, and Fahrenheit temperature scales. Figure 5-11 depicts quantitatively how the radiation tram a dense object depends on its Kelvin temperature. Each curve in this figure shows the intensity of light emitted at each wavelength by a dense object at a given temperature: 3000 K (the temperature at which molten gold boils), 6'OOUK (the temperature of an iron-welding arc], and 12,000 K (a temperature found in special industrial furnaces). In other words, the curves show the spectrum of light emitted by such an object. At any temperature, a hot, The higher the temperature of a blackbnHv, the shorter the wavelength of maximum emission (the wavelength ar which the curve peaks). sible light pox 5-1 Tools of the Astronomer's Trade The higher the temperature of a blackborly, the more light is emitted at all wavelengths. 2000 3000 Wavelength (nm) —■— aFigure 5-11 Blackbmy Curves Each of these curves snows the intensity Df light at every wavelength that is emitted by a blacKbudy (an idealized case of a dense abject) at a particular temperature. The i ainbow-coiored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen, the ppak intensity for the 12,000-K curve is actually about 1000 times grealei than the peak intensity for the 3030-K cuwe. Temperatures and Temperature Scales Three temperature scales are in common use. Throughout most of the world, temperatures are expressed in degrees Celsius I'Cf. The Celsius lem-peraiurc scale is based on the behavior of watei, which freezes at 0°C and boils at 100X' at sea level on Earth. This scale is named after the Swedish astronomer Anders Celsius, who proposed it in 1742. Astronomets usually prefer the Kelvin temperature scale. This is named after the nineteenth-century British physicist Lord Kelvin, who made many important contributions to our understanding of heat and temperature. Absolute zero, the temperaiure at which atomic motion is at the absolute minimum, is -273°C in the Celsius scale but 0 K in the Kelvin scale. Atomic motion cannot be any less than the minimum, so nothing can be colder than 0 K; hence, there are no negative temperatures on the Kelvin scale. Note that we do r.ot use degree C) with the Kelvin temperature scale. A temperature expressed in kelvins is always equal to the temperature m degrees Celsius plus 273. On the Kelvin scale, watei freezes at 273 K and boils at 373 K. Water must be heated through a change of 100 IC or 100°C to go from its freezing point to its boiling point. Thus, the "size" of a kelvin is the same as the "size" of a Celsius degree. When considering temperature changes, measurements in kelvins and Celsius degrees are the same. For extremely high temperatures the Kelvin and Celsius scales are essentially the same; for example, the Sun's core temperature is either 1.55 X If)7 K or 1.55 X 107 °C. The now-archaic Fahrenheit scale, which expresses temperature in degrees Fahrenheit ("F), is used only in the United States. When the German physicist Gabriel Fahrenheit introduced this scale in the early 1700s, he intended 100"F to represent the temperature of a healthy human body. On the Fahrenheit scale, water, freezes at 32°F and boils at 212°F. There are 180 Fahrenheit degrees between the freezing and boiling points of water, so a degree Fahrenheit is only 100/180 = 5/9 as large as either a Celsius degree or a kelvin. Two simple equations allow you to convert a temperature from the Celsius scale to the Fahrenheit scale and from Fahrenheit to Celsius: 7> = -j 7c + 32 Tc=f - 32) Tp = temperature in degrees Fahrenheit Tc = temperature in degrees Celsius EXAMPLE: A typical room temperature is 68aF. We can convert this to the Celsius scale using the second equation: Tc = ~ (68 - 32) = 20aC To convert this to the Kelvin scale, we simply add 273 to :he Celsius temperature. Thus, 68° = 20°C= 293 K The diagram displays the relationships among these three temperature scales. - Sun's core temperature s surface temperature & ft J® 4 d Jal Set? .rrl 1 3 % )* 1 1 -*Mfl (Ě j Ja id fey «1 *, .M - ^ k J tt. f - Boiling point of wa - Freezing poinc of v. dense object emits at all wavelengths, so its spectrum is a smooth, continuous curve with no gaps in it. The shape of the spectrum depends on temperature, however. An object at relatively low temperature (say, 3000 K) has a low curve, indicating a low intensity of radiation. The wavelength of maximum emission, at which the curve has its peak and the emission of energy is strongest, is at a long wavelength. The higher the temperature, the higher the curve (indicating greater intensity) and the shorter the wavelength of maximum emission. Figure S-U shows that for a dense object at a temperature ot 3000 K, the wavelength of maximum emission is around 1000 nm (1 urn). Because this wavelength corresponds to the infrared range and is well outside the visible range, you might think that you cannot see the radiation from an object at this tempetature. In fact, the 106 Chapter 5 The Nature of Light glow fmm such an object is visible; the curve shows that this object emits plenty of light within the visible range, as well as at even shorter wavelengths. The 30OO-K curve is quite a bit higher at the red end of the visible spectrum than at the violet end, so a dense object at this temperature will appear red in color. Similarly, the 12,000-K carve has its wavelength of maximum emission in the ultraviolet part of the spectrum, at a wavelength shorter than visible light. But such a hot, dense object also emits copious amounts of visible light {much mote than at 6000 K or 3000 K, for which the curves are lower) and thus will have a very visible glow. The curve for this temperature is higher for blue light than for red light, and so the color of a dense object at 12,000 K is a brilliant blue or blue-white. These conclusions agree with the color changes of a heated rod shown in Figure 5-9. The same principles apply to stars: A star that looks blue, such as Bellatrix in the constellation Orion {sec Figure 2-2«), has a high surface temperature, while a red star such as Rerelgeuse (Figure 2-2a) has a relatively cool surface. These observations lead to a general rule: The higher an object's temperature, the more intensely the object emits electromagnetic radiation and the shorter the wavelength at which it emits most strongly. We will make frequent use of this general rule to analyze the temperatures of celestial objects such as planets and stars. The curves in Figure 5-11 are drawn for ar. idealized type of dense object called a blackbody. A perfect blackbody does not reflect any light at all; instead, it absorbs all radiation falling on it. Because it reflects no electromagnetic radiation, the radiation that it does emit is entirely the result of its temperature. Ordinary objects, like tables, textbookss and people, are not perfect blackbodies; they reflect light, which is why they are visible. A star such as the Sun, however, behaves very much like a perfect blackbody, because it absorbs almost completely any radiation falling on it from outside. The light emitted by a blackbody is called blackbody radiation, and the curves in Figure 5-11 are often called blackbody curves. CAUTION! Despite its name, a blackbody does not necessarily look black. The Sun, for instance, does not look black because its temperature is high (around 5800 K), and so it glows brightly. But a room-temperature {around 300 K) blackbody would appear very black indeed. Even if it were as large as the Sun, it would emit only about 1/100,000 as much energy. (Its black-body curve is far too low to graph in Figure 5-11.) Furthermore, most of this radiation would be at wavelengths that are too long for our eyes to perceive. Figme 5-12 shows the blackbody curve for a temperature of 5800 K. It also shows the intensity curve for light from the Sun, as measured from above Earth's atmosphere. (This is necessary because Earth's atmosphere absorbs certain wavelengths.) The peak of both curves is at a wavelength of about 500 nm, near the middle of the visible spectrum. Note how closely the observed intensity curve for the Sun matches the blackbody curve. This is a strong indication that the temperature of the Sun's glowing surface is about 5800 K— a temperature that we can measure across a distance of 150 million kilometers! The close correlation between blackbody curves and the J curve: Sunlight - 5300 dashed curve; Blackbody ___0 1300 Wavelength (nm) Figure 5-12 The Sun as a Blackbody This graph shows that ^he intensity of sunlight over a wide range cf wavelengths (solid cirve) is a remarkably close match to the in:ensity of radiation coming from a blackbody at a temperature of 5800 K (dashed curve). The measurements of the bun's intensity were made above Earth's atmosphere twitch absorbs ard scatters certain wavelengths of sunlight), it's not surprising that the range of visible wavelengths includes the peak of the Sun's spectrum; the human eye evolved to take advantage of the most plentiful light available. observed intensity curves for most stars is a key reason why astronomers are interested in rhe physics of blackbody radiation. Blackbody radiation depends only on the temperature of the object emitting the radiation, not on the chemical composition of the object. The light emitted by molten gold at 2000 K is very nearly the same as that emitted by molten lead at 2000 K. Therefore, it might seem that analyzing the light from the'Sun or from a star can tell astronomers the object's temperature but not what the star is made of.. As Figure 5-12 shows, however, the intensity curve for the Sun (a typical star) is not precisely that of a black-body. We will see later in this chapter that the differences between a star's spectrum and that of a blackbody allow us to determine the chemical composition of the star. 5-4 Wien's law and the Stefan-Boltzmann law are useful tools for analyzing glowing objects like stars The mathematical formula that describes the blackbody curves in Figure 5-11 is a rather complicated one. But there are two simpler formulas for blackbody radiation that prove to be. very useful in many branches of astronomy. They are used by astronomers who investigate the stars as well as by those who study the planets (which are dense, relatively c,ool objects that, ■■ emit infrared radiation]. One of the/e formulas relates the tem- Two simple marhematicai formulas describing blackbodies are essential tools For studying the universe perature of a blackbody to its wavelength of/maximum emission, and the other relates the temperature to the amount of energy that the blackbody emits. These formulas, which we will use throughout this book, restate in precise mathematical terms the qualitative relationships that we described in Section 5-3. Wien's Law Figure 5-11 shows that the higher the temperature (T) of a black-body, the shorter its wavelength of maximum emission {\max). In 1893 the German physicist Wilhelm Wien used ideas about both heat and electromagnetism to make this relationship quantitative. The formula that he derived, which today is called Wien's law, is Wien's law for a blackbody 0.0029 K m Xim = wavelength of maximum emission of the object (in meters) T = temperature of the object (in kelvins) oSiiii^ According to Wien's law, the wavelength of maximum emission of a blackbody is inversely proportional to its temperature in kelvins. In other words, if the temperature of the blackbody doubles, its wavelength of maximum emission is halved, and vice versa. For example, Figure 5-11 shows blackbody curves for temperatures of 3000 K, 6000 K, and 12,000 K. From Wien's law, a blackbody with a temperature of 6000 K has a wavelength of maximum emission Xmax — (0.0029 K m)/(6000 K) = 4.8 X 10"7 m = 480 nm, in the visible part of the electromagnetic spectrum. At 12,000 K, or twice the temperature, the blackbody has a wavelength of maximum emission half as great, or >Lmax = 240 nm, which is in the ultraviolet. At 3000 K, just half our original temperature, the value of \max is twice the original value—960 nm, which is an infrared wavelength. You can see that these wavelengths agree with the peaks of the curves in Figure 5-11. CAUTION! Remember rhat Wien's law involves the wavelength : of maximum emission in meters. If you want to convert the i wavelength to nanometers, you must multiply the wavelength in '■ meters by (109 nm)/(l m). Wien's law is very useful for determining the surface temperatures of stars. It is not necessary tu know how far away the star is, how large it is, or how much energy it radiates into space. All we need to know is the dominant wavelength of the star's electromagnetic radiation. The Stefan-Boltzmann Law The other useful formula for the radiation from a blackbody involves the total amount of energy the blackbody radiates at all wavelengths, (By contrast, the curves in Figure 5-11 show how much energy a blackbody radiates at each individual wavelength.) Energy is usually measured in joules (J), named after the nineteenth-century English physicist James Joule. A joule is the amount of energy contained in the motion of a 2-kilogram mass moving at a speed of 1 meter per second. The joule is a convenient unit of energy because it is closely related to the familiar watt (W): 1 watt is 1 joule per second, or 1 W = 1 J/s = 1 J s_1. (The superscript — 1 means yon are dividing by that quantity.) For example, a 100-watt lightbulb uses energy at a rate of 100 joules per second, or 100 J/s. The energy content of food is also often measured in joules; in most of the world, diet soft drinks are labeled as "low joule" rather than "low calorie." The amount of energy emitted by a blackbody depends both on its temperature and on its surface area. These characteristics make sense: A large burning log radiates much more heat than a burning match, even though the temperatures are the same. To consider the effects of temperature alone, it is convenient to look at the amount of energy emitted from each square meter of an object's surface in a second. This quantity is called the energy flux (F). Flux means "rate of flow," and thus F is a measure of how rapidly enetgy is flowing out of the object. It is measured in joules per square meter per second, usually written as J/m2/s or J m~2 s"1. Alternatively, because 1 watt equals 1 joule per second, we can express flux in watts per square meter (W/m2, or W m~2). The nineteenth-century Irish physicist David Tyndall performed the first careful measurements of the amount of radiation emitted by a blackbody. (He studied the light from a heated platinum wire, which behaves approximately like a blackbody.) By analyzing Tyndall's results, the Slovenian physicist Josef Stefan deduced in 1879 that the flux from a blackbody is proportional to the fourth power of the object's temperature (measured in kelvins). Five years after Stefan announced his law, Austrian physicist Ludwig Boltzrrtann showed how it could be derived mathematically from basic assumptions about atoms and molecules. For this reason, Stefan's law is commonly known as the Stefan-BoUzmann law. Written as an equation, the Stefan-Boltzmann law is Stefan-Boltzmann law for a blackbody F = o-T4 F = energy flux, in joules per square meter of surface per second c = a constant = 5.67 X 10"8 W m"2 K"4 T = object's temperature, in kelvins The value of the constant a (the Greek letter sigma) is known from laboratory experiments. The Stefan-Boltzmann law says that if >'du double the temperature of an object (for example, from 300 K to 600 K), then the energy emitted from the object's surface each second increases by a factor of 24 = 16. If you increase the temperature by a factor of 10 (for example, from 300 K to 3000 K), the rate of energy emission increases by a factor of 104 = 10,000. Thus, a chunk of iron at room temperature (around 300 K) emits very little electromagnetic radiation (and essentially no visible light), but an iron bar heated to 3000 K glows quite intensely. Box 5-2 gives several examples of applying Wien's law and the Stefan-Boltzmann law to typical astronomical problems. 46 108 Chapter 5 The Nature of Light 109 Tools of the Astronomer's Trade Using the Laws of Blackbody Radiation The Sun and stars behave like nearly perfect blackbodies. Wien's law and the Stefan-Boltzmann law can therefore be used to relate the surface remperarure of the Sun or a distant star to the energy flux and wavelength of maximum emission of its radiation. The following examples show how to do this. EXAMPLE: The maximum intensity of sunlight is at a wavelength of roughly 500 am = 5.0 X 10~7 m, Use this information to determine the surface temperature of the Sun. Situation: We are given the Sun's wavelength of maximum emission Xmax, and our goal is to find the Sun's surface temperature, denoted by To. (The symbol Q is the standard astronomical symbol for the Sun.) Tools: We use Wien's law to relate the values of Xluax and T0. Answer: As written, Wien's law tells how to find \max if we know the surface temperature. To find the surface temperature from Xmax, we first rearrange the formula, then substitute the value of X™ax: 0.0029 K m 0.0029 K m 5.0 X 10 7 x. -- 5800 K Review: This temperature is very high by Earth standards, about the same as an iron-welding arc. EXAMPLE: Using detectors above Earth's atmosphere, astronomers have measured the average fiux of solar energy arriving at Earth. This value, called the solar constant, is equal to 1370 W m~2. Use rhis information to calculate the Sun's surface temperature. (This calculation provides a check on our result from the preceding example.) Situation: The solar constant is the flux of sunlight as measured at Earth. We want to use the value of the solar constant to calculate To. At a distance of 1 AU from the Sun, this squaie meter of area receives 1370 watts at light power from the Sun. Earth's DtW Tools: Ir may seem that all we need is the Stefan-Boltzmann law, which relates flux to surface temperature. However, the quantity F in this law refers to the flux measured at the Sun's surface, not at Earth. Hence, we will first need to calculate F from the given information. Answer: To determine the value of F, we first imagine a huge sphere of radius 3 AU with the Sun at its center, as shown in the figure. Each square meter of that sphere receives 1370 watts of power from the Sun, so the total energy radiated by the Sun per second is equal to the solar constant multiplied by the sphere's surface area. The result, called the luminosity of the Sun and denoted by the symbol Lq, is L© = 3.90 X 1026 W, That is, in 1 second the Sun radiates 3.90 X 102* joules of energy into space. Because we know the size of the Sun, we can compute the energy flux (energy emitted per square metet per second) at its surface. The radius of the Sun is R0 - 6.96 X 108 m, and the Sun's surface area is 4itR02. Therefore, its energy flux F© is the Sun's luminosity (total energy emitted by the Sun per second) divided by the Sun's surface area (the number of square meters uf surface): Iq ^ 3.90 X 1026 W 4ttR02 4 = crT-4, where the subscripts o and * refer to the Sun and Sirius, respectively. If we divide one equation by the other to find the ratio of fluxes, the Stefan-Boltzmann constants cancel out and we get Fo T»4 To4 (10,000 K)4 (5800 K)4 Review: Recatise Sirius has such a high surface temperature, each square meter of its surface emits 8.8 times more energy per second than a square meter of the Sun's relatively cool surface. Sirius is actually a larger star than the Sun, so it has more square meters of surface area and, hence, its total energy output is more than 8.8 times that of the Sun. 5-5 Light has properties of both waves and particles At the end of the nineteenth century, physicists mounted a valiant effort to explain all the characteristics nf blackbody radiation. To this end they constructed theories based on Maxwell's description of light as electromagnetic waves. But all such theories failed to explain the characteristic shapes of blackbody curves shown in Figure 5-11. The Photnn Hypothesis Tn 1900, however, the German physicist Max Planck discovered that he could derive a formula that correctly described blackbody curves if he made certain assumptions. In 1905 the great German-bom physicist Albert Einstein realized that these assumptions implied a radical new view of the nature of light. One tenet of this new view is that electromagnetic energy is emitted in discrete, particle- ———-------------- like packets, or light quanta (the The revolutionary photon plural of quantum, from a Latin concept is necessary to word meaning "how much"). The explain blackbody second tenet is that the energy of radiation and the photoelectric effect each light quantum—today called i photon—is related to the wavelength of light: the greater the wavelength, the lower the energy of a photon associated with that wavelength. Thus, a photon of red light (wavelength X = 700 nm) has less en- ergy than a photon of violet light (k = 400 nm). In this picture, light has a dual personality; it behaves as a stream of particlelike photons, but each photon has wavelike properties. In this sense, the best answer to the question "Is light a wave or a stream of particles?" is "Yes!" It was soon realized that the photon hypothesis explains more than just the detailed shape of blackbody curves. For example, it explains why only ultraviolet light causes suntans and sunburns. The reason is that tanning or burning involves a chemical reaction in the skin. High-energy, short-wavelength ultraviolet photons can trigger these reactions, but the lower-energy, longer-wavelength photons of visible light cannot. Similarly, normal photographic film is sensitive to visible light but not to infrared light; a long-wavelength infrared photon does not have enough energy to cause the chemical change that occurs when him is exposed to the higher-energy photons of visible light. Siajj^ Another phenomenon explained by the photon hypothesis is the photoelectric effect. In this effect, a metal plate is illuminated by a light beam. If ultraviolet light is used, tiny negatively charged particles called electrons are emitted from the metal plate. (We will see in Section 5-7 that the electron is one of the basic particles of the atom.) But if visible light is used, no matter how bright, no electrons are emitted. ^SSJjjL Einstein explained this behavior by noting that a certain minimum amount of energy is required to remove an electron from the metal piate. The energy of a 110 Chapter 5 The Nature of Light 111 short-wavelength ultraviolet photon is greater than this minimum value, so an electron that absorbs a photon of ultraviolet tight will have enough energy ro escape from the plate. Bui an electron that absorbs a photon of visible light, with its longer wavelength and lower energy, does not gain enough energy to escape and so remains within the metal. Einstein and Pianck both won Nobel prizes for their contributions to understanding the nature of light. The Energy of a Photon The relationship between the energy £ of a single photon and the wavelength of the electromagnetic radiation can be expressed in a simple equation: Energy of a photon (in terms of wavelength) E — energy of a photon b = Planck's constant c - speed of light X ~ wavelength of light The value of the constant h in this equation, now called Planck's constant, has been shown in laboratory experiments to be h = 6.625 X 10~34 J s The units of h are joules multiplied by seconds, called "joule-seconds" and abbreviated j s. Because the ralue of b is so tiny, a single photon carries a very small amount of energy. For example, a photon of red light IM____B___H___i Photons at the Supermarket Abeam of light can be regarded as a stream of tiny packets of energy called photons. The Planck relationships E — hclX and E = hv can be used to relate the energy E carried by a photon to its wavelength X and frequency v. As an example, the laser bar-code scanners used at stores and supermarkets emit orange-red light of wavelength 633 inn. To calculate the energy of a single photon of this light, we must first express the wavelength in meters. A nanometer (nra) is equal to 10~9 ra, so the wavelength is with wavelength 633 nm has an energy of only 3.14 X 10~19 J {Box 5-3}, which is why we ordinarily do not notice that light comes in the form of photons. Even a dim light source emits so many photons per second that it seems to be radiating a continuous stream of energy. The energies of photons are sometimes expressed in terms of a small unit of energy called the electron volt |eV). One electron volt is equal to 1.602 X It)-19 J, so a 633-nm photon has an energy of 1.96 eV. If energy is expressed in electron volts, Planck's constant is best expressed in electron volts multiplied by seconds, abbreviated eV s: h = 4.135 x 10"15 eVs Because the frequency v of light is related to the wavelength V by v = cf\, we can rewrite the equation for the energy of a photon as Energy of a photon (in terms of frequency) E = bv E = energy of a photon h = Planck's constant v = frequency of light The equations E = hcl\ and E = hv are together called Planck's law. Both equations express a relationship between a particlelike property of light (the energy £ of a photon) and a wavelike property (the wavelength X orTrequencyT?)>^ The photon picture of light inessential for understanding the detailed shapes of blackbody curves. As we will see, it also helps to explain how and why the Spectra of the Sun and stars diffeF from those of perfect biackbodics, Astronomy Down to Earth E = hs. = (6-625 x 1Q-3" | s)!3xlQB rn/s) = 19 X 6.33 X 1(T7 m ' J This amount of enetgy is very small. The laser in a typical bar-code scanner emits 10~3 joule of light energy per second, so the number of photons emitted per second is 10 3 joule per second 3.14 X lO-19 joule per photon = 3.2 X 1015 photons per second X = (633 nm) ' io- = 633 X 10~9 m = 6.33 X 10~7 m Then, using the Planck formula E = kc/X, we find that the energy of a single photon is This number is so large that the laser beam seems like a continuous flow of energy rather than a stream of little energy packets. 5-6 Each chemical element produces its own unique set of spectral lines In 1814 the German master optic^n Joseph von Fraunhofer repeated the classic experiment of shining a beam of sunlight through a prism (see Figure 5-3). But this time Fraunhofer subjected the resulting rainbow-colored spectrum to incense magnification. To his surprise, he discovered that the_______________ solar spectrum contains hundreds of Spectroscopy is the key to determining the chemical composition of fine, dark lines, now called spectral lines. By contrast, if the light from a perfect blackbody were sent through a prism, it would produce a smooth, Planefs ant* stars continuous spectrum with no dark lines. Fraunhofer counted more than 600 dark lines in the Sun's spectrum; today we know of more than 30,000. The photograph of the Sun's spectrum in Figure 5-13 shows hundreds of these spectral lines. Spectral Analysis Half a century later, chemists discovered that they could produce spectral lines in the laboratory and use these spectral lines to analyze what kinds of atoms different substances are made of. Chemists had long known that many substances emit distinctive colors when sprinkled into a flame. To facilitate study of these colors, around 1857 the German chemist Robert Bunsen invented a gas burner (today called a Bunsen burner) that produces a clean flame with no color of its own. Bunsen's colleague, the Prussian- Figure 5-13 riQuxg The Sun's Spectrum Numeruus dark spectrallines are seen in tl~is i-nage of the Sun's spectrum. The spectrum is spread out so much that it had to be cut into segments to fit on this page. (N a Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF] 2. Send light from the flame through a narrow slit, then through a prism 3. Bright lines in the spectrum show that the substance emits light at specific wavelengths only Figure 5-14 The Kirchnoff-Bunsen Experiment In the mid-1850s, Gustav Kirchhoff and Robert Bunsen discovered that when a chemical substance is heated and vaporized, the spectrum of the emitted light exhibits a series of bright spectral lines- Tney also found that each chemical element produces its own characteristic pattern oF spectral lines. (In an actual laboratory sxperurent, lenses would be needed"to focus che :mage of th2 slit ontD the screen.) born physicist Gustav Kirchhoff, suggested that the colored light produced by substances in a flame might best be studied by passing the light through a prism (bigure 5-14). The two scientists promptly discovered that the spectrum from a flame consists of a paiLcrn of thin, bright spectral lines against a dark background. The same kind of spectrum is produced by heated gases such as neon or argon. Kirchhoff and Bunsen then found that each chemical element produces its own unique pattern of spectral lines. Thus was born in 1859 the technique of spectral analysis, the identification of chemicai substances by their unique patterns of spectral lines. A chemicai element is a fundamental substance that cannot be broken down into more basic chemicals. Some examples are hydrogen, oxygen, carbon, iron, gold, and silver. After Kirchhoff and Bunsen had recorded the prominent spectral lines of all the then-known elements, they soon began to discover other spectral lines in the spectra of vaporized mineral samples. In this way they discovered elements whose presence had never before been suspected. In 1860, Kirchhoff and Bunsen found a new line in the blue portion of the spectrum of a sample of mineral water. After isolating the previously unknown element responsible for making the line, they named it cesium (from the Latin caesium, "gray-blue"). The next year, a new line in the red portion of the spectrum of a mineral sample led rhem to discover the element rubidium (Latin rubidium, "red"). Spectral analysis even allowed the discovery of new elements outside Earth. During the solar eclipse of 1868, astronomers found a new spectral line in light coming from the hot gases at the upper surface of the Sun while the main body of the Sun was hidden by the Moon. This line was attributed to a new element 112 Chapter 5 The Nature üf Light 113 Figure 5-15 riQuxg Various Spectra These photographs show the spectra of different types of gases as measured in a laboratory on Earth. Each type or gas has a unique spectrum that is the same wherever ir the universe the gas is found. Water vapor h2c1) *s a compound whose molecules are made up of hydrogen and oxygen atoms: the hydrogen rralecule ;h2} is made up of two hydrogen atoms. (Ted Kinsman/Science Photo Library) Water vapor (H20) (a) Continuous spectrum (bhdibodv emits htrfir .it iill wavelengths) (h) Absorption lint: spectrtim (atoms in gas cloud absorb lij;ht of certain specific wavelengths, producing dark lines in spectrum) (0 kmissnw line ipcctntin (utonu in tins cloud rccmil .ibsorhed 11 f»Ii t enemy •« tltt; siime wavelengths at which fhevalistnbeil il) Figure 5-16 Cnnfinunus, Absorption Line, and Emission Line Spectra A hot, opaque body (like a biackbody) emits a continuous spectrum of light (spectrum a). If ihis light is passed through a cloud of a coolei gas, the cloud absorbs light of certain specific wavelengths, and the spectrum of light that passes directly through the cloud has dark absorption lines (spectrum b). The cloud does not retain all the light energy that \t absorbs but radiates it outward in all directions. The spectrum of this reradiated light contains bright emission lines (spect urn c) witl i exactly the same wavelengths as the daik absorption lines in spectrum b. The specific wavelengths observed depend on the chemical composition of the cloud. that was named helium (from the Greek belios, "sun"). Helium was not discovered on Earth until 1895, when it was found in gases obtained from a uranium mineral. A sample of an element contains only a single type of atom; carbon contains only carbon atoms, helium contains only helium atoms, and so on. Atoms of the same or different elements can combine to form molecules. For example, two hydrogen atoms (symbol H) can combine with an oxygen atom (symbol O) to form a water molecule (symbol h2o). Substances like water whose molecules include atoms of different elements are called compounds. Just as each type of atom has its own unique spectrum, so does each type of molecule. Figure 5-15 shows the spectra of several types of atoms and molecules. Kirchhoff s Laws -^Swli.?' "^ie sPectrum or" me Sun, with its dark spectral lines superimposed on a bright background (see Figure 5-13), may seem to be unrelated to the spectra of bright lines against a dark background produced by substances in a flame {see Figure 5-14). But by the,early 1860s, KJrchhofPs experiments had revealed a direct connection between these two types of spectra. His conclusions are summarized in three important statements about spectra that are today called Kuxhhoff's laws. These laws, which are illustrated in Figure 5-16, are as follows: Law 1 A hot opaque body, such as a perfect biackbody, or a hot, dense gas produces a continuous spectrum—a complete rainbow uf colors without any spectral lines. Law 2 A hot, transparent gas produces an emission line spectrum—a series of bright spectral lines against a dark background. Law 3 A cool, transparent gas in front of a source of a continuous spectrum produces an absorption line spectrum—a series of dark spectral lines among the colors of the continuous spectrum. Furthermore, the dark lines in the absorption spectrum of a particular gas occur at exactly the same wavelengths as the bright lines in the emission spectrum of that same gas. Kirchhoff's laws imply that if a beam of white light is passed through a gas, the atoms of the gas somehow extract light of very specific wavelengths from the white light. Hence, an observer who looks straight through the gas at the white-light source (the biackbody in Figure 5-16) will receive light whose spectrum has dark absorption lines superimposed on the continuous spectrum of the white light. The gas atoms then radiate light of precisely these same wavelengths in all directions. An observer at an oblique angle (that is, one who is not sighting directly through the cloud toward the biackbody) will receive only this light radiated by the gas cloud; the spectrum uf this light is bright emission lines on a dark background. CAUTION! Figure 5-16 shows that light can either pass through a cloud of gas or be absorbed by the gas. But there is also a third possibility: The light can simply bounce off the atoms or molecules that make up the gas, a phenomenon called light scattering. In other words, photons passing through a gas cloud can miss the gas atoms altogether, be swallowed whole by the atoms (absorption), or bounce off the atoms like billiard balls colliding (scattering). Box 5-4 describes how light scattering explains the blue color of the sky and the red color Df sunsets. ^jw^ Whether an emission line spectrum or an ahsorptmn l^ne spectrum is observed from a gas cloud depends on <^c^y the relative temperatures of the gas cloud and its background. Absorption lines are seen if the background is hotter than the gas, and emission Sines are seen if the background is cooler. For example, if sodium is placed in the flame of a Bunsen burner in a darkened room, the flame will emit a characteristic orange-yellow glow. (This same glow is produced if we use ordinary table salt, which is a compound of sodium and chlorine.) If we pass the light from the flame through a prism, it displays an emission line spectrum with two closely spaced spectral lines at wavelengths of 588.99 and 589.59 nm, in the orangc-ycllow part of the spectrum. We now turn on a lighthulh whose filament is hotter than the flame and shine the bulb's white light through the flame. The spectrum of this light after it passes through the flame's sodium vapor is the continuous spectrum from the lightbulb, but with two closely spaced dark lines at 588.99 and 589.59 nm. Thus, the chemical composition of the gas is revealed by either bright emission lines or dark absorption lines. Spectroscopy Spectroscopy is the systematic study of spectra and spectral lines. Spectral lines arc tremendously important in astronomy, because they provide reliable evidence about the chemical composition of distant objects. As an example, the spectrum of the Sun shown in Figure 5-13 is an absorption line spectrum. The continuous spectrum comes from the hot surface of the Sun, which acts like a biackbody. The dark absorption lines are caused by this light passing through a cooler gas; this gas is the atmosphere that surrounds the Sun. Therefore, by identifying the spectral lines present in the solar spectrum, we can determine the chemical composition of the Sun's atmosphere. Figure 5-17 shows both a portion of the Sun's absorption line spectrum and the emission line spectrum of iron vapor over the same wavelength range. This pattern of bright spectral lines in the lower spectrum is iron's own distinctive "fingerprint," which no other substance can imitate. Because some absorption lines in the Sun's spectrum coincide with the iron lines, some vaporized iron must exist in the Sun's atmosphere. Spectroscopy can also help us analyze gas clouds in space, such as the nebula surrounding the star cluster NGC 346 shown Emission spectrum of (in the laboratory on Earth) For each emission line of iron, there is a corresponding absorption line in the solar spectrum; hence there must be iron in the Sun's atmosphere Figure 5-17 riQuxg Iron in the Sun The upper part cf thus figure is a portion of the Sun's line spectrum of vaporized iron. The iron lines coincide with some of the spectrum at violet wavelengths, showing numerous dark absorption lines. so'.ar lines, which proves that there is some iron (albeit a relatively small The lower part of the figure is a corresponding portion ot the emission amount) in the Sun's atmosphere. (Carnegie Observatories) 114 Chapter 5 I I The Nature Df Light 115 A.._______ Astronomy Down to Earth Light Scattering Light scattering is the process whereby photons bounce off particles in their path. These particles can be atoms, molecules, or clumps of molecules. You are reading these words using photons from the Sun or a lamp that bounced off the page—that is, were scattered by the particles that make up the page. An important fact about light scattering is that very small particles—ones that are smaller than a wavelength of visible light—are quite effective at scattering short-wavelength photons of blue light, but less effective at scattering long-wavelength photons of red light. This fact explains a number of phenomena that you can see here on Earth. The light that comes from the daytime sky is sunlight that has been scattered by the molecules that make up our atmosphere (see part a of the accompanying figure). Air molecules are less than 1 nm across, far smaller than the wavelength of visible light, so they scatter blue light more than red light— which is why the sky looks blue. Smoke particles are also quite small, which explains why the smoke from a cigarette or a fire has a bluish color. Distant mountains often appear blue thanks to sunlight being scattered from the atmosphere between the mountains and your eyes. (The Blue Ridge Mountains, which extend from Pennsylvania to Georgia, and Australia's Blue Mountains derive their names from this effect.) Sunglasses often have a red or orange tint, which blocks out blue light. This cuts down on the amount of scattered light from the sky reaching your eyes and allows you to see distant objects more clearly. Light scattering also explains why sunsets are red. The light from the Sun contains photons of all visible wavelengths, but as this light passes through our atmosphere the blue photons arc scattered away from the straight-line path from the Sun to your eye. Red photons undergo relatively little scattering, so the Sun always looks a bit redder than it really is. When you look toward the setting sun, the sunlight that teaches your eye has had to pass through a relatively thick layer of atmosphere (part b of the accompanying figure). Hence, a large fraction of the blue light from the Sun has been scattered, and the Sun appears quite red. The same effect also applies to sunrises, hut sunrises seldom look as red as sunsets do. The reason is that dust is lifted into the atmosphere during the day by the wind (which is typically stronger in the daytime dian at night), and dust particles in the atmosphere help to scatter even more blue light. If the small particles that scatter light are sufficiently concentrated, there will be almost as much scattering of red light as of blue light, and the scattered light will appear white. This explains the white color of clouds, fog, and haze, in which the scattering particles are ice crystals or water droplets. Whole milk looks white because of light scattering from tiny fat globules; nonfat milk has only a very few of these globules and so has a slight bluish cast. Light scattering has many applications to astronomy. For example, it explains why very distant stars in our Galaxy appear surprisingly red. The reason is that there are tiny dust particles in the space between the stars, and this dust scatters blue photons. By studying how much scattering takes place, astronomers have learned about the tenuous material that fills interstellar space. (a) Why the sky looks blue Tin? utnmsrtiiciv sen iters blue lij;ht imirc tlk-ciivi-lv ili.m iL'il li^lii— hence niosrtv red lijjhr readies vottr eye when vmi look rlirmiftli ,\ duck slice of .itii'ospliere at the semnu íum. [b] Why the setting Sun looks red Figure 5-18 R1ÜUXG Analyzing the Composition of a Distant Nebula The glowing gas "loud in this Hubble Space Telescope image lies 210.000 light-years away in the constellation Tucana (the Toucan). Ho: stars within the nebula emit high-energy, ultraviolet photons, which are absorbed by the surrounding gas and heat tie gas to high temperature. This heated gas produces light with an emission line spectrum. The particular wavelength of red light emitted by the nebula is bbb" nm, characteristic of hydrogen gas. (NASA, ESA, and A. Nota, jTScI/ESA) in Hgiii-e 5-IS, Such glowing clouds have emission line spectra, because we see them against the black background of space. The particular shade of red that dominates the color of this nebula is due to an emission line at a wavelength near 656 nm. This is one ot the characteristic wavelengths emitted by hydrogen gas, so we can conclude that this nebula contains hydrogen. More detailed analyses of this kind show that hydrogen is the most common element in gaseous nebulae, and indeed in the universe as a whole. The spectra of other nebulae, such as the Ring Nebula shown in the image that opens this chapter, also reveal the presence of nitrogen, oxygen, helium, and other gases. What is truly remarkable about spectroscopy is that it can determine chemical composition at any distance. The 656-nm red light produced by a sample of heated hydrogen gas on Earth (the bright red line in the hydrogen spectrum in Figure 5-15) is the same as that observed coming from the nebula shown in Figure 5-18, located about 210,000 light-years away. By using the basic principles outlined by Kirchhoff, astronomers have the tools to make chemical assays of objects that are almost inconceivably distant. Throughout this book we will see many examples of how astronomers use Kirchhoff s laws to determine the nature of celestial objects. To make full use of Kirchhoffs laws, it is helpful to understand why they work. Why does art atom absorb light of only particular wavelengths? And why does it then emit light of only these same wavelengths? Maxwell's theory of electromagnetism (see Section 5-2) could not answer these questions. The answers did not come until early in the twentieth century, when scientists began to discover the structure and properties of atoms. 5-7 An atom consists of a small, dense nucleus surrounded by electrons The first important clue about the internal structure of atoms came from an experiment conducted in 1910 by Ernest Rutherford, a gifted physicist from New Zealand. Rutherford and his colleagues at the University of Manchester in England had been investigating the recently discovered phenomenon of radioactivity. Certain radioactive elements, such as uranium and radium, were known to emit particles of various types. One type, the alpha particle, has about the same ____.„..„__.__^_„_„. mass as a helium atom and is emitted from some radioactive substances with considerable speed. In unc scries of experiments, Rutherford and his colleagues were using alpha particles as projectiles to probe the structure of solid matter._______ They directed a beam of these particles at a thin sheet of metal (hgirc 5-lc,'). Almost all the alpha particles passed through the metal sheet with little or no deflection from their straight-line paths. To the surprise of the experimenters, however, an occasional alpha particle bounced back from the metal sheet as though it had struck something quite dense. Rutherford later remarked, "It was almost as incredible as Most alpha particles pass through the foil with very little deflection. B 1 Gold foil i seen edge-on) Occasionally an alpha particle rebounds (like A or B), indicating that it has collided with the massive nucleus of a gold atom. Figure 5-19 Rutherford's Experiment Alpha particles from a radioactive source are directed at a thin metal foil. This experiment provided the first evidence that the nuclei of atoms are relatively rrassive and compact To decode the information in the light from immense objects like stars and galaxies, we must understand the structure of atoms s alpha particles. 116 Chapter 5 The Nature of Light 117 Figure 5-20 Rutherford's Model of the Atom In this model, electrons orbit the atom's nucleus, which contains rrost of the atom's mass. The nucleus contains two types of particles, protons and neutrons. if you fired a fifteen-inch shell at a piece of tissue paper and it came back and hit you." Rutherford concluded from this experiment that most of the mass of an atom is concentrated in a compact, massive lump of matter that occupies only a small part of the atom's volume. Most of the alpha particles pass freely through the nearly empty space that makes up most of the atom, but a few particles happen to strike the dense mass at the center of the atom and bounce back. The Nucleus of an Atom Rutherford proposed a new model for the structure of an atom, shown in Figure 5 20. According to this model, a massive, positively charged nucleus at the center of the atom is orbited by tiny, negatively charged electrons. Rutherford concluded that at least 99.98% of the mass of an atom must be concentrated in its nucleus, whose diameter is only about 10-i4 m. (The diameter of a typical atom is far larger, about 10~10m.) i&NALQGLY To appreciate just how tiny the nucleus is, imagine expanding an atom by a factor of 10u to a diameter of 100 meters, about the length of a football field. To this scale, the nucleus would be just a centimeter across—no larger than your thumbnail. We know today that the nucleus of an atom contains two types of particles, protons and neutrons. A proton has a positive electric charge, equal and opposite to that of an electron. As its name suggests, a neutron has no electric charge;—it is electrically neutral. As an example, an alpha particle (such as those Rutherford's team used) is actually a nucleus of the helium atom, with two protons and two neutrons. Protons and neutrons are held together in a nucleus by the so-called sttong nuclear force, whose great strength overcomes the electric repulsion between the posi- tively charged protons. A proton and a neutron have almost the same mass, 1.7 X 10"27 kg, and each has about 2000 times as much mass as an electron (9,1 X 10-31 kg). In an ordinary atom there are as many positive protons as there are negative electrons, so the atom has no net electric charge. Because the mass of the electron is so small, the mass of an atom is not much greater than the mass of its nucleus. That is why an alpha particle has nearly the same mass as an atom of helium. While the solar system is held together by gravitational forces, atoms are held together by electrical forces. Opposites attract: The -negative charges on the orbiting electrons are attracted to the positive charges on the protons in the nucleus. Box 5-5 on page 118 describes more about the connection between the structure of atoms and the chemical and physical properties of substances made of those atoms. Rutherford's experiments clarified the structure of the atom, but they did not explain how these tiny particles within the atom give rise to spectral lines. The task of reconciling Rutherford's atomic model with Kirchhoff s laws of spectral analysis was undertaken by the young Danish physicist Niels Bohr, who joined Rutherford's group at Manchester in 1912. 5-8 Spectrallines are produced when an electron jumps from one energy level to another within an atom Niels Bohr began his study of the connection between atomic spectra and atomic structure by trying to understand the structure of hy- Shorter wavelength Niels Bohr explained spectra! lines with s radical new model of the atom drogen, the simplest and lightest of the elements. (As we discussed in Section 5-6, hydrogen is also the most common element in the universe.) When Bohr was done, he had not only found a way to explain this atom's spectrum but had also found a justification for Kirchhoff's laws in terms of atomic physics. Hydrogen and the Balmer Series The most common type of hydrogen atom consists of a single electron and a single proton. Hydrogen atoms have a simple visible-light spectrum consisting of a pattern of lines that begins at a wavelength of 656.3 nm and ends at 364.6 nm. The first spectral line is called Ha (H-alpha), the second spectral line is called Hp (H-beta), the third is Hy (H-gamma), and so forth. (These are the bright lines in the spectrum of hydrogen shown in Figure 5-15. The fainter lines between these appear when hydrogen atoms form into molecules.} The closer you get to the short-wavelength end of the spectrum at 364.6 nm, the more spectral lines you see. The regularity in this spectral pattern was described mathematically in 1885 by Johann Jakob Balmer, a Swiss schoolteacher. The spectral lines of hydrogen at visible wavelengths are today called Balmer lines, and the entire pattern from Ha onward is called the Balmer series. Eight Balmer lines are seen in the spectrum of the star shown in Figure 5-21. Stars in general, including Figure 5-21 riQ [Qxg Balmer Lines in the Spectrum of a 5tar This portion of the spectrum of the star Vega in the constellation Lyra (the Harp) shows eight Balmer Sires, from H„ at 656.3 nm through H9 (H-theta) at 388.9 nm. The senes the Sun, have Balmer absorption lines in their spectra, which shows they have atmospheres that contain hydrogen. Using trial and error, Balmer discovered a formula from which the wavelengths (\) of hydrogen's spectral lines can be calculated. Baimer's formula is usually written HO i) In this formula R is the Rydberg constant (R = 1.097 X 107m~1), named in honor of the Swedish spectroscopist Johannes Rydberg, and n can be any integer (whole number) greater than 2. To get the wavelength ka of the spectral line HQ, you first put n = 3 into Baimer's formula: ~~ = (1,097 X 107 m"1} (~ - -■ 1.524 X 106 m'1 Then take the reciprocal: 1 1.524 X 106 rrr = 6.563 X 10~7 m = 656.3 nrr To get the wavelength of Hp, use n = 4, and to get the wavelength of H^, use n = 5. If you use n = °o (the symbol <*> stands for infinity), you get the short-wavelength end of the hydrogen spectrum at 364.6 nm. (Note that 1 divided by infinity equals zero.) Bohr's Model of Hydrogen Bohr realized that to fully understand the structure of the hydrogen atom, he had to be able to derive Baimer's formula using the laws of physics. He first made the rather wild assumption that the electron in a hydrogen atom can orbit the nucleus only in certain specific orbits. (This idea was a significant break with the ideas of Newton, in whose mechanics any orbit should be possible.) h^iifc 5-22 shows the four smallest of these Bohr orbits, labeled by the numbers n = 1, n = 2, n = 3, and so on. Although confined to one of these allowed orbits while circling the nucleus, an electron can jump from one Bohr orbit to another. For an electron to jump, the hydrogen atom must gain or lose a specific amount of energy. The atom must absorb energy for the electron to go from an inner to an outer orbit; the atom must release energy for the electron to go from an outer to an inner orbit. As an example, Figure 5-23 shows an electron converges at 364.6 nm, slightly to the left of HB. Parts of this image were made using ultraviolet radiation, which is indicated by the highlighted U in the wavelength tab. (NOAC) jumping between the n = 2 and n = 3 orbits of a hydrogen atom as the atom absorbs or emits an Ha photon. When the electron jumps from one orbit to another, the energy of the photon that is emitted or absorbed equals the difference in energy between these two urbits. This energy difference, and hence the photon energy, is the same whether the jump is from a low orbit to a high orbit (Figure 5-23a) or from the high orbit back to the low one (Figure 5-236). According to Planck and Einstein, if two photons have the same energy E, the relationship E = hc/k tells us that they must also have the same wavelength X. It follows that if an atom can emit photons of a given energy and wavelength, it can also absorb photons of precisefy the same energy and wavelength. Thus, Bohr's picture explains Kirchhoff's observation that atoms emit and absorb the same wavelengths of light. The Bohr picture also helps us visualize what happens to produce an emission line spectrum. When a gas is heated, its atoms move around rapidly and can collide forcefully with each other. These energetic collisions excite the atoms' electrons into high orbits. The electrons then cascade back down to the innermost Figure 5-22 The Bohr Model of the Hydrogei i Atom In this model, an electron circles the hydrogen nucleus (a proton) only in allowed orbits n = 1, 2, 3, and so forth. The first four Bohr orbits are shown here. Tnis figure is not drawn to scale; in the Bohr model, the n = 2,3, and 4 orbits are respectively 4, 9, and 16 times larger than the n = 1 orbit. 118 Chapter 5 The Nature of Light Atoms, the Periodic Table, and Isotopes Each different chemical element is made uf a specific type of atom. Each specific atom has a characteristic number of protons in its nucleus. For example, a hydrogen atom has 1 proton in its nucleus, an oxygen atom has 8 protons in its nucleus, and so on. The number of protons in an atom's nucleus ts the atomic number fur that particular element. Tire chemical elements are most conveniently listed in the form of a periodic table (shown in the figure). Elements are arranged in the periodic table in otder of increasing atomic number. With only a few exceptions, this sequence also corresponds to increasing average mass of the atoms of the elements. Thus, hydrogen (symbol H), with atomic number 1, is the lightest element. Iron (sym bol Fe) has atomic number 26 and is a relatively heavy element. All the elements listed in a single vertical column of the periodic table have similar chemical properties. For example, the elements in the far right column are ai! gases under the conditions of temperature and pressure found at Earuh's surface, and they are all very reluctant to react chemically with other elements. In addition to nearly 100 naturally occurring elements, the periodic table includes a number of artificially produced elements. Most of these elements are heavier than uranium (symbol U) and are highly radioactive, which means that they decay into lighter elements within a short time of being created in laboratory experiments. Scientists have succeeded in creating only a few atoms of elements 104 and above. The number of protons in the nucleus of an atom determines which element that atom is. Nevertheless, the same clement may have different numbers of neutrons in its nncleu1;. For example, oxygen (O) has atomic number 8, so every oxygen nucleus has exactly 8 protons. But oxygen nuclei can have 8, 9, or 10 neutrons. These three slightly different kinds ot Tools of the Astronomer's Trade oxygen are called isotopes, The isotope with 8 neutrons is by far the most abundant variety. It is written as lfiO, or nxygen-16. The rarer isotopes with 9 and 10 neutrons are designated as 170 and ,sO, respectively. The superscript that precedes the chemical symbol for an element equals the total number of protons and neutrons hi a nucleus of that particular isotope. For example, a nucleus of the most common isotope of iron, 5*Fe or iron-56, contains a total of 56 protons and neutrons. From the periodic table, the atomic number of iron is 26, so every iron atom has 26 protons in its nucleus. Therefore, the number of neutrons in an irort-56 nucleus is 56 — 26 ~- 30. (Most nuclei have more neutrons than protons, especially in the case of the heaviest elements.) It is extremely difficult to distinguish chemically between the various isotopes of a particular element. Ordinary chemical reactions involve only the electrons that orbit the atom, never the neutrons buried in its nucleus. But there are small differences in the wavelengths of the spectral lines for different isotopes of the same element. For example, the spectral line wavelengths of the hydrogen isotope 2H are about 0.03% greater than the wavelengths for the most common hydrogen isotope, 1H. Thus, different isotopes can be distinguished by careful spectroscopic analysis. Isotopes are important in astronomy for a variety of reasons. By measuring the relative amounts of diffetent isotopes of a given element in a Moon rock or meteorite, the age of that sample can be determined. The mixture of isotopes left behind when a star explodes into a supernova (see Section 1-3) tells astronomers about the processes that led to the explosion. And knowing the properties of different isotopes of hydrogen and helium is crucial to understanding the nuclear reactions that make the Sun shine. Look for these and other applications of the idea of isotopes in later chapters. Figure 5-23 The Absorption and Emission of an H„ Photon This schematic diagram, drawr according to the Bohr nodel, shows vvhat happens when a hydrogen atom (a) absorbs or (b) emits a photon whose wavelength is 556.3 nm. (a) Atom absorbs a 556.3-nm photon; absorbed energy causes electron to jump from the n = 2 orbit up the n = 3 orbit (b) Electron falls from the n = 3 orbit to the n = 2 orbit; energy lost by atom goes into emitting a 656.3-nm photon Periodic Table of the Elements H Hydrogen He 3 , Li ti'liiym 4 Be 15 .'''Boron-: C o % 10 SÄ 31.. ' . ■ Na ■• Sodium 12 . JUL 13 a: Si p S 17 ." • ■ Cl \f 19 K 20 Ca c Sc Ti Cr Mn ■ F-e ■• Ca Vi --'■'^ičkeí.'; fii 'Zn Ca Gallium Ji-.'-.::; Ce As 'iÄpstňíČ-' Se Br PII!! tu iipIII 37; -"• Tib- 38 Sr Y /j fe .Pft*; Nb Mo 44 Hu Rh I'd "ab (Cd 49 In ladsun Sn Sb Tc S3.-I ; lodias-. ; flllfj \l lllllltl 55 ' Cs 56 Ba & La Hf Ta Rc iß 77'',-Ii Iridium Pi ýM';0'ä: Au Hg M-rcuiy 81 Tl Pl> Iii 84"':^ ■ 'Ä ťo 85;..-;;aV; fSS Rn 87 88 - 109: " Fr Ka Rí Rf Ob Bil 11, -. . TO Mt Ds i. . J*. Cc Pi 60' Nd Ntodyjnluin Pra , řlDmtdlJUtn Sm 63 Eu , Eiujpiun; 64 Gd 'l b -Dy,,, III) fcr Tm /Thulium 70.:. •• Yb Vfterbiiwp n , , LU Th Pa .'■ PfOUOiiiluqi 92 U Uranium 93' Np' NcpHjnigm 94 PiT M u ionium 95; , Ani ' Amtrjcium 96 Cm Curium 97 Bk Berkel j um u CtUfotlwm 59?%t;v Ii* Fm 101 . ' . Md 102 No 03 Lr' possible orbit, emitting photons whose energies are equal to the energy differences between different Bohr orbits. In this fashion, a hot gas produces an emission line spectrum with a variety of different wavelengths. To produce an absorption líne spectrum, begin with a relatively cool gas, so that the electrons in most of the atoms are in inner, low-energy orbits. If a beam of light with a continuous spectrum is shone through the gas, most wavelengths will pass through undisturbed. Only those photons will be absorbed whose energies are just right to excite an electron to an allowed outer orbit. Hence, only certain wavelengths will be absorbed, and dark iines will appear in the spectrum at those wavelengths. Using his picture of allowed orbits and the formula E = hc/\, Bohr was able to prove mathematically that the wavelength \ of the photon emitted or absorbed as an electron jumps between an inner orbit N and an outer orbit « is Bohr formula for hydrogen wavelengths N = number of inner orbit n = number of outer orbit R = Rydberg constant = 1.097 X 107 m"1 , X. = wavelength (in meters) of emitted or absorbed photon If Bohr let N = 2 in this formula, he got back the formula that Baimer discovered by trial and error. Hence, Bohr deduced the meaning of the Baimer series: All the Baimer lines are produced by electrons jumping between the second Bohr orbit 120 Chapter 5 Figure 5-24 "«LJ Fl.^rrmn Transitions in the Hydroger ^■f^."1' Atom This diagram shows the photon wavelengths associated with different electron transitions in hydrogen, In each case, the same wavelength occurs whether a photon is emitted (when the electron drops from a high orbit to a tow one] or absorbed (when the electron jjmps from a tow orbit to a high one). The orbits are not shown to scale. (N - 2) and higher orbits (n = 3, 4, 5, and so on). Remarkably, as part of his calculation Rnhr was able to derive the value of the Rydberg constant in terms of Planck's constant, the speed of light, and the mass and electric charge of the electron. This gave particular credence to his radical model. Bohr's formula also correctly predicts the wavelengths of other series of spectral lines that occur at nonvisible wavelengths (Figure 5-24i. Using N = 1 gives the Lyman series, which is entirely in the ultraviolet. All the spectral lines in this series involve electron transitions between the lowest Bohr orbit and all higher orbits (« = 2, 3, 4, and so on). This pattern of spectral lines begins with La (Lyman alpha) at 122 nm and converges on L™ at 91.2 nm. Using N = 3 gives a series of infrared wavelengths called the Paschen series. This series, which involves transitions between the third Bohr orbit and all higher orbits, begins with Pa (Paschen alpha) at 1875 nm and converges on Pm at 822 nm. Additional series exist at still longer wavelengths. Atomic Energy Levels Today's view of the atom owes much to the Bohr model, but is different in certain ways. The modem picture is based on quantum mechanics, a branch of physics developed during the 1920s that deals with photons and subatomic particles, As a result of this work, physicists no longer picture electrons as moving in specific orbits dhniir the nucleus Instead, electrons are now known to have both particle and wave properties and are said to occupy only certain energy levels in the atom. An extremely useful way of displaying the structure of an atom is with an energy-level diagram. Figure ^-25 shows such a diagram for hydrogen. The lowest energy level, called the ground state, corresponds to the « = 1 Rohr orbit. Higher energy levels, called excited states, correspond to successively larger Bohr orbits. An electron can jump from the ground state up to the n = 2 level if the atom absorbs a Lyman-alpha photon with a wavelength of 122 nm. Such a photon has energy £ = hc/K = 10.2 eV (electron volts; see Section 5-5). That's why the energy level of n - 2 is shown in Figure 5-25 as having an energy 10.2 eV above that of the ground state (which is usually assigned a value of 0 eV). Similarly, the n - 3 level is 12.1 eV above the ground state, Lyman series (ultraviolet) of spectral lines: produced by electron transitiun;; between the m = 1 orbit and higher orbit: {n =2,3,4,...) Balmer series (visible and ultraviolet) of spectral lines: produced by elzcrron transitions between then =2 orbit and higher orbits ( r. = 3, 4,5, ...) Paschen series (infrared] of spectral lines: produced by electron transitions between the n = 3 orbit and higher orbits (« = 4, 5,6,...) and so forth. Electrons can make transitions to higher energy levels by absorbing a photon or in a collision herween atoms; rhey can make transitions to lower energy levels by emitting a photon. On the energy-level diagram for hydrogen, the n = « level has an energy of 13.6 eV. (This corresponds to an infinitely large orbit in the Bohr model.) If the electron is initially in the ground state and rhe atom absorbs a photon of any energy greater than 13.6 eV, the electron will be removed completely from the atom. This process is called ionization. A 13.6-eV photon has a wave- ( Visible am ! Ultraviole -12.8 eV -12.1 eV Figure 5-25 Energy-Level Diagram of Hydrogen A convenient way to display the structure of the hydrogen atom is in a diagram like this, which shuws He allowed energy levels. The diagram shows a number of possible electron jumps, or transitions, between energy levels. An upward transition occurs when the atom absorbs a photon; a downward transition occurs when the atom emits a photon. (Compare with Figure 5-24) length of 91.2 nm, equal to the shortest wavelength in the ultraviolet Lyman series (LMJ, So any photon with a wavelength of 91-2 nm or less can ioniie hydrogen. (The Planck formula £ = hc/k tells us that the higher the photon energy, the shorter the wavelength.) i As an example, the gaseous nebula shown in Figure 5-18 surrounds a cluster of hot stars which produce copious amounts of ultraviolet photons with wavelengths less than 91.2 nm. Hydrogen atoms in the nebula that absorb' these photons become ionized and lose their electrons. When the electrons recombine with the nuclei, they cascade down the energy levels to the ground state and emit visible light in the process. This process is what makes the nebula glow. The Spectra of Other Elements .-r&sa&k The same basic principles that explain the hydrogen spectrum also apply to the atoms of other elements. Electrons in each kind of atom can be only in certain energy levels, so only photons of certain wavelengths can be emitted or absorbed. Because each kind of atom has its own unique arrangement of electron levels, the pattern of spectral Icnes is likewise unique to that particular type of atom [see the photograph that opens this chapter). These patterns are in general much more complicated than for the hydrogen atom. Hence, there is no simple relationship analogous to the Bohr formula that applies to the spectra of all aLouis. The idea of energy levels explains the emission line spectra and absorption line spectra of gase*. Rut what about the continuous spectra produced by dense objects like the filament of a lightbulb or the coils of a toaster? These objects are made of atoms, so why don't they emit light with an emission line spectrum characteristic of the particular atoms of which they are made? The reason is directly related to the difference between a gas on the one hand and a liquid or solid on the other. In a gas, atoms are widely separated and can emit photons without interference from other atoms. But in a liquid or a solid, atoms are so close that they almost touch, and thus these atoms interact strongly with each other. These interactions interfere with the process of emitting photons. As a result, the pattern of distinctive bright spectral lines that the atoms would emit in isolation becomes "smeared out" into a continuous spectrum. Think of atoms as being like tuning forks. If you strike a single tuning fork, it produces a sound wave with a single clear frequency and wavelength, just as an isolated atom emits light of definite wavelengths. But if you shake a box packed full of tuning forks, you will hear a clanging noise that is a mixture of sounds of all different frequencies and wavelengths. This is directly analogous to the continuous spectrum of light emitted by a dense object with closely packed atoms. With the work of such people as Planck, Einstein, Rutherford, and Bohr, the interchange between astronomy and physics came full circle. Modern physics was born when Newton set out to understand the motions of the planets. Two and a half centuries later, physicists in their laboratories probed the properties of light and the structure of atoms. Their labors had immediate applica- The Nature of Light tions in astronomy. Armed with this new understanding nf light and matter, astronomers were able to probe in detail the chemical and physical properties of planets, stars, and galaxies. 5-9 The wavelength of a spectral line is affected by the relative motion between the source and the observer In addition to telling us about temperature and chemical composition, the spectrum of a planet, star, or galaxy can also reveal something about that object's motion through space. This idea dates from 1842, when Christian Doppler, a professor of mathematics in Prague, pointed out that the observed wavelength of light must be affected by motion. The Doppler effect makes it possible to tell whether astronomical objects are moving toward us or away From us The Doppler Effect In Pigure 5-26 a light source is moving from right to left; the circles represent the crests of waves emitted from the moving source at various positions. Each successive wave crest is emitted from a posidon slightly closer to the observer on the left, so she sees a shorter wavelength—the distance from one crest to the next—than she would if the source were stationary. All the line*; in the spectrum Wave crest 1: emitted when light source was a: Sj v Wave crest 2: emitted when lighr source was at S2 Wave crests 3 and emitted when light source was at S3 and X S4, respectively Figure 5-2G The Doppler Effect The wavelength of light is affected by motion hptween the light source and an observer. The light source shown here is moving, so wave costs 1. 2. etc.. emit-.ed when the sojree was at points 5i, S2, etc., are crowded together in front of the source but are spread out behind it. Consequently, wavelengths are shortened (biLes.hift.ed) if the source is moving toward the observer ana lengthened (redshifted) if the source is moving away from the observer. Motion perperdicular to an observer's line nf sight does not affect wavelength. 122 Chapter 5 The Nature of Light 123 Tools of the Astronomer's Trade Applications of the Doppier Effect Doppler's formula relates the radial velocity of an astronomical object to the wavelength shift of its spectral lines. Here are two examples that show how to use this remarkably powerful formula. EXAMPLE: As measured in the laboratory, the prominent Ha spectral line of hydrogen has a wavelength Xo ~ 656.2S5 nm. But in the spectrum of the star Vega (Figure 5-21), this line has a wavelength X. = 656.255 nm. What can we conclude about the motion of Vega? Situation: Our goal is to use the ideas of the Doppier effect to find the velocity of Vega toward or away from Earth. TdoIs: We use the Doppier shift formula, X/Xq = vfc, to determine Vega's velocity v. Answer: The wavelength shift is AX = X - X0 = 656.255 nm - 656.285 nm = -0.030 nm The negative value means that we see the light from Vega shifted to shorter wavelengths—that is, there is a blueshift. (Note that the shift is very tiny and can be measured only using specialized equipment.) From the Doppier shift formula, the star's radial velocity is c— - (3.00 x 10s km/s) I Xo ' -0.030 nm ^ 656.285 nm I Review: The minus sign indicates that Vega is coming toward us at 14 km/s. The star may also be moving perpendicular to the line from Earth to Vega, but such motion produces no Doppier shift. By plotting the motions of stars such as Vega toward and away from us, astronomers have been able to learn how the Milky Way Galaxy (of which our Sun is a part] is rotating. From this knowledge, and aided by Newton's universal law of gravitation (see Section 4-7), they have made the surprising discovery that the Milky Way contains roughl/ 10 times more matter than had once been thoughtl The nature of this unseen dark matter is still a subject of debate. EXAMPLE: In the radio region of the electromagnetic spectrum, hydrogen atoms emit and absorb photons with a wavelength of 21.12 cm, giving rise to a spectral feature commonly called the 21-centimeter line. The galaxy NGC 3840 in the constellation Leo (the Lion) is receding from us at a speed of 7370 km/s, or about 2.5% of the speed of light. At what wavelength do we expect to detect the 21-cm line from this galaxy? Situation: Given the velocity of NGC 3840 away from us, our goal is to find the wavelength as measured on Earth of the 21-centimeter hne from this galaxy. Tools: We use the Doppier shift formula to calculate the wavelength shift AX, then use this to find the wavelength X measured on Earth. Answer: The wavelength shift is = (21.12 cm) 3.00 X 105 km/s J Therefore, we will detect the 21-cm line of hydrogen from this galaxy at a wavelength of X = X0 + AX = 21.12 cm + 0.52 cm = 21.64 cm Review: The 21-cm line has been redshifted to a longer wavelength because the galaxy is receding from us. In fact, most galaxies are receding from us. This observation is one of the key pieces of evidence that the universe is expanding, and has been doing so since the Big Bang that took place almost 14 billion years ago. of an approaching source are shifted toward the short-wavelength (blue) cud of the spectrum. This phenomenon is called a blueshift. The source is receding from the observer on the right in Figure 5-26. The wave crests that reach him are stretched apart, so that he sees a longer wavelength than he would if the source were stationary. All the lines in the spectrum of a receding source are shifted toward the longer-wavelength (red) end of the spectrum, producing a redshift. In general, the effect of relative motion on wavelength is called the Doppier effect. Police radar guns use the Doppier effect to check fot cars exceeding the speed limit: The radar gun sends a radio wave toward the car, and measures the wavelength shift of the reflected wave (and thus the speed of the car). ^MALQfiY You have probably noticed a similar Doppier effect for sound waves. When a police car is approaching, the sound waves from its siren have a shorter wavelength and higher frequency than if the siren were at rest, and hence you hear a higher pitch. After the police car passes you and is moving away, you hear a lower pitch from the siren because the sound waves have a longer wavelength and a lower frequency. Suppose that Xo is the wavelength of a particular spectral line from a light source that is not moving. It is the wavelength that you might look up in a reference book or determine in a laboratory experiment for this spectral line. If the source is moving, this particular spectral line is shifted to a different wavelength X. The size of the wavelength shift is usually written as AX, where AX = \ - Xq. Thus, AX is the difference between the wavelength listed in reference books and the wavelength chat you actually observe in the spectrum of a star or galaxy. Doppier proved that the wavelength shift (AX) is governed by the following simple equation: Doppler shift equation AX AX = wavelength shift Xo = wavelength if source is not moving v = velocity of the source measured along the line of sight c = speed of light = 3.0 X 105 km/s CAUTION! The capita] Greek letter A (delta) is commonly used to denote a change in the value of a quantity. Thus, AX is the change in the wavelength X due to the Doppier effect. It is not equal to a quantity A multiplied by a second quantity X! Interpreting the Doppier Effect The velocity determined from the Doppier effect is called radial velocity, because v is the component of the star's motion parallel to our line of sight, or along the "radius" drawn from Earth to the star. Of course, a sizable fraction of a star's motion may be perpendicular to our line of sight. The speed of this transverse movement across the sky does not affect wavelengths if the speed is small compared with c. (iox 5-6 includes two examples of calculations with radial velocity using the Doppier formula. CAUTION! The redshifts and hhieshifts of stars visible to the : naked eye, or even through a small telescope, are only a small ; fraction of a nanometer. These tiny wavelength changes are far too small to detect visually. (Astronomers were able to detect the tiny Doppier shifts of starlight only after they had developed highly sensitive equipment for measuring wavelengths. This was | done around 1890, a half-century after Doppler's original pro-; posal.j So, if you see a star with a red color, it means that the : star really is red; it does not mean that it is moving rapidly away : from us. The Doppier effect is an important tool in astronomy because it uncovers basic information about the motions of planets, starss and galaxies. For example, the rotation of the planet Venus was deduced from the Doppier shift of radar waves reflected from its surface. Small Doppier shifts in the spectrum of sunlight have shown that the entire Sun is vibrating like an immense gong. The back-and-forth Doppier shifting of the spectral lines of certain stars reveals that these stars are being orbited by unseen companions; from this astronomers have discovered planets around other stars and massive objects that may be black holes. Astronomers also use the Doppier effect along with Kepler's third law to measure the masses of galaxies. These are but a few examples of how Doppler's discovery has empowered astronomers in their quest to understand the universe. In this chapter we have glimpsed how much can be learned by analy2ing light from the heavens. To analyze this light, however, it is first necessary to collect as much of it as possible, because most light sources in space are very dim. Collecting the faint light from distant objects is a key purpose of telescopes. In the next chapter we will describe both how telescopes work and how they are used. Key Words Terms preceded by an asterisk (*) are discussed in the Boxes. absolute zero, p. 104 absorption line spectrum, p, 112 atom, p. 104 * atomic number, p. 118 Balmer line, p. 116 Balmer series, p. 116 blackbody, p, 106 blackhody curve, p. 106 blackbody radiation, p. 106 blueshift, p. 122 Bohr orbits, p. 117 compound, p. 112 continuous spectrum, p. 112 * degrees Celsius, p. 105 ""degrees Fahrenheit, p. 105 Doppier effect, p. 122 electromagnetic radiation, p. 101 electromagnetic spectrum, p. 102 electromagnetism, p. 100 electron, p. 109 electron volt, p. 110 element, p. Ill emission line spectrum, p. 112 energy flux, p. 107 energy level, p. 120 energy-level diagram, p. 120 excited state, p. 120 frequency, p. 102 gamma rays, p. 102 ground state, p. 120 infrared radiation, p. ionization, p. 120 ''isotope, p. 101 . 118 joule, p. 107 kelvin, p. 104 Kirchhoff's laws, p. 112 light scattering, p. 112 * luminosity, p. 108 Lyman series, p. 120 microwaves, p. 102 molecule, p. 112 nanometer, p. 101 neutron, p. 116 nucleus, p. 116 Paschen series, p. 120 "periodic table, p. 118 photoelectric effect, p. 109 photon, p. 108 Planck's law, p. 110 proton, p. 116 quantum mechanics, p. 120 radial velocity, p. 123 radio waves, p. 101 redshift, p. 122 "solar constant, p. 108 spectral analysis, p. Ill spectral line, p. Ill spectroscopy, p. 113 spectrum {plural spectra), p. 99 Stefan-Boltzmann law, p. 107 ultraviolet radiation, p. 102 visible light, p. 101 watt, p. 107 wavelength, p. 101 wavelength of maximum emission, p. 105 Wien's law, p. 107 X tays, p. 102 Key Ideas The Natute of Light: Light is electromagnetic radiation. It has wavelike properties described by its wavelength X and frequency v, and travels through empty space at the constant speed c 3.0 X 108 m/s = 3.0 X 105 km/s. Blackbody Radiation: A blackbody is a hypothetical object that is a perfect absorber of electromagnetic radiatior at all wavelengths. Stars closely approximate the behavior of blackbodies, as do other hot, dense objects. 124 Chapter 5 The Nature of Ligh: 125 • The intensities of radiation emitted at various wavelengths by a Mark-body at a given Temperature are shown by a blackbody curve. • Wien's law states that the dominant wavelength at which a blackbody emits electromagnetic radiation is inversely proportional to the Kelvin temperature of the object: Xmax (in meters) = (0.0029 K m)/T. • The Stefan-Boltzmann law states that a blackbody radiates elec-trumagnetic waves with a total energy flux F directly proportional to the fourth power of the Kelvin temperature T of the object: F = o-T4. Photons: An explanation of blackbody curves led to the discovery that light has particlelike properties. The particles of light are called photons. • Planck's law relates the energy E of a photon to its frequency v or wavelength X: E = hv - hci\, where h is Planck's constant. Kirchhoff's Laws: Kirchhoff's three laws of spectral analysis) describe conditions under which different kinds of spectra are produced. • A hot, dense object such as a blackbody emits a continuous spectrum covering all wavelengths. • A hot, transparent gas produces a spectrum that contains bright (emission) lines. • A cool, transparent gas in front of a light source that itself has a continuous spectrum produces dark (absorption) lines in the continuous spectrum. Atomic Structure: An atom has a small dense nucleus composed of protons and neutrons. The nucleus is surrounded by electrons that occupy only certain orbits or energy levels. » When an electron jumps from one energy level to another, it emits or absorbs a photon of appropriate energy (and hence of a specific wavelength). • The spectral lines of a particular element correspond to the various electron transitions between energy levels in atoms of that element. « Bohr's model of the atom correctly predicts the wavelengths of hydrogen's spectral lines. The Doppler Shift: The Doppler shift enables us to determine the radial velocity of a light source from the displacement of its spectral lines. < The spectral lines of an approaching light source are shifted coward short wavelengths (a blueshift); the spectral lines of a receding light source are shirred toward long wavelengths (a redshift). • The size of a wavelength shirt is proportional to the radial velocity of the light source relative to the observer. Questions Review Questions 1. When Jupiter is undergoing retrograde motion as seen from Earth, would you expect the eclipses of Jupiter's moons to occur several minutes early, several minutes late, or neither? Explain your answer. Approximately how many times around Earth could a beam of light travel in one second? How long does it take light to travel from the Sun to Earth, a distance of 1.50 X 103 km? -tQ^lrV „ 4. How did Newton show that a prism breaks white light into its component colors, but does not add any color to the light? 5. For each of the following wavelengths, state whether it is in the radio, microwave, infrared, visible, ultraviolet, X-ray, or gamma-ray portion of the electromagnetic spectrum. Explain your reasoning, (a) 2.6 urn, (b) 34 m, (c) 0.54 nm, (d) 0.0032 nm, (e) 0.620 u,m, (f) 310 nm, (g) 0.012 m 6. What is meant by the frequency of light? How is frequency related to wavelength? 7. A cellular phone is actually a radio transmitter and receiver. You receive an incoming call in the form of a radio wave of frequency 880.65 MHz. What is the wavelength (in meters) of this wave? 8. A light source emits infrared radiation ar a wavelength of 1150 nm. What is the frequency of this radiation? 9. (a) What is a blackbody? (b) In what way is a blackbody black? (c) If a blackbody is black, how can it emit light? (d) If you were to shine a flashlight beam on a perfect black-body, what would happen to the light? 10. Why dn astronomers find it convenient to use the Kelvin temperature scale in their work rather than the Celsius or Fahrenheit scale? 11. Explain why astronomers are interested in blackbody radiation. S^At.t- *2- Using Wicn's law and the Stefan-Boltzmann law, explain the color and intensity changes that are _ observed as the temperature of a hot, glowing object increases. 13. If you double the Kelvin temperature of a hot piece of steel, how much more energy will it radiate per second? 14. The bright star Bcllatnx in the constellation Orion has a surface temperature of 21,500 K. What is its wavelength of maximum emission in nanometers? What color is this star? 15. The bright star Antares in the constellation Scorpius (the Scorpion) emits the greatest intensity of radiation at a wavelength of 853 urn. What is the surface temperature of Antares? What color is this star? 16. (a) Describe an experiment in which light behaves like a wave, (b) Describe an experiment in which light behaves like a particle. 17. How is the energy of a photon related to its wavelength? What kind of photons carry the most energy? What kind oi photons carry the least energy? To emit the same amount of light energy per second, which must emit more photons per second: a source of red light, or a source of blue light? Explain your answer. 19. Explain how we know that atoms have massive, compact nuclei. 20. (a) Describe the specrrnm of hydrogen at visible wavelengths, (b) Explain how Bohr's model of the atom accounts for the Baimer lines. 18. 21. Why do different elements display different patterns of lines m tneir spectra? 22. What is the Doppler effect? Why is it important to astronomers? 23. If y°u see a D'ue srar» what does'its color tell you about how the star is moving through space? Explain your answer. Advanced Questions Questions preceded by an asterisk (*) involve topics discussed in the Boxes. Problem-solving tips and tools You can find formulas in Box 5-1 for converting between temperature scales. Box 5-2 discusses how a star's radius, luminosity, and surface temperature are related. Box 5-3 shows how to use Planck's law to calculate the energy of a photon. To learn how to do calculations using the Doppler effect, see Box 5-6. 24. Your normal body temperature is 98.6"F. What kind of radiation do you predominantly emit? At what wavelength (in nm) do you emit the most radiation? 25. What is the temperature of the Sun's surface in degrees Fahrenheit? 26. What wavelength of electromagnetic radiation is emitted with greatest intensity by this book? To what region of the elec-ttomagnetic spectrum does this wavelength correspond? 27. Black holes are objects whose gravity is so strong that not even an object moving at the speed of light can escape from their surface. Hence, black holes do not themselves emit light. But it is possible to detect radiation from material falling toward a black hole. Calculations suggest that as this matter falls, it is compressed and heated to temperatures around 106 K. Calculate the wavelength of maximum emission for this temperature. In what part of the electromagnetic spectrum does this wavelength lie? ""28. Use the value of the solar constant given in Box 5-2 and the distance from Earth to the Sun to calculate the luminosity of the Sun. *29. The star Alpha Lupi (the brightest in the constellation Lupus, the Wolf) has a surface temperature of 21,600 K. How much more energy is emitted each second from each square meter of the surface of Alpha Lupi than from each square meter of the Sun's surface? *30. Jupiter's moon lo has an active volcano named Pele whose temperature can be as high as 320°C. (a) What is the wavelength of maximum emission for the volcano at this temperature? In what part of the electromagnetic spectrum is this? (b) The average temperature of lo's surface is — 150°C. Compared with a square meter of surface at this temperature, how much more energy is emitted per second from each square meter of Pele's surface? *31. The bright star Sirius in the constellation of Canis Major (the Large Dog) has a radius of 1.67 RQ and a luminosity of 25 L©, (a) Use this information to calculate the energy flux at the surface of Sirius. (b) Use your answer in part (a) to cal- culate the surface temperature of Sinus. How does your answer compare to the value given in Box 5-2? 32. In Figure 5-13 you can see two distinct dark lines at the boundary between the orange and yellow parts of the Sun's spectrum [in the center of the third colored band from the top of the figure). The wavelengths of these dark lines are 588.99 and 589.59 nm. What do you conclude from this about the chemical composition of the Sun's atmosphere? [Hint: See Section 5-t>.) 33. Instruments on board balloons and spacecraft detect 511-keV photons coming from the direction of the center of our Galaxy. (The prefix k means kilo, or thousand, so 1 keV = 103 eV.) What is the wavelength of these photons? To what part of the electromagnetic spectrum do these photons belong? 34. (a) Calculate the wavelength of P& (P-delta), the fourth wavelength in the Paschen series, (b) Draw a schematic diagram of the hydrogen atom and indicate the electron transition that gives rise to this spectral line, (c) In what part of the electromagnetic spectrum does this wavelength lie? 35. (a) Calculate the wavelength of H,, (H-eta), the spectral line for an electron transition between the n = 7 and n = 2 orbits of hydrogen, (b) In what part of the electromagnetic spectrum does this wavelength lie? Use this to explain why Figure 5-21 is labeled r IQ Q x g. 36. Certain interstellar clouds contain a very cold, very thin gas of hydrogen atoms. Ultraviolet radiation with any wavelength shorter than 91.2 nm cannot pass through this gas; instead, it is absorbed. Explain why. 37. (a) Can a hydrogen atom in the ground state absorb an H-alpba (Ha) photon? Explain why or why not. (b) Can a hydrogen atom in the n = 2 state absorb a Lyman-alpha (L^,) photon? Explain why or why not. 38. An imaginary atom has just 3 energy levels: 0 eV, 1 eV, and 3 eV. Draw an energy-level diagram for this atom. Show all possible transitions between these energy levels. For each transition, determine the photon energy and the photon wavelength. Which transitions involve the emission or absorption of visible light? 39. The star cluster NGC 346 and nebula shown in Figure 5-18 are located within the Small Magellanic Cloud (SMC), a small galaxy rhat orbits our Milky Way Galaxy. The SMC and the stars and gas within it are moving away from us at 158 km/s. At what wavelength does the red Ha line of hydrogen (which causes the color of the nebula) appear in the nebula's spectrum? 40. The wavelength of HQ in the spectrum of the alar Mcgrez in the Rig Dipper (part of the constellation Ursa Major, the Great Bear) is 486.112 nm. Laboratory measurements demonstrate that the normal wavelength of this spectral line is 486.133 nm. Is the star coming toward us or moving away fioin us? At what speed? 41. You are given a traffic ticket foi going through a red light (wavelength 700 nm). You tell the police officer that because you wete approaching the light, the Doppler effect caused a blueshift that made the light appear green (wavelength 500 nm). How fast would you have had to be going foe this to be true? Would the speeding ticket be justified? Explain your answer. 138 Chapters Optics and Telescopes 139 Figure 6-13 Spherical Aberration (a) Different parts of a spherically concave mhur reflect light to slightly different points. This effect, called spherical aberration, causes image blurring. This difficulty can be corrected by either (b) using a parabolic mirror or (c] using a correcting lens in front of the mirror. from a defect called coma, wherein star images far from the center of the field of view are elongated to look like tiny teardrops. A different approach is to use a spherical mirror, thus minimizing coma, and to place a thin correcting lens at the front of the telescope to eliminate spherical aberration (Figure 6-l3c). This approach is only used on relatively small reflecting telescopes for amateur astronomers. The Largest Reflectors There are over a dozen optical reflectors in operation « with primary mirrors between 8 meters (26.2 feet) and _V 11 meters (36.1 feet) in diameter. figure 6-14<7 shows the objective mirror of one of the four Very Large Telescope (VLT) units in Chile, and Figure 6-14b shows the objective and secondary mirrors oi the Gemini North telescope in Hawaii. A near-twin of Gemini North, cailed Gemini South, is in Cerro Pachon, Chile. These twins aJlow astronomers to observe both the northern and southern parrs of the celestial sphere with essentially the same state-of-the-art instrument. Two other "twins" are the side-by-side 8.4-m objective mirrors of the Large Binocular Telescope in Arizona. Combining the light from these two mirrors gives double the light-gathering power, equivalent to a single 11.8-m mirror. [b) A large Cassegrain telescope Figure 6-14 RlffuxG Reflecting Telescopes (a) This photograph shows technicians preparing an objective mirror 8.2 meters in diameter for the European Southern Observatory in Chile. The minor was ground to a curved shape with a remarkable precision of 8.5 nanometers (b) This view o* the Gemini North telescope shews its 8.1-meter objective mirror (1). Light incident on this mirror is reflected toward the 1.0-meter secondary mirror (2), then through Lhe hole in the objective mirror (3) to the Cassegrain focus (see Figure 6-115). {a: SAGEM; b: N0AO/AURA/N5F) Several other reflectors around the world have objective mirrors between 3 and 6 meters in diameter, and dozens of smaller but still powerful telescopes have mirrors in the range of 1 to 3 meters. There are thousands of professional astronomers, each of whom has several ongoing research projects, and thus the demand for all of these telescopes is high. On any night of the year, nearly every research telescope in the world is being used to explore the universe. ?6-3 Telescope images are degraded by the blurring effects of the atmosphere and by light pollution /SEgmLe In addition to providing a brighter image, a large tele-■^0 sc0Pe a'so helps achieve a second major goal: It pro-duces star images that are sharp and crisp. A quantity :alled angular resolution gauges how well fine details can be seen. Poor angular resolution causes star images to be fuzzy and blurred ■ogether. To determine the angular resolution of a telescope, pick out wo adjacent stars whose separate images are just barely dis-:ernible (Hguie 6-15). The angle 8 (the Greek letter theta) be-ween these stars is the telescope's angular resolution; the smaller rhat angle, the finer the details that can be seen and the sharper :he image. When you are asked to read the letters on an eye chart, that's being measured is the angular resolution of your eye. If tou have 20/20 vision, the angular resolution 6 of your eye is ibout 1 arcminute, or 60 arcseconds. (You may want to review the definitions of these angular measures in Section 1-5.) Hence, with the naked eye it is impossible to distinguish two stars less than 1 arcminute apart or to see details on the Moon with an angular size smaller than this. All the planets have angular sizes (as seen from Earth) of 1 arcminute or less, which is why they appear as featureless points of light to the naked eye. Limits to Angular Resolution One factor limiting angular resolution is diffraction, which is the tendency of light waves to spread out when they are confined to a small area like the lens or mirror of a telescope. (A rough analogy is the way water exiting a garden hose sprays out in a wider angle when you cover part of the end of the hose with your thumb.) As a result of diffraction, a narrow beam of light tends to spread out within a telescope's optics, thus blurring the image. If diffraction were the only limit, the angular resolution of a telescope would be given by the formula Diffraction-limited angular resolution 9 = 2.5 X 105 ~ 6 = diffraction-limited angular resolution of a telescope, in arcseconds X — wavelength of light, in meters D = diameter of telescope objective, in meters Two light sources with anguiar separation greater than angular resolution of telescope: Two sources easily distinguished Light sources moved closer so that angular separation equals angular resolution of telescope: Just barely possible to tell that there are two (b) Figure 6-15 riQuxg Angular Resolution The angular resolution of a telescope incicates the sharpness of the telescope's images, (a) This telescope view shows two sources of light whose angular separation is greater than the angular resolution, (b) The light sources have been moved together so that their angular separation is equal to the angular resoluticn. If the sources were moved any closer together, the telescope image would show them as a single source. For a given wavelength of light, using a telescope with an objective of larger diameter D reduces the amount of diffraction and makes the angular resolution 9 smaller (and hence better). For example, with red light with wavelength 640 nm, or 6.4 X 10-7 m, the diffraction-limited resolution of an 8-meter telescope (see Figure 6-15) would be 9 = (2.5 X 105) 6.4 X 10~7 r 8 m = 0.02 arcsec In practice, however, ordinary optical telescopes cannot achieve such fine angular resolution. The problem is that turbulence in the air causes star images to jiggle around and twinkle. Even through the largest telescopes, a star still looks like a tiny blob rather than a pinpoint of light. A measure of the limit that atmospheric turbulence places on a telescope's resolution is called the seeing disk. This disk is the angular diameter of a star's image broadened by turbulence. The size of the seeing disk varies from one observatory site to another and from one night to another. At the observatories on Kkt Peak in Arizona and Cerro Tololo in Chile, the seeing disk is typically around 1 arcsec. Some 140 Chapter 6 Figure 6-1G riHuxg The Telescopes of Mauna Kea The summit of Mauna Kea—an extinct Hawaiian volcano that reaches more than 4100 m (13,400 ft) above the waters of the Pacific -has nighttime skies that are unusually clear, still, and dark. To take advantage of these superb viewing conditions, Mauna Kea has become the home of many powerful telescopes. (Richard J. Wainscoat, University of Hawaii) of the very best conditions in the world can be found at the observatories atop Mauna Kea in Hawaii, where the seeing disk is often as small as 0.5 arcsec. These great conditions are one reason why so many telescopes have been built there (Fi^im: (vlí>). Active Optics and Adaptive Optics In many cases the angular resolution of a telescope is even worse than the limit imposed by the seeing disk. This occurs if the objective mirror deforms even slightly due to variations in air temperature or flexing of the telescope mount. To combat this, many large telescopes are equipped with an active optics system. Such a system adjusts the mirror shape every few seconds to help keep the telescope in optimum focus and properly aimed at its target. Changing the mirror shape is also at the heart of a more refined technique called adaptive optics. The goal of this technique is to compensate for atmospheric_______ turbulence, so that the angular reso- Adaptive optics produces i be smaller than the s eof the seeing disk and can even ap- sharper images by proach the theoretical limit set by "undQN" atmospheric diffraction. Turbulence causes the turbulence ^ ________ ^ image of a star to "dance" around erratically. In an adaptive optics system, sensors monitor this dancing motion 10 to 100 times per second, and a powerful computer rapidly calculates the mirror shape needed to compensate. Fast-acting mechanical devices called actuators then deform the mirror accordingly, at a much faster rate than in an active optics system. In some adaptive optics systems, the actuators deform a small secondary mirror rather than the large objective mirror. One difficulty with adaptive optics is that a fairly bright star must be in or near the field of the telescope's view to serve as a "target" for the sensors that track atmospheric turbulence. This is seldom the case, since the field of view of most telescopes is rather narrow. Astronomers get around this limitation by shining a laser beam toward a spot in the sky near the object to be observed (Figure 6-17). The laser beam causes atoms in the upper atmosphere to glow, making an artificial "star." The light that comes down to Earth from this "star" travels through the same part of our atmosphere as the light from the object being observed, so its image in the telescope will "dance" around in the same erratic way as the image of a real star. FiiiiLf l' Ci-1 S shows the dramatic improvement in angular resolution possible with adaptive optics. Images made with adaptive optics are nearly as sharp as if the telescope were in the vacuum of space, where there is no atmospheric distortion whatsoever and the only limit on angular resolution is diffraction. A number of large telescopes are now being used with adaptive optics systems. CAUTION! The images in Figure 6-18 are false color images: They do not represent the true color of the stars shown. False color is often used when the image is made using wavelengths that the eye cannot detect, as with the infrared images in Figure 6-18. A different use of false color is to indicate the relative brightness of different parts of the image, as in the infrared im- . age of a person in Figure 5-10. Throughout this book, we'll always point out when false color is used in an image. Interferometry Several large observatories are developing a technique called interferometry that promises to further improve the angular resolution of telescopes. The idea is to have two widely separated telescopes observe the same object simultaneously, then use fiber optic cables to "pipe" the light signals from each telescope to a central location where they "interfere" or blend together. This method makes the combined signal sharp and clear. The effective resolution of such a combination of telescopes is equivalent to that of one giant telescope with a diameter equal to the baseline, or distance between the two telescopes. For example, the Keck I Figure 5-17 riQuxg Creating an Artificial "Sta " A laser beam shines upward from Yepun, an 8,2-meter telescope at the European Southern Observatory in the Atacama Desert of Chile. (Figure 6-14a shows the objective mirror for this telescope.) The beam strikes sodium atoms that lie about 90 km (56 miles) above Earth's surface, causing them to glow and iiake an artificial "star." Tracking Ore twinkling of this "star" makes it possible to undo the effects of atmospheric turbulence on telescope images. [European Southern Observatory) and Keck II telescopes atop Mauna Kea (Figure 6-16) are 85 meters apart, so when used as an interferometer the angular resolution is the same as a single 85-meter telescope. Interferometry has been used for many years with radio telescopes (which we will discuss in Section 6-6), but is still under development with telescopes for visible light or infrared wavelengths. Astronomers are devoting a great deal of effort to this development because the potential rewards are great. For example, the Keck I and II telescopes used together should give an angular resolution as small as 0.O05 arcsec, which corresponds to being able to read the bottom row on an eye chart 36 km (22 miles) away! Optics and Telescopes 141 Light Pollution ^fS&j^ Light from city street lamps and from buildings also degrades telescope images. This light pollution illumi-^^0f nates the sky, making it more difficult to see the stars. You can appreciate the problem if you have ever looked at the night sky from a major city. Only a few of the very brightest stars can be seen, as against the thousands that can be seen with the naked eye in the desert or the mountains. To avoid light pollution, observatories are built in remote locations far from any city lights. Unfortunately, the expansion of cities has brought light pollution to observatories that in former times had none. As an example, the growth of Tucson, Arizona, has had deleterious effects on observations at the nearby Kitt Peak National Observatory. Efforts have been made to have cities adopt light fixtures that provide safe illumination for their citizens but produce little light pollution. These efforts have met with only mixed success. One factor over which astronomers have absolutely no control is the weather. Optical telescopes cannot see through clouds, so it is important to build observatories where the weather is usually good. One advantage of mountaintop observatories such as Mauna Kea is thai most clouds form ar altitudes below the observatory, giving astronomers a better chance of having clear skies. In many ways the best location for a telescope is in orbit around Earth, where it is unaffected by weather, light pollution, or atmospheric turbulence. We will discuss orbiting telescopes in Section 6-7. Figure 5-18 rQvuxg Using Adaptive Optics to "Unbtur" Telescope Images The two false-color, inset images show the same 1-arcsecond-wide regior of the sky at infrared wavelengths as observed with the 10.0-m Keck 11 telescope on Mauna Kea (see Figure 6-16). Without adaptive optics, it is impossible to distinguish individual stars in this region. With adaptive optics turned on, more than two dozen stars can be distinguished. (UCLA Galactic Center Group) Chapter 15 Pluto and the Kuiper Belt (continued) Mercury, Venus, Earth and Mars are terrestrial planets whose compositions are dominated by rock. Jupiter and Saturn are gas giant planets dominated by their hydrogen and helium envelopes. Uranus and Neptune are ice gianl planets dominated by gases other than hydrogen and helium. The trans-Neptunian objects or "ice dwarf planets," as some are calling them, are probably composed of large amounts of volatiles such as methane ice and water ice. The International Astronomical Union (IAU) recently choose to use a combination of the second and third definitions above to define a planet. That is, a planet is an object that is both spherical and has a unique orbit in which it is gravitationally dominant. An object that only satisfies definition two above and not three is now being called a dwarf planet, of which Ceres, Pluto arid Eris qualify, as well as several more objects in the Kuiper belt. In reality, it's the public that must accept this definition, and we will only know if that is the case a few generations from now. Defining the word "planet" is like defining what an ocean is. At first it appears to be a simple term, but is very hard to precisely define. Further planet discoveries will be made and there are sure to be borderline cases. This is just the way nature is; it does not have little bins to nicely classify objects, but there is usually a continuous array of objects. The important thing to take away from all of this is to understand this array of objects by using our rapidly expanding scientific knowledge and understanding our place in the solar system. 16 Our Star. The Sun is by far the brightest object in the sky. By earthly standards, the temperature of its glowing surface is remarkably high, about 5800 K. Yet there are regions of the Sun at reach far higher temperatures of tens of thousands or even millions of kelvins. Gases at such temperatures emit ultraviolet light, which makes them prominent in the accompanying image from an ultraviolet telescope in space. Some of the hottest and mnst energetic regions nn the Sun spawn immense disturbances and can propel solar material across space to reach Earth and ■ other planets. In recent decades, we have learned that the Sun shines be- ; cause at its core hundreds of millions of tons of hydrogen are converted to helium every second. We have confirmed this picture by detecting the by-products of this transmutation— -• strange, ethereal particles called neutrinos—streaming outward from the Sun into space. We have discovered that the Sun has . a surprisingly violent atmosphere, with a host of features such as sunspots whose numbers rise and fall on a predictable 11- .-. year cycle. By studying the Sun's vibrations, we have begun to probe beneath its surface into hitherto unexplored realms. And we have just begun to investigate how changes in the Sun's ac- . tivity can affect Earth's environment as well as our technoiogi- ■v cal society. Learning Goals By reading the sections of this chapter, you will learn 16-1 The source of the Sun's heat and light 16-2 How scientists model the Sun's internal structure 16-3 How the Sun's vibrations reveal what lies beneath its glowing surface 16-4 How scientists are able to probe the Sun's energy-generating core 16-5 Why the gaseous Sun appears to have a sharp outer edge A composite view of the Sun (at ultraviolet wavelengths) and an upheaval in the Sun's outer atmosphere, or corona (at visible wavelengths) (SOHO'LASCO/EIT/ESA/NASA) 16-1 The Sun's energy is generated by thermoniidorir reactions in its core _ The Sun is the largest member of the solar system. It /i>jf!y%!-.'.. has almost a thousand dmes more mass than all the mjP0 planets, moons, asteroids, comets, and meteoroids put together. But the Sun is also a star. In fact, it is a remarkably typical star, with a mass, size, surface temperature, and chemical composition that are roughly midway between the extremes exhibited by the myriad other stars in the heavens. !(- I lists essential data about the Sun. 16-6 Why the upper regions of the solar atmosphere have an emission spectrum 16-7 The relationship between the Sun's corona and the solar wind 16-8 The nature of sunspots 16-9 The connection between sunspots and the Sun's magnetic field 16-10 How magnetic reconnection can power immense solar eruptions 404 Chapter 16 Our Star, the Sun Table 16-1 Sun Data Distance from Earth: Distance from Light travel time to Earth: Mean angular diameter: Radius: Mass: Composition (by mass): Composition |by number of atoms): Mean density: Mean temperatures: Luminosity: Distance From center of Galaxy: Orbital period around center of Galaxy: Orbital speed around center of Galaxy: Solar Energy For most people, what matters most about the Sun is the energy that it radiates into space. Without the Sun's warming rays, our atmosphere and oceans would freeze into an icy layer coating a desperately cold planet, and life on Earth would be impossible, To understand why we are here, we must understand the nature of the Sun. Why is the Sun such an important source of energy? An important part of the answer is that the Sun has a far higher surface temperature than any of the planets or moons. The Sun's spectrum is close to that of an idealized blackbody with a temperature of 5800 K (see Sections 5-3 and 5-4, especially Figure 5-12). Thanks to this high temperature, each square meter of the Sun's surface emits a tremendous amount of radiation, principally at visible wavelengths. Indeed, the Sun is the only object in the solar system that emits substantial amounts of visible light. The light that we see from the Moon and planets is actually sunlight that struck those worlds and was reflected toward Earth. The Sun's size also helps us explain its tremendous energy output. Because the Sun is so large, the total number of square meters Mean: 1 AU = 149,598,000 km Maximum: 152,000,000 km Minimum: 147,000,000 km 8.32 min 32 arcmin 696,000 km = 109 Earth radii 1.3891 X 1030 kg = 3.33 X 10s Earth masses 74% hydrogen, 25% helium, 1% other elements 92.1% hydrogen, 7.8% helium, D.1% other elements 1410 kg/m3 Surface: 5800 K; Center: 1.55 x 107 K 3.90 x 10Z6W 8000 pc = 26,000 ly 220 million years " li. v U X G INUAOI of radiating surface—that is, its surface area—is immense. Hence, the total amount of energy emitted by the Sun each second, called its luminosity, is very large Indeed or about 3.9 X 1026 watts, {3.9 X 102°' joules of energy emitted per second.) (We discussed the relation among the Sun's surface temperature, radius, and luminosity in Box 5-2.) Astronomers denote the Sun's luminosity by the symbol L©. A circle with a dot in die center is the astronomical symbo- for the Sun and was also used by ancient astrologers. The Source of the Sun's Energy: Early Ideas These ideas lead us to a more fundamental question: What keep! the Sun's visible surface so hot? Or, put another way, what is the fundamental source of the tremendous energies that the Sun radiates into space? For centuries, this question was one of the greatest mysteries in science. The mystery deepened in the nineteenth century, when geologists and biologists found convincing evidence that life has existed on Earth for at least several hundred million years. (We now know that Earth is 4.56 billion years old and that life had existed on it for most of its history,) Since life as we know it depends crucially on sunlight, the Sun must be *s ate the Sun's luminosity of 3.9 X 1026 joules per second is approximately F.rjure 16-1 r iEBuxg this temperature, all solids and liquids vaporize to form gases. It was only , the twentieth century that scientists discovered what has kept the Sun i hot for billions of ysars: the thermonuclea' fusion of hydrogen nuclei in ie Sun's core. (Jeremy woodhouse/PhotoDlsc) Id- The source of the Sun's energy posed a severe problem for bysicists. What source of energy could have kept the Sun shin-ig for so long (Figure Ib-i)? One attempt to explain solar energy was made in the mid-300s by the English physicist Lord Kelvin (for whom the temperature scale is named) and the German scientist Hermann von ■ Helmholtz. They argued that the tremendous weight of the Sun's uter layers should cause the Sun to contract gradually, compress-ig its interior gases. Whenever a gas is compressed, its tempera-ite rises, {You can demonstrate this with a bicycle pump: As you Limp air into a tire, the temperature of the air increases and the amp becomes warm to the touch.) Kelvin and Helmholtz thus suggested that gravitational contraction could cause the Sun's . „ases to become hot enough to radiate energy out into space. This process, called Ketvin-Helmboltz contraction, actually dees occur during the earliest stages of the birth af a star like the . Sun (see Section 8-4). But Kelvin-Helmholtz contraction cannot be the major source of the Sun's energy today. If it were, the Sun would have had to be much larger in the relatively recent past. Helmholtz's own calculations showed that the Sun could have arted its initial collapse from the solar nebula no more than )out 25 million years ago. But the geological and fossil record lows that Earth is far older than that, and so the Sun must be ■ well. Hence, this model of a Sun that shines because it shrinks innot be correct. On Earth, a common way to produce heat and light is by .•■•binning fuel, such as a log in a fireplace or coal in a power plant. Is .t possible that a similar process explains the energy released by 'he Sun? The answer is no, because this process could not con-"nue for a long enough time to explain the age of Earth. The chemical reactions involved in burning release roughly 10-19 • !uule of energy per atom. Therefore, the number of atoms that .. >^ould have to undergo chemical reactions each second to gener- 3.9 X 1026 joules per second 10"19 joul, joule per atom ■ 3.9 X 1045 atoms per second From its mass and chemical composition, we know that the Sun contains about 1057 atoms. Thus, the length of time that would be required to consume the entire Sun by burning is _1057 atoms_ 3.9 X 104i atoms per second = 3 x 1011 seconds There are about 3 X 107 seconds in a year. Hence, in this model, the Sun would bum itself out in a mere 10,000 (104) years! This period of time is far shorter than the known age of Earth, so chemical reactions also cannot explain how the Sun shines. The Source of the Sun's Energy: Discovering Thermonuclear Fusion The source of the Sun's luminosity could be explained if there were a process that was like burning but released much more energy per atom. Then the rate at which atoms would have to be consumed would be far less, and the lifetime of the Sun could be long enough to be consistent with the known age of Earth. Albert Einstein discovered the key to such a process in 1905. According to his special theory of relativity, a quantity tn of mass can in principle be converted into an amount of energy E according to a now-famous equation: Einstein's mass-energy equation £ = mc2 m = quantity of mass, in kg c = speed of light = 3 X 10s m/s £ = amount of energy into which the mass can be converted, in joules The speed of light c is a large number, so c1 is huge. Therefore, a small amount of matter can release ait awesome amount of energy. Inspired by Einstein's ideas, astronomers began to wonder if the Sun's energy output might come from the conversion of matter into energy. The Sun's low density of 1410 kg/m3 indicates that it must be made of the very lightest atoms, primarily hydrogen and helium. In the 1920s, the British astronomer Arthur Ed-dington showed that temperatures near the center of the Sun must be so'high that atoms become completely ionized. Hence, at the Sun's center we expect to find hydrogen nuclei and electrons flying around independent of each other. Another British astronomer,____________ __._______________________ Robert Atkinson, suggested that un- Ideas from relativity and der these conditions hydrogen nuclei nuc|ear physics ted to an could fuse together to produce he- untJerstanding of how the hum nuclei in a nuclear reaction that transforms a tiny amount of mass Sun shines T F •406 Chaptei 16 II" .. f : Converting Mass into Energy The Cosmic Connections figure shows the steps involved in the thermonuclear fusion of hydrogen ar the Sun's center. In these steps, four protons are converted into a single nucleus of 4He, an isotope of helium with rwo protons and two neutrons. (As we saw in Rox 5-5, different isotopes of the same element have the same number of protons but different numbers of neutrons.) The reaction depicted in the Cosmic Connections: The Proton-Proton Chain Step 1 also produces a neutral, nearly massless panicle called the neutrino. Neutrinos respond hardly at all to ordinary matter, so they travel almost unimpeded through the Sun's massive bulk. Hence, the energy that neutrinos carry is quickly lost into space. This loss is not great, however, because the neutrinos carry relatively little energy. (See Section 16-4 for more about these curious particles.) Most of the energy released by thermonuclear fusion appears in the form of gamma-ray photons. The energy of these photons remains trapped within the Sun for a long time, thus maintaining the Sun's intense internal heat. Some gamma-ray photons are produced by the reaction shown as Step 2 in the Cosmic Connections figure. Others appear when an electron in the Sun's interior annihilates a positively charged electron, or positron, which is a by-product of the reaction shown in Step 1 in the Cosmic Connections figure. An electron and a positron are respectively matter and antimatter, and they convert entirely into energy when they meet. (You may have thought that "antimatter" was puce science fiction. In fact, tremendous amounts of antimatter are being created and annihilated in the Sun as you read these words.) We can summarize the thermonuclear fusion of hydrogen as follows: 4 1H-~» 4He + neutrinos -f- gamma-ray photons To calculate how much energy is released in this process, we use Einstein's mass-energy formula; The energy released is equal to the amount of mass consumed multiplied by c2, where c is the speed of light. To see how much mass is consumed, we compare the combined mass of four hydrogen atoms (the ingredients) to the mass of one helium atom (the product): 4 hydrogen atoms = 6.693 X 10"~27 kg -1 helium atom = 6.645 X 10~37 kg Mass lost - 0.048 x 10"27 kg Tools of the Astronomer's Trade Thus, a small fraction (0.7%) of the mass of the hydrogen going into the nuclear reaction does not show up in the mass of the helium. This lost mass is converted into an amount of energy E'= mc2: E = mc2 = (0.048 X 10~27 kg)(3 X 10s m/s)2 = 4.3 X 10~u joule This amount of energy is released by the formation of a single helium atom. It would light a 10-watt lightbulb for almost one-half of a trillionth of a second. EXAMPLE: How much energy is released when 1 kg of hydrogen is converted to helium? Situation: "We are given the initial mass of hydrogen. We know that a fraction of the mass is lost when the hydrogen undergoes fusion to make helium; our goal is to find the quantity of energy into which this lost mass is transformed. Tools: We use the equation £ = mc2 and the result that 0.7% of the mass is lost when hydrogen is converted into hydrogen. Answer: When 1 kilogram of hydrogen is converted to helium, the amount of mass lost is 0.7% of 1 kg, or 0.007 kg. (This means that 0.993 kg of helium is produced.) Using Einstein's equation, we find that this missing 0.007 kg of matter is transformed into an amount of energy equal to E = mc2 = (0.007 kg)(3 X 108 m/s)2 = 6.3 X 1014 joules Review: The energy released by the fusion of 1 kilogram of hydrogen is the same as that released by burning 20,000 metric tons (2 X 107 kg) of coal! Hydrogen fusion is a much more efficient energy source than ordinary burning. The Sun's luminosity is 3.9 X 1026 joules per second. To generate this much power, hydrogen must be consumed at a rate of 3.9 X 102S joules per second 6.3 X 1014 joules per kilogram = 6 X 10n kilograms per second That is, the Sun converts 600 million metric tons of hydrogen into helium every second. into a large amount of energy. Experiments in the laboratory using individual nuclei show that such reactions can indeed take place. The process of converting hydrogen into helium is called hydrogen fusion. (It is also sometimes called hydrogen burning, even though nothing is actually burned in the conventional sense. Ordinary burning involves chemical reactions that rearrange the outer electrons of atoms but have no effect on the atoms' nuclei.) Hydrogen fusion provides the devastating energy released in a hydrogen bomb (see Figure 1-6). The fusing together of nuclei is also called thermonuclear fusion, because it can take place only at extremely high temperatures. The reason is rhat all nuclei have a positive electric charge The most common form of hydrogen fusion in the Sun involves (b) One of (shown form the protons changes int in blue). The proton and neutron hydrogen isotope fH). (a) Two proions ''---.» (hydrogen nuclei, ]H) collide. (c) One byproduct of converting a ,' proton to a neutron is a neutral nearly massless neutrino (v), which escapes from the San. (d) The other byproduct of converting a proton positively charged electron, or positron (e+). This encouni an ordinary electron (e~), annihilating both particles and converting them into gamma-ray photons (-y). The energy these photons goes into sustaining the Sun's internal heat. STEP 2 (a) The !H r.ucleus '-produced in Step 1 collides with a third proton ('Hi. (b) The result of the collision is a helium isotope (3He) with two protons and one neutron. (c) This nuclear reaction releases another gamma-ray phot' (7). Its energy also goes into sustaining the internal hea the Sun. (1)) Two protons and two neutrons from the two 3He nuclei rearrange themselves into a different helium isotope (AHe). (c) The two remaining protons are ' released. The energy of their moLioii contributes to the Sun's internal heat. 408 Chapter 16 and so tend to repel one another- But in the extreme heat and pressujc di the Sun's center, hydrogen nuclei (protons) are moving so fast that they can overcome their electric repulsion and actually touch one another. When that happens, thermonuclear fusion can take place. AHALizSY, can think of protons as tiny electrically charged ! spheres that are coated with a very powerful glue. If the spheres (. are not touching, the repulsion between their charges pushes ! them apart. But if the spheres are forced into conract, the strength i of the glue "fuses" them together. CAUTION! Be careful not to confuse thermonuclear fusion with the similar-sounding process of nuclear fission. In nuclear 1 fusion, energy is released by joining or fusing together nuclei of lightweight atoms such as hydrogen. In nuclear fission, by contrast, the nuclei of very massive atoms such as uranium or plu- i tonium release energy by fragmenting into smaller nuclei, Nuclear power plants produce energy using fission, not fusion. (Generating power using fusion has been a goal of researchers for decades, but no one has yet devised a commercially viable way to do this.) Converting Hydrogen to Helium We learned in Section 5-H that the nucleus of a hydrogen atom (H) ccnsins of a single proton. The nucleus of a helium atom (He) consists of two protons and two neutrons. In the nuclear process that Atkinson described, four hydrogen nuclei combine to foim one helium nucleus, with a concurrent release of energy: In several separate reactions, two of the four protons arc changed into neutrons, and eventually combine with the remaining protons to produce a helium nucleus. This sequence of reactions is called the proton-proton chain. The Cosmic Connections figure depicts the proton-proton chain in detail. Each time this process takes place, a small fraction (0.7%) of the initial combined mass of the hydrogen nuclei does not show up in the Final mass of the helium nucleus. This "lost" mass is converted into energy. Box 16-1 describes how to use Einstein's mass-energy equation to calculate the amount of energy released. CAUTION! You may have heard the idea that mass is always conserved (that is, it is neither created nor destroyed), or that energy is always conserved in a reaction. Einstein's ideas show that neither of these statements is quite correct, because mass can be converted uuu energy and vice versa. A more accurate statement is that the total amount of mass plus energy is con- , served. Hence, the destruction of mass in the Sun docs not violate any laws of nature. For cvciy four hydrogen nuclei converted into a hehum nucleus, 4.3 x joule of energy is released. This amount of energy may seem tiny, bur it is about 107 times larger than the amount of energy released in a typical chemical reaction, such as occurs in otdinaty burning. Thus, thermonuclear fusion explains how the Sun could have been shining for billions of years. To produce the Sun's luminosity of 3.9 x "i02S joules per ^ * ond, 6 X 1011 kg (600 million metric tons) of hydrogen muSI ^ ^ converted into helium each second. This rate is prodigious, there is a literally astronomical amount of hydrogen in the Sn„ In particular, the Sun's core contains enough hydrogen to hjvj "l" been giving off energy at the present rate for as long as the sojar i system has existed, about 4,56 billion years, and to continue JQ. <■■ ing so for mote than 6 billion years into the future. . ,r,oie^ jne proton-proton chain is also the energy sourci ' many of the stars in the sky. In stars win central t?m, A. peraturcs that are much hotter than that of the ;. however, hydrogen fusion proceeds according to a different sc nuclear reactions, called the CNO cycle, in which carbon, m gen, and oxygen nuclei absorb protons to produce helium niu Still other thermonuclear reactions, such as helium fusion, carton fusion, and oxygen fusion, occur late in the lives of many stars 16-2 A theoretical model of the Sun shows how energy gets from its center to its surface . 0piA; While thermonuclear fusion is the source of the Sun's energy, this process cannot take place everywhere within xnt ^un' we nave seen, extremely high temperatures— in excess of 107 K—'are required for atomic nuclei to fuse together to form larger nuclei. The temperature of the Sun's vis- 1 ible surface, about 5800 K, is too low for these reactions to occur ■■ there. Hence, thermonuclear fusion can be taking place only within ; the Sun's interior, But precisely where does it take place? And how does the energy produced by fusion make its way to tiie surface, where it is emitted into space in the form of photons? To answer these questions, we must understand conditions in the Sun's interior. Ideally, we would send an exploratory spacecraft to probe deep into the Sun; in practice, the Sun's intense heat would vaporize even the sturdiest spacecraft. Instead, astronomers use the laws of physics to constmct a theoretical model of the Sun. {We discussed the use of models in science in Section 1-1.} Let's see what ingredients go into building a model of this kind. Hydrostatic equilibrium Note fiist that the Sun is not undergoing any dramatic charges The Sun is not exploding or collapsing, nor is it stgniticandy heating or cooling. The Sun is thus said to be in both hydrostatic equilibrium and thermal equilibrium. To understand what is meant by hydrostatic equilibrium, imagine a slab of material in the solar interior (Figmc- 16-2-0- 'n equilibrium, the slab on average will move neither up nor down, (in fact, there are upward and downward motions of material inside the Sun, but these motions average out.) Equilibrium is maintained by a balance among three forces that art on this slab: 1. The downward pressure of the layers of solar material above the slab. 2. The upward pressure of the hot gases beneath the slab. 3. The slab's weight—that is, the downward gravitational pul) it feels from the rest of the Sun. MM t Pressure from gases below the slab [, weight of the slab Y a) Material inside the sun is in hydrostatic equilibrium, so forces balance IPressure from water above the fish Weight of tht fish I ■ Pressure from water T ■ beneath the fish ••' (h} A fish floating in water is in hydrostatic equilibrium, so forces balance Figure 16-2 Hydrostatic tquilibnum (a) Material in the Sun's interior tends to move ■ neither up nor down. The upward ^orcss on a slab of solar material (due to nressure of gases nelcw the slab) must balance the downward forces (due to the slab's weight and the pressure of gases above the slab). ■ Hence, the pressure must increase with increasing depth, (b) The same pnnciple applies to a fish 'loa;ing in water. Ir equilibrium, the forces Daiance and the fish neither rises nor sinks. (Ken Usami/FhotoDisc) The pressure from below must balance both the slab's weight and the pressure from above. Hence, the pressure below the slab must be greater than that above the slab. In other words, pressure has to increase with increasing depth. For the same reason, pressure increases as you dive deeper into the ocean (Figure 16-2£>i or as you move toward lower altitudes in our atmosphere. Hydrostatic equilibrium also tells us about the density of the slab. If the stab is too dense, its weight will be too large and it will sink; if the density is too low, the slab will rise. To prevent this, the density of solar material must have a certain value at each depth within the solar interior. (The same principle applies to objects that float beneath the surface of the ocean. Scuba divers Our Star, the Sun wear weight belts to increase their average, density so that they will neither rise nor sink but will stay submerged at the same level.) Thermal Equilibrium Another consideration is that the Sun's interior is so hot that it is completely gaseous. Gases compress and become more dense when you apply greater pressure to them, so density must increase along with pressure as you go to greater depths within the Sun. Furthermore, when you compress a gas, its temperature tends to increase, so the temperature must also increase as you move toward the Sun's center. While the temperature in the solar interior is different at different depths, the temperature ar each depth remains constant in time. This principle is called thermal equilibrium. For the Sun to be in thermal equilibrium, all the energy generated by thermonuclear reactions in the Sun's core must be transported to the Sun's glowing surface, where ii can be radiated into space. If too much energy flowed from the core to the surface to be radiated away, the Sun's interior would cool down; alternatively, the Sun's interior would heat up if too little energy flowed to the surface. Transporting Energy Outward from the Sun's Core But exactly how is enetgy transported from the Sun's center to its surface? There are three methods of energy transport: conduction, convection, and radiative diffusion. Only the last two arc important inside the Sun. If you heat one end of a metal bar with a blowtorch, energy flows to the other end of the bar so that it tDo becomes warm. The efficiency of this method of energy transport, called conduction, varies significantly from one substance to another. For example, metal is a good conductor of heat, but plastic is not (which is why metal cooking pots often have plastic handles). Conduction is not an efficient means of energy transport in substances with low average densities, including the gases inside stars like the Sun. Inside stars like our Sun, energy moves from center to surface by two other means: convection and radiative diffusion. Convection is the circulation of fluids—gases or liquids—berween hot and cool regions. Hot gases (with lower density) rise toward a star's surface, while cool gases (with higher density) sink back down toward the star's center. This physical movement of gases transports heat energy outward in a star, just as the physical movement of water boiling in a pot transports energy from the bottom of the pot (where the heat is applied) ro the cooler water at the surface. In radiative diffusion, photons created in the thermonuclear inferno at a star's center diffuse outward toward the star's surface. Individual photons are absorbed and reemiCted by atoms and electrons inside the st3r. The overall result is an outward migration from the hot core, where photons are constantly created, toward the cooler surface, where they escape into space. Modeling the Sun To construct a model of a star like the Sun, astrophysicists express the ideas of hydrostatic equilibrium, thermal equilibiiuni, and energy transport as a set of equations. To ensure that the model applies to the particular star under study, they also make 410 Chapter 16 Table 16-2 A Theoretical Model of the Sun Distance from the Sun's center (solar radii) Fraction of luminosity Fraction of mass Temperature (x 10« K) Density (kg/m3) Pressure relative to pressure at center 0.0 0.00 0.00 15.5 160,000 1.00 0.1 0.42 0.07 13.0 90,000 0.46 0.2 0.94 0.35 9.5 40,000 0.15 0.3 1.00 0.64 6.7 13,000 0.04 0.4 1.00 0.85 4.8 4,000 0.007 0.5 1.00 0.94 3.4 1,000 0.001 0.6 1.00 0.98 2.2 400 0.0003 0.7 1.00 0.99 1.2 80 4 x 10"' 0.8 1.00 1.00 0.7 20 5 x 10-' 0.9 1.00 1.00 0.3 2 3 x 10-' 1.0 1.00 1.00 0.006 0.00030 4 x lO-" Note: The distance from the Sun's center is expressed cs a fraction of the Sun's radius (Rq). Thus, 0.0 is at the center of the Sun and 1.0 is at the surface. The fraction of luminosity is that portion of the Sun's total luminosity produced within each distance from the center; this is equal to 1.00 for distances of 0.25 Rq or more, which means that all of the Sun's nuclear reactions occur within 0.25 solar radius from the Sun's center. The fraction of mass is that portion of the Sun's total mass lying within each distance from the Sun's center. The pressure is expressed as a fraction of the pressure at the center of the Sun. use of astronomical observations of the star's surface. (For example, to construct a model of the Sun, they use the data that the Sun's surface temperature is 580O K, its luminosity is 3.9 X 1026 W, and the gas pressure and density at the surface are almost zero.) The astrophysicists then use a computer to solve their set of equations and calculate conditions layer by layer in toward the star's center. The result is a model of how temperature, pressure, and density increase with increasing depth below the star's surface. Table 16-2 and Figure 16-3 show a theoretical model of the Sun that was calculated in just this way. Different models of the Sun use slightly different assumptions, but all models give essen- Center of Sun Surface of Sun «Iii) i I Distance from Sun's center {solar radii) | Center of Sun Surface of Sun 0.3 0.4 0.6 0.8 1.0 | Distance from Sun's center (solar radii) | Center of Sun Ä Figure 16-3 A Theoretical Model of the Sun's Interior These graphs depict what percentage of the Sun's total luminosity is produced within each distance from the center (upper left), what percentage of the total mass lies within each distance from the center (lower left), the temperature at each distance (upper right), and the density at each distance (lower right). (See Table 16-2 for a numerical version of this model.) nally tne same results as those shown here. From such computer yodels we have learned that at the Sun's center the density is 160,000 kg/m3 (14 times the density of lead!), the temperature is ] 55 x 107 K, and the pressure is 3.4 x 1011 atm. (One atmo-■ sphere, or 1 atm, is the average atmospheric pressure at sea level on Earth.) Table 16-2 and Figure 16-3 show that the solar luminosity rises to 100% at about one-quarter of the way from the Sun's center to its surface. In other words, the Sun's energy production occurs within a volume that extends out only to 0.25 R©. (The svmbol Rq denotes the solar radius, or radius of the Sun as a whole, equal to 696,000 km.) Outside 0.25 R©, the density and temperature are too low for thermonuclear reactions to take place. Also note that 94% of the total mass of the Sun is found within [he inner 0.5 Rq. Hence, the outer 0.5 Rq contains only a relatively small amount of material. How energy flows from the Sun's center toward its surface depends on how easily photons move through the gas. If the solar gases are comparatively transparent, photons can travel moderate disranccs before being scattered or absorbed, and energy is thus transported by radiative diffusion. If the gases are comparatively opaque, photons are frequently scattered or absorbed and can't easily get through the gas. In an opaque gas, heat builds up and convection then becomes the most efficient means of energy transport. The gases start to churn, with hot lower-density moving upward and cooler gas sinking downward. From the center of the Sun out to about 0.71 Rq, energy is transported by radiative diffusion. Hence, this region is called the radiative zone. Beyond about 0.71 Rq, the temperature is low enough (a mere 2 X 106 K or so) for electrons and hydrogen nuclei to join into hydrogen atoms. These atoms are very effective at absorbing photons, much more so than free electrons or nuclei, Figure 1G-4 The Sun's Internal Structure Tnermonuclear reactions occur in the Sun's core, which extends out to a distance of 0.25 Rs from the center. Energy is transported outward, via radiat.ve diffusion, to a distance of about 0.71 R0. In :he outer layers between 0.71 RQ and 1.00 R0, energy flows outward by convection. Our Star, the Sun and this absorption chokes off the outward flow of photons. Therefore, beyond about 0.71 Rq, radiative diffusion is not an effective way to transport energy. Instead, convection dominates the energy flow in this outer region, which is why it is called the convective zone, figure 16-4 shows these aspects of the Sun's internal structure. Although energy travels through the radiative zone in the form of photons, the photons have a difficult time of it. Table 16-2 shows that the material in this zone is extremely dense, so photons from the Sun's core take a long time to diffuse through the radiative zone. As a result, it takes approximately 170,000 years for energy created at the Sun's center to travel 696,000 km to the solar surface and finally escape as sunlight. The energy flows outward at an average rate of 50 centimeters per hour, or about 20 times slower than a snail's pace. Once the energy escapes from the Sun, it travels much faster— at the speed of light. Thus, solar energy that reaches you today took only 8 minutes to travel the 150 million kilometers from the Sun's surface to Earth. But this energy was actually produced by thermonuclear reacrions that took place in the Sun's core hundreds of thousands of years ago. The sunlight thai reaches Earth today results from thermonuclear reactions that took place about 170,000 years ago 16-3 Astronomers probe the solar interior using the Sun's own vibrations We have described how astrophysicists construct models of the Sun. But since we cannot sec into the Sun's opaque interior, how can we check these models to see if they are accurate? What is needed is a technique for probing the Sun's interior. A very powerful technique of just this kind involves measuring vibrations of the Sun as a whole. This field of solar research is called helioseismology. Vibrations are a useful tool for examining the hidden inceri ors of all kinds of objects, Food shoppers teSt whether melons are ripe by tapping on them and listening to the vibrations. Geologists can determine the structure of Earth's interior by using seismographs to record vibrations during earthquakes. Although there are no true "sunquakes," the Sun does vibrate at a variety of frequencies, somewhat like a ringing bell. These vibrations were first noticed in 1960 by Robert Leighton of the California Institute of Technology, who made high-precision Doppler shift observations of the solar surface. These measurements revealed that parts of the Sun's surface move up and down about 10 meters every 5 minutes. Since the mid-1970s, several astronomers have reported slower vibrations, having periods ranging from 20 to 160 minutes. The detection of extremely slow vibrations has inspired astronomers to organize networks of telescopes around and in orbit above Earth to monitor the Sun's vibrations on a continuous basis. The vibrations of the Sun's surface can be compared with sound waves. If you could somehow survive within the Sun's outermost layers, you would first notice a deafening roar, somewhat like a jet engine, produced by 432 Chapter 16 Activities Observing Projects T Observing f.ps and tools At the risk of repeating ourselves, we remind you tD never look directly at the Sun, because it can easily cause permanent blindness. You can view the Sun safely without a telescope just by using two pieces of white cardboard. First, use a pin to poke a small hole in one piece of cardboard; this will be your "lens," and the other piece of cardboard will be your "viewing screen." Hold the "lens" piece of cardboard so that it is face-on to the Sun and sunlight can pass through the hole. With your other hand, hold the "viewing screen" so that the sunlight from the "lens" falls on it. Adjust the distance between the two pieces of cardboard so that you see a sharp image of the Sun on the "viewing screen." This image is perfectly safe to view. It is actually possible to see sunspots with this iow-tech apparatus. For a better view, use a telescope with a solar filter that fits on the front of the telescope. A standard solar filter is a piece of glass coated with a thin layer of metal to give it a mirrorlike appearance. This coating reflects almost all the sunlight that falls on it, so that only a tiny, safe amount of sunlight enters the telescope. An IIa filter, whkh looks like a red piece of glass, keeps the light at a safe level by admitting only a very narrow range of wavelengths. (Filters that fit on the back of the telescope are not recommended. The telescope focuses concentrated sunlight on such a filter, heating it and making it susceptible to cracking—and if the filter cracks when you are looking through it, your eye will be ruined instantly and permanently.) To use a telescope with a solar filter, first aim the telescope away from the Sun, then pin on the filter. Keep the lens cap on the telescope's secondary wide-angle "finder scope" (if it has one), because the heat of sunlight can fry the finder scope's optics. Next, aim the telescope toward the Sun, using the telescope's shadow to judge when you are pointed in the right direction. You can then safely look through the telescope's eyepiece. When you are done, make sure you point '.he telescope away from the Sun before removing the filter and storing the telescope. Note that the amount of solar activity that you can see (sunspots, filaments, flares, prominences, and so on) will depend on where the Sun is in its 11-year sunspot cycle, 58. Use a telescope with a solar filter to observe the surface of the Sun. Do you see any sunspots? Sketch their appearance. Can you distinguish between the umbrae and penumbrae of the sunspots? Can you see limb darkening? Can you see any granulation? 59. If you have access to an Ha filter attached to a telescope especially designed for viewing the Sun safely, use this instrument to examine the solar surface. How does the appearance of the Sun differ from that in white light? What do sunspot look like in Ha? Can you see any prominences? Can you see any filaments? Are the filaments in the H„ image near an sunspots seen in white light? (Note that the amount ol actiy ity that you see will he much greater at some times durng t]le solar cycle than at others.) 60. Use the Starry Night Enthusiast'^1 program to measure the Sun's rotation. Display the entire celestial sphere by selecting Guides > Atlas in the Favorites menu and center on the Sun by double-clicking on Sun in the Find pane. Using the controls at the right-hand end of the toolbar, zoom in until y0u can see details on the Sun's surface clearly. In the toolbar, set the Time Flow Rate to 1 day. Using the time forward and backward buttons in the toolbar, step through enough time to determine the rotation period of the Sun. Which part of the actual Sun's surface rotates at the rate shown in Stony Night Enthusiast'^} (Note: The program does not show the Sun's differential rotation.) 61. Use the Starry Night Enthusiast''1 program to examine the Sun. Open the Favorites pane and double-click on Solar System > Inner Solar System to display the inner planets surrounding the Sun. Stop Time Advance and use the down arrow in the toolbar under Viewing Location to approach to within about 0.015 AU of the Sun. You can rotate the Sun by placing the mouse cursor over die image and, while holding down the Shift key, bold down the niuuse button while moving the mouse. (On a two-button mouse, hold down the left mouse button.) (a) The Sun's equator lies close to the plane of the ecliptic. Where do most of the sunspots visible on the image of the Sun lie relative to the solar equator? Check Figure 16-18 for more realistic images of sunspots and Figure 16-19 for the latitude distribution of sunspots. (b) Based on your observations in (a), does the image in Sltmy Night Enthusiast'" show the Sun near the beginning, middle, or end of the 11-year sunspot cycle? Explain your reasoning. You can see current solar images from both ground and space-based solar telescopes by opening the LiveSky pane if you have an Internet connection on your computer. Collaborative Exercises 62. Figure 16-19 shows variations in the average latitude of sunspots. Estimate the average latitude of sunspots in the year you were born and estimate the average latitude on your twenty-first birthday. Make rough sketches of the Sun during those years to illustrate your answers. 63. Create a diagram showing a sketch of how limb darkening on the Sun would look different if the Sun had either a thicket or thinner photosphere. Be sure to include a caption explaining your diagram. 64. Solar granules, shown in Figure 16-9, are about 1000 km ' across. What city is about that distance away from where you are right now? What city is that distance from the birthplace of each group member? 65. Magnetic arches in the corona are shown in Figure 16-25«. How many Earths high are these arches, and how many Earths could fit inside one arch? 17 The Nature of the Stars To the unaided eye, the night sky is spangled with several thousand stars, each appearing as a bright pinpoint of light. With a pair of binoculars, you : can see some 10,000 other, fainter stars; with a 15-cm ■ (6-in) telescope, the total rises to more than 2 million. Astronomers now know that there are in excess of 1 00 ;1 billion (10n) stars in our Milky Way Galaxy alone. But what are these distant pinpoints? To the great ^ thinkers of ancient Greece, the stars were bits of light embedded in a vast sphere with Earth at the center. They thought the stars were composed of a mysterious » "fifth element," quite unlike anything found on Earth. Today, we know that the stars are made of the same chemical elements found on Earth. We know their sizes, their temperatures, their masses, and something of their internal structures. We understand, too, why the stars in the accompanying Image come in a range of beautiful colors: Blue stars have high surface temperatures, while the surface temperatures of red and yellow stars are relatively low. How have we learned these things? How can we know the nature of the stars, objects so distant that their light takes years or centuries to reach us? In this chapter, wc will learn about the measurements and calculations that astronomers make to determine the properties of stars. We will also take a first look at the Hertzsprung-Russell diagram, an important tool that helps as- Learning Goals By reading the sections of this chapter, you will learn 17-1 How we can measure the distances to the stars 17-2 How we measure a star's brightness and luminosity 17-3 The magnitude scale for brightness and luminosity 17-4 How a star's color indicates its temperature 17-5 How a star's spectrum reveals its chemical composition 17-6 How we can determine the sizes of stars 17-7 How H-R diagrams summarize our knowledge of the stars Some stars in this cluster (called M39) are distinctly blue in color, while others are yellow or red. (Heidi Schweiker/NOACVAURA/NSF) tronomers systematize the wealth of available information about the stars. In later chapters, we will use this diagram to help us understand how stars are born, evolve, and eventually die. i71 '■^Hfe^- vast majority of stars are objects very much like "f/«"J the Sun. This understanding followed from the discov- ^S^P ery that the stars are tremendously far from ns, at distances so great that their light takes years to reach us, Because the stars at night are clearly visible to the naked eye despite these 17-8 How we can deduce a star's size from its spectrum 17-9 How we can use binary stars to measure the masses of stars 17-10 How we can learn about binary stars in very close orbits 17-11 What eclipsing binaries are and what they tell us about the sizes of stars 433 f 434 Chapter 17 huge distances, it must be thai the luminosity of the stars—that is, how much energy they emit into space per second—is comparable to or greater than that of the Sun. Just as for the Sun, the onfy explanation for such tremendous luminosities is that thermonuclear reactions are occurring within the stars (see Section 16-1). Clearly, then, it's important to know how distant the stars are. But how do we measure these distances? You might think these distances are determined by comparing how bright different stars appear. Perhaps the star Betelgeuse in the constellation Orion appears bright because it is relatively close, while the dimmer and less conspicuous star Polaris (the North Star, in the constellation Ursa Minor) is farther away. But this line of reasoning is incorrect: Polaris is actually closer to us than Betelgeuse! How bright a star appears is not a good indicator of its distance. If you see a light on a darkened road, it could be a motorcycle headlight a kilometer away or a person holding a flashlight just a few meters away. In the same way, a bright star might be extremely far away but have an unusually high luminosity, and a dim star might be relatively close but have a rather low luminosity. Astronomers must use other techniques to determine the distances to the stars. Parallax and the Distances to the Stars ^tAr The most sttaightforward way of measuring stellar Äá^^Wt- distances uses an effect called parallax, which is the ^^jj^ apparent displacement of an object because of a change in the observer's point of view (FitAuio 17-!). To see how parallax works, hold your arm out straight in front of you. Now look at the hand on your outstretched arm, first with your left eye closed, then with your right eye closed. When you close one eye and open the other, your hand appears to shift back and forth against the background of more distant objects. When you are position B, the tree appears to be in horn of this mountain. When you ate a. position A, [he tret appcat* (o L in Jroni of this mountain. Figure 17-1 PdraUax Imagine looking at some nearby object (a tree) against a distant background (mountains). When you move from one location to another, the nearby object appears to shift witi respect to the distant background scenery This familiar phenomenon is called parallax You measure distances around you by comparing the images from your left and right eyes—we find the distances to stars using the same principle The closer the object you are viewing, the greater the parallax shift. To see this increased shift, repeat the experiment with your hand held closer to your face. Your brain analyzes such parallax shifts constantly as it compares the images from your left and right eyes, and in this way determines the distances to objects around you. This analysis is the basis for depth perception. To measure the distance to a star, astronomers measure the paiallax shift of the star using two points of view that are as fat apart as possible—at opposite sides of Earth's orbit. The direction from Earth to a nearby star changes as our planet orbits tie Sun, and the nearby star appears to move back and forth against the background of more distant stars (Figure J 7-2). This motion is called stellar parallax. The parallax (p) of a star is equal to half the angle through which the star's apparent position shifts as Earth moves from one side of its orbit to the other. The larger the parallax p, the smaller the distance d to the star (compare Figure 17~2a with Figure 17'-lb). It is convenient to measure the distance d in parsecs. A star with a parallax angle of 1 second of arc (p ~ 1 arcsec) is at a distance of 1 parsec {d ~ 1 pc). (The word "parsec" is a contraction of the phrase "the distance at which a star has a parallax of one arcsecond." Recall from Section 1-7 that 1 parsec equals 3.26 light-years, 3.09 X 1013 km, or 206,265 AU; see Figure 1-14,) If the angle p is measured in arcseconds, then the distance d to the star in parsecs is given by the following equation: Relation between a star's distance and its parallax d = distance to a star, in parsecs p = parallax angle of that star, in arcseconds This simple relationship between parallax and distance m parsecs is one of the main reasons that astronomers usually measure cosmic distances in parsecs rather than light-years. For example, a star whose parallax is p = 0.1 arcsec is at a distance d - 1/(0.1} = 10 parsecs from Earth. Barnard's star, named for the American astronomer Edward E. Barnard, has a parallax of 0.547 arcsec. Hence, the distance to this star is Because 1 parsec is 3.26 light-years, this distance can also be expressed as d = 1.83 pcX -^-^ =5.97 lv 1 pc All known stars have parallax angles less than one arcsecond. In other wordb, the closest star is more than 1 parsec away. Such The Nature of the Stars (a) Parallax of a nearby star Figure 17-2 Stellar Parallax [a] As Earth orbits the Sun, a nearby star appears to shift its position against the background of distant stars. The parallax (p) of the star is equal to the angular radius of small parallax angles are difficult to detect, so it was not until 1338 that the first successful parallax measurements weie made by the German astronomer and mathematician Friedrich Wilhelm Bessel. He found the parallax angle of the star 61 Cygni to be just 1/3 arcsec—equal to the angular diameter of a dime at a distance of 11 kilometers, or 7 miles. He thus determined that this star is about 3 pc from Earth. (Modern measurements give a slightly smaller parallax angle, which means that 61 Cygni is actually more than 3 pc away.) The star Proxima Cencauri has the largest known parallax angle, 0.772 arcsec, and hence is the closest known star (other than the Sun); its distance is 1/(0.772) = 1.30 pc. %iin*V >$f& Appendix 4 at the back of this book lists all the stars within 4 pc of the Sun, as determined by parallax measurements. Most of these stars . ate far too dim to be seen with the naked eye, which is why their ;: tumes are probably unfamiliar to you. By contrast, the majority ■ of the familiar, bright stars in the nighttime sky (listed in Appendix 5) are so far away that their parallaxes cannot be measured from Earth's surface. They appear bright not because they are dose, but because they are far more luminous than the Sun. The brightest stars in the sky are not necessarily the nearest stars! Measuring Parallax from Space Parallax angles smaller than about 0.01 arcsec are extremely difficult to measure from Earth, in part because of the blurring ef- (b) Parallax of an even closer star Earth's orbit a;, beer from the star, (b) She closer the star is to us, the greater the parallax angle p. The distance d to the star (in paisec^) is equal to the reciprocal of the parallax angle p (in arcseconds]: d = 1/p. fects of the atmosphere. Therefore, the parallax method used with ground-based telescopes can give fairly reliable distances only for stars nearer than about 1/0.01 = 100 pc. But an observatory in space is unhampered by the atmosphere. Observations made fiom spacecraft therefore permit astronomers to measure even smaller parallax angles and thus determine the distances to more remote stars. & In 1989 the European Space Agency (ESA) launched the satellite Hipparcos, an acronym for H/gh Precision Parallax Collecting Satellite (and a commemoration of the ancient Greek astronomer Hipparchus, who created one of the first star charts). Over more than three years of observations, the telescope aboard Hipparcos was used to measure the parallaxes of 118,000 stars, some with an accuracy of 0.001 arcsec-ond. This telescope has enabled astronomers to determine stellar distances out to several hundred parsecs, and with much greater precision than has been possible with ground-based observations. In the years to come, astronomers will increasingly turn to space-based observations to determine stellar distances. Unfortunately, most of the stars in the Galaxy arc so far away that their parallax angles are too small to measure even with an orbiting telescope. Later in this chapter, we will discuss a technique that can be used to find the distances to these more remold stars. In Chapters 24 and 26 we will learn about other techniques that astronomers use to determine the much larger distances to galaxies beyond the Milky Way. These techniques aiso 436 Chapter 17 Stellar Motions Stars can move through space in any direction. The space velocity of a star describes how fast and in what direction it is moving. As the accompanying figure shows, a star's space velocity v can be broken into components parallel and perpendicular to our line of sight. The component perpendicular to our line of sight—that is, across the plane of the sky—is called the star's tangential velocity (vx). To determine it, astronomer's must know the distance to a star [d) and its proper motion (p., the Greek letter mu), which is the number of arcseconds that the star appears to move per year on the celestial sphere. Proper motion does not repeat itself yearly, so it can be distinguished from the apparent back-and-forth motion due to parallax. In terms of a star's distance and proper motion, its tangential velocity Jin km/s) is v, = 4.74u,af where u. is in arcseconds per year and d is in parsecs. For example, Barnard's star (Figure 17-3) has a proper motion of 10.35S arcseconds per year and a distance of 1.83 pc. Hence, its tangential velocity is i't - 4.74(10.3581(1.83) = 89.S km/s The component of a star's motion parallel to our line of sight—that is, eicher directly toward us or directly away from us—is its radial velocity (t;,). It can be determined from measurements of the Doppler shifts of the star's spectra! lines (see Section 5-9 and Box 5-6). If a star is approaching us, the wavelengths of all of its spectral lines are decreased (blueshifted); if the star is receding from us, the wavelengths are increased (redshifted). The radial velocity v, is related to the wavelength shift by the equation X - X,a _ Vj_ Xo c In this equation, X is the wavelength of light coming from :he star, X0 is what the wavelength would be if the star were not moving, and c is the speed of light. As an illustration, a particular spectral iine of iron in the spectrum of Barnard's star has a wavelength (X) of 516.445 ran. As measured in a laboratory on Earth, the same spectral line has a wavelength {Xn) of 516.629 nm. Thus, for Barnard's star, our equation becomes 516.445 nm - 516.629 nm . „„„ _ - vr Tools of the Astronomer's Trade Solving this equation for the radial velocity vIS we find vT = (-0.000356) c = (-O.000356)(3.OO X 1U5 km/s) = -107 km/s The minus sign means that Barnard's star is moving coward us. You can check this interpretation by noting that the wavelength X = 516.445' nm received Írom Barnard's star is less than the laboratory wavelength Xo - 516.629 nm; hence, the light from the star is blueshifted, which indeed means that the star is approaching. If the star were receding, its light would be redshifted, and its radial velocity would be positive. The illustration shows that the tangential velocity and ra dial velocity form two sides of a right triangle. The long side (hypotenuse) of this triangle is the space velocity (ľ). From the Pythagorean theorem, the space velocity is For Barnard's star, the space velocity is v = V(89.4 km/s)2 + (-107 km/s}2 = 140 km/s Therefore, Barnard's star is moving through space at a speed of 140 km/s (503,000 km/h, nr 312,000 mi/h) relative to the Sun. Determining the space velocities of stars is essential for understanding the structure of the Galaxy. Studies show that the stars in our local neigbborhuud are moving in wide orbits around the center of the Galaxy, which lies some 8000 pc (26,000 light-years] away in the direction of the constellation Sagittarius (the Archer). While many of the orbits are roughly circular and lie in nearly the same plane, others are highly elliptical ot steeply inclined to the galactic plane. We will see in Chapter 23 how the orbits of stars and gas clouds leveal the Galaxy's spiral structure. - tilt st.ii's i:idi.il \iTin.ii> = tllo St.l!'\ i.idjíihii.iI vvltK'il) .^ms. Figure 17-3 riQuxg The Motion of Barnard's Star Tree photographs taken over a four-year period were combined to show the motion • of Barnard's star, which lies 1.32 parsecs away in the corstellation - ophiucius. Over this time interval Barnard's star moved more than 41 arcseconds on the celestial sphere (about 069 arcminutes, or 0.012s], more than any other star {John Sanford/Sdence Photo Library) help us understand the overall size, age, and structure of the universe. The Importance of Parallax Measurements Because it can be used only on relatively close stars, stellar parallax might seem to be of limited usefulness. But parallax measurements are the cornerstone for all other methods of finding the distances to remote objects. These other methods require a precise and accurate knowledge of the distances to nearby stars, as determined by stellar parallax. Hence, any inaccuracies in the parallax angles for nearby stars can translate into substantial errors in measurement for the whole universe. To minimize these errors astronomers are continually trying to perfect their parallax-measuring techniques. Stellar parallax is an apparetit motion of stars caused by Earth's orbital motion around the Sun. But stars are not fixed objects and actually do move through space. As a result, stars change their positions on the celestial sphere (Figure 17-3), and they move either toward or away from the Sun. These motions are sufficiently slow, however, that changes in the positions of the slais are hardly noticeable over a human lifetime. [Jox 17-1 describes how astronomers study these motions and what insights they gain from diese studies. 17-2 If a star's distance is known, its luminosity can be determined from its apparent brightness ElIK10 All the stars you can see in the nighttime sky shine by thermonuclear fusion, just as the Sun does (see Section The Nature of the Stars 16-1). But they are by no means merely identical copies of the Sun. Stats differ in their luminosity (Li, the amount of light energy they emit each second. Luminosity is usually measured either in watts (1 watt, or 1 W, is 1 joule per seuond) or as a multiple of the Sun's luminosity (L3, equal to 3.90 x 1026 Most stars are less luminous than the Sun, but some blaze forth with a million times the Sun's luminosity. Knowing a star's luminosity is essential for determining the star's history, its present-day internal structure, and its future evolution. Luminosity, Apparent Brightness, and the Inverse-Square Law To determine the luminosity of a star, we first note that as light energy moves away from its source, it spreads out over increasingly larger regions of space. Imagine a sphere of radius d centered on the light source, as in [;ij>ure 17-4. The amount of energy that passes each second through a square meter of the sphere's surface area ts the total luminosity of the source (L) divided by the total j>urfao: area of the sphere (equal to 4ir/b©). Then we can use the above equation to find how luminous that star is compared to the Sun (the ratio L/L©}. In odier words, this equation gives us a general rule relating the luminosity, distance, and apparent brightness of a star: We can determine the luminosity of a star from its distance and apparent brightness. For a given distance, the brighter the star, the more luminous that star must be. For a given apparent brightness, the more distant the star, the more luminous it must be to be seen at that distance. Box 17-2 shows how to use the above equation to determine the luminosity of the nearby star e (epsilon) Eridani, the fifth brightest star in the constellation Eridanus (named for a river in Greek mythology). Parallax measurements indicate that e Eridani is 3.23 pc away, and photometry shows that the star appears only 6.73 X 10-13 as bright as the Sun. Using the above equation, we find that e Eridani has only 0.30 times the luminosity of the Son. The Stellar Population Calculations of this kind show that stars come in a wide variety of different luminosities, with values that range from about 106 L© (a million times the Sun's luminosity) to only about 10~4 L© (a mere ten-thousandth of the Sun's light output). The most luminous star emits roughly 1010 times more energy each second than the least luminous! (To put this number in perspective, about 1010 human beings have lived on Earth since our species first evolved.) As stars go, our Sun is neither extremely luminous nor extremely dim; it is a rather ordinary, garden-variety star. It is somewhat more luminous than most stars, however. Of more than 30 stars within 4 pc of the Sun (see Appendix 4), only three (a Centauri, Sirius, and Procyon) have a greater luminosity than the Sun. To better characterize a typical population of stars, astronomers count the stars out to a certain distance from the Sun and plot the number of stars that have different luminosities. The resulting graph is called the luminosity function. Figure 17-5 on page 440 shows the luminosity function for stars in our part of the Milky Way Galaxy. The curve declines very steeply for the most luminous stars toward the left side of the graph, indicating that they are quite rare. For example, this graph shows that stars like the Sun are about 10,000 times more common than stars like Spica (which has a luminosity of 2100 L©). The exact shape of the curve in Figure 17-5 applies only to the vicinity of the Sun and similar regions in our Milky Way Galaxy. Other locations have somewhat different luminosity functions. In stellar populations in general, however, low-luminosity stars are much more common than high-luminosity ones. The Nature of the Stars Tools of the Astronomer's Trade Luminosity, Distance, and Apparent Brightness The inverse-square law (Section 17-2) relates a star's luminosity, distance, and apparent brightness to the corresponding quantities for the Sun: L Lo We can use a similar equation to relate the luminosities, distances, and apparent brightnesses of any two stars, which we call star 1 and star 2: U [dij b2 EXAMPLE: The star e (epsilon) Eridani is 3.23 pc from Earth. As seen from Earth, this star appears only 6.73 X 10~13 as bright as the Sun. What is the luminosity of n Eridani compared with that of the Sun? Situation: We are given the distance to e Eridani (d = 3.23 pc) and this star's brightness compared to that of the Sun [b/bo = 6.73 X 10~13). Our goal is to find the ratio of the luminosity of e Eridani to that of the Sun, that is, the quantity L/L©. Tools: Since we are asked to compare this star to the Sun, we use the first of the two equations given above, L/L© = ( wouId take 100 stars of magnitude + 6 to provide as much light ■- energy as we receive from a single star of magnitude + 1. To make computations easier, the magnitude scale was redefined so that a magnitude difference of 5 corresponds exactly to a factor of 100 in brightriess- A magnitude difference of 1 corresponds to a factor of 2.512 in brightness, because 2.512 x 2.512 x 2.512 x 2.512 x 2.512 - (2.512)-* = 100 Thus, it takes 2.512 third-magnitude stars to provide as much light as we receive from a single second-magnitude star. Figure l?-6 illustrates the modern apparent magnitude scale. The dimmest stars visible through a pair of binoculars have an apparent magnitude of +10, and the dimmest stars that can be photographed in a one-hour exposure with the Keck telescopes (see Section 6-2) or the Hubble Space Telescope have apparent - magnitude +-30. Modern astronomers also use negative numbers to extend Hipparchus's scale to include very bright objects. For example, Sirius, the brightest star m the sky, has an apparent -251 -20 -15 "10| i - Venus (at brightest) (-4.4) - Sirius (brightest star) (-1.4) - Naked eye limit (+6.0) +10 I--Binocular limit (+10.0! +1; |--Pluro (+15.1) +20 - J --Large telescope (visual limit) (+21.0) Hubble Space Telescope and large Eanh-based telescopes (photographic limit) (+30.0) (a) 5ome apparent magnitudes Figure 17-& The Apparent Magnitude Scale (a) Astronomers denote the apparent brightness nf objects in the sky by their apparent magnitudes. The greater the apparent magnitude, :he dimmer the object, (b) This photograph of the Pleiades cluster, located acou^: magnitude of -1.43. The Sun, the brightest object in the sky, has an apparent magnitude of —26.7. Absolute Magnitudes Apparent magnitude is a measure of a star's apparent brightness as seen from Earth. A related quantity that measures a star's true energy output—that is, its luminosity—is called absolute magnitude. This is the apparent magnitude a star would have if it were located exactly 10 parsecs from Earth. Apparent magnitude measures a star's brightness; absolute magnitude measures its luminosity If you wanted to compare the light output of two j different lightbulbs, you would naturally place them side by side I so that both bulbs were the same distance from you. In the ab-j solute magnitude scale, we imagine doing the same thing with ! stars to compare their luminosities. If the Sun were moved to a distance of 10 parsecs from Earth, it would have an apparent magnitude of +4.8. The absolute magnitude of the Sun is thus +4.8. The absolute magnitudes of the (b) Apparent magnitudes of stars in the Pleiades RI0UXG 123 pc away in the constellation Taurus, sho^s the apparent magnitudes of snrre of its stars Most are too faint tn he seen by the naked eye. (David Malin/Anglo-Australian Observatory) Chapter 17 T The Nature of the Stars stars range frum approximately +15 for the least luminous to -10 for the most luminous. (Note: Like apparent magnitudes, absolute magnitudes work "backward": The greater the absolute magnitude, the less luminous the star.) The Sun's absolute magnitude is about in the middle of this range. We saw in Section 17-2 that we can calculate the luminosity of a star if we know its distance and apparent brightness. There is a mathematical relationship between absolute magnitude and luminosity, which astronomers use to convert one to the orher as they see fit. It is also possible to rewrite the inverse-square law, which we introduced in Section 17-2, as a mathematical relationship that allows you to calculate a star's absolute magnitude (a measure of its luminosity) from its distance and apparent magnitude (a measure of its apparent brightness). Box !7-3 describes these relationships and how to use them. Because the "backward" magnitude scales can be confusing, we will use them only occasionally in this book. We will usually speak of a star's luminosity rather than its absolute magnitude and will describe a star's appearance in terms of apparent brightness rather than apparent magnitude. But if you go on to study more about astronomy, you will undoubtedly make frequent use of apparent magnitude and absolute magnitude. 17-4 A star's color depends on its surface temperature The image that opens this chapter shows that stars come in different colors. You can see these colors even with the naked eye. For example, you can easiiy see the red □ t500 2000 500 3000 Wavelength (nm) -- (a) A cool star with surface temperature 3000 K emits much more red light than blue light, and so appears red. color of Betelgeuse, (the star in the "armpit" of the constellatio Orion), and the blue tint of Bellatrix at Orion's other "shoulder" (see Figure 2-2). Colors are most evident for the brightest stars be cause human color vision works poorly at low light levels. CAUTION! It's true that the light from a star will appear rerj. shifted if the star is moving away from you and blueshifted if it's moving toward you. But for even the fastest stars, these color shifts are so tiny that it takes sensitive instruments to measure them. The red color of Betelgeuse and the blue color of Bellatrix are not due to their morions; they are the actual colors of the stars. Color and Temperature We saw in Section 5-3 that a star's color is directly related to its surface temperature. The intensity of light from a relatively cool star peaks at long wavelengths, making the star look red (Figure 17-7,;). A hot star's intensity curve peaks at shorter wavelengths so the star looks blue (Figure 17-7c). For a star with an intermediate temperature, such as the Sun, the intensity peak is near the middle of the visible spectrum. The human visual system interprets an object with this spectrum of wavelengths as yellowish in color (Figure 17-76}. This leads to an important general iule about star colors and surface temperatures: Red stars are relatively cold, with low surface temperatures; blue stars are relatively hot, xvitb high surface temperatures. Figure 17-7 shows that astronomers can accurate!y^tdetsrmine the surface temperature of a star by carefully measuring its color. Tools of the Astronomer's Trade 1 Inflated M \5800K^ 5UU 1500 1000 Wavelength (nm) (b) A warmer star with surface temperature 5800 K (like the Sun) emits similar amounts of all visible wavelengths, and so appears yellow-white. 500 1000 1500 Wavelength (nm) —*-(c) A hot star with surface temperature 10,000 K emits much more blue light than red light, and so appears blue. Figure 17-7 temperature and CnlorThese graphs show the intensity of light emitted by three hypotherical stars plotted against wavelength (compare with Figure 5-11). The rainbow band indicates the range of visible wavelengths, "he star's apparent color depends on whether die intensity curve hdb larger values at the short-wavelength or long-wavelength end of the visible spectrum. The insets show stars of about these suface temperatures. UV stands for ultraviolet, which extends from 10 to" 400 nm. See Figure 3-4 for mnrp nn wavelengths of the spectrum, (inset a Andrea Dupree/Haivard-Smithsonian CFA, Ronald Gilhland/STSc:, NASA and ESA; inset b: NSO/AURA/NSF; inset c: Till Credner, Allthesky.com) Apparent Magnitude and Absolute Magnitude Astronomers commonly express a star's apparent brightness in terms of apparent magnitude (denoted by a lowercase m), and the star's luminosity in terms of absolute magnitude (denoted by a capital M). While we do not use these quantities extensively in this buuk, it is useful to know a few simple ic-lationships involving them. Consider two stars, labeled 1 and 2, with apparent magnitudes wi\ and m2 and brightnesses b\ and bz, respectively. The ratio of their apparent brightnesses (bilbi) corresponds to a difference in their apparent magnitudes (m2 - mi). As we learned in Section 17-3, each step in magnitude corresponds to a factor of 2.512 in brightness; we receive 2.512 times more energy per square meter per second from a third-magnitude star than from a fourth-magnitude star. This idea was used to construct the following table: Apparent magnitude Ratio of apparent difference [m2 - »h) brightness (&1/62) 1 2.512 2 (2.512)2 = 6.31 3 (2.512)3 = 15.85 4 (2.512)4 = 39.82 5 (2.512)5 = 100 10 i'2.512]10 = 104 15 (2.512)15 = 106 20 (2.512)20 = 10s A simple equation relates the difference between two stars' apparent magnitudes to the ratio of their brightnesses: Magnitude difference related to brightness ratio m2 ~ «i =2.5 l°g^!j) mi, m2 - apparent magnitudes of stars 1 and 2 b\, b2 = apparent brightnesses of stars 1 and 2 In this equation, log (b\!bi) is the logarithm of the brightness ratio. The logarithm of 1000 = 103 is 3, the logarithm of 10 = 101 is 1, and the logarithm of 1 = 10° is 0. EXAMPLE: At their most brilliant, Venus has a magnitude of about —4 and Mercury has a magnitude of about —2. How many times brighter are these planets than the dimmest stars visible to the naked eye, with a magnitude of + 6? Situation: In each case we want to find a ratio of two apparent brightnesses (the brightness of Venus or Mercury compared to that of the dimmest naked-eye stars). Tools: In each case we will convert a difference in apparent magnitude between the planet and the naked-eye star into a ratio of their brightnesses. Answer; The magnitude difference between Venus and the dimmest stars visible to the naked eye is +6 - (-4) = 10. From the table, this difference corresponds to a brightness ratio of (2.512)10 = 104 = 10,000, so Venus at it most brilliant is 10,000 times brighrer than the dimmest naked-eye stars. The magnitude difference between Mercury and the dimmest naked-eye stars is +4 - (-4) = 8. While this value is not in the table, you can see that the corresponding ratio of brightnesses is (2.512)8 = (2.512)5+3 - (2.512)5 X (2.512)3. From the table, (2.512)5 - 100 and (2.512)3 = 15.85, so the ratio of brightnesses is 100 X 15.85 = 1585. Hence, Mercury at its most brilliant is 1585 times brighter than the dimmest stars visible to the naked eye. Review: Can you show that when at their most brilliant, Venus is 6.31 times brighter than Mercury? (Hint: No multiplication or division is required—just notice the difference in apparent magnitude between Venus and Mercury, and consult the table.) EXAMPLE: The variable star RR Lyrae in the constellation Lyra (the Harp) periodically doubles its light output. By how-much does its apparent magnitude change? Situation: We are given a ratio of two brightnesses (the star at its maximum is twice as bright as at its minimum). Our goal is to find the corresponding difference in apparent magnitude. Tools: We let 1 denote the star at its maximum brightness and 2 denote the same star at its dimmest, so the ratio of brightnesses is b-Jbi = 2. Wc then use the equation m2 - m-\ = 2.5 log (bilbi) to solve for the apparent magnitude difference mi - «i. Answer: Using a calculator, we find m2 - mj = 2.5 log (2) = 2.5 X 0.30 = 0.75. RR Lyrae therefore varies periodically in brightness by 0.75 magnitude. Review: Our answer means that at its dimmest, RR Lyrae has an apparent magnitude m2 that is 0.75 greater than its apparent magnitude mi when it is brightest. (Remember that s greater value of apparent magnitude means the star is dimmer, not brighter!) (continued on the next page) 444 Chapter 17 The Nature of the SLars 445 BOX 17-3 (continued), -T • •> WS « meg*'? The inverse-square law relating a star's apparent brightness and luminosity can be rewritten in terms of the star's apparent magnitude (m), absolute magnitude |M), and distance from Earth (d). This can be expressed as an equation; Relation between a star's apparent magnitude and absolute magnitude m - M = 5 log d - 5 m = star's apparent magnitude M = star's absolute magnitude d — distance from Earth to the atar in parsecs In this expression m - M is called the distance modulus, and log d means the logarithm of the distance d in parsecs. For convenience, the following table gives rhe values of the distance d corresponding to different values of m - M. Distance modulus m ~ M Distance d (pc) -4 1.6 -3 2.5 -2 4.0 -1 6.3 0 10 1 16 2 25 3 40 4 63 5 100 30 103 15 104 20 10s This table shows that it a sur is less than 10 pc away, its distance modulus m - M is negative. Thar is, its apparent magnitude \m) is less than its absolute magnitude (M). If the star is more than 10 pc away, m - M is positive and m is greater than M As an example, the star e fepsilon) Indi, which is in the direction of the southern constellation Indus, has apparent magnitude m = +4.7. It is 3.6 pc away, which is less than 10 pc, so its apparent magnitude is less than its absolute magnitude. EKAMPLE: Find ihe absolute magnitude ot e Indi. Situation: We are given the distance to e Indi (d = 3.6 pc) and its apparent magnitude iw = +4.7). Our goal is to find the star's absolute magnitude M. Tools; We use the formula m -for M. M = 5 log d - 5 to solve Answer: Since d = 3.6 pc, we use a calculator to find log d - log 3.6 = 0.56. Therefore the star's distance modulus [s m - jvf = 5(0.56) - 5 = -2.2, and the star's absolute magnitude is Ai = m - (-2.2) = +4.7 + 2.2 = +6.9. .Review: As a check on our calculations, note that this star's distance modulus m — M = -2.2 is less than zero, as it should be for n star less than 10 pc away. Note that our Sun has absolute magnitude +4.8; e Indi has a greater absolute magnitude, so it is less luminous than the Sun. EXAHPLF: Suppose you were viewing the Sun from a planet orbiting another srar 100 pc away. Could you see it without using a telescope? Situation: We learned in the preceding examples that the Sun has absolute magnitude M — +4.8 and that the dimmest stars visible to the naked eye have apparent magnitude m = +6. Our goal is to determine whether the Sun would be visible to the naked eye at a distance of 100 pc. Tools: We use the relationship m — M = 5 log d - 5 to find the Sun's apparent magnitude at d = 100 pc. If this is greater than 46, the Sun would not be visible at that distance. (Remember that the greater the apparent magnitude, the dimmer the star.) Answer: From the table, ar d = 100 pc the distance modulus is m - Tví = i. So, as seen from this distant planet, the Sun's apparent magnitude would be m = M + 5 = +4.8 + 5 ~ + 9.8. This is greater than the naked-eye limit ?u = +6, so the Sun could not be. seen. Review: The Sun is oy far rhe brightest object in Earth's sky. But our result teils us that to an inhabitant of a planetary system 100 pc away—a rather small distance in a galaxy that is thousands of parsecs across—our own Sun would be just another insignificant star, visible only through binoculars or a telescope. The magnitude system is also used by astronomers to express the colors of stars as seen thiough different filters, as we describe in Section 17-4. For example, rather than quantifying a star's color by the color ratio b\j/b& (a star's apparent brightness as seen through a V filter divided by the brightness through a B filter), astronomers commonly use the color index B-V, which is the difference in the star's apparent magnitude as measured with these two filters. We will not use this system in this book, however (but see Advanced Questions 53 and 54). 400 500 Wavelength (nm) ■ figure 17-8 ■' n b, aid V Filters This graph sh^ws the wavelengths to which the standard titers are transparent The U filter is transparent to near- ■ ultraviolet light. 1 he b filter is transparent to violet, blue, and green light, '" W|nle the V filter is transparent to gresn snd yellow light. By "Measuring the apparent brightness of a star with ear/h of these filters and comparing the results, an astronomer can determine the star's surface -- temperature. Astronomers use a set oF filters in their telescopes to measure the surface temperatures of stars < To measure color, rhe star's light is collected by a telescope and passed : through various color-filters. For ex-. ample, a red filter passes red light while blocking other wavelengths. The filtered light is then collected by a light-sensitive device such as a CCD (see Section 6-4). The process is then repeated with each of the filters in the set. The star's image will have a different brightness through each colored filter, and by comparing these brightnesses astronomers can find the wavelength at which the star's intensity curve has its peak— and hence the star's temperature. UBV Photometry Let's look at this procedure in more detail. The most commonly used filters are called U, B, and V, and the technique that uses them is called UBV photometry. Each fi-ter is transparent to a different band of wavelengths: the ultraviolet (U), the blue (B), and the yellow-green (V, for visual) region in and around the visible spectrum (Hi;mi: 17-Sj. The transparency of the V filter uuinics the sensitivity of the human eye. To determine a star's temperature using UBV photometry, the astronomer first measures the star's brightness through each of the filters individually. This gives three apparent brightnesses for the star, designated bij, 6B, and by. The astronomer then compares the intensity of starlight in neighboring wavelength bands by taking rhe ratios of these brightnesses: bvlb^ and b^lby. Table 1 7-1 gives values for these color ratios for several stars with different surface temperatures. If a star is very hot, its radiation is skewed toward short, ultraviolet wavelengths as in Figure 17-7t. This makes the star dim through rhe V filter, brighter through the B filter, and brightest through che U filter. Hence, for a hot star bv is less than 6B, which in turn is less than by, and the ratios b\rfbi and b^/bjj are both less than 1. One such star is Bellatrix (see Table 17-1), which has a surface temperature of 21,500 K. In contrast, if a stdi is coo!, us ladiation peaks ar long wavelengths as in Figure 17-la. Such a star appears brightest through the V filter, dimmer through the B filter, and dimmest through the U filter (see Figure 17-8). In other words, for a cool star bv is greater than bg, which in turn is greater than b\j. Hence, the ratios by/b-n and b%lb\i will both be greater than 1. The star Betel-geuse (surface temperature 3500 K) is an example. You can see these differences between hot and cool stars in parts a and c of Figure 6-27, which show the constellation Orion at ultraviolet wavelengths (a bit shorter than those transmitted by the U filter) and at visible wavelengths that approximate the transmission of a V filter. The hot star Bellatrix is brighter in the ultraviolet image (Figure 6-27 giaphs the relaLionsdiip between a stai's b\lb\w color ratio and its temperature. If you know the value of the bylbw color ratio for a given srar, you can use this graph to find the star's surface temperature. As an example, for the Sun b\>!b% 1 Table 17-1 Colors of Selected Stars Star Surface temperature (K) by/bB Apparent color Bellatrix (-y Ononis) Regulus (a Leonis) Sirius (a Canis Majoris) Megrez (S Ursae Majoris Altair (ct Aquiiae) Sun Aldebaran (a Tauri) Betelgeuse (ot Ononis) 21,500 12,000 9400 8630 7800 5800 4000 3500 0.81 0.90 1.00 1.07 1.23 1.87 4.12 5.55 0.45 0.72 0.96 1.07 1.08 1.17 5.76 6.66 Blue Blue-white Blue-white White Yellow-white Yellow-white Orange Ked Somes: j.-C. Mermilltod, B. Eauck, and M. Mermiiliod, University of Lausanne 446 Chapter 17 The Nature of the Stars 447 30,000 27,000 24,000 21,000 18,000 15,000 12,000 9000 6000 3000 1.50 2.00 Color ratio by/bo 3.00 4.00 5.00 Figure 17-9 Temperature, Color and Color Ratio The bv/bB color ratio is the ratio of a star's apparent bnghtnesses through a V filter and through a B filter. This ratio is small for hot, blue stars but large for cool red stars After measuring a star's brightness with the B and V niters, an astronomer can estimate the star's surface temperature from a graph like this one equals 1.87, which corresponds to a surface 5800 K. temperature of CAUTION! As we will see in Chapter 18, tiny dust particles that pervade interstellar space cause distant stars to appear redder than they really are. (In the same way, particles in Earth's : atmosphere make the seutug Sun look redder; see Box 5-4.) As-. rronomers must take this reddening into account whenever they , attempt to determine a star's surface temperature from its color ratios. A star's spectrum provides a more precise measure of a star's surface temperature, as we will see next. But it is quicker and easier to observe a star's colors with a set of U, B, and V filters than it is to take the star's spectrum with a spectrograph. 17-5 The spectra of stars reveal their chemica" corrpositions as wetl as their surface temperatures We have seen how the color of a star's light helps astronomers determine its surface temperature. To determine the other properties of a star, astronomers must analyze the spectrum of its light in more detail. This technique of stellar spectroscopy began in 1817 when Joseph Fraunhofer, a German instrument maker, attached a spectroscope to a telescope and pointed it toward the stars. Fraunhofer had earlier observed that the Sun has an absorption line spectrum—that is, a continuous spectrum with dark absorption lines (see Section 5-6). He found that stars have the same kind of spectra, which reinforces the idea that our Sun is a rather typical star. But Fraunhofer also found that the pattern of absorption lines is different for different stars. Classifying Stars: Absorption Line Spectra and Spectral Classes We see an absorption line specttum when a cool gas lies betwe us and a hot, glowing ob]ect (recall Figure 5-16). The light fro- ' the hot, glowing object itself has a continuous spectrum. In j si case of a star, light with a continuous spectrum is produced low-lying levels of the star's atmosphere where the gases are h and dense. The absorption lines are created when this light fi0i outward through the upper layers of the star's atmosphere. Atoi in these cooler, less dense layers absorb radiation at specific wa\ ! lengths, which depend on the specific kinds of atoms present hydrogen, helium, or other elements—and on whether or not t atoms are ionized. Absorption lines in the Sun's spectrum are pi duced in this same way (see Section 16-5). ^vAf^jr, Some stars have spectra in which the Balmer absor ° tion lines of hydrogen are prominent. But in the spec-tra of other stars, including the Sun, the Balmer lines are nearly absent and the dominant absorption lines are those of heavier elements such as calcium, iron, and sodium. Still other stellar spectra are dominated by broad absorption lines caused by molecules, such as titanium oxide, rather than single atoms. To cope with this diversity, astronomers group similar-appearing stellar spectra into spectral classes. In a popular classification scheme that emerged in the late 1890b, a star was assigned a letter from A through O according to the strength or weakness of the hydrogen Balmer lines in the star's spectrum. Nineteenth-century science could not explain why or how the spectral lines of a particular chemical are affected by the temperature and density of the gas. Nevertheless, a team of astronomers at the Harvard College Observatory forged ahead with a monumental project of examining the---------------------------------- spectra of hundreds of thousands of Deciphering the stars. Their goal was to develop a inFormatian in starlight system of spectral classification in took the painstaking which all spectral features, nut just Balmer lines, change smoothly from one spectral class to the next. The Harvard project was financed by the estate of Henry Draper, a wealthy New York physician and amateur astronomer who in 1872 became the first person to photograph stellar absorption lines. Researchers on the project included Edward C. Pickering, Williamina Fleming, Antonia Maury, and Annie Jump Cannon (Figure 17-10). As a result of their efforts, many of the original A-through-0 classes were dropped and others were consolidated. The remaining spectral classes were reordered in the sequence OBAFGKM, You can remember this sequence with the mnemonic: "Oh, Be A Fine Girl (or Gay), iviss Ale!" Refining the Classification: Spectral Types Cannon refined the original OBAEGKM sequence into smaller steps called spectral types. These steps are indicated by attaching an integer from 0 through 9 to the original letter. For example, the spectral class F includes spectral types F0, Fl, F2, . . . , F8, F9, which are followed by the spectral types GO, Gl, G2, . . . , G8, G9, and so on. work oF generations of astronomers Figure 17-10 riIuxg Classifying the Spectra of the Stars The modern scheme of classifying stars by their spectra was developed at ths Harvard College Obsen/atory in the late nineteenth century. A team of women astronomers led by Edward C. Pickering and Williamina Fleming ■>. (standing) analyzed hundreds of thousands of spectra. Social conventions • of the time prevented most women astronomers from using research telescopes or receiving salaries comparable to men's. (Harvard College observatory] \-igure 17-11 shows representative spectra of several spectral types. The strengths of spectral lines change gradually from one spectral type to the next. Fur example, the Balmer absorption lines of hydrogen become increasingly prominent as you go from spectral type B0 to AO. From AO onward through the F and G classes, the hydrogen lines weaken and almost fade from view. The Sun, whose spectrum is dominated by calcium and iron, is a G2 star. The Harvard project culminated in the Henry Draper Catalogue, published between 1918 and 1924. It listed 225,300 stars, each of which Cannon had personally classified. Meanwhile, physicists had been making important discoveries about the structure of atoms. Ernest Rutherford had shown that atoms have nuclei (recall Figure 5-19), and Niels Bohr made the remarkable hypothesis that electrons circle atomic nuclei along discrete orbits (see Figure 5-22). These advances gave scientists the conceptual and mathematical tools needed to understand stellar spectra. In the 1920s, the Harvard astronomer Cecilia Payne and the Indian physicist Meghnad Saha demonstrated that the OBAFGKM spectral sequence is actually a sequence in temperature. The hottest stars are O stars. Their absorption lines can occur only if these stars have surface temperatures above 25,000 K. M stars are the coolest stars. The spectral features of M stars are consistent with stellar surface temperatures of about 3000 K. Why Surface Temperature Affects Stellar Spectra To see why the appearance of a star's spectrum is profoundly affected by the star's surface temperature, consider the Balmer lines of hydrogen. Hydrogen is by far the most abundant element in the universe, accounting for about three-quarters of the mass of a typical star. Yet the Balmer lines do not necessarily show up in a star's spectrum. As we saw in Section 5-8, Balmer absorption lines are produced when an electron in the n ~ 2 orbit of hydrogen is lifted into a higher orbit by absorbing a photon with the right amount of energy (see Figure 5-24). If the star is much hotter than 10,000 K, the photons pouring out of the star's interior have such high energy that they easily knock electrons out of hydrogen atoms in the star's atmosphere. This process ionizes the gas. With its only electron torn away, a hydrogen atom cannot produce absorption lines. Hence, the Balmer lines will be relatively weak in the spectra of such hot stars, such as the hot O and B2 stars in Figure 17-11. Conversely, if the star's atmosphere is much cooler than 10,000 K, almost all the hydrogen atoms are in the lowest (« = 1) energy state. Most of the photons passing through the star's atmosphere possess too little energy to boost electrons up from the n = 1 to the n = 2 orbit of the hydrogen atoms. Hence, very few of these atoms will have electrons in the n — 2 orbit, and only these few can absorb the photons characteristic of the Balmer lines. As a result, these lines are nearly absent from the spectrum of a cool star. {You can see this in the spectra of the cool MO and M2 stars in Figure 17-11.) For the Balmer lines to be prominent in a star's spectrum, the star must be hot enough to excite the electrons out of the ground state but not so hot that all the hydrogen atoms become ionized. A stellar surface temperature of about 9000 K produces the strongest hydrogen lines; this is the case for the stars of spectral types AO and A5 in Figure 17-11. •i£JmkSp Every other type of atom or molecule also has a char-aaeiislic temperature range in which it produces ^■P' prominent absorption lines in the observable part of the specttum. Figure 1 "-12 shows the relative strengths of absorption lines produced by different chemicals. By measuring the details of these lines in a given star's spectrum, astronomers can accurately determine that star's surface temperature. For example, the spectral lines of neutral (that is, un-ionized) helium are strong around 25,000 K. At this temperature, photons have enough energy to excite helium atoms without tearing away the electrons altogether. In stars hotter than about 30,000 K, helium atoms become singly ionized, that is, they lose one of their two electrons. The remaining electron produces a set of spectral lines that is recognizably different from those of neutral helium. Hence, when the spectral lines of singly ionized helium appear in a star's spectrum, we know that the star's surface temperature is greater than 30,000 K. Astronomers use the term metals to refer to all elements other than hydrogen and helium. This idiosyncratic use of the term "metal" is quite different from the definition used by chemists and other scientists, To a chemist, sodium and iron are metals but carbon and oxygen are not; to an astronomer, all of these substances are metals. In this terminology, metals dominate the Chapter 17 The Nature of the Stars t tt tt t t HI I CN Ca n Fe I Ca I CH Fe I Fe I (K+H) Wavelength (run Figure 17-11 RiBfuxG Principal Types of Stellar Specti a Stars of different spectral classes and different surface temperatures have spectra dominated by differen: absorption lines. Notice how tie Balrrer lines of hydrogen (Ha, Hp, HT, and H6) are strongest for hot stars of spectral class A. while absorption lines due to calcium (Ca) are strongest in cooler K and M stars. The speclid uf M stars also have broad, dark hand? caused by molecules of titanium oxide (TiOj, which can only exist at relatively low temperatures. A roman numeral after a chemical symbol shows whether the absorption hne is caused by un-ionized atoms (roman rumera! I) or by atoms that have lost one electron (/oman numeral II). (R. Bell University of Maryland, and M. Briley, University ot Wisconsin at Oshkosh) 50,000 25,000 10,000 1 <-Surface temperature (K) 8000 6000 5000 4000 3000 Figure 17-12 The Strengths of Absorption Lines Each curve in this graph peaks at the stellar surface temperature for which that chemical's absorption line '.s strongest tor example, hydrogen (H) absorpton lines are strongest in A stars with surface terrperatures near 10,000 K, Roman numeral I denotes neutral, un-ionized atoms; X III, and IV denote atoms that are singly, doubly, or triply ionized (that is, have lost one, two, or tfree electrons). .pectra of stars cooler than 10,000 K. Ionized metals are promi-ien[ for surface temperatures between 6000 and 8000 K, while antral metals are strongest between approximately 5500 and (000 K. Below 4000 K, certain atoms in h star's atmosphere combine 0 form molecules. (At higher temperatures aroms move so fasr hat when they collide, they bounce off each other rather than 'sticking together" to form molecules.) As these molecules vibrate md rotate, they produce bands of spectral lines that dominate he star's spectrum. Most noticeable are the lines of titanium ox-dc (TiO), which are strongest for surface temperatures of about !000 K. Spectral Classes for Brown Dwarfs *?£m& Since 1995 astronomers have found a number of stars *Sri» w^tn sur^ace temperatures even lower than those of spectral class M. Strictly speaking, these are not stars put brown dwarfs, which we introduced in Section 8-6. Brown Iwarfs are too small to sustain thermonuclear fusion in their ores. Instead, these "substars" glow primarily from the heat released by Kelvin-Hetmholtz contraction, which we described in . Section 16-1. (They do undergo fusion reactions for a brief period during their evolution.) Brown dwarfs arc so cold that they are best observed with infrared telescopes (see Figure 17-13). Such observations reveal that brown dwarf spectra have a rich variety ■ of absorption lines due to molecules. Some of these molecules actually form into solid grains in a brown dwarfs atmosphere. To describe brown dwarf spectia, astronomers have defined two new spectral classes, L and T. Thus, the modern specrral sequence of stars and brown dwarfs from hottest to coldest surface temperature is OBAFGKMLT, {Can you think of a new mnemonic that includes L and T?) For example, Figure 17-13 shows a star of spectral class K and a brown dwarf of spectral class T. Table 17-2 summarizes the relationship between the temperature and spectra of stars and brown dwarfs. teTable 17-2 The Spectral Sequence HI) Wo ('itar "I spivrr.il Figure 17-13 rQv uxg An Infrared Image of Brown Dwarf HD 3651B The star HD 3561 is of spectral class K, with a surface temperature of about 5200 K. ("HD" refers to the Henry Draper Catalogue.) In 2006 it was discovered that HD 3651 is orbited by a brown dwa'f named HD 3651B with a surface temperature between 800 and 300 K and a luminosity just It J00.UUU that of the bun. The brown dwarf emit-: most of its light at infrared wavelengths, so an infrared telescope was used to rernrd this image. The hotter and more luminous star HD 3651 is greatly overexposed in this image and appears much larger than its true size. HD 3651 and HD 3651B are both 11 pc (3E ly] from Earth in the constellation Pisces (the Fish); the other stars in this image are much farther away. (M. Mugrauer and R. NeuhaTiser, U. of Jena; A. Seifahrt, ESO; and T. Maseh, Tel Aviv U.) Spectral class Color Temperature (K) Spectral lines Examples O Blue-violet 30,000-50,000 Ionized atoms, especially helium Naos (£ Puppis), Mintaka {S Orionis) B Blue-white 11,000-30,000 Neutral helium, some hydrogen Spica (a Virginia), Rigel (ß Ononis) A White 7500-11,000 Strong hydrogen, some ionized metals Sirius (a Canis Majoris), Vega (a Lyrae) F Yellow-white 5900-7500 Hydrogen and ionized metals such as calcium and iron Canopus (a Carinae), Procyon (a Cams Minoris) C, Yellow 5200-5900 Both neutral and ionized metals, especially ionized calcium . Sun, Capella (a Aurigae) K Orange 3900-5200 Neutral metals Arcturus (a Boötis), Aldebaran (a Tauri) M Red-orange 2500-3900 Strong titanium oxide and some neutral calcium Antares (a Scorpii), Betelgeuse (a Orionis) L Red 1300-2500 Neutral potassium, rubidium, and cesium, and metal hydrides Brown dwarf Teide 1 T Red below 1300 Strong neutral potassium and some water (H2O) Brown dwarfs Gliese 229B, HD 3651B 450 Chapter 17 The Nature of ihe Stars 451 When the effects of temperature are accounted for, astronomers find that all stars have essentially the same chemical composition. We can state the results as a general rule: By mass, almost all stars (including the Sun) and brown dwarfs are about three-quarters hydrogen, one-quarter helium, and 1% or less metals. Our Sun is about 1% metals by mass, as are most of the stars you can see with the naked eye. But some stars have an even lower percentage of metals. We will see in Chapter 19 that these seemingly minor differences tell an important tale about the life stories of stars. 17-6 Stars come in a wide variety of" sizes "With even the best telescopes, stars appear as nothing more than bright points of light. On a photo- -....._________.........._______________ graph or CCD image, brighter stars A star's radius can be appear larger than dim ones (see calculated IF we know its F.gures 17-3, 17-6fc. and 17-13), but |um|nos|1y and surface temperature these apparent sizes give no indica tion of the star's actual size. To di Hü termme the size of a star, astronomers combine information about its luminosity {determined from its distance and apparent brightness) and its surface temperature (determined from its spectral type). In this way, they find that some stars are quite a hit smallec than the Sun, while others are a thousand times larger. Calculating the Radii of Stars The key to finding a star's radius from its luminosity and surface temperature is the Stefan-Boltzmann law (see Section 5-4). This law says that the amount of energy radiated per second from a square meter of a blackbody's surface—that is, the energy flux (F)—is proportional to the fourth power of the temperature of that surface (T), as given by the equation F = oT4. This equation applies very well to stars, whose spectra are quite similar to that of a perfect blackbody. (Absorption lines, while important for determining the star's chemical composition and surface temperature, make only relatively small modifications to a star's blackbody spectrum.) A star's luminosity is the amount of energy emitted per second from its entire surface. This quantity equals the energy flux F multiplied by the total number of square meters on the star's surface (that is, the star's surface area). We expect that most stars are nearly spherical, like the Sun, so we can use the formula for the surface area of a sphere. The formula is 4xR2, where R is the Tools of the Astronomer's Trade Stellar Radii, Luminosities, and Surface Temperatures jQecause stars emit light in almost exactly the same fashion fc—=as blackbodies, we can use the Stefan-Boltzmann law to relate a star's luminosity (L), surface temperature (T), and radius {R). The relevant equation is L = 4ttR2o-T4 As written, this equation involves the Stefan-Boltzmann constant flowchart shows how astronomers determine •. properties of a relatively nearby star (oae close enough th its parallax can be measured). The rounded purple Doxes s t'-ie measurements that must be made of the star, the btu* ovals show tne key equations that are usee (from Section: 17-2,17-5, and 17-6), and the green rectangles show the inferred properties of the stars. A different Drocedure is followed for more distant stars (see Sectior 17-8, especial Figure 17 17'.. A graph of luminosity versus surface temperature reveals tl j stars Fall inta a few be. categories (as we saw in Section 17-6 and Box 17-4). We also relegate the positions and space velocities of stars to secondary importance. (In a similar way, a physician is more interested in your weight and blood pressure than in where you live or how fast you drive.) We can then ask the following question: What do we learn when we graph luminosities of stars versus their surface temperatures? The first answer to this question was given in 1911 by the Danish astronomer Ejnar Hertzsprung. He pointed nut thit a regular pattern appears when the absolute magnitudes of stars {which measure their luminosities) are plotted against their colors (which measure their surface temperatures). Two years later, the American astronomer Henry Norris Russell independently discovered a similar regularity in a graph using spectral types (another measure of surface temperature) instead of colors. In recognition of their originators, graphs of this kind are today known as Hertzsprung-Russell diagrams, or H-R diagrams (Figure 17-15). Figure 17-lSd is a typical Hertzsprung-Russell diagram. Each dot represents a star whose spectral type and luminosity have been determined. The most luminous stars are near the top of the diagram, the least luminous stars near the bottom. Hot stars of spectral classes O and B are toward the left side of the graph and cool stars of spectral class M are toward the right. CAUTION! You are probably accustomed to graphs in which ; the numbers on the horizontal axis increase as you move to the . right. (For example, the business section of a newspaper includes a graph of stock market values versus dates, with later (a) A Hertzsprung-Russell (H-R) diagram A«flfiL\ Figure 17-15 Hertzspmng-RusseU (H-R) Diagrams On an H-R diagram, ^*c7sTr the luminosities (or absolute magnitudes) of stars are plotted against uVir ^pecLidl types [or surface temperatures"], (a) Tfe data points ate grouped in, jus", a few regions on the graph, showing -.hat luminosity and spectral type are correlated. Most stars lie along the red curve called the main sequence. Giants like Arcturus as well as supergiants like Rigel and Betelgeusa are above the main sequence, and white dwarfs like dates to the right of earlier ones.) But on an H-R diagram the temperature scale on the horizontal axis increases toward the left. This practice stems from the original diagrams of Hertzsprung and Russell, who placed hot O stars on the left and : cool M stars on the right. This arrangement is a tradition that ■ no one has seriously tried to change. Star Varieties: Main-Sequence Stars, Giants, Supergiants, White Dwarfs, and Brown Dwarfs The most striking feature of the H-R diagram is that the data points are not scattered randomly over die graph but are grouped in a few distinct regions. The luminosities and surface temperatures of stars do not have random values; instead, these two quantities are related! (b) The sizes of stars on an H-R diagram Sirius B are below it. (b) The blue curves on this H-R diagram enclose the regions of the diagram in which different types of stars are found. The dashed diagonal lines indicate different stellar radii. For a given stellar radius, as the sui fan; temperature increases (that is, moving from nght to left in the diagram], the star glows mere intersely and the luminosity increases (that is, moving upward in =tip digram) Note that the Sun is intermediate in luminosity, surface temperature, anc radius. The band stretching diagonally across the H-R diagram includes about 90% of the stars in the night sky. This band, called the main sequence, extends from the hot, luminous, blue stars in the upper lelt corner of the diagram to the conl, dim, red stars in the lower right corner. A star whose properties place it in this region of an H-R diagram is called a main-sequence star. The Sun (spectral type G2, luminosity 1 LQ, absolute magnitude +4.8) is such a star. Wc will find that all main-sequence stars are like the Sun in that hydrogen fusion—thermonuclear reactions that convert hydrogen into helium (see Section 16-1)—is taking place in their cores. The upper right side of the H-R diagram shows a second major grouping of data points. Stars represented by these points are both luminous and cool. From the Stefan-Boltzmann law, we 454 Chapter 17 The Nature of the Stars 455 know that a cool star radiates much less light per unit of surface area than a hot star. In order for these stars to be as luminous as chey are, they must be huge (see Section 17-6), and so they are called giants. These stars are around 10 to 100 times larger than the Sun. You can see this size difference in Figure 17-15£>, which is an H-R diagram to which dashed lines have been added to represent stellar radii. Most giant stars are around 100 to 1000 times more luminous than the Sun and have surface temperatures r»f about 3000 to 6000 K. Cooler members of this class of stars (those with surface temperatures from about 3000 to 4000 K) are often called red giants because they appear reddish, in the image that opens this chapter, the yel- " lowish stars, as well as the red star just left of center, are red qiants. A number of red giants can easily be seen with the naked eye, including Aldebarau in the constellation Taurus and Arc-turus in Bootes. A few rare stats are considerably bigger and brighter than typical red giants, with radii up to 1000 R©. Appropriately enough, these superlunnnous stars are called supergiants. Betel-geuse in Orion (see Box 17-4) and Antares in Scorpius are rwo supergiants you can find in the nighttime sky. Together, giants and supergiants make up about 3 % of the stars in the sky. Both giants and supergiants have thermonuclear reactions occurring in their interiors, but the character of those reactions and where in the star they occur can be quite different than for a main-sequence star like the Sun. We will study these stars in more detail in Chapters 21 and 22. The remaining 9% of stars form a distinct grouping of data points toward the lower left corner of the Hertzsprung-Russell diagram. Although these stars are hot, their luminosities are quite low; hence, they mus; be small. They are appropriately called white dwarfs. These stars, which are so dim that they can be seen only with a telescope, are approximately the same size as Earth. As we will learn in Chapter 20, no thermonuclear reactions take place within white dwarf stars. Rather, like embers left from a fire, they are the still-glowing remnants of what were once giant stars. By contrast, brown dwarfs (which lie at the extreme lower right of the main sequence, off the bortom and right-hand edge of Figure 17-15rt or Figure 17-1 S2>) are objects that will never become stars. They are comparable in radius to the planet Jupiter (that is, intermediate in she between Earth and the Sun; see Figure 7-2). The study of brown dwarfs is still in its infancy, but it appears that There may be twice as many brown dwarfs as there are "real" stars. ANcUQftY You can think of white dwarfs as "has-been" stars , whose days of glory have passed. In this analogy, a brown dwarf ' IS a "never-will-be." The existence of fundamentally different types of stars is the first important lesson to come from the H-R diagram In later chapters we will find that these different types represent various stages m the lives of stars. We will use the H-R diagram as an essential tool for understanding how stars evolve. 17-0 Details or a star's spectrum reveal whether it is a giant, a white dvv^rf, or n main-sequence star A star's surface temperature largely determines which lines a-e prominent in its spectrum. Therefore, classifying stars by spectra] type is essentially the same as categorizing rhem by surface teii\. perature. But as the H-R diagram ir> Figure 17-156 shows, stars of the same surface temperature can have very different luminosities. As an example, a star with surface temperature 5800 K could be 3 white dwarf, a main-sequence srar, a giant, or a supergiant, depending on irs luminosity. By examining the details of a star's spectrum, however, astronomers can determine to which of these categories a star belongs. This gives astronomers a tool to determine the distances to stars millions of parsecs away, far beyond the: maximum distance that can be measured using stellar parallax. Determining a Star's Size from Its Spectrum ritiuic 17- compares the spectra of two stars of the same spec-tral type but different luminosity (and hence different size): a B8 supergiant and a main-sequence star. Note that the Balmer lines of hydrogen are narrow in the spectrum of the very large, ' very luminous supergiant but quite broad in the spectrum of the small, less luminous main-sequence star. In general, for stars of spectral types B through F, the larger and more luminous the star, the narrower its hydrogen lines. The smaller a star and the denser its atmosphere, the broader the absorption lines in its spectrum (a) A supergiant star has a low-density, low-pressure atmosphere: its spectrum has narrow absorption lines (b) A main-sequence star has a denser, higher-pressure atmosphere-its spectrum has broad absorption lines Figure 17-16 ri||uxg Hnw a Star's Size Affectb its Spectrum These are the spectra of two stars of ;he same spectra! type (00) and burface temperature (13,400 K) but different radii and luminosities: (a) the BO supeigiant Rigel (luminosity 58,000 LG) tn Orion, and (b) the B8 main-sequence star Algol [luminosity 100 LQ) in Perseus. (From W. W. Morgan, P. C. Keenan, and E. Kellman, An Atlas of Stellar Spectra) Fundamentally, these differences between stars of different luminosity are due to differences between the stars' atmospheres, where absorption lines ate produced. Hydrogen lines in particu-|a[ ate affected by the density and pressure of the gas hi a star's atmosphere. The higher the density and pressure, the more frequently hydrogen atoms collide and interact with other atoms and jons in the atmosphere. These collisions shift the energy levels in [hi hydrogen atoms and thus broaden the hydrogen spectral lines. In the atmosphere of a luminous giant star, the density and prsssiire are quite low because the star's mass is spread over a huge volume, Atoms and ions in the atmosphere are relatively far apart; hence, collisions between them are sufficiently infrequent that hydrogen atoms can produce narrow Balmer lines. A main-sequence star, however, is much more compact than a giant or supergiant. In the denser atmosphere of a main-sequence star, frequent interatomic collisions perturb the energy levels in the hydrogen atoms, thereby producing broader Balmer fines. Luminosity Classes In the 1930s, W. W. Morgan and P. C. Keenan of the Yerkes Ob-setvatory of the Univetsity of Chicago developed a system of luminosity classes based upon the subtle differences in spectral lines. When these luminosity classes are plotted on an H-R. diagram [l-igurc 17-17), they provide a useful subdivision of the star types in the upp^r Tight of the diagram. Luminosity classes la and lb are composed of supergiants; luminosity class V includes all the main-sequence stars. The intermediate classes distinguish giant stars of various luminosities. Note that for stars of a given surface temperature (that is, a given spectral type), the higher the number of the luminosity class, the loiter the star's luminosity. As we will see in Chapters 19 and 20, different luminosity classes represent different stages tn the evolution of a star. White dwarfs are not always given a luminosity class of their own; as we mentioned in Section 17-7, they represent a final stage in stellar evolution in which nu thermonuclear reactions take place. Astronomers commonly use a shorthand description that combines a star's spectral type and irs luminosity class. For example, the Sun is said to be a G2 V star. The spectral type indicates the star's surface temperature, and the luminosity class indicates its luminosity. Thus, an astronomer knows immediately rhar any G2 V star is a main-sequence star with a luminosity of about 1 L© and a surface temperature of ahout 5S00 K. Similarly, a description of Aldebaran as a K5 111 star tells an astronomer that it is a red giant with a luminosity of around 370 Lq and a surface temperature of about 4UO0 K. Spectroscopic Parallax A star's spectral type and luminosity class, combined with the information on the H R diagram, enable astronomers to estimate the srsr's distance from Earth. As an example, consider the star Pleione in the constellation Tauius. Its spectrum reveals Pleione to be a B8 V star (a hot, blue, main-sequence star, like the one in Figure 17-16f>). Using Figure 17-17, we can read off that such a star's luminosity is 190 Lq. Given the star's luminosity and its apparent brightness—in the case of Pleione, 3.9 x 10~u of the apparent brightness of the Sun—we can use the inverse-square law Figure 17-17 Luminosity Classes The H-R diagram is divided into regions corresponding to stars oF different luminosity classes. (White dwarfs do not have their own luminosity class.) A star's spectrum reveals both its spectral type and its luminosity class; from these, tha star's luminosity can be determined. to determine its distance from Earth. The mathematical details are worked out in Box 17-2. This method for determining distance, in which the luminosity of a star is found using spectroscopy, is called spectroscopic parallax, figure 17-18 summarizes the method of spectroscopic parallax. CAUTION! The name "spectroscopic parallax" is a bit misleading, because no parallax angle is involved! The idea is that measuring the star's spectrum takes the place of measuring its parallax as a way to find the star's distance, A better name for this method, although not the Dne used by astronomers, would be "spectroscopic distance determination." Spectroscopic parallax is an incredibly powerful technique. No matter how remote a star is, this technique allows astronomers 456 Chapter 17 3 The Nature of the Stars 457 to determine its distance, provided only that its spectrum and apparent brightness can be measured. Roy 17-2 gives an example of how spectroscopic parallax has been used to find the distance to stars in other galaxies tens of millions of parsecs away. By contrast, we saw in Section 17-1 that "real" stellar parallaxes can be measured only for stars within a few hundred parsecs. Unfortunately, spectroscopic parallax has its limitations; distances to individual stars determined using this method often have errors greater than 10%. The reason is that the luminosity classes shown in Figure 17-17 ate not thin lines on the H-R diagtam but are moderately broad bands. Hence, even if a star's spectral type and luminosity class are known, there is still some uncertainty in the luminosity that we read off an H-R diagram. Nonetheless, spectroscopic parallax is often the only means that an astronomer has to estimate the distance to remote stars. What has been left out of this discussion is why different stars have different spectral types and luminosities. One key factor, as we shall see, turns out to be the mass of the star. 17-9 Observing binary star systems reveals the masses of stars We now know something abuut the sizes, temperatures, and luminosities of stars. To complete our picture of the physical properties of stars, we need to know their masses. In this section, we will see that Figure 17-18 The Method of SpecLiuSLupic Parallax If astans too far away, its parallax angle is too small to allow a direct determination of its distance. This flowchart shows how astronomers deduce the properties of such a distant star Not that the H-R diagram plays a central role in determining th= star's luminosity from its spectral type and lurrinosity class" Just as for nearby stars (see Figure 17-14), the star's chemical composition is cetermined from its spectrum, and the staf-radius is calculated from the luminosity and surface temperature. For main-sequence stars, there is a direct correlation between mass and luminosity 3 understand what hap- stars come in a wide range of masses. We will also discover an important relationship between the mass and luminosity of main-sequence stars. This relationship is crucial to understanding why some main-sequence stars are hot and luminous, while others are cool and dim. It will also help i pens to a star as it ages and evolves. Determining the masses of stars is not trivial, however. The problem is that there is no practical, direct way to measure the mass of an isolated star. Fortunately for astronomers, about halt of the visible stars in the night sky are noi isolated individuals. Instead, they are multiple-star systems, in which two or more stars orbit each other. By carefully observing the motions of these stars, astronomers can glean important information about their masses. Binary Stars A pair of stars located at nearly the same position in the night sky is called a double star. The Anglo-German astronomer William Herschel made the first organized search for such pairs. Between 1782 and 1821, he published three catalogs listing more than 800 double stars. Late in the nineteenth century, his son, John Herschel, discovered 10,000 more doubles. Some of these double stars are optical double stars, which are two stars that lie along nearly the same line of sight but are actually at very different distances from us. But many double stars are true binary stars, or Figure 17-19 RfUvuXG A Binary Star System As seen from Earth, the two stars tiat make up the binary system ca'.led 2MASSW 30746425 + 2000321 are separated by less than 1/3 arcsecond. The images surrounding the center diagram show the relative positions of the two stars over a four-year period. These images were made by the Hubble Space Telescope (HST), the European binaries—pairs of stars that actually orbit each other. H^ire 17-11> shows an example of this orbital motion. When astronomers can actually see the two stars orbiting each other, a binary is called a visual binary. By observing the binary over an extended period, astronomers can plot the orbit that one star appears to describe around the other, as shown in the center diagram in Figure 17-19. In fact, both stars in a binary system are in motion. They orbit each other because of their mutual gravitational attraction, and their orbital motions obey Kepler's third law as formulated by Isaac Newton (see Section 4-7 and Box 4-4). This law can be written as follows: Kepler's third law for binary star systems M: + M2= ^ Southern Observatory's Very targe Telescope (VLT), anc Keck I and Gemini North in Hawaii (see Figure 6-16). For simplicity, the diagram shows one star as remaining stationary; in realty, both stars move around their common center of mass. (H. Bouy et al, MPt and ESQ) Mi, Mi = masses of two stars in binary system, in solar masses a = semimajor axis of one star's orbit around the other, in AU P = orbital period, in yeais Here a is the semimajor axis of the elliptical orbit that one star appears to describe around the other, plotted as in the center diagram in Figure 17-19. As this equation indicates, if we can measure this semimajor axis (a) and the orbital period (P), we can learn something about the masses of the two stars. In principle, the orbital period of a visual binary is easy to determine. All you have to do is see how long it takes for the two stars to revolve once about each other. The two stars shown in Figure 17-19 are relatively close, about 2.5 AU on average, and their orbital period is only 10 years. Many binary systems have 458 Chapter 17 The center of mass of the systerr. of two children is nearer co the more e child. The center of mass of the binary siar system is nearer to the more massive star. (a) A "Dinary system" of two children Figure 17-20 ■gfll Center of Mass in a Binary Star System (a] A seesaw ^■8^ balances if tie f jlcrurn is at the center of mass of the two children, (b) The members of a binary star system orbit around the center much larger separations, however, and the period may be so long that more than one astronomer's lifetime is needed to complete the observations. Determining the semimajor axis of an orbit can also be a challenge. The angular separation between the stars can be determined by observation. To convert this angle into a physical distance between the stars, we need to know the distance between the binary and Earth. This distance can be found from parallax measurements or by using spectroscopic parallax. The astronomer must also take into account how the orbit is tilted to our line of sight. Once both P and a have been determined, Kepler's third law can be used to calculate M\ -f Mi, the sum of the masses of the two stars in the binary system. But this analysis tells us nothing about the individual masses of the two stars. To obLain these masses, more information about the motions of the two stars is needed. Each of the two stars in a binary system actually moves in an elliptical orbit about the center of mass of the system. Imagine two children sitting on opposite ends of a seesaw (figure f " ■ JU,:). For the seesaw to balance properly, they must position themselves so that their center of mass—an imaginary point that lies along a line connecting their two bodies—is at the fulcrum, or pivot point of the seesaw. If the two children have the same mass, the center of mass lies midway between them, and they should sit equal distances from the fulcrum. If their masses arc different, the center of mass is closer to the heavier child. Just as the seesaw naturally balances at its center of mass, the two stars that make up a binary system naturally orbit around their center of mass (Figure 17-20b). The center of mass always lies along the line connecting the two stars and is closer to the more massive star. The center of mass of a visual binary is located by plotting the separate orbits of the two stars, as in Figure 17-206, using the background stars as reference points. The center of mass lies at (b) A binary star system of mass of the two stars. Although their elliptical orbits cross each othf the two stars are always on opposite sides of the center of mass and thus never collide. the common focus of the two elliptical orbits. Comparing the relative sizes of the two orbits around the center of mass yields the ratio of the two stars' masses, M\IM.i. The sum M\ + M.i is already known from Kepler's third law, so the individual masses of the two stars can then be determined. Main-Sequence Masses and the Mass-Luminosity Relation Yeats of careful, patient observations of binaries have slowly yielded the masses uf many stars. As the data accumulated, an important trend began to emerge: For main-sequence stars, there is a direct correlation between mass and luminosity. The more massive a main-sequence star, the more luminous it is. Hgi.iT 17-21 depicts this mass-luminosity relation as a graph. The range of stellar masses extends from less than 0.1 of a solar mass to more than 50 solar masses. The Sun's mass lies between these extremes. The Cosmic Connections figure on the next page depicts the mass-luminosity relation for main-sequence stars on an H-R diagram. This figure shows the main sequence on an H-R diagram is a progression in mass as well as in luminosity and surface temperature. The hot, bright, bluish stars in the upper left corner of an H-R diagram are the most massive main-sequence stars. Likewise, the dim, cool, reddish stars in the lower right corner of an H-R diagram are the least massive. Main-sequence stars of intermediate temperature and luminosity also have intermediate masses. The mass of a main-sequence star also helps determine its radius. Referring back to Figure 17-iSb, wc sec that if we move along the main sequence from low luminosity to high luminosity, the radius of the star increases. Thus, we have the following general rule for main-sequence stars: The greater the mass of a main-sequence star, the greater its luminosity, its surface temperature, and its radius. The main sequence is an arrangement oF stars according to their mass. The most massive main-sequence stars have the greatest . ___-+„^+. =nrt nroa+OC-t-ClirfarP tpmOeratUre. Chapter 17 For a ma;n-sequence star, high mass means high U ...while low mass ! means low luminosity. Mass (M0) - Figure 17-21 The Mass-Luminosity Relation For main-sequence stars, there is a direct correlation between mass and luminosity—the more massive a star, the mere luminous it is. A main-sequence star of mass 10 [that is. 10 titles the Sun's mass) has roughly 3000 times tne Sun's luminosity (3000 L3); one with 0.1 MG has a luminosity of only about 0.001 L0. Mass and Main-Sequence Stars Why is mass the controlling factor in determining the properties of a main-sequence star? The answer is that all main-sequence stars are objects like the Sun, with essentially the same chemical composition £S the Sun but with different masses. Like the Sun, all mam-sequence stars shine because thermonuclear reactions at their cores convert hydrogen to helium and release energy. The greater the total mass of the star, the greater the pressure and temperature at the core, the more rapidly thermonuclear reactions take place in the core, and the greater the energy output—that is, the luminosity—of the star. In other words, the greater the mass of a main-sequence star, the greater its luminosity. This statement is just the mass-luminosity relation, which we can now recognize as a natural consequence of the nature of main-sequence stars. Like the Sun, main-sequence stars are in a state of both hydrostatic equilibrium and thermal equilibrium. Calculations using models of a main-sequence star's interior (like the solar models we discussed in Section 16-2) show that to maintain equilibrium, a more massive star must have a larger radius and a higher surface temperature. This result is just what we see when we plot the curve of the main sequence on an H~R diagram (see Figure 17-156). As you move up the main sequence from less massive stars (at the lower right in the H-R diagram) to m( massive stars (at the upper left}, the radius and surface tempe ture both increase. Calculations using hydrostatic and thermal equilibrium a show that if a star's mass is less than about O.OSMq, the core pressure and temperature are too low for thermonuclear reaction to take place. The "star" is then a brown dwarf. Brown dwatf$ also follow a mass-luminosity relation: The greater the mass, th? faster the brown dwarf contracts because of its own gravity, the more rapidly it radiates energy into space, and, hence, the more luminous the bjown dwarf is. CAUTION'. The mass-luminosity relation we have discussed applies to main-sequence stars only. There are no simple mass-luminosity relations for giant, supergiant, or white dwarf stars, i Why these stars lie where they do on an H-R diagram will be-I come apparent when we study the evolution of stars in Chap-1 ters 19 and 20. We will find that main-sequence stars evolve into giant and supergiant stars, and that some of these eventually end their lives as white dwarfs. 17-10 Spectroscopy makes it possible to study oinary systems in which the two stars are close together We have described how the masses of stars can be determined from observations of visual binaries, in which the two stars can be distinguished from each other. But if the two stars in a binary system are too close together, the images of the two stars can blend to produce the semblance of a single star. Happily, in many cases we can use spectroscopy to decide whether a seemingly single star is in fact a binary system. Spectroscopic observations of binaries provide additional useful information about star masses. Some binaries are discovered when the spectrum of a star shows incongruous spectral lines. For example, the spectrum of what appears to be a single star may include both strong hydrogen lines (characteristic of a type A star) and strong absorption bands of manium oxide (typical of a type M star). Because a single star cannot have the differing physical properties of these two spectral types, such a star must actually be a binary system that is too far away for us to resolve its individual stars, A binary system detected in this way is called a spectrum binary. Other binary systems can be detected using the Doppler effect. If a star is moving toward Earth, its spectral lines are displaced toward the short-wavelength (blue) end of the spectrum, Conversely, the spectral lines of a star moving away from us are shifted toward the long-wavelength (red) end of the spectrum. The upper portion of Figure 17-22 applies these ideas to a hypothetical binary star system with an orbital plane that is edge-on to our line of sight. As the two stars move around their orbits, they periodically approach and recede from us. Hence, the spectral lines of the two stars are alternately blueshifted and redshifted. The two stars in this hypothetical system are so close together that they appear through a telescope as a single star with a single spectrum. Stage 1 Center /of mass The Nature of the Stars Stage 4 Figure 17-22 Radial v'elodl/ Curves The lower ^r^ph displays the radial — velocity curves of the binary system HD 1710.78. The rimwngs at the top indicate the positions of the s:ars (labeled A and B) and the spectra of the binary at four selected moments (stages l, 2. 3, and A) during ar orbital period. Note that at stages 1 and 3, the Doppler Because one star shows a Wueshift while the other is showing a red-shift, the spectral lines of the binary system appear to split apart and rejoin periodically. Stars whose binary character is revealed by such shifting spectral lines are called spectroscopic binaries. Exploring Spectroscopic Binary Stars To analyze a spectroscopic binary, astronomers measure the wavelength shift of each star's spectral lines and ase the Doppler shift formula (introduced in Section 5-9 and Box 5-6} to determine the radial velocity of each star—that is, how fast and in what direction it is moving along our line of sight. The lower portion of Figure 17-22 shows a graph of the radial velocity versus time, called a radial velocity curve, for the binary system HD 171978, Fach of the two stars alternately ap- Stars in close binary systems move so rapidly that we can detect their motion using the Doppler eFfect effect splits apart the absorption lines from stars A and B; compare with figure 17-23. The entire binary star system is moving away from us at 12 km/s. which is why the entire pattern of radial velocity curves is displaced upward from the zero-velocity line. preaches and recedes as it orbits around the center of mass. The pattern of the curves repeats every 15 days, which is the orbital period of the binary. Fijmfc J "'-23 shows two spectra of the spectroscopic binary k (kappa) Arictis taken a few days apart. In Figure 17-23<3, two sets of spectral line.'; are visible, offset slightly in opposite directions from the normal positions of these lines. This corresponds ' to stage 1 or stage 3 in Figure 17-22; one of the orbiting stars is moving toward Earth and has its spectra! lines blueshifted, and the other star is moving away from Earth and has its lines red-shifted. A few days later, the stars have progressed along their orbits so that neither star is moving toward or away from Earth, corresponding to stage 2 or stage 4 in Figure 17-22. At this time there are no Doppler shifts, and the spectral lines of both stars are at the same positions. That is why only one set of spearal lines appears in Figure 17-236. It is important to emphasize that the Doppler effect applies only to motion along the line of sight- Motion perpendicular to 462 Chapter 17 The Ndtuie of the Stars 463 When one of the stats in a spectroscopic binary is moving toward us and the other is receding Írom us, wc sec two sets of specual lines due to ihe Doppler shift. To E When both stars are moving perpendicular to our line of sight, there is no Doppler splitting and we see a single szc of spectral lines. To Earth | Figure 17-23 riQuxg A Spectroscopic Binary The visible-light spectrum of the double-tine spectroscopic binary k (kappd) Arietis has spectral lines that shift Dack and forth as the two stars revolve obout each other. (Lick Observatory) the line of sight does not affect the observed wavelengths of spectral lines. Hence, the ideal orientation for a spectroscopic binary-is to have the stars orbit in a plane that is edge-on to our line of sight. (By contrast, a visual binary is best observed if the orbital plane is face-on to our line of sight.) For the Doppler shifts to be noticeable, the orbital speeds of the two stars should be at least a few kilometers per second. The binaries depicted in Figures 17-22 and 17-23 are called double-line spectroscopic binaries, because the spectral lines of both stars in the binary system can be seen. Most spectroscopic binaries, however, are single-line spectroscopic binaries, in which one of the stars is so dim that its spectral lines cannot be detected. The star is obviously a binary, however, because its spectral lines shift back and forth, thereby revealing the orbital motions of two stars about their center of mass. As for visual binaries, spectroscopic binaries allow astronomers to learn about stellar masses. From a radial velocity curve, one can find the ratio of the masses of the two stars in a binary. The sum of the masses is related to the orbital speeds of the two stats by Kepler's laws and Newtonian mechanics, if both the ratio of the masses and their sum are known, the individual masses can be determined using algebra. However, determining the sum of the masses requires that we know how the binary orbits are tilted from our line of sight. This is because the Doppler shifts reveal only the radial velocities of the stars rather than their true orbital speeds. This tilt is often impossible to determine, because we cannot see the individual scars in the binary. Thus, the masses of stars in spectroscopic binaries tend to be uncertain. There is one important case in which we can determine the orbital tilt of a spectroscopic binary. If the two stars are observed Eclipsing binaries can reveal the sizes and shapes qF stars to eclipse each other periodically, then we must bp viewing the or bit nearly edge-on. As we will see next, individual stellar masses as well as other useful data—can be determined if a spectroscopic binary also happens to be such an eclipsing binary. 17-11 Light curves of eclipsing binaries provide detailed information about the two stars Some binary systems are oriented so that the two stars periodically eclipse each other as seen from Earth. These eclipsing binaries can be detected even when the two stars cannot be resolved visually as two distinct images in the telescope. The apparent brightness of the image of the binary dims briefly each time one star blocks the light from, the other. Using a sensitive detector at the focus of a telescope, an as tronomer can measure the incoming light intensity quite accurately and create a light curve (Figure l?-24). The shape of the light curve for an eclipsing binary reveals at a glance whether the eclipse is partial or total (compare Figures 17-24^ and 17-24£>). Figure 17-24(i shows an observation of a binary system undergoing a total eclipse. In fact, the light curve of an eclipsing binary can yield a surprising amount of information. For example, the ratio of the surface temperatures can be determined from how much their combined light is diminished when the stars eclipse each other. Also, the duration of a mutual eclipse tells astronomers about the relative sizes of the stars and their orbits. If the eclipsing binary is also a double-line spectroscopic binary, an astronomer can calculate the mass and radius of each star from the light curves and the velocity curves. Unfortunately, very few binary stars are of this ideal type, Stellar radii determined in this way agree well with the values found using the Srefan Boltzmann law, as described in Section 17-6. The shape of a light curve can reveal many additional details about a binary system. In some binaries, for example, the gravitational pull of one star distorts the other, much as the Moon distorts Earth's oceans in producing tides (see Figure 4-26). Figure 17-24c shows how such tidal distortion gives the tight curve a dif' ferent shape than in Figure \7-1Ab, Information about stellar atmospheres can also be derived from light curves. Suppose that one star of a binary is a luminous main-sequence star and the other is a bloated red giant. By observing exactly how the light from the bright main-sequence star is gradually cur off as it moves behind the edge of the red giant during the beginning of an eclipse, astronomers can infer the pres-sure and density in the upper atmosphere of the red giant. Binary systems are tremendously important because they enable asttonomers to measure stellar masses as well as other key properties of stars. In the next several chapters, we will use this information to help us piece together the story of slelltir evolution—how stars are born, evolve, and eventually die. «MMR {a} Partial eclipse --- *— » ' - * Y / Time Incite f j~| <_disk ipf toriíí (b) Total eclipse (c) Tidal distortion Tims *" Figure 17-24 RlQuXG Repiebftntativs Light Curves of Eclipsing Binaries (a], (b), (c) The shape of the light curve of an eclipsing binary can reveal many defaib about the two stars that make up the binary, (d) Tiis image shows the Dinary star NN Serpens (indicated by the arrow) undergoing a total eclipse. The telescope wa5 moved during tne exposure so that the sky Key Words Terms preceded by an asterisk (*) are discussed in the Boxes. luminosity function, p. 438 magnitude scale, p. 440 main sequence, p. 453 main-sequence star, p. 453 mass-luminosity relation, p. 458 metals, p. 447 OBAFGKM, p. 446 optical double star, p. 456 parallax, p. 434 parsec, p. 434 photometry, p. 438 * proper motion, p. 436 radial velocity, p. 461 radial velocity curve, p. 461 red giant, p. 454 'space velocity, p. 436 spectral classes, p. 446 absolute magnitude, p. 441 apparent brightness (brightness), p. 437 apparent magnitude, p. 440 binary star (binary), p. 456 brown dwarf, p. 449 center of mass, p. 458 color ratio, p. 445 ""distance modulus, p. 444 double star, p. 456 eclipsing binary, p. 462 giant, p. 454 Hertzsprung-Russell diagram (H-K diagram), p. 452 inverse-square law, p. 437 light curve, p. 462 luminosity, p. 434 luminosity class, p. 455 (d) Eclipse of a binary star drifted slowly from left to right across the field of view. During the lO.E-minute duration q< the eclipse, the di-nmer star of the binary system ;an M6 main-sequence star) passed in front of the other, more lumincus star (a white dwarf) The binary became so dim that it almost disappeared. (European Southern Ocservatory) spectral types, p. 446 spectroscopic binary, p. 461 spectroscopic parallax, p. 455 spectrum binary, p. 460 stellar parallax, p. 434 supergiant, p. 454 ^tangential velocity, p. 436 TlfYV photometry, p. 445 visual binary, p. 457 white dwarf, p. 454 Key Ideas Measuring Distances to Nearby Stars: Distances to the nearer stars can be determined by parallax, the apparent shift of a star against the background stars observed as Earth moves along its orbit. • Parallax measurements made from orbit, above the blurring effects of the atmosphere, are much more accurate than those made with Farth-hased telescopes. • Stellar parallaxes can only he measured for stars within a few hundred parsecs. The Inverse-Square Law: A star's luminosity (total light output), apparent brightness, and distance from Earth are related by the 1 T of Birth OLl b The stars that illuminate our nights seem eternal and unchanging. But this permanence is an illusion. Each of the stars visible to the naked eye shines due to thermonuclear :•• reactions and has only a finite amount of fuel available for these -•' reactions. Hence, stars cannot last forever: They form from ma-. renal in interstellar space, evolve over millions or billions of years, and eventually die. In this chapter our concern is with how stars are born and become part of the main sequence. ! Stars form within cold, dark clouds of gas and dust that are scattered abundantly throughout our Galaxy. One such cloud appears as a dark area on the far right-hand side of the photograph at the top of this page. Perhaps a dark cloud like this encounters one of the Galaxy's spiral arms, or perhaps a supernova detonates nearby. From the shock of events like these, the cloud begins to contract under the pull of gravity, forming protostars—the fragments that will one day become stars. As a protostar develops, its internal pressure builds and its temperature rises. In time, hydrogen fusion begins, and a star is born. The hottest, bluest, and brightest young stars, like those in the accompanying image, emit ultraviolet radiation that excites the surrounding interstellar gas. Ihe result is a beautiful glowing nebula, which typically has the red color characteristic of excited hydrogen (as shown in the photograph). In Chapters 19 and 20 we will see how stars mature and grow old. Some even blow themselves apart in death throes that enrich interstellar space with the material for future generations of stars. Thus, like the mythical phoenix, new stars arise from the ashes of the old. Learning Goals B? reading the sections of this chapter, you will learn 18-1 How astronomers have pieced together the story of stellar evolution 18-2 What interstellar nebulae are and what they are made of 18-3 What happens as a star begins to form 18-4 The stages of growth from young protostars to main-sequence stars RIBUXG A region of star formation about 1400 pc (4000 ly) from Earth in the southern constellation Ara (the Altar). (European Southern Observatory) 18-1 Understanding how stars evolve requires observation as well as ideas from physics Over the past several decades, astronomers have labored to develop an understanding of stellar evolution, that is, how stars are born, live their lives, and finally die. Our own Sun provides evidence that stars are nor permanent. The energy radiated by the Sun comes from thermonuclear reactions in its core, which consume 6 X 1011 kg of hydrogen each second and convert it into helium (see Section 16-1). "While the amount of hydrogen in the Sun's core is vast, it is not infinite; therefore, the Sun cannot always have been shining, nor can it continue to shine forever. The same is true for all other main-sequence stars, which are fundamentally the same kinds of objects as the Sun but with different masses (see Section 17-9). Thus, stars must have a beginning as well as an end. Stars consume the material of which they are made, and so cannot last Forever 18-5 How stars gain and lose mass during their growth 18-6 What insights star clusters add to our understanding of stellar evolution 18-7 Where new stars form within galaxies 18-8 How the death of old stars can trigger the birth of new 471 472 Chapter 18 T The Sirth of Stars Stars last very much longer than the lifetime of any astronomer—indeed, far longer than the entire history of human civilization. Thus, it is impossible to watch a single star go through its formation, evolution, and eventual demise. Rather, astronomers have to piece together the evolutionary history of stars by studying different stars at different stages in their life cycles. To see the magnitude of this task, imagine that you are a biologist from another planet who sets out to understand the life cycles of human beings. You send a spacecraft to fly above Earth and photograph humans in action. Unfortunately, the spacecraft fails after collecting only 20 seconds of data, but during that time its sophisticated equipment sends back observations of thousands of different humans. From this brief snapshot of life on Earth—only 10~8 (a hundred-millionth) of a typical human lifetime—how would you decide which were the young humans and which were the older ones? Without a look inside our bodies to see the biological processes that shape our lives, could you tell how humans are born and how they die? And how could you deduce the various biological changes that humans undergo as they age? Astronomers, too, have data spanning only a tiny fraction of any star's lifetime. A star like the Sun can last for about 1010 years, whereas astronomers have been observing stars in detail for only about a century—as in our analogy, roughly 10"8 of the life span of a typical star. Astronomers are also frustrated by being unable to see the interiors of stars. For example, we cannot see the thermonuclear reactions that convert hydrogen into helium. But astronomers have an advantage over the biotogist in our story. Unlike humans, stars are made of relatively simple substances, primarily hydrogen and helium, that are found almost exclusively in the form of gases. Of the three phases of matter—gas, liquid, and solid—gases are by far the simplest to understand. Astronomers use our understanding of gases to build theoretical models of the interiors of stars, like the model of the Sun we saw in Section 16-2. Models help to complete the stoty of stellar evolution. In fact, like all great dramas, the stoiy of stellar evolution can be regarded as a struggle between two opposing and unyielding forces: Gravity continually tries to make a star shrink, while the star's internal pressure tends to make the star expand. When these two opposing forces are in balance, the star is in a state of hydrostatic equilibrium (see Figure 16-2). But what happens when changes within the star cause cither pressure or gravity to predominate? The star must then either expand or contract until it reaches a new equilibrium. In the process, it will change not only in size but also in luminosity and color. In the following chapters, we will find that giant and super-giant stars are the result of pressure gaining the upper hand over gravity. Roth giants and supergiants turn out to be aging stars that have become tremendously luminous and ballooned to hundreds or thousands of times their previous size. White dwarfs, by contrast, are the result of the balance tipping in gravity's favor. These dwarfs are even older stars that have collapsed to a fraction of the size they had while on the main sequence. In this chapter, however, we will see how the opposing influences of gravity and pressure explain the birth of stars. We start our journey within the diffuse clouds of gas and dust that permeate our galaxy. 18-2 interstellar gas and dust pervade the galaxy DiFFerent types of nebulae emit, absorb, i reflect light Where do stars come from? As we saw in Section 8-4, our Sun condensed from a solar nebula, a collection of gas and dust in interstellar space. Observations suggest that ~~~~ ~~ other stars originate in a similar way (see Figure 8-8). To undei ■ stand the formation of stars, we must first understand the natur of the interstellar matter from which the stars form. Nebulae and the Interstellar Medium At first glance, the space between the stars seems to be empty. O closer inspection, we find that it is filled with a thin gas laced wit microscopic dust particles. This combination of gas and dust i called the interstellar medium. Evidence we'll discuss for thi medium includes interstellar clouds of various types, curious line in the spectra of binary star systems, and an apparent dimming and reddening of distant stars. You can see evidence for the interstellar medium with the naked eye. Look carefully at the constellation Orion (hgurc I'Mi/), visible on winter nights in the northern hemisphere and summer nights in the southern hemisphere. While most ot the stars in the constellation appear as sharply defined points of light, the middle "star" in Orion's sword has a fuzzy appearance. This fuzziness becomes more obvious with binoculars or a telescope. As Figure 18-lfc shows, this "star" is actually not a star at all, but the Orion Nebula—a cloud in interstellar space. Any interstellar cloud is called a nebula (plural nebulae) or nebulosity. Emission Nebulae: Clouds of Excited Gas The Orion Nebula emits its own light, with the characteristic emission line spectrum of a hot, thin gas. For this reason it is called an emission nebula. Many emission nebulae can be seen with a small telescope, Figure 18-2 shows some of these nebulae in a different part of the constellation Orion. Emission nebulae are direct evidence of gas atoms in the interstellar medium. Typical emission nebulae have masses that range from about 100 to about 10,000 solar masses. Because this mass is spread over a huge volume that is light-years across, the density is quite tow by Earth standards, only a few thousand hydrogen atoms per cubic centimeter. (By comparison, the air you are breathing contains more than 1019 atoms per cm3.) Emission nebulae are found near hot, luminous stars of spectral types O and B. Such stars emit copious amounts of ultraviolet radiation. When atoms in the nearby interstellar gas absorl these energetic ultraviolet photons, the atoms become ionized. Indeed, emission nebulae are composed primarily of ionized hydrogen atoms, that is, free protons (hydrogen nuclei) and electrons, Astronomers use the notation H I for neutral, un-ionized hydrogen atoms and H II for ionized hydrogen atoms, which is why emission nebulae are also called H II regions. H II regions emit visible light when some of the free protons and electrons get back together to form hydrogen atoms, a process (a) A wide-angle view of Orion ^ Figure 18-1 The Orion Nebula (a) The middle "star" of the three that make up Orion's swerd is actuaty an interstellar cloud called - the Onon Nebula (b) The nebula is about 450 pc (1500 ly) from Earth and ' contains about 300 solar masses of material. Within the area shown by NGC2024 (b) A doseup of the Orion Nebula R 11 the box are four hot, massive stars called the Trapezium. They produce the ultraviolet light that makes the nebjta glow, (a: R. C. Mitchell, central Washington University; b: Anglu-Austi alian Observatory) called recombination (Figuri: H-t). When an atom forms by recombination, the electron is typically captured into a high-energy orbit. As the electron cascades downward through the atom's energy levels toward the ground state, the atom emits photons with lower energies and longer wavelengths than the photons that originally caused the ionization. Particularly important is the transition from n - 3 to n = 2, It produces HQ photons with a wavelength of 656 nm, in the red portion of the visible spectrum {see Section 5-8, especially Figure 5-23r?}. These photons give H II regions their distinctive reddish color. For each high-energy, ultraviolet photon absorbed by a hydrogen atom to ionize it, several photons of lower energy are emitted when a proton and electron recombine. As Bom 18-1 describes, a similar effect takes place in a fluorescent lightbulb. In this sense, H II regions are immense fluorescent light fixtures! Figure 18-2 RIHuxg Emission, Reflection, and Dark Nebulae in Or.on A variety of different nebulae appear In the sky around Alnitak, the easternmost star in Orion's belt (see Tigure 181a) All the nebulae lie approximately 500 pc (1600 ly) from Earth They are actually nowhere near Alnitak, which is only 250 pc (820 ly) distant. This photograph shows an area of the sky about 1.5" across. [Royal Observatory, Edinburgh) 482 Chapter 18 The Birth of Stars 483 (a) Visible-light image Figure 18-13 Mess Loss from Young. Massive; Stars (a] The Omega Nebula, also known as M17, is a regien of star formation in the constellation Sagittarius asout 1700 pc (5500 ly) from Earth, (b) This infrared image allows us to see through dust, revealing recently formed stars that cannot be seen in (a), (c) The most massive young stars ejsct copious amounts of hot gas Red indicates X-ray emission from gas at a mass. This process is called accretion, and the disk of material being added to the protoscar in this way is called a circumstellar accretion disk, Figure IS-I.S is an edge-on view of a circumstellar accretion disk, showing two oppositely directed jets emanating from a point at or near the center of the disk (where the proto-star is located). What causes some of the material in the disk to be blasted outward in a pair of jets? One model involves the magnetic field of the dark nebula in which the star forms (Figure I H-lo}. As material in the circumstellar accretion disk falls inward, it drags the magnetic field lines along with it. (V/e saw in Section 16-9 how vuQ temperature of 1.5 x 106 K; blue indicates even hotter gas at a temperature of 7 x 1C6 K. Astronomer do not see such X-ray emissior from the Ohon Nebula (Figure 1B-1), which has many young stars but ver/ few massive ones, (a: Palomar Observatory DSS; b: 2MAS5/UMass/ IPAC-CaltechVNASA/NSF; c: NASA/CXC/PSU/L. Townsley et aL) a similar mechanism may explain the Sun's 22-year cycle.) P; of the disk at different distances from the central protostar oi at different speeds, and this can twist the magnetic field lines i two helix shapes, one on each side of the disk. The helices tl act as channels that guide infalling material away from die p tostar, forming two opposing jets. Many astronomers suspect that interactions among the p tostar, the accretion disk, and the jets help to slow the protost; rotation, li so, this would explain why main-sequence stars g... erally spin much more slowly than protostars of the same fir mass. Figure 18-14 riEJuxg Bipolar Outflow and Herbig-Haro Objects The two bright knots of glowing, ionized gas called HH 1 and HH 2 are Herbig-Haro objects. They are created when fast-moving gas ejected from a protostar slams into the surrounding interstellar medium, healing the gas to high temperature. HH 1 and Hh 2 are C.34 parsec (1.1 light-ye apart and lie 470 pc (1500 ly) from Earth in the constellation Orion. (1 Hester, the WFPC-2 Investigation Definiticn Team, anc NASA) 1^ Figure 18-15 RlBuxG A Circumstellar Accretion Disk and Jets This False-color image shows a star surrounded by an accretion disk, wh.ch i see nearly edge-on. Red denotes emission from ionized gas, while ;en denotes starlight scattered from dust particles in the disk. The rjplane oF the accretion disk is so dusty and opaque that it appears ik. Two oppcsitely directed jets flow away from the star, perpendicular the disk and along the disk's rotation axis. This star lies 140 pr (450 ly) im Earth. (C. Burrows, the WFPC-2 Investigation Definition Team, and NASA) In the 1990s, astronomers using the Hubble Space Telescope discovered many examples of disks around newly formed stars in the Orion Nebula (see Figure 18-, one of the most prominent star-forming regions in the north-n sky. Figure 8-8 shows a number of these protoplanetary disks, proplyds, that surround young stars within the nebula. As the accrciion ilikk ! t \ i: Magnetic In-ill 1 ; lnic-i thread la) Figure 18-16 ■ A Magnetic Model for Bipolar Outflow (a) Observations suggest that ■-' Wcumstellar accretion disks are threaded by magnetic field lines, as ■ shown here (b)r (c) The contraction and rotation of the disk make the magnetic field lines distort and twist into helices. I hese helices stee' name suggests, protoplanetary disks are thought to contain the material from which planets form around stars. They are what remains of a circumstellar accretion disk after much of the material has eirher fallen onto the star or been ejected by bipolar outflows. Not all stars are thought to form protoplanetary disks; the exceptions probably include stars with masses in excess of about 3 M.Q, as well as many stars in binary systems. But surveys of the Orion Nebula show that disks are found around most young, low-mass stars. Thus, disk formation may be a natural stage in the birth of many stars. 18-6 Young star clusters give insight into star formation and evolution Dark nebulae contain tens or hundreds of solar v. : of gas and dust, enough to form many stars. As a consequence, these nebulae rend to form groups or clusters of young stars. One such cluster is Ml 6, shown in Figure 18-17; another is NGC 6520, visible in Figure 18-4. Star Clusters as Evolutionary Laboratories In addition to being objects of great natural beauty, star clusters give us a unique way to compare the evolution of different stars. That's because clusters typically include stars with a range of different masses, all of which began to form out of the parent nebula at roughly the same time. ftfJALQGY A foot race is a useful way to compare the performance of sprinters because all the competitors start the race simultaneously. A young star cluster gives us the same kind of opportunity to compare the evolution of stars of different masses that all began to form roughly simultaneously. Unlike a foot Swirling moiiuns in tlm ilhk diMort tin.' field , line* into helical shapes Some infalling disk materi.ii is channeled LKu.ird long the [idicei some of the disk material into jets that stream perpendicular to the plare of the disk, as .n Figure 18-15. (Adapted from Alfred T. Kamajian/Thomas P. Ray, "Fountain of Youth: Early Days in the Life of a Star," Scientific Anerican, August 2000) 484 Chapter 18 The Birth of Stars 485 1. This emission nebula (about 2200 pc away and about 20 pc across) sun™'*"4, :he star cluster M16. 2. Scar formation is still caking place wirhi . dark, dusty nebuli 3. Hot, luminous stars (beyond the upper edge of the closeup image) emit ultraviolet radiation: This makes the dark nebula evaporate, leaving these pillars. 4. At the tip of each of these "fingers" is a cocoon nebula young i evaporate, revealing the stars. Figure 18-17 riQuxg A Star Cluster with an H II Region The star cluster M16 is thought to be no more tian 800,000 years old, and star formation is still taking place within adjacent dark, dusty globules. The inset shows three dense, cold oillars of gas and dust silhouetted against the glowing background of the red emission race, however, the entire "race" of stellar evolution in a single cluster happens too slowly for us to observe; as Figure 18-10 shows, protostars take many thousands or millions of years to evolve significantly. Instead, we must compare different star clusters at various stages in their evolution to piece together the history of star formation in a cluster. All the stars in a cluster may begin to form nearly simultaneously, but they do not all become main-sequence stars at the same time. As you can see from their evolutionary tracks (see Figure 18-10), high-mass stars evolve more rapidly than low-mass stars. The more massive the protostar, the sooner it develops the central pressures and temperatures needed for steady hydrogen fusion to begin, thus joining the main sequence. Upon reaching the main sequence, high-mass, protostars become hot, uitraluminous stars of spectral types O and B. As we saw in Section 18-2, these types of stars have ultraviolet radiation that ionize the surrounding interstellar medium to produce an H nebula (called the Eagle Nebula for its shape). The pillar at the upper lert extends about 0.3 parsec (1 light-year) from base to tip, ar.d each of its "fingers" is somewhat broader than our entire sclar system. (Anglo-Australian Observatory; l Hester and P. Scowen, Arizona State University, NASA) II region. Figure 18-17 shows such an H II region, called the Eagle Nebula, surrounding the young star cluster M16. A few hundred thousand years ago, this region of space would have had a far less dramatic appearance. It was then a dark nebula, with protostars just beginning to form. Over the intervening millennia, mass ejection from these evolving protostars swept away the obscuring dust. The exposed young, hot stars heated the relatively thin remnants of the original dark nebula, creating the H H region thai we see today. When the most massive protostars to form out of a dark nebula have reached the main sequence, other low-mass protostars are still evolving nearby within their dusty cocoons. The evolution of these low-mass stars can be disturbed by their more massive neighbors. As an example, the inset in Figure 18-17 is a closc-up of part of the Eagle Nebula. Within these opaque pillars of cold gas and dust, protostars are still forming. At the same time, however, the pillars are heing eroded by intense ultraviolet light from hot, massive stars that have already shed their cocoons. young that most of its cool, low-mass stars have not yet arrived ar the main sequence. ) ihe star cluster NGC 2264 RlQlJXG -igure 18-18 Young Star Cluster and Its H-R Diayiam (a) This photograph shows i HII region and the young star cluster NGC 2264 in the constellaticn Moraceros {the Unicorn). It lies about 800 pc (2600 ly) from Earth. (b) Each dot plotted on this H-R diagram represents a star \n NGC 2264 As each pillar evaporates, the embryonic stars within have their , surrounding material stripped away prematurely, limiting the total mass that these stars can accrete. Analyzing Young Clusters Using H-R Diagrams Star clusters tell us still more about how high-mass and low-mass stars evolve. Figure 18-iSu' shows the young star cluster NGC 2264 and its associated emission nebula. Astronomers have mea-'.- sured each star's apparent brightness and color ratio. Knowing . the distance to the cluster, they have deduced the luminosities and . surface temperatures of the stars (see Section 17-2 and Section 17-4). Figure 18-186 shows all these stars on an H-R diagram. Note that the hottest and most massive stats, with surface tem-. peratures around 20.000 K, are on the main sequence. Stars cooler than about 10,000 K, however, have not • yet quite arrived at the main sequence. These are less massive stars sn the final stages of pre-main-sequence contraction and are just The H-R diagram oFa young cluster reveals how much time has elapsed since its stars began to Form [b) An H-R diagram of the stars in NGC 2264 whose luminosity and surface temperature have been determined. This star cluster probably started forming only 2 million years ago. (Anglo-Australian Observatory) now beginning to ignite thermonuclear reactions at their centers. To find the ages of these stars, we can compare Figure 18-186 with the theoretical calculations of protostar evolution in Figure 18-10. It turns out that this particular cluster is probably about 2 million years old. Figure XH-W'a shows another young star cluster called the Pleiades. The photograph shows gas that must once have formed an H II region around this cluster and has dissipated into interstellar space, leaving only traces of dusty material that forms reflection nebulae around the cluster's stars. This implies that the Pleiades must be older than NGC 2264, the cluster in Figure 18-18a, which is still surrounded by an H II region. The H-R diagram for the Pleiades in Figure 18-196 bears out this idea. In contrast to the H-R diagram for NGC 2264, nearly all the stars in the Pleiades are on the main sequence. The cluster's age is about 50 million years, which is how long it takes for the least massive stars to finally begin hydrogen fusion in their cores. CAUTION! Note that the data points for the most massive stars in the Pleiades (at the upper left of the H-R diagram in Figure 486 Chapter 18 The Birth of Stars 487 (a) The Pleiades star cluster R I Q U X G Figure 18-19 The Pleiades and Its H-R Diagram (a) The P'.eiades star cluster is 117 pc (380 ly) from Earth in the constellation Taurus, and ran he seen with the naked eye. (b) Each dot plotted on this hR diagram represents a star in the Pleiades whose luminosity and surface temperature have been 18-196) lie above the main sequence. This is not because these stars have yet to arrive at the main sequence. Rather, these stars were the first members of the cluster to arrive at the main sequence some time ago and are now the first members to leave it. They have used up the hydrogen in their cores, so the steady process of core hydrogen fusion that characterizes main-sequence stars cannot continue. In Chapter 19 we will see why massive stars spend a rather short time as main-sequence stars and will study what happens to stars after the main-sequence phase of their lives. •?-2}LIg> A loose collection of stars such as NGC 2264 or the |rJ Pleiades is referred to as an open cluster (or galactic cluster, since such clusters are usually found in the plane of the Milky Way Galaxy). Open clusters possess barely enough mass to hold themselves together by gravitation. Occasionally, a star moving faster than average will escape, or "evaporate," from an open cluster. Indeed, by the time the stars are a few billion years old, they may be so widely separated that a cluster no longer exists. If a group of stars is gravitationally unbound from the very beginning—that is, if the stars are moving away from one another (b) An H-R diagram of the stars in the Pleiades measured. (Note: The scales on this H-R diagram are different from thos in Figure 18-18M The Pleiades is about 50 million (5 x 107) years old (Anglo-Australian Observatory) so rapidly that gravitational forces cannot keep them together then the group is called a stellar association. Because young st lar associations are typically dominated by luminous O and main-sequence stars, they are also called OB associations. The ii age that opens this chapter shows part of an OB association the southern constellation Ara (the Altar). 18-7 Star birth can begin in giant molecular clouds We have seen that star formation takes place within dark ner. lae. But where within our Galaxy are these dark nebulae foun Does star formation take place everywhere within the Milky Wi or only in certain special locations? The answers to such tions can enhance our understanding of star formation and of f nature of our home Galaxy. Exploring the Interstellar Medium at Millimeter Wavelengths Dark nebulae are a challenge to locate simply because they < dark—they do not emit visible light. Nearby dark nebulae can Observing the Galaxy at millimeter wavelengths reveals the cold gas that spawns new stars ;en silhouetted against background stars or H II regions (see jgure 18-2), but sufficiently distant dark nebulae are impossible j see in contrast with background visible light because of inter-:e|lar extinction from dust grains. They can, however, be deleted using longer-wavelength radiatipn that can pass unaffected ,rough interstellar dust. In fact, dark nebulae actually emit radi-■ ation at millimeter wavelengths. Such emission takes place because in the cold depths of inter-cllar space, atoms combine to form molecules. The laws of lanmm mechanics predict that just as electrons within atoms n occupy only certain specific en-gy levels (see Section 5-8), mole-jes can vibrate and rotate only at rtain specific rates. When a mole-le goes from one vibrational state rotational state to another, it ei- _ er emits or absorbs a photon. (In e same way, an atom emits or absorbs a photon as an electron mps from one energy level to another.) Most molecules are rong emitters of radiation with wavelengths of around 1 to I millimeters (mm). Consequently, observations with radio tele-apes tuned to millimeter wavelengths make it possible to detect rellar molecules of different types. More than 100 different of molecules have so far been discovered in interstellar and the list is constantly growing. I hydrogen is by far the most abundant element in the universe. • IWortunately, in cold nebulae much of it is in a molecular form ■,[■[;) that is difficult to detect. The reason is that the hydrogen ule is symmetric, with two atoms of equal mass- joined to- j------, and such molecules do not emit many photons at radio fre- enries. In contrast, asymmetric molecules that consist of two ■)ms of unequal mass joined together, such as carbon monoxide 0), are easily detectable at radio frequencies. When a carbon anoxide molecule makes a transition from one rate of rotation another, it emits a photon at a wavelength of 2.6 mm or shorter. The ratio of carbon monoxide to hydrogen in interstellar ■ ace is reasonably constant; For every CO molecule, there arc out 10,000 h2 molecules. As a result, carbon monoxide is an excellent "tracer" for molecular hydrogen gas. Wherever as-Jnomers detect strong emission from CO, they know molecular drogen gas must be abundant. Molecular Clouds st systematic surveys of our Galaxy looking for 2.6-mm CO radiation were undertaken in 1974 by the American astronomers fl'.Jip Solomon and Nicholas Scoville. In mapping the locations of ■-0 emission, they discovered huge clouds, now called giant molec-ukr clouds, that must contain enormous amounts of hydrogen, douds have masses in the range of 105 to 2 X 106 solar masses d diameters that range from about 15 to 100 pc (50 to 300 ly). ■ide one of these clouds, there are about 200 hydrogen molecules f cubic centimeter. This density is several thousand times greater in the average density of matter in the disk of our Galaxy, yet only 17 as dense as the air we breathe. Astronomers now estimate that r Galaxy contains about 5000 of these enormous clouds. l'i[;me ] H-20 is a map of radio emissions from carbon monox-: "i the constellations Orion and Monoceros. Note the exten- Figure 18-20 Hivuxg Mapping Moiecu.ar Clouds A radio telescope was :uned to a wavelength of Z.b mm to detect emissions from :arbon monoxide [CO) molecules in the constellatiors Orion and Monoceros. The result was this false-color man. which shows a 35" x 40° section of the sky. The Orion and Hcrsehead star-forming nebulae are located at sites of intense CO emission (shown in red and yellow), indicating the preserce of a particularly dense molecular cloud at these sites of star Formation. The molecular cloud is much thinner at the positions of the Cone and Rosette nebulas, where star formation is less intense {Courtesy of R. Maddalena. M. Morris, 3. Moscowitz, and P. Thaddeus) sive areas of the sky covered by giant molecular clouds. This part of the sky is of particular interest because it includes several star-forming regions, By comparing the radio map with the star chart overlay, you can see that the areas where CO emission is strongest, and, thus, where giant molecular clouds are densest, are sites di" star formation. Therefore, giant molecular clouds are associated with the formation of stars. Particularly dense regions within these clouds form dark nebulae, and within these stars are born. By using CO emissions to map out giant molecular clouds, astronomers can find the locations in our Galaxy where star formation occurs. These investigations reveal that molecular clouds clearly outline our Galaxy's spiral arms, as Figure 11-2 I shows. These clouds lie roughly 1000 pc (3000 ly) apart and are strung along the spiral arms like beads on a string. This arrangement resembles the spacing of H II regions along the arms of other spiral galaxies, such as the galaxy shown in Figure 18-8a. The presence of both molecular clouds and H II regions shows that spiral arms are sites of ongoing star formation. Star Formation in Spiral Arms In Chapter 23 we will learn that spiral arms are locations where matter "piles up" temporarily as it orbits the center of the Galaxy. 496 Chapter 13 for observing with a telescope? Explain how you determined this. 54. Use the Stany Night Enthusiast'1'-' program ro examine the Milky Way Galaxy. Open the Favorites pane and click on Stars > Sun in Milky Way to display our Galaxy from a position 0.150 million light-years above the galactic plane. (You can remove the astronaut's feet from this view if de-sited by clicking on View > Feet.) You can zoom in or out on the Galaxy using the 4- and - buttons at the upper right end of the toolbar. You can move the Galaxy by holding down the mouse button while moving the mouse. You can also rotate the Galaxy by putting the mouse cursor over the image and holding down the Shift key while holding down the mouse button and moving the mouse, (a) You can identify H II regions by their characteristic magenta color. Describe where in the Galaxy you find these. Are most found in the inner part of the Galaxy or in its outer regions? (b) Where do you find dark lanes of dust—in the inner part of the Galaxy or in its outer regions? Do you see any connection between the locations of dust and of H II regions? If there is a connection, what do you think causes it? If there is not a connection, why is this the case? You can examine the location of our Galaxy in relation to neighboring galaxies by turning the Milky Way edge-on and by increasing the distance from Earth using the up key below the Viewing Location on the toolbar. Collaborative Exercises 55. Imagine that your group walks into a store that specialize in selling antique clothing. Prepare a list of observable char acteristics that you would look for to distinguish whici, items were from the early, middle, and late twentieth cen * tury. Also, write a paragraph that specifically describes hoy this task is similar to how astronomers understand the evrj lution of stars. 56. Consider advertisement signs visible at night in your conirrig nity and provide specific examples of ones that are example of the three different types of nebulae that astronomers ob serve and study. If an example doesn't exist in your commu nity, creatively design an advertisement sign that could serv. as an example. 57. The pre-main-sequence evolutionary tracks shown in FigUr, 18-10 describe the tracks of seven protostars of differen masses. Imagine a new sort of H-R diagram that plots a hu man male's increasing age versus decreasing hair density oi the head instead of increasing luminosity versus decreasing remperature. Create and carefully lahel a sketch of this imag inary HaiR diagram showing both the majority of the US male population and a few oddities. Finally, draw a line tha clearly labels your sketch to show how a typical male under going male-pattern baldness might slowly change position oi the HaiR diagram over the course of a human life span. 1 Stellar Evolutioi 0 t Sequence Imagine a world like Earth, but orbiting a star more than 100 times larger and 2000 times more luminous than our Sun. Bathed in the star's intense light, the surface of this world is utterly dry, airless, and hot enough to melt iron. If you could somehow survive on the daytime side of this world, you would see the star filling almost the entire sky. This bizarre planet is not a creation of science fiction—it is our own Earth some 7.6 billion years from now. The bloated star-is our own Sun, which in that remote era will have become a red-giant star. In this chapter, we'll learn how a main-sequence star evolves into a red giant when all the hydrogen in its core is consumed. The star's core contracts and heats up, but its outer layers expand and cool. In the hot, compressed core, helium fusion becomes a new energy source. The more massive a star, the more rapidly it consumes its core's hydrogen and the sooner it evolves into a giant. The interiors of stars are hidden from our direct view, so much of the story in this chapter is based on theory. We back up those calculations with observations of star clusters, which con-tun stars of different masses but roughly the same age. (An ex- R l£5jjU XG The red stars in this image of open cluster NGC 290 are red giants, a late stage in stellar evolution (ESA/NASA/Edware w. Olszewski, U of Arizona) ample is the cluster shown here, many of whose stars have evolved into luminous red giants.) Other observations show that some red-gianr stars actually pulsate, and that stars can evolve along very different paths if they are part of a binary srar system. In their cores, main-sequence stars are all fundamentally alike. As we saw in Section 18-4, it is in their cores that ail such stars convert hydrogen into helium by thermonuclear reactions. This process is called core hydrogen fusion. The total time that a star will spend fusing hydrogen into helium in its core, and thus the total time that it will spend as a main-sequence stat, is called its main-sequence lifetime. For our Sun, the main-sequence lifetime is about 12 billion (1.2 x 1010) years. Hydrogen Over the past 4.56 hillion years, thermonuclear reactions have caused an accumulation of helium in our 5un's core Learning Goals By reading the sections uf this chapter, you will learn 19-1 How a main-sequence star changes as it converts hydrogen to helium 19-2 What happens to a star when it runs out of hydrogen fuel 19-3 How aging stars can initiate a second stage of thermonuclear fusion 19-4 How H-R. diagrams for star clusters reveal the later stages in the evolution of stars 19-5 The two kinds of stellar populations and their significance 19-6 Why some aging stars pulsate and vary in luminosity 19-7 How stars in a binary system can evolve very differently from single, isolated stars Chapter 19 Stellar Evolution: On and After the Main Sequence 499 100 Dashed line: 4.56 billion yeais ago 75 / 50 - I Solid curve: today 25 1 I 1 / Sun's surface / 1 200,000 400,000 600,000 800,000 Distance from Sun's center (km (a) Hydrogen in the Sun's interior Figure 19-1 Charges in the Sun's Ohpmirnl Composition These graphs show the percentage by mass of (a) hydrogen and (b) helium at different points within the Sun's interior. The dashed horizontal lines show that these percentages were the same throughout the Sun's volume when it first fusion has been going on in the Sun's core for the past 4.56 billion (4.56 x 10s) years, so our Sun is less than halfway through its main-sequence lifetime. What happens to a star like the Sun after the core hydrogen has been used up, so that it is no longer a main-sequence star? As we will see, it expands dramatically to become a red giant. To understand why this happens, it is useful to first look at how a star evolves during its main-sequence lifetime. The nature of that evolution depends on whether its mass is less than or greater than about 0.4 Mo. Main-Sequence Stars of 0.4 M,,-, or Greater: Consuming Core Hydrogen A protostar becomes a main-sequence star when steady hydrogen fusion begins in its core and it achieves hydrostatic equilibrium-Si balance between the inward force of gravity and the outward pressure produced by hydrogen fusion (see Section 16-2 and Section 18-4). Such a freshly formed main-sequence star is called a zero-age main-sequence star. We make the distinction between "main sequence" and "zero-age main sequence" because a star undergoes noticeable changes in luminosity, surface temperature, and radius during its main-sequence lifetime. These changes are a result of core hydrogen fusion, which alters the chemical composition of the core. As an example, when our Sun first formed, its composition was the same at all points throughout its volume: by mass, about 74% hydrogen, 25% helium, and 1% heavy elements. But as Figure 1.9-1 shows, the Sun's core now contains a greater mass of helium than of hydrogen. {There is still enough hydrogen in the Sun's core for another 7 billion years or so of core hydrogen fusion.) CAUTION! Although the outer layers of the Sun are also predominantly hydrogen, there are two reasons why this hydrogen cannot undergo fusion. The first reason is that while the temperature and pressure in the core are high enough for thermonu- ~ 100 I 75 e 50 .Solid curve: today NDashed line: 4.56 billion years Astronomy Down to Earth 200,000 400,000 600,000 800,000 Distance from Sun's center (km) .......> (b) Helium in the Sun's interior formed. As the solid curves show, over the past 4.56 x 109 years, thermonuclear reactions at the core have depleted hydrogen in th and increased the amount of helium in the core. clear reactions to take place, the temperatures and pres the outer layers are not. The second reason is that thet flow of material between the Sun's core and outer layers hydrogen in the outer layers cannot move into the ho: pressure core to undergo fusion. The same is true foi sequence stars with masses of about 0.4 M© or greater, f -see below that the outer layers can undergo fusion k sequence stars with a mass less than about 0.4 Mq.) Thanks to core hydrogen fusion, the total number of nuclei in a star's core decreases with time: In each reactic hydrogen nuclei are converted to a single helium nucleus ' Cosmic Connections figure in Section 16-1, as well as Bo> With fewer particles bouncing around to provide the core' nal pressure, the core contracts slightly under the weight star's outer layers. Compression makes the core denser creases its temperature. {!lo\ S9-I gives some everyday ex of how the temperature of a gas changes when it comprc expands.) As a result of these changes in density and tempt the pressure in the compressed core is actually higher than As the star's core shrinks, its outer layers expand an more brightly. Here's why: As the core's density and temp increase, hydrogen nuclei in the core collide with one i more frequently, and the rate of core hydrogen fusion ini Hence, the star's luminosity increases. The radius of the si whole also increases slightly, because increased core p pushes outward on the star's outer layers. The star's surfa perature changes as well, because it is related to the lurr and radius (see Section 17-6 and Box 17-4). As an examp oretical calculations indicate that over the past 4.56 X 101 our Sun has become 40% more luminous, grown in radi 6%, and increased in surface temperature by 300 K (Fi;;tm As a main-sequence star ages and evolves, the increasi ergy outflow from its core also heats the material imme surrounding the core, As a result, hydrogen fusion can b Compressing and Expanding Gases As a star evolves, various parts of the star either contract or expand. When this happens, the gases behave in much the same way as gases here on Earth when they are forced to compress or allowed to expand. When a gas is compressed, its temperature rises. You know this by personal experience if you have ever had ro inflate a bicycle tire with a hand pump. As you pump, the compressed air gets warm and makes the pump warm to the touch. The same effect happens on a larger scale in southern California during Santa Ana winds or downwind from the Rocky Mountains when there are Chinook winds. Both of these strong winds blow from the mountains down to the lowlands. Even though the mountain air is cold, the winds that reach low elevations can be very hot. (Chinook winds have been known to raise the temperature by as much as 27°C, or 49°F, in only 2 minutes!) The explanation is compression. Air blown downhill by the winds is compressed by the greater air pressure at lower altitudes, and this compression raises the temperature of the air. Expanding gases tend to drop in temperature. When you open a bottle of carbonated beverage, the gases trapped in the bottle expand and cool down. The cooling can be so great that a little cloud forms within the neck of the bottle. Clouds form in the atmosphere in the same way. Rising air cools as it goes to higher altitudes, where the pressure is lower, and the cooling makes water in the air condense into droplets. Here's an experiment you can do to feel the cooling of expanding gases. Your breath is actually quite warm, as you can feel if you open your mouth wide, hold the back of your hand next to your mouth, and exhale. But if you bring your lips together to form an "o" and again blow on your hand, your breath feels cool. In the second case, your exhaled breath has to expand as it passes between your lips to the outside, which makes its temperature drop. lis surrounding material. By tapping this fresh supply of hydro-;n, a star manages to eke out a few million more years of main-■quence existence, Main-Sequence Stars of Less than 0.4 M©: □nsuming All Their Hydrogen he story is somewhat different for the least massive main-;quence stars, with masses between 0.08 Mq (the minimum mass ■ gure 13-2 te Zeto-Age Sun and Today's Sun ever the past 4.56 x 109 years, jch Df the hydrogen in the Sun's core has been converted into helium, e core has contracted a bit, and the Sun's luminosity has gone up by out 40%. These changes ir the core have made the Sun's outer layers pand in radius by 6% aid increased the surface temperature from WO K to 5800 K. for sustained thermonuclear reactions to take place in a star's core) and about 0.4 Mo. These stars, of spectral class M, are called red dwarfs because they are small in size and have a red color due to their low surface temperature. They are also very numerous; about 85% of all stars in the Milky Way Galaxy are red dwarfs. In a red dwarf, helium does not accumulate in the core to the same extent as in the Sun's core. The reason is that in a red dwarf there are convection cells of rising and falling gas that extend throughout the star's volume and penetrate into the core (see Figure 18-"12c). These convection cells drag helium outward from the core and replace it with hydrogen from the outer layers (Figure* 19-.i). The fresh hydrogen can undergo thermonuclear fusion that releases energy and makes additional helium. This helium is then dragged out of the core by convection and replaced by even more hydrogen from the red dwarf's outer layers. As a consequence, over a red dwarf's main-sequence lifetime essentially all of the star's hydrogen can be consumed and converted to helium. The core temperature and pressure in a red dwarf is less than in the Sun, so thermonuclear reactions happen more slowly than in our Sun. Calculations indicate that it takes hundreds of billions of years for a red dwarf to convert all of its hydrogen completely to helium. The present age of the universe is only 13.7 billion years, so there has not yet been time for any red dwarfs to become pure helium. A Star's Mass Determines Its Main-Sequence Lifetime The main-sequence lifetime of a star depends critically on its mass. As Tabic 19-[ shows, massive stars have short main-sequence lifetimes because they are also very luminous (see Section 17-9, and particularly the Cosmic Connections figure for Chapter 17). To emit energy so rapidly, these stars must be Chapter 19 H He Figure 19-3 A Fully Convective Red Dwarf In a red dwarf—a main-sequence star with less than about 0.4 solar masses—helium (He] created in the core by thermonuclear reacticns is carried to the star's outer layers by convection. Convection also brings fresh hydrogen (H) from the outer layer; into the core, "his process continues until the entire star is helium. depleting the hydrogen in their cores at a prodigious rate. Hence, even though a massive O or B main-sequence star contains much more hydrogen fuel in its core than is in the entire volume of a red dwarf of spectral class M, the O or B star exhausts its hydrogen much sooner. High-mass O and B stars gobble up the available hydrogen fuel in only a few million years, while red dwarf stars of very low mass take hundreds of billions of years to use up their hydrogen. Thus, a main-sequence star's mass determines not only its luminosity and spectral type, but also how long it can remain a main-sequence star (sec Box 19-2 for details), We saw in Section 1 8-4 how more-massive stars evolve more quickly through the protostar phase to become main-sequence stars (see Figure 18-10). In general, the more massive the star, the rapidly it goes through all the phases Df its life. Still, most of stars we are able to detect are in their main-sequence phase oe cause this phase lasts so much longer than other luminous phases In the remainder of this chapter we will look at the luminous phases that can take place after the end of a star's rnain-sequerice lifetime. (In Chapters 20, 21, and 22 we will explore the fina| phases of a star's existence, when it ceases to have an apprecia ble luminosity.) 19-2 When core hydrogen fusion ceases, a main-sequence star like the Sun becomes a red giant ^IAi Like so many properties of stars, what happens at the "nd of a star's main-sequence lifetime depends on its mass. If the star is a red dwarf of less than about 0.4 Mq, after hundreds of billions of years the stat has converted all of its hydrogen to helium. It is possible for helium to undergo thermonuclear fusion, but this requires temperatures and pressures far higher than those found within a red dwarf. Thus this red dwarf will end its life as an inert ball of helium, which has no further nuclear reactions, but still glows due to its internal heat. As it radiates energy into space, it slowly cools and shrinks. This slow, quiet demise is the ultimate fate of the 85% of stars in the Milky Way that are red dwarfs. (As we have seen, there has not yet been time in the history of the universe for any red dwarf to reach this final stage in its evolution.) What is the fate of stars more massive than about 0.4 Mq, including the Sun? As we will see, the late stages of their evolution are far more dramatic. Studying these stages will give us insight into the fate of our solar system and of life on Earth. Stars of 0.4 Mq or Greater: From Main-Sequence Star to Red Giant When a star of at least 0.4 solar masses reaches the end of its main-sequence lifetime, all of the hydrogen in its core has been used up and hydrogen fusion ceases there. In this new stage, hydrogen fusion continues only in the hydrogen-rich material just outside the core, a situation called shell hydrogen fusion. At first, this process occurs only in the hottest region just outside the core, Table 19-1 Approximate Main-Sequence Lifetimes Mass (Mo) Surface temperature (K) Spectral class Luminosity (Lq) Main-sequence lifetime (106 years) 25 35,000 O 80,000 4 IS 30,000 B 10,000 15 3 11,000 A 60 800 1.5 7000 F 5 4500 1.0 : 6000 G 1 12,000 0.75 5000 K 0.5 25,000 0.50 1000 M 0.03 700,000 The main-sequence lifetimes were estimated using the elationship t cc 1/M2-5 (see Box 19-2). box 19-2 Main-Sequence Lifetimes Hydrogen fusion converts a portion of a star's mass into energy. We can use Einstein's famous equation relating mass and energy to calculate how long a star will remain on the main sequence. Suppose that M is the mass of a star and f is the fraction of the star's mass that is converted into energy by hydrogen fusion. During its main-sequence lifetime, the total energy E supplied by the hydrogen fusion can be expressed as E = fMc1 In this equation c is the speed of light. This energy from hydrogen fusion is released gradually over millions or billions of years. If L is the star's luminosity (energy released per unit time) and t is the star's main-sequence lifetime (the total time over which the hydrogen fusion occurs), then we can write (Actually, this equation is only an approximation. A star's luminosity is not quite constant over its entire main-sequence lifetime. But the variations are not important for our purposes.) We can rewrite this equation as £ - Lt From this equation and E — fMc2, wc sec that Lt ■■= fMc2 Wc can rearrange this equation as Thus, a star's lifetime on the main sequence is proportional to its mass (M) divided by its luminosity (L). Using the symbol « to denote "is proportional to," we write Stellar Evolution: On and After the Main Sequerce Tools of the Astronomer's Trade M 106 T We can carry this analysis further by recalling that main-sequence stars obey the mass-luminosity relation (see Section 17-9, especially the Cosmic Connections figure). The distribution of data on the graph in the Cosmic Connections figure in Section 17-9 tells us that a star's luminosity is roughly proportional to the 3.5 power of its mass: L <* M3-5 Substituting this relationship into the previous proportionality, we find that AI M3.5 M2 VM This approximate relationship can be used to obtain rough estimates of how long a star will remain on the main sequence, It is often convenient to relate these estimates to the Sun (a typical 1-Mq star), which will spend 1.2 X 1010 years on the main sequence. example: How long will a star whose mass is 4 Mo remain on the main sequence? Situation: Given the mass of a star, we are asked to determine its main-sequence lifetime. Tools: We use the relationship t « 1/M2'5. Answer: The star has 4 times the mass of the Sun, so it will be on the main sequence for approximately 1 = 1 42.5 4i v4 ' times the Sun's main-sequence lifetime Thus, a 4-Mq main-sequence star will fuse hydrogen in its core for about (1/32) x 1.2 x 1010 years, or about 4 x 10s (400 million) years. Review: Our result makes sense: A star more massive than the Sun must have a shorter main-sequence lifetime. where the hydrogen fuel has not yet been exhausted. Outside this region, no fusion reactions take place. Strangely enough, the end of the core hydrogen fusion process leads to an increase in the core's temperature. Here's why: When thermonuclear reactions first cease in the Core, nothing remains to generate heat there. Hence, the core starts to cool and the pressure in the core starts to decrease. This pressure de- ln the transition From main-sequence star to red giant, the star's core contracts while its outer layers expand crease allows the star's core to again compress under the weight of the outer layers. As the core contracts, its temperature again increases, and heat begins to flow outward from the core even though no nuclear reactions are taking place there. (Technically, gravitational energy is converted into thermal energy, as in Kelvin-Helmholtz contraction; see Section 8-4 and Section 16-1), This new flow of heat warms the gases around the core, increasing the rate of shell hydrogen fusion and making the shell eat further outward into the surrounding matter. Helium produced by reactions in the shell falls down onto the core, which continues 502 Chapter 19 Stellar Evolution: On and After the Main Sequence 503 Ea) The Sun today and as a ran" giant JP Red Giants (a) he present-day Sun produces energy in a hydrogen- fusing core about 100,000 km in diameter. Some 7.6 billion years from now, when the Sun becomes a red giant, its energy sourcs will be a shell only about 30,000 km in diameter within which hydrogen fus'.on will :ake place at a furious rate. The Sun's luminosity will to contract and heat up as it gains mass. Over the course of hundreds of millions of years, the core of a 1-Mg star compresses to about one-third of its original radius, while its central temperature increases from about 15 million (1.5 X 107] K to about 100 million (10s) K. During this post-main-sequence phase, the star's outer layers expand just as dramatically as the core contracts. As the hydrogen-fusing shell works its way outward, egged on by heat from the contracting core, the star's luminosity increases substantially. This increases the star's internal pressure and makes the star's outer layers expand to many times the original radius. This tremendous expansion causes those outer layers to cool down, and the star's surface temperature drops (see Box 19-1). Once the temperature of the star's bloated surface falls to about 3500 K, the gases glow with a reddish hue, in accordance with Wien's law (see Figure 17-7a). The star is then appropriately called a red giant (Figure 19-4). Thus, we see that red-giant stars are former main-sequence stars that have evolved into a new stage of existence. We can summarize these observations as a general rule: Stars join the main sequence when they begin hydrogen fusion in their cores. They leave the main sequence and become giant stars when the core hydrogen is depleted. Red-giant stars undergo substantial mass loss because of their large diameters and correspondingly weak surface gravity. This makes it relatively easy for gases to escape from the red giant into (b) Red giant stars in the star cluster M50 Rfi0UX(3 be about 2000 times greater than today, and the increased luminosity will make the Sun's outer layers expand to approximately 100 times they present si2e. {b} This composite of visible aid infrared images shows bright red giant stars in the open cluster M50 in the constellation Moncceros (the Unicorn). (T. Credner and S. Kohle, Calar Alto Observatory) space. Mass loss can be detected in a star's spectrum, because gas escaping from a red giant toward a telescope on Earth produces narrow absorption lines that are slightly blueshifted by the Doppler effect (review Figure 5-26). Typical observed blueshifts correspond to a speed of about 10 km/s. A typical red giant loses roughly 10~7 Mo of matter per year. For comparison, the Sun's present-day mass loss rate is only 10-1"1 Mo per year. Hence, an evolving star loses a substantial amount of mass as it becomes a red giant. Figure 19-5 shows a star losing mass in this way, f he Distant Future of Our Solar System We can use these ideas to peer into the future of our planet and our solar system. The Sun's luminosity will continue to increase as it goes through its main-sequence lifetime, and the temperature of Earth will increase with it. One and a half billion years from now Earth's average surface temperature will be 50°C (122°F). By 3V2 billion years from now the surface temperature of Earth will exceed the boiling temperature of water. All the oceans will boil away, and Earth will become utterly incapable of supporting life. These increasingly hostile conditions will pose the ultimate challenge to whatever intelligent beings might inhabit Earth in the distant future. About 7 billion years from now, our Sun will finish converting hydrogen into helium at its core. As the Sun's core contracts, its atmosphere will expand to envelop Mercury and perhaps reach to the orbit of Venus. Roughly 700 million years after leaving the main sequence, our red-giant Sun will have swollen to a diameter Figure 19-5 RiSHuXG A Ma^-Loss Star As stars age and become giant star?, they expand tremendously and shed matter into soace. This star, HD148937, is losing matter at a high rate. Other strong outbursts in the past ejected the clouds that surround HD 148937. These clouds absorb ultraviolet radiation from the star, which excites the atoms in the Uuuds and causes them to glow. The characteristic red color of the clouds reveals the preserce of hydrogen [see Section 5-61 bat was ejected from the stars outer layers. (David Matin, Anglo-Australian Observatory) of about 1 AU—roughly 100 times larger than its present size— and its surface temperature will have dropped to about 3500 K. Shell hydrogen fusion will proceed at such a furious rate that our star will shine with the brightness of 2000 present-day Suns. Some of the inner planets will be vaporized, and the thick atmospheres of the outer planets will evaporate away to reveal tiny, rocky cores. Thus, in its later years, the aging Sun may destroy the planets that have accompanied it since its birth. 19-3 Fusion of helium into carbon and oxygen begins at the center of a red giant When a star with a mass greater than 0.4 Mq first changes from a mam-sequence star (Figure 19-ha) to a red giant (Figure 19~6b), its hydrogen-fusing shell surrounds a small, compact core of almost pure helium. In a red giant of moderately low mass, which the Sun will become 7 billion years from now, the dense helium core is about twice the diameter of Earth. Most of this core helium was produced by thermonuclear reactions during the star's main-sequence lifetime; during the red-giant era, this helium will undergo thermonuclear reactions. Core Helium Fusion Helium, the "ash" of hydrogen fusion, is a potential nuclear fuel: Helium fusion, the thermonuclear fusion of helium nuclei to make heavier nuclei, releases energy. But this reaction cannot take place within the core of our present-day Sun because the temperature there is too low. Each helium nucleus contains two protons, so it has twice the positive electric charge of a hydrogen nucleus, and there is a much stronger electric repulsion between two helium nuclei than between two hydrogen nuclei. For helium nuclei to overcome this repulsion and get close enough to fuse together, they must be moving at very high speeds, which means that the temperature of the helium gas must be very high. (For more on the relationship between the temperature of a gas and the speed of atoms in the gas, see Box 7-2.) When a star first becomes a red giant, the temperature of the contracted helium core is still too low for helium nuclei to fuse. But as the hydrogen-fusing shell adds mass to the helium core, the core contracts even more, further increasing the star's central temperature. When the central temperature finally reaches 100 million (10s) K, core helium fusion—that is, thermonuclear fusion of helium in the core—begins. As a result, the aging star again has a central energy source for the first time since leaving the main sequence (Figure 19-6c). (a) (b) (c) Figure 19-G Stages in I he Involution of a Star wi:h More than U.4 -Tcist' '* Solar Masses (a) During the star's main-sequence lifetime hydrogen is cbnverted into helium in the star's core, (b) When the core hydrogen is exhausted, hydrogen fusion continues in a shell, and the star expands to become a red giant, (c) When the temperature in the red giant's core becomes high enough because of contraction, core helium fusion begins (right). (These three pictures are not drawn to scale. The star is about IOC times larger in its red-giant phase than in its main-sequence phase, then shrinks somewhat when core helium fusion begins.) ' 504 Chapter 19 Helium fusion occurs in two steps. First, two helium nuclei combine to form a beryllium nucleus: 4He 4- "He -> 8Be This particular beryllium isotope, which has four protons and four neutrons, is very unstable and breaks into two helium nuclei soon after it forms. However, in the star's dense core a third helium nucleus may strike the "Be nucleus before it has a chance to fall apart. Such a collision creates a stable isotope of carbon and releases energy in the form of a gamma-ray photon {y}: 8Be + 4He 12C - 7 This process of fusing three helium nuclei to form a carbon nucleus is called the triple alpha process, because helium nuclei (4He) are also called alpha particles by nuclear physicists. Some of the carbon nuclei created in this process can fuse with an additional helium nucleus to produce a stable isotope of oxygen and release more energy: 12C + 4He-» 160 +■ -y Thus, both carbon and oxygen make up the "ash" of helium fusion. The Cosmic Connections figure summarizes the reactions involved in helium fusion. It is interesting to note that 12C and l6Q are the most common isotopes of carbon and oxygen, respectively; the vast majority of the carbon atoms in your body are 12C, and almost all the oxygen you breathe is 160. We will discuss the significance of this in Section 19-5. The second step in the triple alpha process and the process of oxygen formation both release energy. The onset of these reactions reestablishes thermal equilibrium and prevents any further gravitational contraction of the star's core, A mature red giant fuses helium in its core for a much shorter time than it spent fusing hydrogen in its core as a main-sequence star. For example, in the distant future the Sun will sustain helium core fusion for only about 100 million years—this period is only about 1 % of the time that hydrogen fusion occurs. (While this is going on, hydrogen fusion is still continuing in a shell around the core.) The Helium Flash and Electron Degeneracy How helium fusion begins at a red giant's center depends on the mass of the star. In high-mass red giants (greater than about 2 to 3 Mo), helium fusion begins gradually as temperatures in the star's core approach 10a K. In red giants with a mass less than about 2 to .3 Mq, helium fusion begins explosively and suddenly, in what is called the helium flash. Tabic 19-2 summarizes these differences. The helium flash occurs because of unusual conditions that develop in the core of a moderately low-mass star as it becomes a red giant. To appreciate these conditions we must first understand how an ordinary gas behaves. Then we can explore how the densely packed electrons at the star's center alter this behavior. When a gas is compressed, it usually becomes denser and warmer. To describe this process, scientists use the convenient concept of an ideal gas, which has a simple relationship between pressure, temperature, and density. Specifically, the pressure ex- : Table 19-2 How Helium Core Fusion Begins ; : • in Different Red Giants Stars with less than about 0,4 solar masses do not become red giants (see Section 19-2). erted by an ideal gas is directly proportional to both the density and the temperature of the gas. Many real gases actually behave like an ideal gas over a wide range of temperatures and densities, Under most circumstances, the gases inside a star act like an ideal gas. If the gas expands, it cools down, and if it is compressed, it heats up (see Box 19-1). This behavior serves as a safety valve, ensuring that the star remains in thermal equilibrium (see Section 16-2). For example, if the rate of thermonuclear reactions in the star's core should increase, the additional energy releases heat and expands the core. This expansion cools the core's gases and slows the rate of thermonuclear reactions back to the original value. Conversely, if the rate of thermonuclear reactions should decrease, the core will cool down and compress under the pressure of the overlying layers. The compression of the core will make its temperature increase, thus speeding up the thermonuclear reactions and returning them to their original rate. In a red giant with a mass between about 0.4 M© and 2-3 Mq, however, the core behaves very differently from an ideal gas. The core must be compressed tremendously in order to become hut enough for helium fusion to begin. At these extreme pressures and temperatures, the atoms are completely ionized, and most of the core consists of nuclei and detached electrons. Eventually, the free electrons become so closely crowded that a limit to further compression is reached, as predicted by a remarkable law of quantum mechanics called the Pauli exclusion principle. Formulated in 1925 by the Austrian physicist Wolfgang Pauli, this principle states that two electrons cannot simultaneously occupy the same quantum state. A quantum state is a particular set of circumstances concerning locations and speeds that are available to a particle. In the submicroscopic world of electrons, the Pauli exclusion principle is analogous to saying that you can't have two things in the same place at the same time. Just before the onset of helium fusion, the electrons in the core of a low-mass star are so closely crowded together that any further compression would violate the Pauli exclusion principle. Because the electrons cannot be squeezed any closer together, they produce a powerful pressure that resists further core contraction. This phenomenon, in which closely packed particles resist compression as a consequence of the Pauli exclusion principle, is called degeneracy. Astronomers say that the electrons in the helium-rich core of a low-mass red giant are "degenerate," and Before helium fusion begins in a red giant's core, the helium gas there behaves like a metal Mass of star Onset of helium fusion in core More than about 0.4 but less Explosive (helium flash) i than 2-3 solar masses i More than 2-3 solar masses Gradual A star becomes a red giant after the Fusion oFhydrogen into helium in its core has come to an end. As the red giant's core shrinks aru heats up, a new cycle of reactions can occur that creatE the evon ____....._____________„_____temperatures and pressures become high enough for helium nuclei (4He) to and fuse togethei. " 2. Fusing two4Me nuclei produces a beryllium nucleus (aBe) with four protons and four neutrons. The "Be nucleus is very unstable; it breaks apait, leaving two 1He nuclei again, with a half-life of just 7 x 10"r's. 3. However, if a third 4He nucleus collides with the "Be nucleus during its brief existence, thi stable nucleus of carbon (12C) with six protons and six neutrons. - 4, This nuclear reaction releases a gamma-ray photon {-(). The photon's energy goe; inio sustaining the internal heat of the red giant. 5. Some 12C nuclei collide with an -' additional 4He nucleus to form a stable nucleus of oxygen |160) with eight protons and eiglit Chapter 19 Figure 19-7 riQuxg Degenerate Electrons The electrons in an ordinary piece of metal, like the chrome grille on this classic car, are so close together that they are affected by the Pauli exclusion principle. The resulting degenerate electron pressure helps make metals strong and difficult to compress. A mare powerful version of this same effect happens inside the cores of low-mass red-giant stars. (Sp.ntokh Kochar/PhotoDisc) that the core is supported by degenerate-electron pressure. This degenerate pressure, unlike the pressure of an ideal gas, does not depend on temperature. Remarkably, you can find degenerate electrons on Earth in an ordinary piece of metal (Figure 19-7). When the temperature in the core of a low-mass red giant reaches the high level required for the triple alpha process, energy begins to be released. The helium heats up, which makes the triple alpha process happen even faster. However, the pressure provided by the degenerate electrons is independent of the temperature, so the pressure does not change. Without the "safety valve" of increasing pressure, the star's core cannot expand and cool. The rising temperature causes the helium to fuse at an ever-increasing rate, producing the helium flash. Eventually, the temperature becomes so high that the electrons in the core are no longer degenerate. The electrons then behave like an ideal gas and the star's core expands, terminating the helium flash. These events occur so rapidly that the helium flash is over in seconds, after which the star's core settles down to a steady rate of helium fusion. CAUTION! The term "helium flash" might give you the impression that a star emits a sudden flash of light when the helium flash occurs. If this were true, it would be an incredible sight. During the brief time interval when the helium flash occurs, the helium-fusing core is 10u times more luminous than the present-day Sun, which is similar to the total luminosity of all the stars in the Milky Way Galaxy! But, in fact, the helium flash has no immediately visible consequences—for two reasons. First, much of the energy released during the helium flash goes into heating the core and terminating the degenerate state of the electrons. Second, the energy that does escape the core is largely absorbed by the star's outer layers, which are quite opaque (just like the Sun's present-day interior; see Section 16-2). Therefore the explosive drama of the helium flash takes place where it can' not be seen directly. The Continuing Evolution of a Red Giant Whether a helium flash occurs or not, the onset of core helium fusion actually causes a decrease in the luminosity of the star This decrease is the opposite of what you might expect—after all turning on a new energy source should make the luminosity greater, not less. What happens is that after the onset of core helium fusion, a star's superheated core expands like an ideal gas (If the star is of sufficiently low mass to have had a degenerate core, the increased temperature after the helium flash makes the core too hot to remain degenerate. Hence, these stars also end up with cores that behave like ideal gases.) Temperatures drop around the expanding core, so the hydrogen-fusing shell reduces its energy output and the star's lumi nosity decreases. This temperature decrease allows the star's outer layers to contract and heat up. Consequently, a post-helium-fiash star is less luminous, hotter at the surface, and smaller than a red giant. Core helium fusion lasts for only a relatively short time. Calculations suggest that a 1-M© star like the Sun sustains core Core helium fusion and hell hydrogen fusion 12.1 12.2 of Che Sun (billions of years) Figure 19-8 Stages in the Evolution of the Sun This diagram shows how the luminosity of the Sun (a 1-M0 star) changes over tine. The Sun began as a protostar whose lumnosity decreased rapidly as the protostar contracted. Once estabtohec as a main-sequence star with core hydrogen fusion, the Sun's luminosity increases slowly over billions of yeers. The post-main-sequence evolution is much more rapid, so a different tiTie scale is used in the right-hand porticn of the graph. (Adapted from Mark A. Garlick, based on calculations by l.Ouliana Sackmann and Kathleen E. Kramer) hydrogen fusion for about 12 billion (1.2 X 1010) years, followed hj- about 250 million (2,5 X 10s) years of shell hydrogen fusion leading up to the helium flash. After the helium flash, such a star can fuse helium in its core (while simultaneously fusing hydrogen ^ a shell around the core) for only 100 million (10s) years, a niere 1% °f its main-sequence lifetime. Figure 19-8 summarizes these evolutionary stages in the life of a 1-Mo star. In Chapter 20 art will take up the story of what happens after a star has consumed all the helium in its core. Here is the story of post-main-sequence evolution in its briefest form: Before the beginning of core helium fusion, the star's core compresses and the outer layers expand, and just after core helium fusion begins, the core expands and the outer layers compress. We will see in Chapter 20 that this behavior, in which [he inner and outer regions of the star change in opposite ways, occurs again and again in the final stages of a srar's evolution. [19-4 H-R diagrams and observations of star clusters reveal how red giants evolve To see how stars evolve during and after their main-sequence lifetimes, it is helpful to follow them on a Hertzsprung-Russell (H-R) diagram. On such a dia- (a) Post-main-sequence evolutionary tracks of five stars with different n Figure 19-9 H-R Diagrams of Stellar Evolution on and off the Main Sequence (a) The two lowest-mass stars shown here (1 MQ and 2 M©) undergo a helium flash at their centers, as shown by the asterisks. In the high-mass stars, core helium fusion ignites more gradually where the evolutionary tracks make a sharp downward turn in Stellar Evolution; On and After the Main Sequence gram, zero-age main-sequence stars lie along a line called the zero-age main sequence, or ZAMS (Figure These stars have just emerged from their protostar stage, are steadily fusing hydrogen into helium in their cores, and have attained hydrostatic equilibrium. With the passage of time, hydrogen in a main-sequence star's core is converted to helium, the luminosity slowly increases, the star slowly expands, and the star's position on the H-R diagram inches away from the ZAMS. As a result, the main sequence on an H-R diagram is a fairly broad band rather than a narrow line (Figure 19-9/?). Post-Main-Sequence Evolution on an H-R Diagram The dashed line in Figure \9-9a denotes stars whose cores have been exhausted of hydrogen and in which core hydrogen fusion has ceased. These stars have reached the ends of their main-sequence lifetimes. From there, the points representing high-mass stars (3 Mo, 5 Mo, and 9 Mo) move rapidly from left to right across the H-R diagram. This means that, although the star's surface temperature is decreasing, its surface area is increasing at a rate that keeps its overall luminosity roughly constant. During this transition, the star's core contracts and its outer layers expand as energy flows outward from the hydrogen-t shell. 103. WHITE DwARFS 1 10 Colors indicate number ^of stars per point. - Temperacure (K) (b) H-R diagram of 20,853 stars-note the width of the main sequsnce the red-giant region on the right hand side of the I l-R diagram, (b) Data from the Hipparcos satellite (see Section 17-1) was used to create this H-R diagram. The thickness of the main sequence :s due in large part to stars evolving during their nair-sequence lifetimes, (a: Adapted from I Iben; b: Adapted from M. A. C. Perryman; 508 Chapter 19 Just before core helium fusion begins, the evolutionary tracks of high-mass stars turn upward in the red-giant tegion of the H-R diagram (to the upper right of the main sequence). After core helium fusion begins, however, the cores of these stars expand, the outer layers contract, and the evolutionary tracks back away from these temporary peak luminosities. The tracks then wander back and forth in the red-giant region while the stars readjust to their new energy sources. Figure 19-9a also shows the evolutionary tracks of two stars of moderately low mass (1 Mo and 2 Mo). The onset of core helium fusion in these stars occurs with a helium flash, indicated by the red asterisks in the figure. As we saw in the previous section, after the helium flash, these stars shrink and become less luminous. The decrease in size is proportionately greater than the decrease in luminosity, and so the surface temperatures increase. Hence, after the helium flash, the evolutionary tracks for the 1-M© and 2-M© stars move down and to the left. A Simulated Star Cluster: Tracking 4V2 Billion Years of Stellar Evolution We can summarize our understanding of stellar evolution from birth through the onset of helium fusion by following the evolution of a hypothetical cluster of stars. We saw in Section 18-6 that the stars that make up a cluster all begin to form at essentially the same time but have different initial masses. Hence, studying star clusters allows us to compa re how stars of different masses evolve. The eight H-R diagrams in Figure l^-l 0 are from a computer simulation of the evolution of 100 stars that all form at the same moment and differ only in initial mass. All 300 stars begin as cool protostars on the right side of the H-R diagtam (see Figure 19-10tf). The protostars are spread out on the diagram according to their masses, and the greater the mass, the greater the proto-star's initial luminosity. As we saw in Section 18-3, the source of a protostar's luminosity is its gravitational energy. As the proto-star contracts, this gravitational energy is converted to thermal energy and radiated into space. The most massive protosrars contract and heat up very rapidly. After only 5000 years, they have already moved across the H-R diagram toward the main sequence (see Figure 19-106). After 100,000 years, these massive stars have ignited hydrogen fusion in their cores and have settled down on the main sequence as O stars (see Figure 19-10c). After 3 million years, stars of moderate mass have also ignited core hydrogen fusion and become main-sequence stars of spectral classes B and A (see Figure 19-10i). Meanwhile, low-mass protostars continue to inch their way toward the main sequence as they leisurely contract and heat up. After 30 million years (see Figure 19-10e), the most massive stars have depleted the hydrogen in their cores and become red giants. These stars have moved from the upper left end of the main sequence to the upper right corner of the H-R diagram. (This simulation follows stars only to the red-giant stage, after which they are simply deleted from the diagram.) Intermediate-mass stars lie on the main sequence, while the lowest-mass stars are still in the protostar stage and lie above the main sequence. After 66 million years (see Figure 19-10/"), even the lowest-mass protostars have finally ignited core hydrogen fusion and I have settled down on the main sequence as cool, dim, M stars These lowest-mass stars can continue to fuse hydrogen in thei cores for hundreds of billions of years. In the final two H-R diagrams (Figures 19-10g and 19-ifj^j the main sequence stars get "peeled" or "eaten away" from th upper left to the lower right as stars exhaust their core supply of hydrogen and evolve into red giants. The stars that leave th main sequence between Figure 19-10g and Figure 19-10/j hav masses between about 1 Mo and 3 M© and undergo the helmn flash in their cores. For all stars in this simulation, the giant stage lasts only a brief time compared to the star's main-sequence lifetime. Compared to a 1-Mq star (see Figure 19-8), a more massive star has a shorter main-sequence lifetime and spends a shorter time as a giant star. Thus, at any given time, only a small fraction of the stellar population is passing through the giant stage. Hence, most o: the stars we can see through telescopes are main-sequence stars. As an example, of the stats within 4.00 pc (13.05 ly) of the Sun listed in Appendix 4, only one—Procyon A—is presently evolving from a main-sequence star into a giant. Two other nearby stars are white dwarfs, an even later stage in stellar evolution that we will discuss in Chapter 20. (By contrast, most of the brightest stars listed in Appendix 5 are giants and supergiants. Although they make up only a small fraction of the stellar population, these stars stand out due to their extreme luminosity.) Real Star Clusters: Cluster Ages and Turnoff Points ft^liií'^ The evolution of the hypothetical cluster displayed in Figure 19-10 helps us interpret what we se^ in actual star clusters. We can observe the early stages of stellar evolution in open clusters, which typically contain a few hundred to a few thousand stars. Many open clusters are just a few million years old, so their H-R diagrams resemble Figure 19-lQd, 19-10e, or 19-10/(see Section 18-6, especially Figure 18-18 and Figure 1H-19). Figure 19-! 1 shows two open clusters of different ages. The nearer cluster, called M35, must be relatively young because it contains several dozen luminous, blue, high-mass main-sequence stars. These stars lie in the upper______ part of the main sequence on an H-R diagram. They have main-sequence lifetimes of only a few hundred million years, so M35 can be no older than that. Some of the most luminous stars in M35 are red or yellow in color; these are stars that ended their main-sequence lifetimes some time ago anc have evolved into red giants. The H-R diagram for this cluster resembles Figure 19-10#. There are no high-mass blue main-sequence stars at all in NGC 2158, the more distant cluster shown in Figure 19-11. Any such stars that were once in NGC 2158 have long since come to the end of their main-sequence lifetimes. As a result, the main se quence in this cluster has been "eaten away" more than that of M35, leaving only stars that are yellow or red in color. This tells us that NGC 2158 must be older than M35 (compare Figures As a duster ages and Its stars end their main-sequence lifetimes, the duster's color changes from blue to red Stellar Evolution; On and After the Main Sequence 509 the main sequence: This means thathydrogen fusion is taking place in [heir cores. Surface temperature (K) \4. All of these stars ha ncd the m 5. The least massive stars cvo vc the id have not ye: joi icel the mainjeq v:"'''// *\\ 40,000 10,000 3000 (b) -«— Surface temperature (K) -\6. Tints parr of the main sequence is empty: The must massive a have depleted rhc hydrogcr thcir cores .. v- ...and have 40,000 10,000 3000 (c) -»-Surface temperature (K) Age: 30 rnillio 40,000 10,000 3000 -*-Surface temperature (K) *\\ 9. Stars of ever-lower mass have ' depleted their core hydrogen, cof the main ; now empty. - Surface temperature (K) 40.000 10,000 3000 (g) ■* ■ Surface temperatute (K) 40,000 10,000 3000 [h) Surface temperature (K) 40,000 10,000 3000 (f) -*-Surface temperature (K) iSSSfci. Fi3ure 19-10 The Evolution of a Theoretical Cluster This seiies of H-R diagrams shows the evolution of 100 ^rars of different masses in a hypothetical cluster. Each dot represents a star, and the "age" indicates the time that has elapsed since all the stars formed. At each age, the luminosity and sui face tempeiatuie of each star were calculated using the equations of stelar structure. After a star passes through the red-giant stage, it is deleted from the diagram. (Adapted from R. Kippenhahn) 510 Chapter 19 T Stellar Evolution: On and After the Main Sequence 511 Figure 19-11 RiBuxg Two Open Clusters The two dusters in this image, M35 and NG; 2158, lie in almost the same direction in the constellation Gemini. The nearer cluster, M35, has a number of luminous hlue ma-n-sequence stars with surface temperatures around 10,000 K as well as a few red giants. Hence its H-R diagram resembles that shown in Figu'e 19-10g, and its age is around 100 million years [more accurately, around 150 million). The more distant cluster, NGC 2158, has no blue main-sequence stars; long ago, all of these massive stars came to the end of their main-sequence lifetimes and became giants. The H-R diagram for NGC 2158 is intermediate hetween Figure 19-10g and Figure 19-lOh, and its age (1.05 billion years) is as well. (Canada--rance-Hawaii Telescope; 1-C. Cuillandre, CFHT; and Coeium) 19-10g and 19-10h), This example shows that as a cluster ages, it generally becomes redder in its average color. We can see even later stages in stellar evolution by studying globular clusters, so called because of their spherical shape. A typical globular cluster contains up to 1 million stars in a volume less than 100 parsecs across li-igurc 19-12}. Among these are many highly evolved post-main-sequence stars. Globular clusters must be old, because they contain no high-mass main-sequence stars. To determine that these clusters are old, you would measure the apparent magnitude (a measure of apparent brightness, which we introduced in Section 17-3) and color ratio of many stars in a globular cluster, then plot the data as shown in figure 1 9-15. Such a color-magnitude diagram 1 cluster is equivalent to an II-R diagram. The color ratio of a tells you its surface temperature (as described in Section 1 and because all the stars in the cluster are at essentially the .• distance from us, their relative brightnesses indicate their rel luminosities. What you would discover is that a globular elm main sequence has been "peeled" or "eaten away" even mon tensively than the open cluster NGC 2158 in Figure 19-11. Hi globular clusters must be even older than NGC 2158. In a cal globular cluster, all the main-sequence stars with masses i than about IMq or 2 M© evolved long ago into red giants, i low-mass, slowly evolving stars still haye core hydrogen fu. (Compare Figure 19-13 with Figure 19-10/?.) CAUTION! The inset in Figure 19-12 shows something sur ing: There are luminous blue stars in the ancient globular ter M10. This seems to contradict our earlier statements blue main-sequence stars evolve into red giants after just a hundred million years. The explanation is that these are main-sequence stars, but rather horizontal-branch stars. 1 stars get their name because in the color-magnitude diagra a globular cluster, they form a horizontal grouping in the of-center portion of the diagram (see Figure 19-13). Horizo branch stars are relatively low-mass stars that have air become red giants and undergone a helium flash, so the both core helium fusion and shell hydrogen fusion taking j . in their interiors. After the helium flash their luminosit) creased to about 50 L© (compared to about 1000 L© hefor flash) and their outer layers contracted and heated, giving i stars their blue color. In years to come, these stars will rmv: : back toward the red-giant region as their fuel is devoured. Our own Sun will go through a horizontal-branch phase in the distant future; this is the phase labeled by the number 3 at the far right of Figure 19-8. Measuring the Ages of Star Clusters The idea that a cluster's main sequence is progressively "eaten away" is the key to determining the age of a cluster. In the H-R diagram for a very young cluster, all the stars are on or near the main sequence. (An example is the open cluster NGC 2264, shown in Figure 18-18.) As a cluster gets older, however, stars begin to leave the main sequence. The high-mass, high-luminosity stars are the first to consume their core hydrogen and become red giants. As time passes the main sequence gets shorter and shorter, like a candle burning down (see parts d through h of Figure 19-10). The age of a cluster can be found from the turnoff puint, which is the top of the surviving portion of the main sequence stars on the cluster's H-R diagram (see Figure 19-13). The stars at the turnoff point are just now exhausting the hydrogen in their cores, so their main-sequence lifetime is equal to the age of the cluster, For example, in the case of the globular cluster M55 plotted in Figure 19-13, 0.8-Mu stars have just left the main sequence, indicating that the cluster's age is more than 12 billion (1.2 x 1010) years (see Table 19-1). I:igtire 19-14 shows data for several star clusters plotted on a single H-R diagram. This graph also shows turnoff-point times from which the ages of the clusters can be estimated. e:i Figure 19-12 riHuxg A Globular CI ister This cluster, called M10, contains a few hundred thousand stars within a diameter of enly 20 pc (70 ly). It lies approximately 5000 pc (16,000 ly) from Earth in the constellation Ophiuchus (the Serpent Holder), Most of the stars in this image are either red giants or blue, horizontal-branch stars with both core nelium fusion and shell hydrogen fusion. (T. Credner and S. Kohle, Astronomical Institutes of the University of Bonn) Figure 19-13 A Color-Magnitude Diagram of a Globular Cluster Each dot in this diagram represents the apparent visual magnitude (a measure of the brightness as seen through a V filter) and surface temperature (as measured by the color ratio Dv/Ob) of a star in the globular cluster M55 in Sagittarius. Because all the stars in M55 are a: essentially the same distance from Earth (about 6000 pc or 20,000 ly), their apparent visual magnitudes are a direct measure of their luminosities. Note that the upper half of the main sequence is missing. (Adapted from D. Schade, D. VandenBerg, and F. Hartwick) Figure 19-14 An H-R Diagram for Open Star Clusters The black lands indicate where stars from various open clusters fall on the H-R diagram. The age of a cluster can be estimated from the location of the cluster's turnoff point, where the cluster's most massive stars are just now leaving the main sequence. The times for these tu'noff points are listed alongside the main sequence. For example, the Pleiades cluster turnoff point is near the 10a-year point so this cluster is about 10B years old. (Adapted from A. Sandage) 512 Chapter 19 Stellar Evolution: On and After the Main Sequence 513 19-5 Stellar evolution has produced two cistinct populations of stars Studies of star clusters reveal a curious difference between the youngest and oldest stars in our Galaxy. Stars in the youngest clusters (those with most of their main sequences still intact) are said to be metal rich, because their spectra contain many prominent spectral lines nf heavy elements. (Recall from Section 17-5 that astronomers use the term "metal" to denote any element other than hydrogen and helium, which are the two lightest elements.) Such stars are also called Population i stars. The Sun is a relatively young, metal-rich, Population i star. By contrast, the spectra of stars in the oldest clusters show only weak lines of heavy elements. These ancienr stars are thus said to be metal poor, because heavy elements are only about 3% as abundant in these stars as in the Sun. They are also called Population ii stars. The stars in globular clusters are metal poor, Population ii stars. Figure 19-15 shows the difference in spectra between a metal-poor, Population ii star and the Sun (a metal-rich, Population i star). CAUTION! Note that "metal rich" and "metal poor" are relative terms. In even the most metal-rich star known, metals make up just a few percent of the total mass of the star. Stellar Populations and the Origin of Heavy Elements To explain why there are two distinct populations of stars, we must go back to the Big Bang, the explosive origin of the universe that took place some 13.7 billion years ago. As we will discuss in Chapter 27, the early universe consisted almost exclusively of hydrogen and helium, with almost no heavy elements (metals). The first stars to form were likewise metal poor. The least massive of Stars like the Sun zon\& material that was processed through an earlier generation of stars these stars have survived to the present day and are now the ■ cient stars of Population II. The more massive of the original stars evolved more rapid and no longer shine. But as these stars evolved, helium fusion their cores produced metals—carbon and oxygen. In the r massive stars, as we will learn in Chapter 21, further thermonuclear reactions produced even heavier elements. As these massive original stars aged and died, they expelled their metal-enriched gases into space. {The star shown in Figure 19-5 is going through such a mass-loss -phase late in its life.) This expelled material joined the interstellar medium and was eventually incorporated into a second generation of stars that have a higher concentration of heavy elements These metal-rich members of the second stellar generation are the Population I stars, of which our Sun is an example. CAUTION! Be careful not to let the designations of the two stellar populations confuse you. Population 1 stars are members of a second stellar generation, while Population II stars belong to an older first generation. The relatively high concentration of heavy elements in the Sun means that the solar nebula, from which both the Sun and planets formed (see Section 8-4), must likewise have been metal rich. Earth is composed almost entirely of heavy elements, as are our bodies. Thus, our very existence is intimately linked to the Sun's being a Population I star. A planet like Earth probably could not have formed from the metal-poor gases that went into making Population II stars. The spectrum of this Population II star shows absorption lines of hydrogen (such as Hy and H5) but only very weak absorptior lines of metals... such a star is metal-poor. w T-'inT The spectrum of this Popula absorption lines of metals .. Figure 19-15 . riQuxg Spectra of a Metal- Poor Star and £ Metal-Rich Star The abundance of metals (elements heavier than hydrogen and helium) in a star can be inferrec'froTi its spectrum. These spectra compare (a) a metal-poor. Population II star and (b) a metal-rich, Population I star (the Sun) of the ionl star has stronger such a star is metal-rich. same sjrface temperature. We described the hydrogen aDsorption lines 1L, [wavelength 434 nm) and HB (wavelength 410 nrn] in Section 5-8. (tick Observatory] The concept of two stellar populations provides insight into r own origins. Recall from Section 19-3 that helium fusion in 'd-giant stars Pr°duces tne same isotopes of carbon (-2C) and xygen <16(^' tnat are f°und most commonly on Earth. The rea--,n is that Earth's carbon and oxygen atoms, including all of iose in your body, actually were, produced by helium fusion, hese reactions occurred billions of years ago within an earlier ■-neration of stars that died and gave up their atoms to the inter-e|lar medium—the same atoms that later became part of our so-r system, our planet, and our bodies. "We are literally children f the stars. 19-6 Many mature stars pulsate *£12$\.-p We saw in Section 16-3 that the surface of our Sun vi-|,J brates in and out, although by only a small amount. But other stars undergo substantial changes in size, al-■- ternately swelling and shrinking. As these stars pulsate, they also ; vary dramatically in brightness. We now understand that these pulsating variable stars are actually evolved, post-main-sequence . stars. ; Long-Period Variables Pulsating variable stars were first discovered in 1595 by David - Fabricius, a Dutch minister and amateur astronomer.. He noticed that the star o (oiuicron) Ceti is sometimes bright enough to be easily seen wirh the naked eye but at other times fades to invisibility (hiuire i 9-16). By 1660, astronomers realized that these bright- / Mllil .!( IllilKJil (b) Figure 19-16 riQuxg Mira—A Long-Period Variable Star Mira, or o (omicron) Ceti, is a variable star whose lurrinosity varies with a 332-day period. At its dimmest, as in [a] (photographed in December 1961}, Mira is less than 1% as bright as when it is at maximum, as in (b) (January 1S65). These brightness variations occur because Mira pulsates. (Lowell Observatory] e. Figure 19-17 ^ Variable Stars on the H-R Diagram Pulsating variable stcrs -feist''' are found in the upper right of ths H-R diagram. :.ong-period variables like Mira are cool red giant stars that pulsate slowly, changing their brightness in a semi-regular fashion over months or years. Cepheid variables and RR Lyrae variables are located in the instability strip, which lies between the main sequence and the red-giant region. A star passing through this strip along its evolutionary track becomes unstable and pulsates. ness variations repeated with a period of 332 days. Seventeenth-century astronomers were so enthralled by this variable star that they renamed it Mira ("wonderful"). Mira is an example of a class of pulsating stars called long-period variables. These stars are cool red giants that vary in brightness by a factor of 100 or more over a period of months or years. With surface temperatures of about 3500 K and average luminosities that range from about 10 to 10,000 ho, they occupy the upper right side of the H-R diagram (Figure 19-17). Some, like Mira, are periodic, but others are irregular. Many eject large amounts of gas and dust into space. Astronomers do not fully understand why some cool red giants become long-period variables. It is difficult to calculate accurate stellar models to describe such huge stars with extended, tenuous atmospheres. 514 Chapter ig By studying variable stars, astronomers gain insight into late stages of stellar evolution Cepheid Variables Astronomers have a much better understanding at" other pulsating stars, called Cepheid variahles, or simply Cepheids. A Cepheid variable is recognized by the characteristic way in which its light output varies—rapid brightening followed by gradual dimming. They are named lor S (delta) Cephei, an example of this type of star discovered in 1784 by John Goodricke, a deaf, mute, 19-year-oid English amateur astronomer. He found that at its most brilliant, o Cephei is 2.3 times as bright as at its dimmest. The cycle of brightness variations repeats every 5.4 days. (Sadly, Goodricke paid for his discoveries with his life; he cauglu pneumonia while making his nightly observations and died before bis twenty-second birthday.) The surface temperatures and luminosities of the Cepheid variables place them in the upper middle the H-R diagram (see Figure 19-17). 5 Cephei reaches f-—maximum brightness -every 5.4 days : of Time (days) W The tight curve of 6 Cephei (a graph of brightness versus time) When 5 Cephei is at rnajirn,™ brighlnes!| the star ,s near ,B maximum surface temperamre Time (days) (O Surface temperature versus time for 8 Cephei " ~"J Figure 19-18 S Cephei-4 Pulsating Gtar (a) As s Cepne, pulsates it After core helium fusion begins, mature stars move across !',,„ middle of the H-R- diagram. Figure \9-9a shows the evolutions tracks of high-mass stars crisscrossing the H-R diagram. \>Qi helium-flash stars of moderate mass also cross the middle of t|lf' H-R diagram between the red-giant region and the horizon branch. During these transitions across the H-R diagram, a star can become unstable and pulsate. In fact, there is a region on f.; H-R diagram between the upper main sequence and the rcd-giL branch called the instability strip (see Figure 19-17). When evolving star passes through this region, the star pulsates and ,. ■ brightness varies periodically. Figure 19-18(7 shows the brightrt ;; variations of 8 Cephei, which lies within the instability strip. A Cepheid variable brightens and fades because the stars outer envelope cyclically expands and contracts. The first to <}fy serve this was the Russian astronomer Aristarkh BelopoPskn, who noticed in 1894 that spectral lines in the spectrum of K Cephei shift back and forth with the same 5.4-day period as that of the magnitude variations. From the Doppler effect, we can When 5 Cephei is ar maximum brightness, the star is expanding most rapidly Time (days! (b) Radial velocity versus time for 8 Cephei (positive: star is contracting; negative: star is expanding] When 8 Cephei is at maximum brightness, die star » expanding (its diameter is increasing) 1.15 f 1 5 6 7 Time (days) (d) Diameter versus time for á Cephei away from us, negative when the star expands and the .urfacP ItZlm.Tn h-we"T"(c)'the5tar'ss,jrfacete^erature-m> nslate these wavelength shifts into radial velocities and draw a vj|cicity curve (Figure 19-186). Negative velocities mean that the star's surface is expanding toward us; positive velocities mean l^t the star's surface is receding. Note that the light curve and .elDcity curve are mirror images of each other. The star is brighter (nan average while it is expanding and dimmer than average while rontracting. When a Cepheid variable pulsates, the star's surface oscillates ip and down like a spring. During these cyclical expansions and -onttactions, the star's gases alternately heat up and cool down. :;gure 19-18t shows the resulting changes in the star's surface ernperature. Figure 19-18J graphs the periodic changes in the „tar's diameter. Just as a bouncing ball eventually comes to rest, a pulsating tar would soon stop pulsating without something to keep its os-Jllations going. In 1914, the British astronomer Arthur Edding-[on suggested that a Cepheid pulsates because the star is more opaque when compressed than when expanded. When the star is compressed, trapped heat increases the internal pressure, which pushes the star's surface outward. When the star expands, the heat escapes, the internal pressure drops, and the star's surface falls inward. In the 1960s, the American astronomer John Cox followed up on Eddington's idea and proved that helium is what keeps Cepheids pulsating. Normally, when a star's helium is compressed, the gas increases in temperature and becomes more transparent. But in certain layers near the star's surface, compression may ionize helium (remove one of its electrons) instead of raising its temperature. Ionized helium gas is quite opaque, so these layers effectively trap heat and make the star expand, as Eddington suggested. This expansion cools the outer layers and makes the helium ions recom-bine with electrons, which makes the gas more transparent and releases the trapped energy. The star's surface then falls inward, recompressing the helium, and the cycle begms all over again. CAUTION! In our discussion of the behavior of gases (see Box j 19-1, Section 19-1. and Section 19-3) we saw that a gas cools ■ when it expands and heats up when it is compressed. Hence, . you would expect that the gases in a pulsating star like S Cephei would reach their maximum temperature when the star is at its smallest diameter, so that the gases are most compressed. The hotter the gas, the more brightly it glows, so 8 Cephei should : also have its maximum brightness when its diameter is smallest. But Figure 19-18 shows that the star's brightness and the temperature of the gases at the surface reach their maximum values when the star is expanding, some time after the star has con-! tracted to its smallest diameter. How can this be? The explana-: tion is again related to how opaque the gases are inside the star. The rate at which energy is emitted from the central regions of the star is indeed greatest when the star is at its minimum diameter, but the opaque gases in the star's outer layers impede the flow of energy to the surface, Hence, S Cephei reaches its maximum brightness and maximum surface temperature about half a day after the star is at its smallest size. Cepheid variables are important because they have two properties that allow astronomers to determine the distances to very Stellar Evolution: On and After the Main Sequence remote objects. First, Cepheids can be seen even at distances of millions of parsecs, because they are very luminous, ranging from a few hundred times solar luminosity to more than 104 L©. Second, there is a direct relationship between a Cepheid's period and its average luminosity: The dimmest Cepheid variables pul sate rapidly, with periods of 1 to 2 days, while the most luminous Cepheids pulsate with much slower periods of about 100 days. figure 19-19 shows this period-luminosity relation. By measuring the period of a distant Cepheid's brightness variations and using a graph like Figure 19-19, an astronomer can determine the star's luminosity. By also measuring the star's apparent brightness, the distance to the Cepheid can be found by using the inverse-square law (see Section 17-2). By applying the period-luminosity relation in this way to Cepheids in other galaxies, astronomers have been able to calculate the distances to those galaxies with great accuracy. (Box 17-2 gives an example of such a calculation.) As we will see in Chapters 24 and 26, such measurements play an important role in determining the overall size and structure of the universe. How a Cepheid pulsaLes depends on the amount of heavy elements in the star's outer layers, because even trace amounts of these elements can have a large effect on how opaque the stellar gases are. Hence, Cepheids are classified according to their metal content. If the star is a metal-rich, Population I star, it is called a Type I Cepheid; if it is a metal-poor, Population II star, it is called Type I Cepheids • Metal-rich Population I si • More luminous Type II Cepheids • Metal-poor Population II si • Less luminous Figure 19-19 Period-Luminosity Relations for Cepheids The greater the average luminosity of a Cepheid variable, the longer its period and the slower its pulsations. Note that there are actually two distinct penod-lnminosity relations—ore for Type 3 Cepheids and one for the less luminous Type 31 Cepheids. (Adapted from H. C. Arp) Koche lubi! of Roche lobe of smaller star larger star , inner I ;igimigian puint 53-6 Chapter 10 a Type II Cepheid. As Figure 19-19 shows, these two types of Cepheids exhibit different period-luminosity relations. In order to know which period-luminosity relation to apply to a given Cepheid, an astronomer must determine the star's metal content from its spectrum (see Figure 19-15). The evolutionary tracks of mature, high-mass stars pass back and forth through the upper end of the instability strip on the II-R diagram. These stars become Cepheids when helium ionization occurs at just the right depth to drive the pulsations. For stars on the high-temperature (left) side of the instability strip, helium ionization occurs too close to the surface and involves only an insignificant fraction of the star's mass. For stars on the cool (right) side of the instability strip, convection in the star's outer layers prevents the storage of the energy needed to drive the pulsations. Thus, Cepheids exist only in a narrow temperature range on the H-R diagram. RR Lyrae Variables Stars of lower mass do not become Cepheids. Instead, after leaving the main sequence, becoming red giants, and undergoing the helium flash, their evolutionary tracks pass through the lower end of the instability strip as they move along the horizontal branch. Some of these stars become RR Lyrae variables, named for rheir prototype in the constellation Lyra (the Harp). RR Lyrae variables all have periods shorter than one day and roughly the same average luminosity as horizontal-branch stars, about 100 L©. In fact, the RR Lyrae region of the instability strip (see Figure 19-17) is actually a segment of the horizontal branch. RR Lyrae stars are all metal-poor, Population II stars. Many have been found in globular clusters, and they have been used to determine the distances to those clusters in the same way that Cepheids are used to find the distances to other galaxies. In Chapter 23 we will see how RR Lyrae stars helped astronomers determine the size of the Milky Way Galaxy. In some cases the expansion speed of a pulsating star exceeds the star's escape speed. When this happens, the star's outer layers are ejected completely. We will see in Chapter 20 that dying stars eject significant amounts of mass in this way, renewing and enriching the interstellar medium for future generations of stars. 19-7 Mass transfer can affect the evolution of stars in a close binary system We have outlined what happens when a main-sequence star evolves into a red giant. Whar we have ignored is that more than half of all stars are members of multiple-star systems, including binaries. If the stars in such a system are widely separated, the individual stars follow the same course of evolution as if they were isolated. In a close binary, however, when one star expands to become a red giant, its outer layers can be gravirationally captured by the nearby companion star. In other words, a bloated red giant in a close binary system can dump gas onto its companion, a process called mass transfer. If the stars in a binary system are suFFicien+Jy close, tidal Forces can pull gases off one star and onto the other esig. Roche Lobes and Lagrangian Points Our modern understanding of mass transfer in close binaries '' based on the work of the French mathematician Edouard R 1 i In the mid-1800s, Roche studied _________ . , °c,lc< how rotation and mutual tidal interaction affect the stars in a binary system. Tidal forces cause the two stars in a close binary to keep the same sides facing each other, just as our Moon keeps its same side facing Earth (see Section 4-8). But because stars are gaseous, not solid, roration and tidal forces can have nificant effects on their shapes. In widely separated binaries, the stars are so far apart that tidal effects are small, and, therefore, the stars are nearly perfect spheres. In close binaries, where the separation between the stats-is not much greater than their sizes, tidal effects are strong, causing the stars to be somewhat egg-shaped. Roche discovered a mathematical surface that marks the grav itational domain of each star in a close binary. (This surface is not a real physical one, like the surface of a balloon, but a mathematical construct.) Figure i^-lOa shows the outline of this surface as a dashed line. The two halves of this surface, each of which encloses one of the .stars, are known as Roche lobes. The more massive star is always located inside the larger Roche iohe If gas from a star leaks over its Roche lobe, it is no longer bound by gravity to that star. This escaped gas is free either to fall onto the companion star or to escape from the binary system. The point where the two Roche lobes touch, called the inner Lagrangian point, is a kind of balance point between the two stars in a binary. It is here that the effects of gravity and rotation cancel each other. When mass transfer occurs in a close binary, gases flow through the inner Lagrangian point from one star to the other. In many binaries, the stars are so far apart that even during their red-giant stages the surfaces of the stars remain welt inside their Roche lobes. As a result, little mass transfer can occur and each star lives out its life as if it were single and isolated. A binary system of this kind is called a detached binary (Figure 19-20a}. However, if the two stars are close enough, when one star expands to become a red giant, it may fill or overflow its Roche lobe. Such a system is called a semidetached binary (Figure 19-206). If both stars fill their Roche lobes, the two stars actually touch and the system is called a contact binary (Figure 19-20t). It is quite unlikely, however, that both stars exactly fill their Roche lobes at the same time. (This would only be the case if the two stars had identical masses, so that they both evolved at exactly the same rate.) It is more likely that they overflow their Roche lobes, giving rise to a common envelope of gas. Such a system is called an overcontact binary (Figure 19-20J). Observations of Mass Transfer The binary star system Algol (from an Arabic term for "demon") provided the first clear evidence of mass transfer in close binaries. Also called ft (beta) Persei, Algol can easily be seen with the naked (a) Detached binary: Neither star fills its Roche lobe. M.tss «in limy liom either stur lu [lit utile across the inner Lagransian point (c) Contact binary: Both stars fill their Roche lobes. Figure 19-20 KJ(1 Close Binary Star Systems The gravitational domain of a ?^t>v star in a close binary system is called its Roche lobe. The two :he lobes meet at the inner Lagrangian point. Tie sizes of the stars Ancient astronomers knew that Algol varies periodically in brightness by a factor of more than 2. In 1782, John Goodricke [the discoverer of S Cephei's variability) first suggested that these brightness variations take place because Algol is an eclipsing binary, (We discussed this type of binary in Section 17-11.) The or-/ bitai plane of the two stars that make up the binary system happens to be nearly edge-on to our line of sight, so one star periodically eclipses the other. Algol's light curve {Figure 19-2Li) and spectium show that Goodricke's brilliant hypothesis is cor-- rect, and that Algol is a semidetached binary. The detached star ' (on the right in Figure \9-21a) is a luminous blue main-sequence star, while its less massive companion is a dimmer red giant that fills its Roche lobe. CAUTION! According to stellar evolution theory, the more i massive a star, the more rapidly it should evolve. Since the two ; stars in a binary system form simultaneously and thus are the : same age, the more massive star should become a red giant be-• fore the less massive one. But in Algol and similar binaries, the : more massive star (on the right in Figure \9-l\a) is still on the : main sequence, whereas the less massive star (on the left in 1 Figure 19-21a) has evolved to become a red giant. How can we explain this apparent contradiction? The answer is that the red Stellar Evolution: On and After the Main Sequence 517 Ma^i can flow from the enlarged star to tlic other aero is the inner L^cui^ian point (b) Semi-detached binary: One star fills its Roche lobe. Both stars share tlic saint outer atmosphere (d) Overcontact binary: Both stars overfill their Roche lobes. relative to their Roche lobes determine whether the system is (a) a detached binary, (b) a semidetached binary, (c) a contact binary, or (d) an overcontact binary. giant in Algol-type binaries was originally the more massive star. . As it left the main sequence to become a red giant, this star expanded until it overflowed its Roche lobe and dumped gas onto its originally less massive companion. Because of the resulting mass transfer, that companion (which is still on the main se-quence) became the more massive star, Mass transfer is also important in another class of semidetached binaries, called B (beta) Lyrae variables, after their prototype in the constellation Lyra. As with Algol, the less massive star in P Lyrae (on the left in Figure 19-21f>) fills its Roche lobe. Unlike Algol, however, the more massive detached star (on the right in Figure 19-216) is the dimmer of the two stars. Apparently, this detached star is enveloped in a rotating accretion disk of gas captured from its bloated companion. This disk partially blocks the light coming from the detached star, making ir appear dimmer. What is the fate of an Algol or 3 Lyrae system? If the detached star is massive enough, it will evolve rapidly, expanding to also fill its Roche lobe. The result will be an overcontact binary in which the rwo stars share the-gases of their outer layers. Such binaries are sometimes called W Ursae Majoris scats, after the prototype of this class (Figure 19-21c). 5f o Evo' The of ir • ution: %tA \*l I %Jf (b) A supernova remnant (a) A planetary nebula «íJÍ2£a. RI0UXG Left: The planetary nebula NGC 7293. (the Helix Nebula) Right The supernova remnant LMC N49. (NASA, NOAO, ESA, the Hutble Helix Nebula Teem, M. Meixner/ STScI, and T. A. Rector/NRAO; NASA and the Hubble Heritage Team, STScI/AURA) | hen a star of 0.4 solar mass or more reaches the end of F its mam-sequence lifetime and becomes a red giant, it has a compressed core and a bloated atmosphere, Finally, the star devours its remaining nuclear fuel and begins to die. As we'll .learn in this chapter, the character of the star's death depends crucially on the value of its mass. A star of relatively low mass—such as our own Sun—ends its evolution by gently expelling its outer layers into space. These ejected gases form a glowing cloud called a planetary nebula such as the one shown here in the left-hand image. The burned-out core that remains is called a white dwarf. In contrast, a high-mass star ends its life in almost inconceivable violence. At the end of its short life, the core of such a star collapses suddenly, which triggers a powerful supernova explosion that can be as luminous as an entire galaxy of stars. A white dwarf, too, can become a supernova if it accretes gas from a companion star in a close binary system, Thermonuclear reactions in supernovae produce a wide variety of heavy elements, which are ejected into the interstellar medium. (The supernova remnant shown here in the right-hand image is rich in these elements.) Such heavy elements are essential building blocks for terrestrial worlds like our Earth. Thus, the deaths of massive stars can provide the seeds for planets orbiting succeeding generations of stars. 20-1 Stars of between 0.4 and 4 solar masses go through two distinct red-giant stages -,p.iA( ^ All main-sequence stars convert hydrogen to helium in ^f^/aXy Erieir cores in a series of energy-releasing thermonuclear reactions. As we saw in Section 19-1, convection within a low-mass main-sequence star—a so-called red dwarf with a mass between 0.08 and 0.4 M©—will eventually bring all of the star's hydrogen into the core. Over hundreds of billions of years a red dwarf evolves into an inett ball of helium. Convection is less important in main-sequence stars with masses greater than 0.4 Mo, so these stars are able to consume only the hydrogen that is present within the core. These stars of greater mass then leave the main sequence. Let's examine what happens next for a star of moderately low mass, between 0,4 and 4 M©, One example for such a star is our own Sun, with a mass of 1 Mq. We'll begin by Learning Goals Sy reading the sections of this chapter, you will learn 20-1 What kinds of thermonuclear reactions occur inside a star of moderately low mass as it ages 20-2 How evolving stars disperse carbon into the interstellar medium 20-3 How stars of moderately low mass eventually die 20-4 The nature of white dwarfs and how they are formed 20-5 What kinds of reactions occur inside a high-mass star as it ages 20-6 How high-mass stars explode and die 20-7 Why supernova SN 1987A was both important and unusual 20-8 What role neutrinos play in the death of a massive star 20-9 How white dwarfs in close binary systems can explode 20-10 What remains after a supernova explosion 525 Chapter 20 Stellar Evolution: The Deaths of Stars [a) Before the helium flash: A red-giant star (b) After the helium flash: A horizontal-branch star (c) After core helium fusion ends: An AGB star Figure 20-1 The Post-Main-Sequence Evolution of a 1 M-.. Star These H-R diagrams show the evolutionary track of a star tike the Sun as it goes through the stages cf being (a) a red-giant star, reviewing what we learned in Chapter 19 about the first stages of post-main-sequence evolution for such a star. (Later in this chapter we'll study the evolution of more massive stars.) The Red-Giant and Horizontal-Branch Stages: A Review We can describe a star's post-main-sequence evolution using an evolutionary track on a H-R diagram. Figure 20-1 shows the track for a 1-Mq star like the Sun. Once core hydrogen fusion ceases, the core shrinks, heating the surrounding hydrogen and triggering shell hydrogen fusion. The new outpouring of energy causes the star's outer layers to expand and cool, and the star becomes a red giant. As the luminosity increases and the surface temperature drops, the post-main-sequence star moves up and to the right along the red-giant branch on an H-R diagram (Figure 20-ltf), Next, the helium-rich core of the star shrinks and heats until eventually core helium fusion begins. This second post-main-sequence stage begins gradually in stars more massive than about 2-3 Mo, but for less massive stars it comes suddenly—in a helium flash. During core helium fusion, the surrounding hydrogen-fusing shell still provides most of the red giant's luminosity, As we learned in Section 19-3, the core expands when core helium fusion begins, which makes the core coo! down a bit. (We saw in Box 19-1 that letting a gas expand tends to lower its temperature, while compressing a gas tends to increase its temperature.) The cooling of the core also cools the surrounding hydrogen-fusing shell, so that the shell releases energy more (b) a horizontal-branch star, and (c) an asymptotic giant branch (AGB] star. The star eventually evolves into a planetary nebula (described in Section 20-3). slowly. Hence, the luminosity goes down a bit after core helium fusion begins. The slower rate of energy release also lets the star's outer layers contract. As they contract, they heat up, so the star's surface temperature increases and its evolutionary track moves to the left on the H-R diagram in Figure 20-16. The luminosity changes relatively little during this stage, so the evolutionary track moves almost horizontally, along a path called the horizontal branch. Horizontal-branch stars have helium-fusing cores surrounded by hydrogen-fusing shells. Figure 19-12 shows horizontal-branch stars in a globular cluster, and Figure 19-8 shows the evolution of the luminosity of a 1-Mq star up to this point in its history, AGB Stars: The Second Red-Giant Stage Helium fusion produces nuclei of carbon and oxygen. After about a hundred million (10s) years of core helium fusion, essentially all the helium in the core of a 1-M© star has been converted into carbon and oxygen, and the fusion of helium in the core ceases. (This corresponds to the right-hand end of the graph in Figure 19-8.) Without thermonuclear reactions to maintain the core's internal pressure, the core again contracts, until it is stopped by degenerate-electron pressure (described in Section 19-3). This contraction releases heat into the surrounding helium-rich gases, and Stars like the Sun go through a second red-giant phase, during which helium Fusion fakes place in a shell around an inert core ■ Almut 20,000 lem . Figure 20-2 Dormant hydrogen- Central regions Helium-taing «hell a new stage of helium fusion begins in a thin shell around the core. This process is called shell helium fusion. History now repeats itself—the star enters a second red-giant phase. A star first becomes a red giant at the end of its main-sequence lifetime, when the outpouring of energy from shell hydrogen fusion makes the star's outer layers expand and cool. In the same way, the outpouring of energy from shell helium fusion causes the outer layers to expand again. The low-mass star ascends into the red-giant region of the H-R diagram for a second time (Figure 20-lc), but now with even greater luminosity than during its first red-giant phase. Stars in this second red-giant phase are commonly called asymptotic giant branch stars, or AGB stars, and their evolutionary tracks follow what is called the asymptotic giant branch. (Asymptotic means "approaching"; the name means that a star on the asymptotic giant branch approaches the red-giant branch from the left on an H-R diagram.) When a low-mass star first becomes an AGB star, it consists nf an inert, degenerate carbon-oxygen core and a helium-fusing shell, both inside a hydrogen-fusing shell, all within a volume not much larger than Earth. This small, dense central region is surrounded by an enormous hydrogen-rich envelope about as big as Earth's orbit around the Sun. After a while, the expansion of the star's outer layers causes the hydrogen-fusing shell to also expand and cool, and thermonuclear reactions in this shell temporarily cease. This leaves the aging star's structure as shown in Figure 20-2. We saw in Section 19-1 that the more massive a star, the shorter the amount of time it remains on the main sequence. Similarly, the greater the star's mass, the more rapidly it goes through the stages of post-main-sequence evolution. Hence, we can see all of these stages by studying star clusters, which contain stars that are all the same age but that have a range of masses (see Section 19-4). Figure 20-3 shows a color-magnitude diagram for the globular cluster M55, which is at least 13 billion years old. The least massive stars in this cluster are still on the main sequence. Progressively more massive stars have evolved to the red giant branch, [he horizontal branch, and the asymptotic giant branch. The Structure of an Old, Moderately Low-Mass AGB Star Near the end of its life, a star like the Sun becomes an immense, red, asymptotic giant branch (AGB) star. The star's inert core, active helium-fusing shell, and dormant hydrogen-fusing shell are all contained within a volume roughly the size of Earth. Thermonuclear reactions in the heiiurr-f using shell are so rapid that the star's luminosity is thousands of times that of the present-day Sun, (The relative sizes of the shells in the stars interior arc not shown to scale.) aflfc*- Figure 2D-3 Stellar Evolution in a Globular Cluster In the old globular cluster M55, stars with masses less than about 0.8 M0 are still on the main sequence, converting hydrogen into helium in their cores. Slightly more massive stars have consumed their core hydrogen and are ascending the red-giant branch; even more massive stars have begun helium core fusion and are found on the horizontal branch. The most massive stars (which still have less than 4 M©) have consumed all the helium in their cores and are ascending the asymptotic giant branch. (Compare with Figure 21.-11.) (Adapted from D. Schade, D. VandenBerg, and F. Hart wick] 528 Chapter 20 A 1-Mq AGB star can reach a maximum luminosity of nearly 104 Lq, as compared with approximately 103 L0 when it reached the helium flash and a relatively paltry 1 Lq during its main-sequence lifetime. When the Sun becomes an AGB star some 7.8 billion years from now, this tremendous increase in luminosity will cause Mars and the Jovian planets to largely evaporate away. The Sun's bloated outer layers will reach to Earth's orbit. Mercury and perhaps Venus will simply be swallowed whole. 20-2 Dredge-ups bring the products cf nuclear fusion to a giant star's surface As we saw in Section 16-2, energy is transported outward from a star's core by one of two processes—radiative diffusion or convection. The first is the passage of energy in the form of electromagnetic radiation, and it dominates only when a star's gases are relatively transparent. The second involves up-and-down movement of the star's gases. Convection plays a very important role in giant stars, and it helps supply the cosmos with the elements essential to life. Convection, Dredge-ups, and Carbon Stars ■^iSi'j In the Sun, convection dominates only the outer layers, from around 0.71 solar radius (measured from the center of the Sun) up to the photosphere (recall Figure 16-4). During the final stages of a star's life, however, the con-vective zone can become so broad that it extends down to the star's core. At these times, convection can "dredge up" the heavy elements produced in and around the core by thermonuclear fusion, transporting them all the way to the star's surface. ■^jj^&> The first dredge-up takes place after core hydrogen fu-oK^^Wf sion stops, when the star becomes a red giant for the ^^^r first time. Convection dips so deeply into the star that material processed by the CNO cycle of hydrogen fusion (see Section 16-1) is carried up to the star's surface, changing the relative abundances of carbon, nitrogen, and oxygen. A second dredge-up occurs after core helium fusion ceases, further altering :he abundances of carbon, nitrogen, and oxygen. Still later, during the AGB stage, a third dredge-up can occur if the star has a mass greater than about 2 M©. This third dredge-up transports large amounts of freshly synthesized carbon to the star's surface, and the star's spectrum thus exhibits prominent absotption bands of carbon-rich molecules like C2, CH, and CN. For this reason, au AGB star that has undergone a third dredge-up is called a carbon star. All AGB stars have very strong stellar winds that cause them to lose mass at very high rates, up to 10~4 M© per year {a thousand times greater than that of a red giant, and 1010 times greater than -— the rate at which our present-day Sun loses mass). The surface temperature of AGB stars is relatively low, around 3000 K, so any ejected carbon-rich molecules can condense lu form tiny grains of soot. Indeed, T The carbon that forms the basis of all life on Earth was ejected billions □ f years ago from giant stars Figure 20-4 Oivuxg A Carbon Star TT Cygni is an AGB star in the constellation Cygnus that ejects some of its carbon rich outer layers into space. Some of the ejected carbon combines with oxygen to form molecules of carbon monoxide (CO), whose emissions can be detected with a radio telescope. This radio image shows the CO emissions from a shell of material that IT Cygni ejected some 7000 years ago. Over that time, the shell has expanded to a diameter of about V2 tight-year. (H. Olnfsson, Stockholm Observatory, et alVNASA) carbon stars are commonly found to be obscured in sooty cocoons of ejected matter {Figure 20-4). Carbon stars are important because they enrich the interstellar medium with carbon and some nitrogen and oxygen. The triple alpha process that occurs in helium fusion is the only way that carbon can be made, and carbon stars are the primary avenue by which this element is dispersed into interstellar space. Indeed, most of the carbon in your body was produced long ago inside a star by the triple alpha process (see Section 19-3). This carbon was later dredged up to the star's surface and ejected into Space. Some 4.56 billion years ago a clump of the interstellar medium which contained this carbon coalesced into the solar nebula from which our Earth—and all of the life on it—eventually formed. In this sense you can think of your body as containing "recycled" material—substances that were once in the heart of a star that formed and evolved long before our solar system existed. 20-3 Stars of moderately low mass die by gently ejecting their outer layers, creating planetary nebulae For a star that began with a moderately low mass (between abour 0.4 and 4 Mq), the AGB stage in its evolution is a dramatic turning point. Before this stage, a star loses mass only gradually through steady stellar winds. But as it evolves during its AGB e a star divests itself completely ■ hi'outer layets. The aging star un-I 'oeS a series of bursts in luminos-• and in each burst it ejects a shell Tiaterial into space. (The shell An aging ABB star casls □ ff much oFthe mass that it possesses and 'makes a beautiful glowing nebula. !hown in Figure 20-4, was probably crested in this way.) Eventually, all that remains of a low-mass star is i fiercely hot, exposed core, surrounded by glowing shells 0f ejected gas. This late stage in the life of a star is called a planetary nebula. The left-hand image on the opening page of this chapter shows one such planetary nehula, called the Ring Nebula for its shape. Making a Planetary Nebula To understand how an AGB star can eject its outer layers in shells, consider the internal structure of such a star as shown in Figure 20-2. As the helium in the helium-fusing shell is used up, the pressure that holds up the dormant hydrogen-fusing shell decreases. Hence, the dormant hydrogen shell contracts and heats up, and hydrogen fusion begins anew. This revitalized hydrogen fusion creates helium, which rains downward onto the temporarily dormant helium-fusing shell. As the helium shell gains mass, it shrinks and heats up. When the temperature of the helium shell reaches a certain critical value, it reignites in a helium shell flash that is similar to (but less intense than) the helium flash that occurred earlier in the evolution of a low-mass star (see Section 19-3). The released energy pushes the hydrogen-fusing shell outward, making it coo! off, so that hydrogen fusion ceases and this shell again becomes dormant. The process then starts over again. When a helium shell flash occurs, the luminosity of an AGB star increases substantially in a relatively short-lived burst called a thermal pulse. Figure 20-5, which is based on a theoretical calculation of the evolution of a 1-M© star, shows that thermal pulses begin when the star is about 12.365 billion years old. The calculations predict that thermal pulses occur at ever-shorter intervals of about 100,000 years. During these thermal pulses, the dying star's outer layers can separate completely from its carbon-oxygen core. As the ejected material expands into space, dust grains condense out of the cooling gases. Radiation pressure from the star's hot, burned-out core acts on the specks of dust, propelling them further outward, and the star sheds its outer layers altogether. In this way an aging 1-Mq star loses as much as 40% of its mass. More massive stars eject even greater fractions of their original mass. As a dying star ejects its outer layers, the star's hot core he-comes exposed. With a surface temperature of about 100,000 K, this exposed core emits ultraviolet tadiation intense enough to ionize and excite the expanding shell of ejected gases. These gases therefore glow and emit visible light through the process of fluorescence (see Box 18-1), producing a planetary nebula like those shown in Figure 20-6. CAUTION! Despite their name, planetary nebulae have nothing to do with planets. This misleading term was introduced in the nineteenth century because these glowing objects looked like distant Jovian planets—a small colored blur—when viewed through the small telescopes then available. The difference be- Stellar Evolution: The Deaths of Stars Core helium fusion and Shell helium shell hydrogen fusion fusion and shell 1 hydrogen fusion ] I I I ' ' I 10 12.1 12.2 12.3 12.3653 12.3055 Age of the Sun (billions of years) Figure 20-5 Further Stages in the Evolution of the Son This diagram, which shows how the luminosity of the Sun (a 1-Mq Star] changes over time, is an extension of figure 19-8. We use different scales for the final stages because the evolution is se rapid. During the AGB stage there are brief Deriods of runaway helium fusion, causing spikes in luminosity called thermal pulses. (Adapted from Mark A. Garlick, based on calculations by I.-Juliana Sackmann and Kathleen E. Kramer) tween planets and planetary nebulae first became obvious with the advent of spectroscopy: Planets have absorption line spectra (see Section 7-3), but the excited gases of planetary nebulae have emission line spectra. The Properties of Planetary Nebulae Planetary nebulae are quite common. Astronomers estimate that there arc 20,000 to 50,000 planetary nebulae in our Galaxy alone. Many planetary nebulae, such as those in Figure 20-6, are more or less spherical in shape. This shape is a result of the symmetrical way in which the gases were ejected. But if the rate of expansion is not the same in all directions, the resulting nebula can rake un an hourglass or dumbbell appearance (Figure 20-7). Spectroscopic observations of planetary nebulae show emission lines of ionized hydrogen, oxygen, and nitrogen. From the Doppler shifts of these lines, astronomers have concluded that the expanding shell of gas moves outward from a dying star at speeds from 10 to 30 km/s. For a shell expanding at such speeds to have attained the typical diameter of a planetary nebula, about 1 light-year, it must have begun expanding about 10,000 years ago. Thus, by astronomical standards, the planetary nebulae we see today were created only very recently. We do not observe planetary nebulae that are more than about 50,000 years old. After this length of time, the shell has spread out so far from the cooling central star that its gases cease to glow and simply fade from view. The nebula's gases then mix with the surrounding interstellar medium. 530 Chapter 20 Stellar Evolution: The Deaths of Stars 531 "IQUXG k iQuxs ■<^- Figure ao-G Planetary Nebulae (a) The pinkish blob is a planetary nebula surrounding a star in the globular duster M15 about 10,000 pc (33,000 ly) from Earth in the constellation Pegasus. (b)The planetary nebula Abell 39 lies about 2200 pc (7000 ly) from Earth in the constellac.on Hercules. The almost perfectly sphencal shell that comprises the nebula is about 1.5 pc (5 !y) in diameter; the thickness of the shell is Astronomers estimate that all the planetary nebulae in the Galaxy return a total of about 5 Mo to the interstellar medium each year. This amount is about 15% of all the matter expelled by all the vanous sorts of stars in the Galaxy each year. Because 2. The stür then ejects visible gas entire surl JV U X C only about 0.1 pc (11.3 ly). (c) This ir NGC 7027 suggests a mere cample Abell 39. NGC 7027 is about 900 pc constellation Cygnus and is roughly Heritage Team, STSclMURA: b: WIYN. Science Center/Caitech. art) NASA) this contribution is so significant, and because the ejected material includes heavier elements (metals) manufactured within a nebula's central star, planetary nebulae play an important role in the chemical evolution of the Galaxy as a whole \ ---O ( (b) 3.The doughnut I channels the ' ejected gas into two oppositely directed streams. / Inmi ihe star Figure 2D-7 Making ar elongated Planetary Nebula (a), (b) These illustrations show one proposed explanation for why many planetary nebulae have an elongated shape, (c) The planetary nebula MyLnlS, shown here in false color, may have acquired its elongated M RIQJUXG shape in this way. It lies seme 2500 pc {8000 ly) from Earth in the constellation Mjsca (the Fly). (R, Sahai and l Trauger. Jet Propulsion .ahnrstory; the WFPC-2 Science Team; and NASA) The burned-out core of a moderately |ovv-mass star cools and contracts until it ^conies a white dwarf BVCte have seen that after a moderately low-mass star (from about ■Q 4 to about 4 solar masses) consumes all the hydrogen in its core, It is able to ignite thermonuclear reactions that convert helium to carbon and oxygen. Given sufficiently high temperature and pressure, carbon and oxygen can also undergo fusion reactions that release energy. But for such a moderately low-mass srar, the core te[nperature and pressure never reach the extremely high values Reeded for these reactions to take place. Instead, as we have seen, the process of mass ejection just strips away the star's outer layers and leaves behind the hot carbon-oxygen core. With no thermonuclear reactions taking place, the core simply cools down like a dying ember. Such a burnt-out relic of a star's former glory is called a white dwarf. Such white dwarfs prove to have exotic physical properties that are wholly unlike any object found on Earth. CAUTION! Unfortunately, the word dwarf is used in astronomy for several very different kinds of small objects. Here's a review of the three kinds that we have encountered so far in this t book. A white dwarf is the relic that remains at the very end of ! the evolution of a star of initial mass between about 0.4 Mq and | 4 Ma. Thermonuclear reactions are no longer raking place in its interior; it emits light simply because it is still hot. A red dwarf, discussed in Section 19-1, is a coot main-sequence star with a mass between about 0.08 M© and 0.4 M©. The energy emitted by a red dwarf in the form of light comes from its core, where fusion reactions convert hydrogen into helium. Finally, a brown dwarf (see Section 8-6 and Section 17-5) is an object like a main-sequence star but with a mass less than about 0.08 M©. Because its mass is so small, its internal pressure and temperature are too low to sustain thermonuclear reactions. Instead, a brown dwarf emits light because ir is slowly contracting, a process that releases energy (see Section 16-1). White dwarfs are comparable in size to Eatth (see Section 17-7); by contrast, brown dwarfs are larger than the planet Jupiter, and red dwarfs are even larger. Properties of White Dwarfs You might think that without thermonuclear reactions to provide internal heat and pressure, a white dwarf should keep on shrinking under the influence of its own gravity as it cools. Actually, however, a cooling white dwarf___ maintains its size, because the burnt-out stellar core is so dense that most of its electrons are degenerate (see Section 17-3). Thus, degenerate-electron pressure supports the star against further collapse. This pressure does not depend on temperature, so it continues to hold up the star even as the white dwarf cools and its temperature drops. Many white dwarfs are found in the solar neighborhood, but all are too faint to be seen with the naked eye. One of the first white dwarfs to be discovered is a companion to Sirius, rhe hright- A white dwarf is kept from collapsing by the pressure of its degenerate electrons est star in the night sky. In 1844 the German astronomer Friedrich Bessel noticed that Sirius was moving back and forth slightly, as if it was being orbited by an unseen object. This companion, designated Sirius B (figure 20-8), was first glimpsed in 1862 by the American astronomer Alvan Clark. Recent Hubble Space Telescope observations at ultraviolet wavelengths, where hot white dwarfs emit most of their light, show that the surface temperature of Sirius B is 25,200 EC. (By contrast, the main-sequence star Sirius A has a surface temperature of 10,500 K, while the Sun's surface temperature is a relatively frosty 5800 K.) Observations of white dwarfs in binar)' systems like Sirius allow astronomers to determine the mass, radius, and density of these stars {see Sections 17-9, 17-10, and 17-11). Such observations show that the density of the degenerate matter in a white dwarf is typically 109 kg/m3 (a million times denser than water). A teaspoonful of white dwarf matter brought to Earth would weigh nearly 5.5 tons—as much as an elephant! The Mass-Radius Relation for White Dwarfs As we learned in Section 17-3, degenerate matter has a very different relationship between its pressure, density, and temperature Figure 20-8 riQuxg Sinus A and Its White Dwarf Companion Sinus, the biightest-appearing star in the sky, is actually a binary star: The secondary star, called Sinus B. is a white dwarf. In this Hubble Space Telescope image, Sirius B is almost obscured by the glare of the overexposed primary star, Siius A, which is about 10A times more luminous than Sirius B. The halo and rays around Sirius A are the result of optical effects within the telescope. [NASA; H E. Bond and E. Nelan, STScI; M. Barstow and M. Burleigh, U. of Leicester, and 1 B. Hdberg, U. of Arizona)