16 properties of stars - cppjanourse/cosmicperspectivextra... · 2003. 7. 15. · ing stars with...

16 Properties of Stars

LEARNING GOALS

16.1 Snapshot of the Heavens• How can we learn about the lives of stars, which last

millions to billions of years? • What are the two main elements in all stars? • What two basic physical properties do astronomers

use to classify stars?

16.2 Stellar Luminosity• What is luminosity, and how do we determine it? • How do we measure the distance to nearby stars? • How does the magnitude of a star relate to its

apparent brightness?

16.3 Stellar Surface Temperature• How are stars classified into spectral types? • What determines a star’s spectral type?

16.4 Stellar Masses• What is the most important property of a star? • What are the three major classes of binary star

systems? • How do we measure stellar masses?

16.5 The Hertzsprung–Russell Diagram• What is the Hertzsprung–Russell (H–R) diagram? • What are the major features of the H–R diagram? • How do stars differ along the main sequence? • What determines the length of time a star spends on

the main sequence? • What are Cepheid variable stars, and why are they

important to astronomers?

16.6 Star Clusters• What are the two major types of star cluster? • Why are star clusters useful for studying stellar

evolution? • How do we measure the age of a star cluster?

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“All men have the stars,” he answered,“but they are not the same things fordifferent people. For some, who aretravelers, the stars are guides. For othersthey are no more than little lights in thesky. For others, who are scholars, theyare problems. For my businessman theywere wealth. But all these stars aresilent. You—you alone—will have thestars as no one else has them.”

Antoine de Saint-Exupéry, from The Little Prince

On a clear, dark night, a few thousand stars

are visible to the naked eye. Many more

become visible through binoculars, and

with a powerful telescope we can see so many stars

that we could never hope to count them. Like indi-

vidual people, each individual star is unique. Like the

human family, all stars share much in common.

Today, we know that stars are born from clouds

of interstellar gas, shine brilliantly by nuclear fusion

for millions or billions of years, and then die, some-

times in dramatic ways. This chapter outlines how

we study and categorize stars and how we have come

to realize that stars, like people, change over their

lifetime.

16.1 Snapshot of the HeavensImagine that an alien spaceship flies by Earth on a simplebut short mission: The visitors have just 1 minute to learneverything they can about the human race. In 60 seconds,they will see next to nothing of each individual person’slife. Instead, they will obtain a collective “snapshot” of hu-manity that shows people from all stages of life engaged intheir daily activities. From this snapshot alone, they mustpiece together their entire understanding of human beingsand their lives, from birth to death.

We face a similar problem when we look at the stars.Compared with stellar lifetimes of millions or billions of years, the few hundred years humans have spent study-ing stars with telescopes is rather like the aliens’ 1-minuteglimpse of humanity. We see only a brief moment in anystar’s life, and our collective snapshot of the heavens con-sists of such frozen moments for billions of stars. From thissnapshot, we try to reconstruct the life cycles of stars whilealso analyzing what makes one star different from another.

Thanks to the efforts of hundreds of astronomersstudying this snapshot of the heavens, stars are no longer

mysterious points of light in the sky. We now know that allstars form in great clouds of gas and dust. Each star beginsits life with roughly the same chemical composition: Aboutthree-quarters of the star’s mass at birth is hydrogen, andabout one-quarter is helium, with no more than about 2%consisting of elements heavier than helium. During mostof any star’s life, the rate at which it generates energy de-pends on the same type of balance between the inward pullof gravity and the outward push of internal pressure thatgoverns the rate of fusion in our Sun.

Despite these similarities, stars appear different fromone another for two primary reasons: They differ in mass,and we see different stars at different stages of their lives.

The key that finally unlocked these secrets of stars wasan appropriate classification system. Before the twentiethcentury, humans classified stars primarily by their bright-ness and location in our sky. The names of the brighteststars within each constellation still bear Greek letters desig-nating their order of brightness. For example, the brighteststar in the constellation Centaurus is Alpha Centauri, thesecond brightest is Beta Centauri, the third brightest isGamma Centauri, and so on. However, a star’s brightnessand membership in a constellation tell us little about its truenature. A star that appears bright could be either extremelyluminous or unusually nearby, and two stars that appearright next to each other in our sky might not be true neigh-bors if they lie at significantly different distances from Earth.

Today, astronomers classify a star primarily accordingto its luminosity and surface temperature. Our task in thischapter is to learn how this extraordinarily effective classi-fication system reveals the true natures of stars and theirlife cycles. We begin by investigating how to determine a star’sluminosity, surface temperature, and mass.

Measuring Cosmic Distances Tutorial, Lesson 2

16.2 Stellar LuminosityA star’s luminosity is the total amount of power it radiatesinto space, which can be stated in watts. For example, theSun’s luminosity is 3.8 � 1026 watts [Section 15.2]. We can-not measure a star’s luminosity directly, because its bright-ness in our sky depends on its distance as well as its trueluminosity. For example, our Sun and Alpha Centauri A (the brightest of three stars in the Alpha Centauri system)are similar in luminosity, but Alpha Centauri A is a feeblepoint of light in the night sky, while our Sun providesenough light and heat to sustain life on Earth. The differ-ence in brightness arises because Alpha Centauri A is about 270,000 times farther from Earth than is the Sun.

More precisely, we define the apparent brightness ofany star in our sky as the amount of light reaching us perunit area (Figure 16.1). (A more technical term for appar-ent brightness is flux.) The apparent brightness of any lightsource obeys an inverse square law with distance, similar to the inverse square law that describes the force of grav-ity [Section 5.3]. If we viewed the Sun from twice Earth’s

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522 p a r t V • Stellar Alchemy


distance, it would appear dimmer by a factor of 22 � 4. Ifwe viewed it from 10 times Earth’s distance, it would ap-pear 102 � 100 times dimmer. From 270,000 times Earth’sdistance, it would look like Alpha Centauri A—dimmer by a factor of 270,0002, or about 70 billion.

Figure 16.2 shows why apparent brightness follows aninverse square law. The same total amount of light mustpass through each imaginary sphere surrounding the star.If we focus our attention on the light passing through asmall square on the sphere located at 1 AU, we see that thesame amount of light must pass through four squares ofthe same size on the sphere located at 2 AU. Thus, eachsquare on the sphere at 2 AU receives only �

212� � �

14

� as muchlight as the square on the sphere at 1 AU. Similarly, the sameamount of light passes through nine squares of the samesize on the sphere located at 3 AU. Thus, each of thesesquares receives only �

312� � �

19

� as much light as the square on the sphere at 1 AU. Generalizing, we see that the amountof light received per unit area decreases with increasing dis-tance by the square of the distance—an inverse square law.

This inverse square law leads to a very simple andimportant formula relating the apparent brightness, lumi-

nosity, and distance of any light source. We will call it theluminosity–distance formula:

apparent brightness ��4p

l

�

um

(d

in

is

o

t

s

a

i

n

ty

ce)2�

Because the standard units of luminosity are watts, theunits of apparent brightness are watts per square meter.Because we can always measure the apparent brightness of a star, this formula provides a way to calculate a star’s

c h a p t e r 1 6 • Properties of Stars 523

COMMON MISCONCEPTIONS

Photos of Stars

Photographs of stars, star clusters, and galaxies convey agreat deal of information, but they also contain a few arti-facts that are not real. For example, different stars seemto have different sizes in photographs, but stars are sofar away that they should all appear as mere points oflight. Stellar sizes in photographs are an artifact of howour instruments record light. Because of the problem ofoverexposure, brighter stars tend to appear larger thandimmer stars.

Overexposure can be a particular problem for photo-graphs of globular clusters of stars and photographs ofgalaxies. These objects are so much brighter near theircenters than in their outskirts that the centers are al-most always overexposed in photographs that show theoutskirts. That is why globular clusters and galaxies oftenlook in photographs as if their central regions contain asingle bright blob, when in fact the centers contain manyindividual stars separated by vast amounts of space.

Spikes around bright stars in photographs, oftenmaking the pattern of a cross with a star at the center,are another such artifact. These spikes are not real butrather are created by the interaction of starlight with thesupports holding the secondary mirror in the telescope[Section 7.2]. The spikes generally occur only with pointsources of light like stars, and not with larger objects likegalaxies. When you look at a photograph showing manygalaxies (for example, Figure 20.1), you can tell whichobjects are stars by looking for the spikes.

Figure 16.1 Luminosity is a measure of power, and apparentbrightness is a measure of power per unit area.

Not to scale!

Luminosity is the total amountof power (energy per second)the star radiates into space.

Apparent brightness isthe amount of starlightreaching Earth (energyper second per squaremeter).

Figure 16.2 The inverse square law for light. At greater distancesfrom a star, the same amount of light passes through an area thatgets larger with the square of the distance. The amount of lightper unit area therefore declines with the square of the distance.

1 AU

2 AU

3 AU


luminosity if we can first measure its distance or to calcu-late a star’s distance if we somehow know its luminosity.(The luminosity–distance formula is strictly correct only if interstellar dust does not absorb or scatter the starlightalong its path to Earth.)

Although watts are the standard units for luminosity,it’s often more meaningful to describe stellar luminositiesin comparison to the Sun by using units of solar luminos-ity : LSun � 3.8 � 1026 watts. For example, Proxima Cen-tauri, the nearest of the three stars in the Alpha Centaurisystem and hence the nearest star besides our Sun, is onlyabout 0.0006 times as luminous as the Sun, or 0.0006LSun.Betelgeuse, the bright left-shoulder star of Orion, has aluminosity of 38,000LSun, meaning that it is 38,000 timesmore luminous than the Sun.

Measuring Apparent Brightness

We can measure a star’s apparent brightness by using a detector, such as a CCD, that records how much energystrikes its light-sensitive surface each second. For example,such a detector would record an apparent brightness of2.7 � 10�8 watt per square meter from Alpha Centauri A.The only difficulties involved in measuring apparent bright-ness are making sure the detector is properly calibratedand, for ground-based telescopes, taking into account theabsorption of light by Earth’s atmosphere.

No detector can record light of all wavelengths, so wenecessarily measure apparent brightness in only some smallrange of the complete spectrum. For example, the humaneye is sensitive to visible light but does not respond toultraviolet or infrared photons. Thus, when we perceive a star’s brightness, our eyes are measuring the apparentbrightness only in the visible region of the spectrum.

When we measure the apparent brightness in visiblelight, we can calculate only the star’s visible-light luminosity.Similarly, when we observe a star with a spaceborne X-raytelescope, we measure only the apparent brightness in X raysand can calculate only the star’s X-ray luminosity. We willuse the terms total luminosity and total apparent bright-ness to describe the luminosity and apparent brightness wewould measure if we could detect photons across the entireelectromagnetic spectrum. (Astronomers refer to the totalluminosity as the bolometric luminosity.)

Measuring Distance Through Stellar Parallax

Once we have measured a star’s apparent brightness, thenext step in determining its luminosity is to measure itsdistance. The most direct way to measure the distances to stars is with stellar parallax, the small annual shifts in a star’s apparent position caused by Earth’s motion aroundthe Sun [Section 2.6].

Recall that you can observe parallax of your finger byholding it at arm’s length and looking at it alternately withfirst one eye closed and then the other. Astronomers mea-sure stellar parallax by comparing observations of a nearbystar made 6 months apart (Figure 16.3). The nearby starappears to shift against the background of more distantstars because we are observing it from two opposite points of Earth’s orbit. The star’s parallax angle is defined as halfthe star’s annual back-and-forth shift.

Measuring stellar parallax is difficult because stars areso far away, making their parallax angles very small. Eventhe nearest star, Proxima Centauri, has a parallax angle ofonly 0.77 arcsecond. For increasingly distant stars, the paral-lax angles quickly become too small to measure even withour highest-resolution telescopes. Current technology


Mathematical Insight 16.1 The Luminosity–Distance Formula

We can derive the luminosity–distance formula by extending theidea illustrated in Figure 16.2. Suppose we are located a distance dfrom a star with luminosity L. The apparent brightness of the staris the power per unit area that we receive at our distance d. Wecan find this apparent brightness by imagining that we are part of a giant sphere with radius d, similar to any one of the threespheres in Figure 16.2. The surface area of this giant sphere is 4p � d2, and the star’s entire luminosity L must pass through this surface area. (The surface area of any sphere is 4p � radius2.)Thus, the apparent brightness at distance d is the power per unitarea passing through the sphere:

apparent brightness �

� �4p �

L

d2�

This is our luminosity–distance formula.

star’s luminosity��surface area of imaginary sphere

Example: What is the Sun’s apparent brightness as seen fromEarth?

Solution: The Sun’s luminosity is LSun � 3.8 � 1026 watts, andEarth’s distance from the Sun is d � 1.5 � 1011 meters. Thus, theSun’s apparent brightness is:

�4p �

L

d2� �

� 1.3 � 103 watts/m2

The Sun’s apparent brightness is about 1,300 watts per squaremeter at Earth’s distance. It is the maximum power per unit areathat could be collected by a detector on Earth that directly facesthe Sun, such as a solar power (or photovoltaic) cell. In reality, solarcollectors usually collect less power because Earth’s atmosphereabsorbs some sunlight, particularly when it is cloudy.

3.8 � 1026 watts��4p � (1.5 � 1011 m)2


allows us to measure parallax only for stars within a fewhundred light-years—not much farther than what we callour local solar neighborhood in the vast, 100,000-light-year-diameter Milky Way Galaxy.

By definition, the distance to an object with a parallaxangle of 1 arcsecond is 1 parsec, abbreviated pc. (The wordparsec comes from the words parallax and arcsecond.) With a little geometry and Figure 16.3 (see Mathematical Insight16.2), it is possible to show that:

1 pc � 3.26 light-years � 3.09 � 1013 km

If we use units of arcseconds for the parallax angle, a simpleformula allows us to calculate distances in parsecs:

d (in parsecs) ��p (in arc

1

seconds)�

For example, the distance to a star with a parallaxangle of �

12

� arcsecond is 2 parsecs, the distance to a star witha parallax angle of �

110� arcsecond is 10 parsecs, and the dis-

tance to a star with a parallax angle of �1

100� arcsecond is

100 parsecs. Astronomers often express distances in par-secs or light-years interchangeably. You can convert quicklybetween them by remembering that 1 pc � 3.26 light-years.Thus, 10 parsecs is about 32.6 light-years; 1,000 parsecs,or 1 kiloparsec (1 kpc), is about 3,260 light-years; and 1 mil-lion parsecs, or 1 megaparsec (1 Mpc), is about 3.26 mil-lion light-years.

Enough stars have measurable parallax to give us afairly good sample of the many different types of stars.For example, we know of more than 300 stars within about33 light-years (10 parsecs) of the Sun. About half are binary star systems consisting of two orbiting stars or


Mathematical Insight 16.2 The Parallax Formula

Here is one of several ways to derive the formula relating a star’sdistance and parallax angle. Figure 16.3 shows that the parallaxangle p is part of a right triangle, the side opposite p is the Earth–Sun distance of 1 AU, and the hypotenuse is the distance d to theobject. You may recall that the sine of an angle in a right triangleis the length of its opposite side divided by the length of thehypotenuse. In this case, we find:

sin p � � �1 A

d

U�

If we solve for d, the formula becomes:

d � �1

sin

AU

p�

By definition, 1 parsec is the distance to an object with a parallax angle of 1 arcsecond (1�), or 1/3,600 degree (be-cause that 1° � 60� and 1� � 60�). Substituting these numbers into the parallax formula and using a calculator to find that sin 1� � 4.84814 � 10�6, we get:

1 pc � �s

1

in

A

1

U

��

4.8481

1

4

A

�

U

10�6�� 206,265 AU

That is, 1 parsec � 206,265 AU, which is equivalent to 3.09 �1013 km or 3.26 light-years. (Recall that 1 AU � 149.6 million km.)

length of opposite side��length of hypotenuse

We need one more fact from geometry to derive the parallaxformula given in the text. As long as the parallax angle, p, is small,sin p is proportional to p. For example, sin 2� is twice as large assin 1�, and sin �

12

�� is half as large as sin 1�. (You can verify theseexamples with your calculator.) Thus, if we use �

12

�� instead of 1� forthe parallax angle in the formula above, we get a distance of 2 pcinstead of 1 pc. Similarly, if we use a parallax angle of �

110��, we get

a distance of 10 pc. Generalizing, we get the simple parallax for-mula given in the text:

d (in parsecs) ��p (in arc

1

seconds)�

Example: Sirius, the brightest star in our night sky, has a mea-sured parallax angle of 0.379�. How far away is Sirius in parsecs?In light-years?

Solution: From the formula, the distance to Sirius in parsecs is:

d (in pc) � �0.3

1

79� � 2.64 pc

Because 1 pc � 3.26 light-years, this distance is equivalent to:

2.64 pc � 3.26 �light

p

-

c

years� � 8.60 light-years

Figure 16.3 Parallax makes the apparent position of a nearbystar shift back and forth with respect to distant stars over thecourse of each year. If we measure the parallax angle p in arc-seconds, the distance d to the star in parsecs is �

1p

�. The angle in this figure is greatly exaggerated: All stars have parallax angles of less than 1 arcsecond.

July

nearby star

distant stars

January

Every January,we see this:

Every July,we see this:

1 AU

p

d

Not to scale

2396_AWL_Bennett_Ch16 6/26/03 1:58 PM 25

multiple star systems containing three or more stars. Mostare tiny, dim red stars such as Proxima Centauri—so dimthat we cannot see them with the naked eye, despite thefact that they are relatively close. A few nearby stars, such as Sirius (2.6 parsecs), Vega (8 parsecs), Altair (5 parsecs),and Fomalhaut (7 parsecs), are white in color and bright in our sky, but most of the brightest stars in the sky lie far-ther away. Because so many nearby stars appear dim whilemany more distant stars appear bright, their luminositiesmust span a wide range.

The Magnitude System

Many amateur and professional astronomers describe stellarbrightness using the ancient magnitude system devised bythe Greek astronomer Hipparchus (c. 190–120 B.C.). Themagnitude system originally classified stars according to howbright they look to our eyes—the only instruments avail-able in ancient times. The brightest stars received the desig-nation “first magnitude,” the next brightest “second magni-tude,” and so on. The faintest visible stars were magnitude 6.We call these descriptions apparent magnitudes becausethey compare how bright different stars appear in the sky.Star charts (such as those in Appendix J) often use dots ofdifferent sizes to represent the apparent magnitudes of stars.

In modern times, the magnitude system has been ex-tended and more precisely defined (see Mathematical In-sight 16.3). As a result, stars can have fractional apparent

magnitudes, and a few bright stars have apparent magni-tudes less than 1—which means brighter than magnitude 1.For example, the brightest star in the night sky, Sirius, hasan apparent magnitude of �1.46. Appendix F gives the ap-parent magnitudes and solar luminosities for nearby starsand the brightest stars.

The modern magnitude system also defines absolutemagnitudes as a way of describing stellar luminosities. Astar’s absolute magnitude is the apparent magnitude itwould have if it were at a distance of 10 parsecs from Earth.For example, the Sun’s absolute magnitude is about 4.8,meaning that the Sun would have an apparent magnitudeof 4.8 if it were 10 parsecs away from us—bright enough to be visible, but not conspicuous, on a dark night.

Understanding the magnitude system is worthwhilebecause it is still commonly used. However, for the cal-culations in this book, it’s much easier to work with theluminosity–distance formula, so we will avoid using magnitude formulas in this book.

The Hertzsprung–Russell Diagram Tutorial, Lessons 1–3

16.3 Stellar Surface TemperatureThe second basic property of stars (besides luminosity)needed for modern stellar classification is surface tempera-ture. Measuring a star’s surface temperature is somewhateasier than measuring its luminosity because the measure-

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Mathematical Insight 16.3 The Modern Magnitude Scale

The modern magnitude system is defined so that each differenceof 5 magnitudes corresponds to a factor of exactly 100 in bright-ness. For example, a magnitude 1 star is 100 times brighter than a magnitude 6 star, and a magnitude 3 star is 100 times brighterthan a magnitude 8 star. Because 5 magnitudes corresponds to afactor of 100 in brightness, a single magnitude corresponds to afactor of (100)1/5 � 2.512.

The following formula summarizes the relationship betweenstars of different magnitudes:

� (1001/5)m2�m1

where m1 and m2 are the apparent magnitudes of Stars 1 and 2,respectively. If we replace the apparent magnitudes with absolutemagnitudes (designated M instead of m), the same formula ap-plies to stellar luminosities:

� (1001/5)M 2�M1

Example 1: On a clear night, stars dimmer than magnitude 5 arequite difficult to see. Today, sensitive instruments on large tele-scopes can detect objects as faint as magnitude 30. How much moresensitive are such telescopes than the human eye?

luminosity of Star 1��luminosity of Star 2

apparent brightness of Star 1��apparent brightness of Star 2

Solution: We imagine that our eye sees “Star 1” with magnitude 5and the telescope detects “Star 2” with magnitude 30. Then wecompare:

� (1001/5)30�5� (1001/5)25

� 1005 � 1010

The magnitude 5 star is 1010, or 10 billion, times brighter than themagnitude 30 star, so the telescope is 10 billion times more sensi-tive than the human eye.

Example 2: The Sun has an absolute magnitude of about 4.8.Polaris, the North Star, has an absolute magnitude of �3.6.How much more luminous is Polaris than the Sun?

Solution: We use Polaris as Star 1 and the Sun as Star 2:

� (1001/5)4.8�(�3.6)� (1001/5)8.4

� 1001.7 � 2,500

Polaris is about 2,500 times more luminous than the Sun.

luminosity of Polaris��

luminosity of Sun

apparent brightness of Star 1��apparent brightness of Star 2


ment is not affected by the star’s distance. Instead, we de-termine surface temperature directly from the star’s coloror spectrum. One note of caution: We can measure only astar’s surface temperature, not its interior temperature. (In-terior temperatures are calculated with theoretical models[Section 15.3].) When astronomers speak of the “tempera-ture” of a star, they usually mean the surface temperatureunless they say otherwise.

A star’s surface temperature determines the color oflight it emits [Section 6.4]. A red star is cooler than a yellowstar, which in turn is cooler than a blue star. The naked eye can distinguish colors only for the brightest stars, butcolors become more evident when we view stars throughbinoculars or a telescope (Figure 16.4).

Astronomers can determine the “color” of a star moreprecisely by comparing its apparent brightness as viewedthrough two different filters [Section 7.3]. For example, a coolstar such as Betelgeuse, with a surface temperature of about3,400 K, emits more red light than blue light and thereforelooks much brighter when viewed through a red filter thanwhen viewed through a blue filter. In contrast, a hotter starsuch as Sirius, with a surface temperature of about 9,400 K,emits more blue light than red light and looks brighterthrough a blue filter than through a red filter.

Spectral Type

The emission and absorption lines in a star’s spectrumprovide an independent and more accurate way to measureits surface temperature. Stars displaying spectral lines ofhighly ionized elements must be fairly hot, while stars dis-playing spectral lines of molecules must be relatively cool[Section 6.4]. Astronomers classify stars according to surfacetemperature by assigning a spectral type determined fromthe spectral lines present in a star’s spectrum.

The hottest stars, with the bluest colors, are called spec-tral type O, followed in order of declining surface tempera-ture by spectral types B, A, F, G, K, and M. The time-honoredmnemonic for remembering this sequence, OBAFGKM,is “Oh Be A Fine Girl/Guy, Kiss Me!” Table 16.1 summarizesthe characteristics of each spectral type.

Each spectral type is subdivided into numbered sub-categories (e.g., B0, B1, . . . , B9). The larger the number, thecooler the star. For example, the Sun is designated spectraltype G2, which means it is slightly hotter than a G3 star butcooler than a G1 star.


Figure 16.4 This Hubble Space Telescopeview through the heart of our Milky WayGalaxy reveals that stars emit light of manydifferent colors.

VIS


Invent your own mnemonic for the OBAFGKM sequence. Tohelp get you thinking, here are two examples: (1) Only BunglingAstronomers Forget Generally Known Mnemonics; and (2) OnlyBusiness Acts For Good, Karl Marx.

History of the Spectral Sequence

You may wonder why the spectral types follow the peculiarorder of OBAFGKM. The answer lies in the history of stel-lar spectroscopy.

Astronomical research never paid well, and many astron-omers of the 1800s were able to do research only because of family wealth. One such astronomer was Henry Draper(1837–1882), an early pioneer of stellar spectroscopy. AfterDraper died in 1882, his widow made a series of large do-nations to Harvard College Observatory for the purpose ofbuilding upon his work. The observatory director, EdwardPickering (1846–1919), used the gifts to improve the facili-ties and to hire numerous assistants, whom he called “com-puters.” Pickering added money of his own, as did otherwealthy donors.

Most of Pickering’s hired computers were women whohad studied physics or astronomy at women’s colleges suchas Wellesley and Radcliffe. Women had few opportunities toadvance in science at the time. Harvard, for example, did notallow women as either students or faculty. Pickering’s projectof studying and classifying stellar spectra provided plentyof work and opportunity for his computers, and many ofthe Harvard Observatory women ended up among the mostprominent astronomers of the late 1800s and early 1900s.

One of the first computers was Williamina Fleming(1857–1911). Following Pickering’s suggestion, Fleming clas-sified stellar spectra according to the strength of their hy-drogen lines: type A for the strongest hydrogen lines, type Bfor slightly weaker hydrogen lines, and so on to type O, forstars with the weakest hydrogen lines. Pickering publishedFleming’s classifications of more than 10,000 stars in 1890.

As more stellar spectra were obtained and the spec-tra were studied in greater detail, it became clear that theclassification scheme based solely on hydrogen lines wasinadequate. Ultimately, the task of finding a better classifi-cation scheme fell to Annie Jump Cannon (1863–1941), whojoined Pickering’s team in 1896 (Figure 16.5). Building onthe work of Fleming and another of Pickering’s computers,Antonia Maury (1866–1952), Cannon soon realized thatthe spectral classes fell into a natural order—but not thealphabetical order determined by hydrogen lines alone.Moreover, she found that some of the original classes over-lapped others and could be eliminated. Cannon discoveredthat the natural sequence consisted of just a few of Picker-ing’s original classes in the order OBAFGKM and alsoadded the subdivisions by number.

Cannon became so adept that she could properly clas-sify a stellar spectrum with little more than a momentary

THINK ABOUT IT

glance. During her lifetime, she personally classified over400,000 stars. She became the first woman ever awarded anhonorary degree by Oxford University, and in 1929 theLeague of Women Voters named her one of the 12 greatestliving American women.


Table 16.1 The Spectral Sequence

Spectral Temperature Type Example(s) Range

O Stars of >30,000 KOrion’s Belt

B Rigel 30,000 K–10,000 K

A Sirius 10,000 K–7,500 K

F Polaris 7,500 K–6,000 K

G Sun, Alpha 6,000 K–5,000 KCentauri A

K Arcturus 5,000 K–3,500 K

M Betelgeuse, <3,500 KProxima Centauri

Figure 16.5 Women astronomers pose with Edward Pickering at Harvard College Observatory in 1913. Annie Jump Cannon isfifth from the left in the back row.


The astronomical community adopted Cannon’s system of stellar classification in 1910. However, no one at that time knew why spectra followed the OBAFGKMsequence. Many astronomers guessed, incorrectly, that the different sets of spectral lines reflected different com-positions for the stars. The correct answer—that all starsare made primarily of hydrogen and helium and that a star’ssurface temperature determines the strength of its spec-tral lines—was discovered by Cecilia Payne-Gaposchkin(1900–1979), another woman working at Harvard Observatory.

Relying on insights from whatwas then the newly develop-ing science of quantum me-chanics, Payne-Gaposchkinshowed that the differences inspectral lines from star to starmerely reflected changes in theionization level of the emittingatoms. For example, O stars haveweak hydrogen lines because,at their high surface tempera-tures, nearly all their hydrogenis ionized. Without an electron to “jump” between energy

levels, ionized hydrogen can neither emit nor absorb itsusual specific wavelengths of light. At the other end of thespectral sequence, M stars are cool enough for some par-ticularly stable molecules to form, explaining their strongmolecular absorption lines. Payne-Gaposchkin describedher work and her conclusions in a dissertation published in1925. A later review of twentieth-century astronomy calledher work “undoubtedly the most brilliant Ph.D. thesis everwritten in astronomy.”


16.4 Stellar MassesThe most important property of a star is its mass, but stellarmasses are harder to measure than luminosities or surfacetemperatures. The most dependable method for “weigh-ing” a star relies on Newton’s version of Kepler’s third law[Section 5.3]. This law can be applied only when we canmeasure both the orbital period and the average distancebetween the stars (semimajor axis) of the orbiting starsystem. Thus, in most cases we can measure stellar massesonly in binary star systems in which we have determinedthe orbital properties of the two stars.

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BrightestKey Absorption WavelengthLine Features (color) Typical Spectrum

Lines of ionized <97 nm helium, weak (ultraviolet)*hydrogen lines

Lines of neutral 97–290 nm helium, moderate (ultraviolet)*hydrogen lines

Very strong 290–390 nm hydrogen lines (violet)*

Moderate hydrogen 390–480 nm lines, moderate lines (blue)*of ionized calcium

Weak hydrogen 480–580 nm lines, strong lines (yellow)of ionized calcium

Lines of neutral and 580–830 nm singly ionized metals, (red)some molecules

Molecular lines >830 nm strong (infrared)

*All stars above 6,000 K look more or less white to the human eye because they emit plenty of radiation at all visible wavelengths.

hydrogen

sodium

O

B

A

F

G

K

M

ionizedcalcium

titaniumoxide

titaniumoxide

Cecilia Payne-Gaposchkin


Types of Binary Star Systems

About half of all stars orbit a companion star of some kind.These star systems fall into three classes:

● A visual binary is a pair of stars that we can see dis-tinctly (with a telescope) as the stars orbit each other.Mizar, the second star in the handle of the Big Dipper,is one example of a visual binary (Figure 16.6). Some-times we observe a star slowly shifting position in the

sky as if it were a member of a visual binary, but itscompanion is too dim to be seen. For example, slowshifts in the position of Sirius, the brightest star in thesky, revealed it to be a binary star long before its com-panion was discovered (Figure 16.7).

● An eclipsing binary is a pair of stars that orbit in theplane of our line of sight (Figure 16.8). When neitherstar is eclipsed, we see the combined light of both stars.When one star eclipses the other, the apparent bright-

Figure 16.8 The apparent brightness ofan eclipsing binary system drops when eitherstar eclipses the other.

app

aren

t brig

htne

ss

time

AA

A A

BB

B

We see light from both A and B.

We see light from all of B, some of A.

We see light from both A and B.

We see light only from A.

Figure 16.6 Mizar looks like one star to the naked eye but is actually a system of four stars. Through atelescope Mizar appears to be a visual binary made up of two stars, Mizar A and Mizar B, that graduallychange positions, indicating that they orbit every few thousand years. However, each of these two “stars”is actually a spectroscopic binary, making a total of four stars. (The star Alcor appears very close to Mizar to the naked eye but does not orbit it.)

Mizar is a visual binary.

Mizar A

Mizar B

Alcor

Mizar Spectroscopy shows that each ofthe visual “stars” is itself a binary.

Figure 16.7 Each frame represents the relative positions of Sirius A and Sirius B at 10-year intervals from 1900 to 1970. The back-and-forth “wobble” of Sirius A allowed astronomers to infer the existenceof Sirius B even before the two stars could be resolved in telescopic photos.

1900 1910 1920

A

B

1930 1940 1950 1960 1970



ness of the system drops because some of the light isblocked from our view. A light curve, or graph of ap-parent brightness against time, reveals the pattern ofthe eclipses. The most famous example of an eclipsingbinary is Algol, the “demon star” in the constellationPerseus (algol is Arabic for “the ghoul”). Algol becomesthree times dimmer for a few hours about every 3 daysas the brighter of its two stars is eclipsed by its dimmercompanion.

● If a binary system is neither visual nor eclipsing, wemay be able to detect its binary nature by observingDoppler shifts in its spectral lines [Section 6.5]. Suchsystems are called spectroscopic binary systems. If onestar is orbiting another, it periodically moves towardus and away from us in its orbit. Its spectral lines showblueshifts and redshifts as a result of this motion (Fig-ure 16.9). Sometimes we see two sets of lines shiftingback and forth—one set from each of the two stars in the system (a double-lined spectroscopic binary).Other times we see a set of shifting lines from only onestar because its companion is too dim to be detected (a single-lined spectroscopic binary). Each of the twostars in the visual binary Mizar is itself a spectroscopicbinary (see Figure 16.6).

Measuring Masses in Binary Systems

Even for a binary system, we can apply Newton’s version ofKepler’s third law only if we can measure both the orbitalperiod and the separation of the two stars. Measuring orbitalperiod is fairly easy. In a visual binary, we simply observehow long each orbit takes (or extrapolate from part of an


Figure 16.9 The spectral lines of a star in a binary system arealternately blueshifted as it comes toward us in its orbit and red-shifted as it moves away from us.

Star B spectrum at time 1:approaching, therefore blueshifted

A

B

B

1approaching us

2receding from us

to Earth

Star B spectrum at time 2:receding, therefore redshifted

Measurements of stellar masses rely on Newton’s version of Kep-ler’s third law [Section 5.3], for which we need to know the orbitalperiod p and semimajor axis a. As described in the text, it’s gen-erally easy to measure p for binary star systems. We can rarelymeasure a directly, but we can calculate it in cases in which wecan measure the orbital velocity of one star relative to the other.

If we assume that the first star traces a circle of radius aaround its companion, the circumference of its orbit is 2pa. Be-cause the star makes one circuit of this circumference in one orbitalperiod p, its velocity relative to its companion is:

v � � �2p

p

a�

Solving for a, we find:

a � �2

p

pv�

Once we know both p and a, we can use Newton’s version of Kepler’s third law to calculate the sum of the masses of the twostars (M1 � M2). We can then calculate the individual masses of the two stars by taking advantage of the fact that the relativevelocities of the two stars around their common center of massare inversely proportional to their relative masses.

Example: The spectral lines of two stars in a particular eclipsingbinary system shift back and forth with a period of 2 years (p �6.2 � 107 seconds). The lines of one star (Star 1) shift twice as faras the lines of the other (Star 2). The amount of Doppler shiftindicates an orbital speed of v � 100,000 m/s for Star 1 relative to

distance traveled in one orbit��

period of one orbit

Star 2. What are the masses of the two stars? Assume that each ofthe two stars traces a circular orbit around their center of mass.

Solution: We will find the masses by using Newton’s version ofKepler’s third law, solved for the masses:

p2 ��G(M

4

1

p�

2

M2)�a3 ⇒ (M1 � M2) � �

4

G

p2

� � �p

a3

2�

We are given the orbital period p � 6.2 � 107 s, and we find thesemimajor axis a of the system from the given orbital velocity v:

a � �2

p

pv� �

� 9.9 � 1011 m

Now we calculate the sum of the stellar masses by substituting thevalues of p, a, and the gravitational constant G [Section 5.3] intothe mass equation above:

(M1 � M2) � ��(9

(6

.9

.2

�

�

1

1

0

0

11

7

m

s)2

)3

�

� 1.5 � 1032 kg

Because the lines of Star 1 shift twice as far as those of Star 2,we know that Star 1 moves twice as fast as Star 2, and hence thatStar 1 is half as massive as Star 2. In other words, Star 2 is twice as massive as Star 1. Using this fact and their combined mass of1.5 � 1032 kg, we conclude that the mass of Star 2 is 1.0 � 1032 kgand the mass of Star 1 is 0.5 � 1032 kg.

4p2

��

�6.67 � 10�11 �kg

m

�

3

s2��

(6.2 � 107 s) � (100,000 m/s)��

2p

Mathematical Insight 16.4 Orbital Separation and Newton’s Version of Kepler’s Third Law


orbit). In an eclipsing binary, we measure the time betweeneclipses. In a spectroscopic binary, we measure the time ittakes the spectral lines to shift back and forth.

Determining the average separation of the stars in abinary system is usually much more difficult. Except in rarecases in which we can measure the separation directly, we cancalculate the separation only if we know the actual orbitalspeeds of the stars from their Doppler shifts. Unfortunately,a Doppler shift tells us only the portion of a star’s velocitythat is directly toward us or away from us [Section 6.5]. Be-cause orbiting stars generally do not move directly alongour line of sight, their actual velocities can be significantlygreater than those we measure through the Doppler effect.

The exceptions are eclipsing binary stars. Because thesestars orbit in the plane of our line of sight, their Dopplershifts can tell us their true orbital velocities.* Eclipsingbinaries are therefore particularly important to the study of stellar masses. As an added bonus, eclipsing binariesallow us to measure stellar radii directly. Because we knowhow fast the stars are moving across our line of sight as oneeclipses the other, we can determine their radii by timinghow long each eclipse lasts.

Suppose two orbiting stars are moving in a plane perpendicularto our line of sight. Would the spectral features of these starsappear shifted in any way? Explain.


16.5 The Hertzsprung–RussellDiagram

During the first decade of the twentieth century, a similarthought occurred independently to astronomers Ejnar Hertz-sprung, working in Denmark, and Henry Norris Russell,working in the United States at Princeton University: Eachdecided to make a graph plotting stellar luminosities on oneaxis and spectral types on the other. Such graphs are nowcalled Hertzsprung–Russell (H–R) diagrams. Soon afterthey began making their graphs, Hertzsprung and Russelluncovered some previously unsuspected patterns in the prop-erties of stars. As we will see shortly, understanding thesepatterns and the H–R diagram is central to the study of stars.

A Basic H–R Diagram

Figure 16.10 displays an example of an H–R diagram.

● The horizontal axis represents stellar surface tempera-ture, which, as we’ve discussed, corresponds to spectraltype. Temperature increases from right to left because

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Hertzsprung and Russell based their diagrams on thespectral sequence OBAFGKM.

● The vertical axis represents stellar luminosity, in unitsof the Sun’s luminosity (LSun). Stellar luminositiesspan a wide range, so we keep the graph compact bymaking each tick mark represent a luminosity 10 timeslarger than the prior tick mark.

Each location on the diagram represents a uniquecombination of spectral type and luminosity. For example,the dot representing the Sun in Figure 16.10 correspondsto the Sun’s spectral type, G2, and its luminosity, 1LSun.Because luminosity increases upward on the diagram andsurface temperature increases leftward, stars near the upperleft are hot and luminous. Similarly, stars near the upperright are cool and luminous, stars near the lower right arecool and dim, and stars near the lower left are hot and dim.

Explain how the colors of the stars in Figure 16.10 help indi-cate stellar surface temperature. Do these colors tell us anythingabout interior temperatures? Why or why not?

The H–R diagram also provides direct informationabout stellar radii, because a star’s luminosity depends onboth its surface temperature and its surface area or radius.Recall that surface temperature determines the amount of power emitted by the star per unit area: Higher tempera-ture means greater power output per unit area [Section 6.4].Thus, if two stars have the same surface temperature, onecan be more luminous than the other only if it is larger insize. Stellar radii therefore must increase as we go from thehigh-temperature, low-luminosity corner on the lower left of the H–R diagram to the low-temperature, high-luminositycorner on the upper right.

Patterns in the H–R Diagram

Figure 16.10 also shows that stars do not fall randomlythroughout the H–R diagram but instead fall into severaldistinct groups:

● Most stars fall somewhere along the main sequence,the prominent streak running from the upper left tothe lower right on the H–R diagram. Our Sun is a main-sequence star.

● The stars along the top are called supergiants becausethey are very large in addition to being very bright.

● Just below the supergiants are the giants, which aresomewhat smaller in radius and lower in luminosity(but still much larger and brighter than main-sequence stars of the same spectral type).

● The stars near the lower left are small in radius andappear white in color because of their high tempera-ture. We call these stars white dwarfs.

THINK ABOUT IT


*In other binaries, we can calculate an actual orbital velocity from thevelocity obtained by the Doppler effect if we also know the system’s orbitalinclination. Astronomers have developed techniques for determiningorbital inclination in a relatively small number of cases.


When classifying a star, astronomers generally reportboth the star’s spectral type and a luminosity class thatdescribes the region of the H–R diagram in which the starfalls. Table 16.2 summarizes the luminosity classes: Lumi-nosity class I represents supergiants, luminosity class IIIrepresents giants, luminosity class V represents main-

sequence stars, and luminosity classes II and IV are inter-mediate to the others. For example, the complete spectralclassification of our Sun is G2 V. The G2 spectral type meansit is yellow in color, and the luminosity class V means it is a main-sequence star. Betelgeuse is M2 I, making it a redsupergiant. Proxima Centauri is M5 V—similar in color and

Figure 16.10 An H–R diagram, one of astronomy’s most important tools, shows how the surface tem-peratures of stars (plotted along the horizontal axis) relate to their luminosities (plotted along the ver-tical axis). Several of the brightest stars in the sky are plotted here, along with a few of those closest toEarth. They are not drawn to scale—the diagonal lines, labeled in solar radii, indicate how large they arecompared to the Sun. The lifetime and mass labels apply only to main-sequence stars (see Figure 16.11).(Star positions on this diagram are based on data from the Hipparcos satellite.)

10 2

102

103

104

Lifetime109 yrs

Lifetime1010 yrs

Lifetime1011 yrs

Lifetime107 yrs

Lifetime108 yrs

Proxima Centauri

Barnard’s Star

Altair

ProcyonSirius

Vega

Arcturus

Canopus

Pollux

Aldebaran

DX Cancri

Wolf 359

Ross 128

Gliese 725 BGliese 725 A

61 Cygni B61 Cygni A

Lacaille 9352

Procyon B

Sun

Achernar

Bellatrix

Rigel

Deneb

Polaris

Betelgeuse

Antares

Spica

Sirius B

Sirius

60MSun

30MSun

10MSun

6MSun

3MSun

0.3MSun

0.1MSun

1.5MSun

1MSun

105

106

0.1

1

10

surface temperature (Kelvin) decreasing temperatureincreasing temperature

30,000 10,000

W H I T E

G I A N T S

S U P E R G I A N T S

M A I N

S E Q U E N C E

D W A R F S

6,000 3,000

10 3

10 3 Solar Radius

10 2 Solar Radius

0.1 Solar Radius

1 Solar Radius

10 Solar Radii

10 2 Solar Radii

10 3 Solar Radii

10 4

10 5

lum

inos

ity (

sola

r un

its)

Ceti EridaniCentauri B

Centauri A

Centauri



surface temperature to Betelgeuse, but far dimmer becauseof its much smaller size. White dwarfs are usually designatedwith the letters wd rather than with a Roman numeral.

The Main Sequence

The common trait of main-sequence stars is that, like ourSun, they are fusing hydrogen into helium in their cores.Because stars spend the majority of their lives fusing hydro-gen, most stars fall somewhere along the main sequence of the H–R diagram.

Why do main-sequence stars span such a wide rangeof luminosities and surface temperatures? By measuringthe masses of stars in binary systems, astronomers have dis-covered that stellar masses decrease downward along themain sequence (Figure 16.11). At the upper end of the mainsequence, the hot, luminous O stars can have masses ashigh as 100 times that of the Sun (100MSun). On the lowerend, cool, dim M stars may have as little as 0.08 times themass of the Sun (0.08MSun). Many more stars fall on thelower end of the main sequence than on the upper end,which tells us that low-mass stars are much more commonthan high-mass stars.

The orderly arrangement of stellar masses along themain sequence tells us that mass is the most importantattribute of a hydrogen-burning star. Luminosity dependsdirectly on mass because the weight of a star’s outer layersdetermines the nuclear burning rate in its core. More weightmeans the star must sustain a higher nuclear burning ratein order to maintain gravitational equilibrium [Section 15.3].

The nuclear burning rate, and hence the luminosity, is verysensitive to mass. For example, a 10MSun star on the mainsequence is about 10,000 times more luminous than the Sun.

The relationship between mass and surface tempera-ture is a little subtler. In general, a very luminous star musteither be very large or have a very high surface tempera-ture, or some combination of both. Stars on the upper endof the main sequence are thousands of times more lumi-nous than the Sun but only about 10 times larger than theSun in radius. Thus, their surfaces must be significantlyhotter than the Sun’s surface to account for their high lu-minosities. Main-sequence stars more massive than theSun therefore have higher surface temperatures than theSun, and those less massive than the Sun have lower sur-face temperatures. That is why the main sequence slicesdiagonally from the upper left to the lower right on theH–R diagram.


Table 16.2 Stellar Luminosity Classes

Class Description

I Supergiants

II Bright giants

III Giants

IV Subgiants

V Main sequence

Mathematical Insight 16.5 Calculating Stellar Radii

Almost all stars are too distant for us to measure their radii directly.However, we can calculate a star’s radius from its luminosity withthe aid of the thermal radiation laws. As given in MathematicalInsight 6.2, the amount of thermal radiation emitted by a star ofsurface temperature T is:

emitted power per unit area � sT 4

where the constant s � 5.7 � 10�8 watt/(m2 � Kelvin4).The luminosity L of a star is its power per unit area multi-

plied by its total surface area. If the star has radius r, its surfacearea is given by the formula 4pr2. Thus:

L � 4pr2 � sT 4

With a bit of algebra, we can solve this formula for the star’sradius r:

r � ��4ps

L

T�4��Example: Betelgeuse has a luminosity of 38,000LSun and a surfacetemperature of about 3,400 K. What is its radius?

Solution: First, we must make our units consistent by convert-ing the luminosity of Betelgeuse into watts. Remembering thatLSun � 3.8 � 1026 watts, we find:

LBet � 38,000 � LSun � 38,000 � 3.8 � 1026 watts

� 1.4 � 1031 watts

Now we can use the formula derived above to calculate the radiusof Betelgeuse:

r � ��4ps

L

T�4��

��

� �� 3.8 � 1011 m

The radius of Betelgeuse is about 380 billion meters or, equiva-lently, 380 million kilometers. Note that this is more than twicethe Earth–Sun distance of 150 million kilometers.

1.4 � 1031 watts��9.6 � 107 �

w

m

at2

ts�

1.4 � 1031 watts��

4p � �5.7 � 10�8 �m2

w

�

att

K4�� (3,400 K)4


Main-Sequence Lifetimes

A star has a limited supply of core hydrogen and thereforecan remain as a hydrogen-fusing main-sequence star foronly a limited time—the star’s main-sequence lifetime(or hydrogen-burning lifetime). Because stars spend the vast majority of their lives fusing hydrogen into helium,we sometimes refer to the main-sequence lifetime as sim-ply the “lifetime.” Like masses, stellar lifetimes vary in anorderly way as we move up the main sequence: Massivestars near the upper end of the main sequence have shorterlives than less massive stars near the lower end (see Fig-ure 16.11).

Why do more massive stars live shorter lives? A star’slifetime depends on both its mass and its luminosity. Itsmass determines how much hydrogen fuel the star initiallycontains in its core. Its luminosity determines how rap-idly the star uses up its fuel. Massive stars live shorter livesbecause, even though they start their lives with a largersupply of hydrogen, they consume their hydrogen at a pro-digious rate.

The main-sequence lifetime of our Sun is about 10 bil-lion years [Section 15.1]. A 30-solar-mass star has 30 timesmore hydrogen than the Sun but burns it with a luminositysome 300,000 times greater. Consequently, its lifetime isroughly 30/300,000 � 1/10,000 as long as the Sun’s—cor-responding to a lifetime of only a few million years. Cos-mically speaking, a few million years is a remarkably shorttime, which is one reason why massive stars are so rare:Most of the massive stars that have ever been born are longsince dead. (A second reason is that lower-mass stars formin larger numbers than higher-mass stars [Section 17.2].)

The fact that massive stars exist at all at the presenttime tells us that stars must form continuously in our galaxy. The massive, bright O stars in our galaxy todayformed only recently and will die long before they have a chance to complete even one orbit around the center ofthe galaxy.

Would you expect to find life on planets orbiting massive O stars? Why or why not? (Hint: Compare the lifetime of an O star to the amount of time that passed from the forma-tion of our solar system to the origin of life on Earth.)

On the other end of the scale, a 0.3-solar-mass staremits a luminosity just 0.01 times that of the Sun and con-sequently lives roughly 0.3/0.01 � 30 times longer than the Sun. In a universe that is now about 14 billion yearsold, even the most ancient of these small, dim M stars stillsurvive and will continue to shine faintly for hundreds ofbillions of years to come.

Giants, Supergiants, and White Dwarfs

Giants and supergiants are stars nearing the ends of theirlives because they have already exhausted their core hydro-gen. Surprisingly, stars grow more luminous when theybegin to run out of fuel. As we will discuss in the next chap-ter, a star generates energy furiously during the last stagesof its life as it tries to stave off the inevitable crushing forceof gravity. As ever-greater amounts of power well up fromthe core, the outer layers of the star expand, making it agiant or supergiant. The largest of these celestial behemothshave radii more than 1,000 times the radius of the Sun. Ifour Sun were this big, it would engulf the planets out toJupiter.

Because they are so bright, we can see giants and super-giants even if they are not especially close to us. Many ofthe brightest stars visible to the naked eye are giants orsupergiants. They are often identifiable by their reddishcolor. Nevertheless, giants and supergiants are rarer thanmain-sequence stars. In our snapshot of the heavens, wecatch most stars in the act of hydrogen burning and rela-tively few in a later stage of life.

Giants and supergiants eventually run out of fuel en-tirely. A giant with a mass similar to that of our Sun ulti-mately ejects its outer layers, leaving behind a “dead” corein which all nuclear fusion has ceased. White dwarfs arethese remaining embers of former giants. They are hot because they are essentially exposed stellar cores, but theyare dim because they lack an energy source and radiateonly their leftover heat into space. A typical white dwarfis no larger in size than Earth, although it may have a massas great as that of our Sun. (Giants and supergiants withmasses much larger than that of the Sun ultimately explode,leaving behind neutron stars or black holes as corpses[Section 17.4].)

THINK ABOUT IT


Figure 16.11 Along the main sequence, more massive stars arebrighter and hotter but have shorter lifetimes. (Stellar masses aregiven in units of solar masses: 1MSun � 2 � 1030 kg.)

10 2

102

103

104

Proxima Centauri

Sun

Achernar

Spica

Sirius

105

106

0.1

1

10

surface temperature (Kelvin)

30,000 10,000 6,000 3,000

10 3

10 4

10 5

lum

inos

ity (

sola

r un

its)

Lifetime108 yrs

Lifetime107 yrs

Lifetime109 yrs

Lifetime1010 yrs

Lifetime1011 yrs

6MSun

60MSun

30MSun

10MSun

3MSun

1.5MSun

1MSun

0.3MSun

0.1MSun

M A I NS E Q U E N C E


Pulsating Variable Stars

Not all stars shine steadily like our Sun. Any star that sig-nificantly varies in brightness with time is called a variablestar. A particularly important type of variable star has a pe-culiar problem with achieving the proper balance betweenthe power welling up from its core and the power beingradiated from its surface. Sometimes the upper layers ofsuch a star are too opaque, so energy and pressure build upbeneath the photosphere and the star expands in size. How-ever, this expansion puffs the upper layers outward, makingthem too transparent. So much energy then escapes thatthe underlying pressure drops, and the star contracts again.

In a futile quest for a steady equilibrium, the atmo-sphere of such a pulsating variable star alternately expandsand contracts, causing the star to rise and fall in luminos-ity. Figure 16.12 shows a typical light curve for a pulsatingvariable star, with the star’s brightness graphed against time.Any pulsating variable star has its own particular periodbetween peaks in luminosity, which we can discover easilyfrom its light curve. These periods can range from as shortas several hours to as long as several years.

Most pulsating variable stars inhabit a strip (called theinstability strip) on the H–R diagram that lies between themain sequence and the red giants (Figure 16.13). A specialcategory of very luminous pulsating variables lies in theupper portion of this strip: the Cepheid variables, or Cepheids (so named because the first identified star ofthis type was the star Delta Cephei).

Cepheids fluctuate in luminosity with periods of a fewdays to a few months. In 1912, another woman astronomerat Harvard, Henrietta Leavitt, discovered that the periods ofthese stars are very closely related to their luminosities: Thelonger the period, the more luminous the star. This period–luminosity relation holds because larger (and hence moreluminous) Cepheids take longer to pulsate in and out in size.

Once we have measured the period of a Cepheid vari-able, we can use the period–luminosity relation to deter-mine its luminosity. We can then calculate its distance with

the luminosity–distance formula. In fact, as we’ll discuss inChapter 20, Cepheids provide our primary means of mea-suring distances to other galaxies and thus teach us the truescale of the cosmos. The next time you look at the NorthStar, Polaris, gaze upon it with renewed appreciation. Notonly has it guided generations of navigators in the North-ern Hemisphere, but it is also one of these special Cepheidvariable stars.

Stellar Evolution Tutorial, Lessons 1, 4

16.6 Star ClustersAll stars are born from giant clouds of gas. Because a singleinterstellar cloud can contain enough material to form manystars, stars almost inevitably form in groups. In our snap-shot of the heavens, many stars still congregate in the groupsin which they formed. These groups are of two basic types:modest-size open clusters and densely packed globularclusters.

Open clusters of stars are always found in the disk ofthe galaxy (see Figure 1.18). They can contain up to sev-eral thousand stars and typically span about 30 light-years(10 parsecs). The most famous open cluster is the Pleiades, aprominent clump of stars in the constellation Taurus (Fig-ure 16.14). The Pleiades are often called the Seven Sisters,although only six of the cluster’s several thousand stars areeasily visible to the naked eye. Other cultures have othernames for this beautiful group of stars. In Japanese it iscalled Subaru, which is why the logo for Subaru automo-biles is a diagram of the Pleiades.

Globular clusters are found primarily in the halo ofour galaxy, although some are in the disk. A globular clus-

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Figure 16.12 A typical light curve for a Cepheid variable star.Cepheids are giant, whitish stars whose luminosities regularly pulsateover periods of a few days to about a hundred days. The pulsationperiod of this Cepheid is about 50 days.

time (days)

app

aren

t brig

htne

ss

250 50 75 100 125 150 175 200

period


Figure 16.13 An H–R diagram with the instability strip highlighted.

10 2

102

103

104

Sun

Polaris

variable stars withperiods of hours(called RR Lyraevariables)

inst

abilit

y st

rip

105

106

0.1

1

10


30,000 10,000 6,000 3,000

10 3

10 4

10 5

lum

inos

ity (

sola

r un

its)

Cepheids withperiods of days

10 3 Solar Radius

10 2 Solar Radius

10 2 Solar Radii

10 3 Solar Radii

0.1 Solar Radius

1 Solar Radius

10 Solar Radii


ter can contain more than a million stars concentrated in aball typically from 60 to 150 light-years across (20 to 50 par-secs). Its innermost part can have 10,000 stars packedwithin a region just a few light-years across (Figure 16.15).The view from a planet in a globular cluster would be mar-velous, with thousands of stars lying closer than AlphaCentauri is to the Sun.

Because a globular cluster’s stars nestle so closely, theyengage in an intricate and complex dance choreographedby gravity. Some stars zoom from the cluster’s core to itsoutskirts and back again at speeds approaching the escapevelocity from the cluster, while others orbit the dense coremore closely. When two stars pass especially close to eachother, the gravitational pull between them deflects theirtrajectories, altering their speeds and sending them careen-ing off in new directions. Occasionally, a close encounterboosts one star’s velocity enough to eject it from the clus-ter. Through such ejections, globular clusters gradually losestars and grow more compact.

Star clusters are extremely useful to astronomers fortwo key reasons:

1. All the stars in a cluster lie at about the same distancefrom Earth.

2. Cosmically speaking, all the stars in a cluster formed at about the same time (i.e., within a few million yearsof one another).

Astronomers can therefore use star clusters as laboratoriesfor comparing the properties of stars, as yardsticks formeasuring distances in the universe [Section 20.3], and astimepieces for measuring the age of our galaxy.

We can use clusters as timepieces because we can de-termine their ages from H–R diagrams of cluster stars.

Figure 16.14 A photo of the Pleiades,a nearby open cluster of stars. The mostprominent stars in this open cluster are ofspectral type B, indicating that the Pleiadesare no more than 100 million years old,relatively young for a star cluster. The regionshown here is about 11 light-years across.

VIS

Figure 16.15 This globular cluster, known as M 80, is over 12 billion years old. The prominentreddish stars in this Hubble SpaceTelescope photo are red giant stars nearing the ends of their lives. The region pictured here is about 15 light-years across.

VIS



To understand how the process works, consider Figure 16.16,which shows an H–R diagram for the Pleiades. Most ofthe stars in the Pleiades fall along the standard main se-quence, with one important exception: The Pleiades’ starstrail away to the right of the main sequence at the upperend. That is, the hot, short-lived O stars are missing fromthe main sequence. Apparently, the Pleiades are old enoughfor its O stars to have already ended their hydrogen-burninglives. At the same time, they are young enough for some B stars to still survive on the main sequence.

The precise point on the H–R diagram at which thePleiades’ main sequence diverges from the standard mainsequence is called the main-sequence turnoff point. In this cluster, it occurs around spectral type B6. The main-sequence lifetime of a B6 star is roughly 100 million years,so this must be the age of the Pleiades. Any star in thePleiades that was born with a main-sequence spectral typehotter than B6 had a lifetime shorter than 100 million yearsand hence is no longer found on the main sequence. Starswith lifetimes longer than 100 million years are still fusinghydrogen and hence remain as main-sequence stars. Overthe next few billion years, the B stars in the Pleiades will die out, followed by the A stars and the F stars. Thus, if wecould make an H–R diagram for the Pleiades every fewmillion years, we would find that the main sequence grad-ually grows shorter.

Comparing the H–R diagrams of other open clustersmakes this effect more apparent (Figure 16.17). In each

case, we determine the cluster’s age from the lifetimes ofthe stars at its main-sequence turnoff point:

age of the cluster � lifetime of stars at main-

sequence turnoff point

Stars in a particular cluster that once resided above theturnoff point on the main sequence have already exhaustedtheir core supply of hydrogen, while stars below the turn-off point remain on the main sequence.

Suppose a star cluster is precisely 10 billion years old. On an H–R diagram, where would you expect to find its main-sequence turnoff point? Would you expect this cluster to haveany main-sequence stars of spectral type A? Would you expectit to have main-sequence stars of spectral type K? Explain.(Hint: What is the lifetime of our Sun?)

The technique of identifying main-sequence turnoffpoints is our most powerful tool for evaluating the ages ofstar clusters. We’ve learned, for example, that most openclusters are relatively young and that very few are older thanabout 5 billion years. In contrast, the stars at the main-sequence turnoff points in globular clusters are usually less massive than our Sun (Figure 16.18). Because stars likeour Sun have a lifetime of about 10 billion years and these

THINK ABOUT IT


Figure 16.16 An H–R diagram for the stars of the Pleiades.Triangles represent individual stars. The Pleiades cluster is missingits upper main-sequence stars, indicating that these stars havealready ended their hydrogen-burning lives. The main-sequenceturnoff point at about spectral type B6 tells us that the Pleiadesare about 100 million years old.

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Figure 16.17 This H–R diagram shows stars from four clusterswith very different ages. Each star cluster has a different main-sequence turnoff point. The youngest cluster, h � Persei, stillcontains main-sequence O and B stars (only the most massivestars are shown), indicating that it is only about 14 million yearsold. Stars at the main-sequence turnoff point for the oldest cluster,NGC 188, are only slightly more luminous and massive than theSun, indicating an age of 7 billion years.

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NGC 188 – 7 billion years

Hyades – 650 million years

Pleiades – 100 million years

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stars have already died in globular clusters, we concludethat globular-cluster stars are older than 10 billion years.

More precise studies of the turnoff points in globularclusters, coupled with theoretical calculations of stellarlifetimes, place the ages of these clusters at between 12 and

16 billion years, making them the oldest known objects inthe galaxy. In fact, globular clusters place a constraint onthe possible age of the universe: If stars in globular clustersare 12 billion years old, then the universe must be at leastthis old.

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

Putting Chapter 16 into Context

We have classified the diverse families of stars visible inthe night sky. Much of what we know about stars, gal-axies, and the universe itself is based on the fundamentalproperties of stars introduced in this chapter. Make sureyou understand the following “big picture” ideas:

● All stars are made primarily of hydrogen and helium,at least at the time they form. The differences betweenstars come about primarily because of differences inmass and age.

● Much of what we know about stars comes from study-ing the patterns that appear when we plot stellar sur-face temperatures and luminosities in an H–R diagram.Thus, the H–R diagram is one of the most importanttools of astronomers.

● Stars spend most of their lives as main-sequence stars,fusing hydrogen into helium in their cores. The mostmassive stars live only a few million years, while theleast massive stars will survive until the universe is manytimes its present age.

● Much of what we know about the universe comes fromstudies of star clusters. Here again, H–R diagramsplay a vital role. For example, H–R diagrams of starclusters allow us to determine their ages.

Figure 16.18 This H–R diagram shows stars from the globularcluster Palomar 3. The main-sequence turnoff point is in the vicin-ity of stars like our Sun, indicating an age for this cluster of around10 billion years. A more technical analysis of this cluster places itsage at around 12–14 billion years. (Stars in globular clusters tendto contain virtually no elements other than hydrogen and helium.Because of their different composition, these stars are somewhatbluer and more luminous than stars of the same mass and compo-sition as our Sun.)

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SUMMARY OF KEY CONCEPTS

16.1 Snapshot of the Heavens

• How can we learn about the lives of stars, which lastmillions to billions of years? By taking observations of many stars, we can study stars in many phases oftheir life, just as we might study how humans age by observing all the humans living in a particularvillage at one time.

• What are the two main elements in all stars? All starsare made primarily of hydrogen and helium at birth.

• What two basic physical properties do astronomers use to classify stars? Stars are classified by their lumi-nosity and surface temperature, which depend pri-marily on a star’s mass and its stage of life.

16.2 Stellar Luminosity

• What is luminosity, and how do we determine it? Astar’s luminosity is the total power (energy per unittime) that it radiates into space. It can be calculatedfrom a star’s measured apparent brightness and dis-tance, using the luminosity–distance formula:

apparent brightness ��4p

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ce)2�

• How do we measure the distance to nearby stars? Thedistance to nearby stars can be measured by paral-lax, the shift in the apparent position of a star withrespect to more distant stars as Earth moves aroundthe Sun.

continued �



• How does the magnitude of a star relate to its appar-ent brightness? The magnitude scale runs backward,so a star of magnitude 5 is brighter than a star of mag-nitude 18.

16.3 Stellar Surface Temperature

• How are stars classified into spectral types? Fromhottest to coolest, the major spectral types are O, B,A, F, G, K, and M. These types are futher subdividedinto numbered categories. For example, the hottestA stars are type A0 and the coolest A stars are typeA9, which is slightly hotter than F0.

• What determines a star’s spectral type? The mainfactor in determining a star’s spectral type is its sur-face temperature. Spectral type does not dependmuch on composition, because the compositions ofstars—primarily hydrogen and helium—are nearlythe same.

16.4 Stellar Masses

• What is the most important property of a star? A star’smost important property is its mass, which deter-mines its luminosity and spectral type at each stageof its life.

• What are the three major classes of binary star sys-tems? A visual binary is a pair of orbiting stars thatwe can see distinctly through a telescope. An eclips-ing binary reveals its binary nature because of peri-odic dimming that occurs when one star eclipses theother as viewed from Earth. A spectroscopic binaryreveals its binary nature when we see the spectrallines of one or both stars shifting back and forth asthe stars orbit each other.

• How do we measure stellar masses? We can directlymeasure stellar mass only in binary systems for whichwe are able to determine the period and separationof the two orbiting stars. We can then calculate thesystem’s mass using Newton’s version of Kepler’sthird law.

16.5 The Hertzsprung–Russell Diagram

• What is the Hertzsprung–Russell (H–R) diagram?The H–R diagram is the most important classifica-tion tool in stellar astronomy. Stars are located onthe H–R diagram by their surface temperature (orspectral type) along the horizontal axis and theirluminosity along the vertical axis. Surface tempera-ture decreases from left to right on the H–R diagram.

• What are the major features of the H–R diagram? Most stars occupy the main sequence, which extends

diagonally from lower right to upper left. The giantsand supergiants inhabit the upper-right region ofthe diagram, above the main sequence. The whitedwarfs are found near the lower left, below the mainsequence.

• How do stars differ along the main sequence? Allmain-sequence stars are fusing hydrogen to heliumin their cores. Stars near the lower right of the mainsequence are lower in mass and have longer lifetimesthan stars further up the main sequence. Lower-massmain-sequence stars are much more common thanhigher-mass stars.

• What determines the length of time a star spends onthe main sequence? A star’s mass determines howmuch hydrogen fuel it has and how fast it fuses thathydrogen into helium. The most massive stars havethe shortest lifetimes because they fuse their hydro-gen at a much faster rate than do lower-mass stars.

• What are Cepheid variable stars, and why are theyimportant to astronomers? Cepheid variables are very luminous pulsating variable stars that follow a period–luminosity relation, which means we cancalculate luminosity by measuring pulsation period.Once we know a Cepheid’s luminosity, we can cal-culate its distance with the luminosity–distanceformula. This technique enables us to measure dis-tances to many other galaxies in which we haveobserved these variable stars.

16.6 Star Clusters

• What are the two major types of star cluster? Openclusters contain up to several thousand stars and are found in the disk of the galaxy. Globular clustersare much denser, containing hundreds of thousandsof stars, and are found mainly in the halo of the gal-axy. Globular-cluster stars are among the oldest starsknown, with estimated ages of up to 12–14 billionyears. Open clusters are generally much youngerthan globular clusters.

• Why are star clusters useful for studying stellar evolu-tion? The stars in star clusters are all at roughly thesame distance and, because they were born at aboutthe same time, are all about the same age.

• How do we measure the age of a star cluster? The ageof a cluster is equal to the main-sequence lifetime of the hottest, most luminous main-sequence starsremaining in the cluster. On an H–R diagram ofthe cluster, these stars sit farthest to the upper leftand define the main-sequence turnoff point of thecluster.



True Statements?

Decide whether each of the following statements is true or falseand clearly explain how you know.

1. Two stars that look very different must be made of differentkinds of elements.

2. Sirius is the brightest star in the night sky, but if we movedit 10 times farther away it would look only one-tenth asbright.

3. Sirius looks brighter than Alpha Centauri, but we knowthat Alpha Centauri is closer because its apparent positionin the sky shifts by a larger amount as Earth orbits the Sun.

4. Stars that look red-hot have hotter surfaces than stars thatlook blue.

5. Some of the stars on the main sequence of the H–R dia-gram are not converting hydrogen into helium.

6. The smallest, hottest stars are plotted in the lower left-handportion of the H–R diagram.

7. Stars that begin their lives with the most mass live longerthan less massive stars because it takes them a lot longer touse up their hydrogen fuel.

8. Star clusters with lots of bright, blue stars are generallyyounger than clusters that don’t have any such stars.

9. All giants, supergiants, and white dwarfs were once main-sequence stars.

10. Most of the stars in the sky are more massive than the Sun.

Problems

11. Similarities and Differences. What basic composition are allstars born with? Why do stars differ from one another?

12. Across the Spectrum. Explain why we sometimes talk aboutwavelength-specific (e.g., visible-light or X-ray) luminosityor apparent brightness, rather than total luminosity andtotal apparent brightness.

13. Determining Parallax. Briefly explain how we calculate astar’s distance in parsecs by measuring its parallax angle inarcseconds.

14. Magnitudes. What is the magnitude system? Briefly explainwhat we mean by the apparent magnitude and absolutemagnitude of a star.

15. Deciphering Stellar Spectra. Briefly summarize the roles ofAnnie Jump Cannon and Cecilia Payne-Gaposchkin in dis-covering the spectral sequence and its meaning.

16. Eclipsing Binaries. Describe why eclipsing binaries are soimportant for measuring masses of stars.

17. Basic H–R Diagram. Draw a sketch of a basic Hertzsprung–Russell (H–R) diagram. Label the main sequence, giants,supergiants, and white dwarfs. Where on this diagram dowe find stars that are cool and dim? Cool and luminous?Hot and dim? Hot and bright?

18. Luminosity Classes. What do we mean by a star’s luminosityclass? On your sketch of the H–R diagram from problem17, identify the regions for luminosity classes I, III, and V.

19. Pulsating Variables. What are pulsating variable stars? Whydo they vary periodically in brightness?

20. H–R Diagrams of Star Clusters. Explain why H–R diagramslook different for star clusters of different ages. How doesthe location of the main-sequence turnoff point tell us theage of the star cluster?

21. Stellar Data. Consider the following data table for severalbright stars. Mv is absolute magnitude, and mv is apparentmagnitude.

Spectral Luminosity Star Mv mv Type Class

Aldebaran �0.2 �0.9 K5 III

Alpha Centauri A �4.4 0.0 G2 V

Antares �4.5 �0.9 M1 I

Canopus �3.1 �0.7 F0 II

Fomalhaut �2.0 �1.2 A3 V

Regulus �0.6 �1.4 B7 V

Sirius �1.4 �1.4 A1 V

Spica �3.6 �0.9 B1 V

Answer each of the following questions, including a briefexplanation with each answer.

a. Which star appears brightest in our sky?

b. Which star appears faintest in our sky?

c. Which star has the greatest luminosity?

d. Which star has the least luminosity?

e. Which star has the highest surface temperature?

f. Which star has the lowest surface temperature?

g. Which star is most similar to the Sun?

h. Which star is a red supergiant?

i. Which star has the largest radius?

j. Which stars have finished burning hydrogen in theircores?

k. Among the main-sequence stars listed, which one is themost massive?

l. Among the main-sequence stars listed, which one hasthe longest lifetime?

22. Data Tables. Study the spectral types listed in Appendix Ffor the 20 brightest stars and for the stars within 12 light-years. Why do you think the two lists are so different? Explain.

*23. The Inverse Square Law for Light. Earth is about 150 millionkm from the Sun, and the apparent brightness of the Sun



in our sky is about 1,300 watts/m2. Using these two factsand the inverse square law for light, determine the apparentbrightness we would measure for the Sun if we were locatedat the following positions.

a. Half Earth’s distance from the Sun.

b. Twice Earth’s distance from the Sun.

c. Five times Earth’s distance from the Sun.

*24. The Luminosity of Alpha Centauri A. Alpha Centauri A liesat a distance of 4.4 light-years and has an apparent bright-ness in our night sky of 2.7 � 10�8 watt/m2. Recall that 1 light-year � 9.5 � 1012 km � 9.5 � 1015 m.

a. Use the luminosity–distance formula to calculate theluminosity of Alpha Centauri A.

b. Suppose you have a light bulb that emits 100 watts ofvisible light. (Note: This is not the case for a standard100-watt light bulb, in which most of the 100 watts goesto heat and only about 10–15 watts is emitted as visiblelight.) How far away would you have to put the lightbulb for it to have the same apparent brightness as AlphaCentauri A in our sky? (Hint: Use 100 watts as L in theluminosity–distance formula, and use the apparentbrightness given above for Alpha Centauri A. Then solvefor the distance.)

*25. More Practice with the Luminosity–Distance Formula. Usethe luminosity–distance formula to answer each of thefollowing questions.

a. Suppose a star has the same luminosity as our Sun (3.8 � 1026 watts) but is located at a distance of 10 light-years. What is its apparent brightness?

b. Suppose a star has the same apparent brightness asAlpha Centauri A (2.7 � 10�8 watt/m2) but is locatedat a distance of 200 light-years. What is its luminosity?

c. Suppose a star has a luminosity of 8 � 1026 watts andan apparent brightness of 3.5 � 10�12 watt/m2. Howfar away is it? Give your answer in both kilometers andlight-years.

d. Suppose a star has a luminosity of 5 � 1029 watts andan apparent brightness of 9 � 10�15 watt/m2. How faraway is it? Give your answer in both kilometers andlight-years.

*26. Parallax and Distance. Use the parallax formula to calculatethe distance to each of the following stars. Give your an-swers in both parsecs and light-years.

a. Alpha Centauri: parallax angle of 0.742�.

b. Procyon: parallax angle of 0.286�.

*27. The Magnitude System. Use the definitions of the magni-tude system to answer each of the following questions.

a. Which is brighter in our sky, a star with apparent mag-nitude 2 or a star with apparent magnitude 7? By howmuch?

b. Which has a greater luminosity, a star with absolutemagnitude �4 or a star with absolute magnitude �6?By how much?

*28. Measuring Stellar Mass. The spectral lines of two stars in aparticular eclipsing binary system shift back and forth witha period of 6 months. The lines of both stars shift by equalamounts, and the amount of the Doppler shift indicatesthat each star has an orbital speed of 80,000 m/s. What arethe masses of the two stars? Assume that each of the twostars traces a circular orbit around their center of mass.(Hint: See Mathematical Insight 16.4.)

*29. Calculating Stellar Radii. Sirius A has a luminosity of26LSun and a surface temperature of about 9,400 K. What is its radius? (Hint: See Mathematical Insight 16.5.)

Discussion Question

30. Classification. Edward Pickering’s team of female “comput-ers” at Harvard University made many important contribu-tions to astronomy, particularly in the area of systematicstellar classification. Why do you think rapid advances inour understanding of stars followed so quickly on the heelsof their efforts? Can you think of other areas in sciencewhere huge advances in understanding followed directlyfrom improved systems of classification?



MEDIA EXPLORATIONS

Astronomy Place Web Tutorials

Tutorial Review of Key ConceptsUse the interactive Tutorials at www.astronomyplace.com toreview key concepts from this chapter.

Hertzsprung–Russell Diagram Tutorial

Lesson 1 The Hertzsprung–Russell (H–R) Diagram

Lesson 2 Determining Stellar Radii

Lesson 3 The Main Sequence

Measuring Cosmic Distances Tutorial

Lesson 2 Stellar Parallax

Stellar Evolution Tutorial

Lesson 1 Main-Sequence Lifetimes

Lesson 4 Cluster Dating

Supplementary Tutorial ExercisesUse the interactive Tutorial Lessons to explore the followingquestions.

Hertzsprung–Russell Diagram Tutorial, Lessons 1–3

1. If one star appears brighter than another, can you be surethat it is more luminous? Why or why not?

2. Answer each part of this question with either high, low,left, or right. On an H–R diagram, where will a star be ifit is hot? Cool? Bright? Dim?

3. Why is there a relationship between stellar radii and loca-tions on the H–R diagram?

astr

onomyplace.com 4. Why is there a relationship between luminosity and mass

for main-sequence stars on the H–R diagram?

Measuring Cosmic Distances Tutorial, Lesson 2

1. Explain how we measure distances with stellar parallax.Give an example.

2. Explain why we cannot use parallax to measure the distanceto all stars.

Stellar Evolution Tutorial, Lesson 4

1. In the animation at the beginning of Lesson 4, list the orderin which you saw the three differently colored stars in thecluster disappear, and explain why they disappeared in thisorder.

2. In the second animation in Lesson 4, in what order did you see stars on the main sequence disappear? Explain thereason for this.

3. How does the age of a dim star cluster of mostly small starscompare to a bright cluster with some giants in it? Explainyour answer.

Exploring the Sky and Solar System

Of the many activities available on the Voyager: SkyGazer CD-ROM accompanying your book, use the following files to observekey phenomena covered in this chapter.

Go to the File: Basics folder for the following demonstrations:

1. Large Stars

2. More Stars

3. Star Color and Size

Go to the File: Demo folder for the following demonstrations:

1. Circling the Hyades

2. Flying Around Pleiades

3. The Tail of Scorpius

Web Projects

Take advantage of the useful web links on www.astronomyplace.com to assist you with the following projects.

1. Women in Astronomy. Until fairly recently, men greatlyoutnumbered women in professional astronomy. Neverthe-less, many women made crucial discoveries in astronomythroughout history. Do some research about the life anddiscoveries of a woman astronomer from any time period,and write a two- to three-page scientific biography.

2. The Hipparcos Mission. The European Space Agency’s Hip-parcos mission, which operated from 1989 to 1993, madeprecise parallax measurements for more than 40,000 stars.Learn about how Hipparcos allowed astronomers to mea-sure smaller parallax angles than they could from the groundand how Hipparcos discoveries have affected our knowl-edge of the universe. Write a one- to two-page report on yourfindings.

Voya

ger: SkyGazer


For a complete list of media resources available, go to www.astronomyplace.com, and choose Chapter 16 from the pull-down menu.


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