surveying the stars - weeblyjasysci.weebly.com/uploads/1/6/3/8/1638942/chapter_11.pdfchapter 11...

308

11Surveying the Stars

11.1 Properties of Stars

� How do we measure stellar

luminosities?


temperatures?


masses?

11.2 Patterns Among Stars

� What is a Hertzsprung-Russell

diagram?

� What is the significance of the

main sequence?

� What are giants, supergiants, and

white dwarfs?

11.3 Star Clusters

� What are the two types of star

clusters?

� How do we measure the age of a

star cluster?

learning goals

Chapter 11 Surveying the Stars 309

On a clear, dark night, a few thousand stars are visible to the

naked eye. Many more become visible through binoculars, and a

powerful telescope reveals so many stars that we could never hope to

count them. Like each individual person, each individual star is

unique. Like the human family, all stars have much in common.

Today, we know that stars are born from clouds of interstellar gas,

shine brilliantly by nuclear fusion for millions to billions of years, and

then die, sometimes in dramatic ways. In this chapter, we’ll discuss

how we study and categorize stars and how we have come to realize

that stars, like people, change over their lifetimes.

11.1 Properties of StarsImagine that an alien spaceship flies by Earth on a simple but shortmission: The visitors have just 1 minute to learn everything they canabout the human race. In 60 seconds, they will see next to nothing ofany individual person’s life. Instead, they will obtain a collective “snap-shot” of humanity showing people from all stages of life engagedin their daily activities. From this snapshot alone, they must piecetogether their entire understanding of human beings and their lives,from birth to death.

We face a similar problem when we look at the stars. Comparedwith stellar lifetimes of millions or billions of years, the few hundredyears humans have spent studying stars with telescopes is rather like thealiens’ 1-minute glimpse of humanity. We see only a brief moment inany star’s life, and our collective snapshot of the heavens consists ofsuch frozen moments for billions of stars. From this snapshot, we havelearned to reconstruct the life cycles of stars.

We now know that all stars have a lot in common with the Sun. Theyall form in great clouds of gas and dust, and each begins its life withroughly the same chemical composition as the Sun: about three quartershydrogen and one quarter helium (by mass), with no more than about 2%consisting of elements heavier than helium. Nevertheless, stars are not allthe same; they differ in size, age, brightness, and temperature. We’ll devotemost of this and the next chapter to understanding how and why starsdiffer. First, however, let’s explore how we measure three of the most fun-damental properties of stars: luminosity, surface temperature, and mass.

� How do we measure stellar luminosities?

If you go outside on any clear night, you’ll immediately see that starsdiffer in brightness. Some stars are so bright that we can use them toidentify constellations [Section 2.1]. Others are so dim that our nakedeyes cannot see them at all. However, these differences in brightness donot by themselves tell us anything about how much light these stars aregenerating, because the brightness of a star depends on its distance aswell as on how much light it actually emits. For example, the starsProcyon and Betelgeuse, which make up two of the three corners of thewinter triangle (see Figure 2.2), appear about equally bright in our sky.However, Betelgeuse actually emits about 5000 times as much light asProcyon. It has about the same brightness in our sky because it is muchfarther away.

essential preparation

1. How does Newton’s law of gravity extend Kepler’slaws? [Section 4.4]

2. How does light tell us what things are made of?[Section 5.2]

3. How does light tell us the temperatures of planetsand stars? [Section 5.2]

4. How does light tell us the speed of a distantobject? [Section 5.2]

This inverse square law leads to avery simple and important formula re-lating the apparent brightness, lumi-nosity, and distance of any light source.

We will call it the inverse square law for light:

Because the standard units of luminosity are watts [Section 10.1],the units of apparent brightness are watts per square meter. The 4π in the

apparent brightness =luminosity

4p * (distance)2

We can understand the difference between apparent brightness andluminosity by thinking about a 100-watt light bulb. The bulb always

puts out the same amount of light,so its luminosity doesn’t vary.However, its apparent brightnessdepends on your distance from the

bulb: It will look quite bright if you stand very close to it, but quite dimif you are far away.

The Inverse Square Law for Light The apparent brightness of astar or any other light source obeys an inverse square law with distance,much like the inverse square law that describes the force of gravity[Section 4.4]. For example, if we viewed the Sun from twice Earth’sdistance, it would appear dimmer by a factor of 22 � 4. If we viewed itfrom 10 times Earth’s distance, it would appear 102 � 100 times dimmer.

Figure 11.2 shows why apparent brightness follows an inverse squarelaw. The same total amount of light must pass through each imaginarysphere surrounding the star. If we focus on the light passing through thesmall square on the sphere located at 1 AU, we see that the same amountof light must pass through four squares of the same size on the spherelocated at 2 AU. Each square on the sphere at 2 AU therefore receivesonly as much light as the square on the sphere at 1 AU. Similarly, the same amount of light passes through nine squares of the same size on the sphere located at 3 AU, so each of these squares receives only

as much light as the square on the sphere at 1 AU. Generalizing, we see that the amount of light received per unit area decreases with increas-ing distance by the square of the distance—an inverse square law.

1

32 = 1

9

1

22 = 1

4

Because two similar-looking stars can be generating very differentamounts of light, we need to distinguish clearly between a star’s bright-ness in our sky and the actual amount of light that it emits into space(Figure 11.1):

• When we talk about how bright stars look in our sky, we are talkingabout apparent brightness. More specifically, we define the appar-ent brightness of any star in our sky as the amount of power (energyper second) reaching us per unit area.

• When we talk about how bright stars are in an absolute sense, re-gardless of their distance, we are talking about luminosity—thetotal amount of power that a star emits into space.

310 Part IV Stars

A star’s apparent brightness in the skydepends on both its true light output, orluminosity, and its distance from us.

Until the 20th century, people classified stars primarilyby their brightness and location in our sky. On the next

clear night, find your favorite constellation and visually rank its stars by brightness.Then look to see how that constellation is represented on the star charts in Appendix I.Why do the star charts use different size dots for different stars? Do the brightnessrankings on the chart differ from what you see?

Not to scale!

Luminosity is the totalamount of power(energy per second)the star radiatesinto space.

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

Figure 11.1

Luminosity is a measure of power, and apparent brightness is a measure of power per unit area.

1 AU 2 AU 3 AU

The same amountof starlight passesthrough eachsphere.

The surface areaof a sphere dependson the square of itsradius (distancefrom the star) . . .

. . . so the amountof light passingthrough each unitof area depends onthe inverse squareof its distance fromthe star.

Figure 11.2

The inverse square law for light: The apparent brightness of astar declines with the square of its distance.

Doubling the distance to a star woulddecrease its apparent brightness by afactor of 22, or 4.


formula for the inverse square law for light comes from the fact that thesurface area of a sphere is given by 4π � (radius)2.

In principle, we can always measure a star’s apparent brightness witha detector that records how much energy strikes its light-sensitive surfaceeach second. We can therefore use the inverse square law to calculate astar’s luminosity if we can first measure its distance, or to calculate astar’s distance if we know its luminosity.

Suppose Star A is four times as luminous as Star B. Howwill their apparent brightnesses compare if they are both the

same distance from Earth? How will their apparent brightnesses compare if Star A istwice as far from Earth as Star B? Explain.

Measuring Cosmic Distances Tutorial, Lesson 2

Measuring Distance Through Stellar Parallax The most directway to measure a star’s distance is with stellar parallax, the small annualshifts in a star’s apparent position caused by Earth’s motion around theSun [Section 2.4]. Astronomers measure stellar parallax by comparingobservations of a nearby star made 6 months apart (Figure 11.3). Thenearby star appears to shift against the background of more distant starsbecause we are observing it from two opposite points of Earth’s orbit.

July

nearby star

distant stars

January

Every January,we see this

Every July,we see this

1 AU

p

d

Not to scale

. . . the position of anearby star appears to

shift against thebackground of

more distantstars.

As Earthorbits theSun . . .

Figure 11.3

Parallax makes the apparent position of a nearby star shift backand forth with respect to distant stars over the course of eachyear. The angle p, called the parallax angle, represents half thetotal parallax shift each year. If we measure p in arcseconds,the distance d to the star in parsecs is (1 parsec �3.26 light-years). The angle in this figure is greatly exaggerated:All stars have parallax angles of less than 1 arcsecond.

d = 1p

cosmicCalculations 11.1

The Inverse Square Law for Light

If we use L for luminosity, d for distance, and b for apparentbrightness, we can write the inverse square law for light as

As noted in the text, we can generally measure apparentbrightness, which means we can use this formula to calcu-late luminosity if we know distance and to calculate dis-tance if we know luminosity.

Example: The Sun’s measured apparent brightness is1.36 � 103 watts/m2 at Earth’s distance from the Sun, 1.5 � 1011 m. What is the Sun’s luminosity?

Solution: In order to solve the inverse square law formulafor the luminosity L, we first multiply both sides by 4π � d2.Then we plug in the given values:

Just by measuring the Sun’s apparent brightness and dis-tance, we can calculate the total power that it radiates intoall directions in space.

= 3.8 * 1026 watts

= 4p * 11.5 * 1011 m22 * A1.36 * 103 watts

m2 B L = 4p * d2 * b

b =L

4p * d2

We can calculate a star’s distanceif we know the precise amount ofthe star’s annual shift due to paral-lax. This means measuring the angle

p in Figure 11.3, which we call the star’s parallax angle. Notice that thisangle would be smaller if the star were farther away, so we conclude thatmore distant stars have smaller parallax angles.

In fact, all stars are so far away that they have very small parallaxangles, which explains why the ancient Greeks were never able to measureparallax. Even the nearest stars have parallax angles smaller than 1 arcsec-ond—well below the approximately 1 arcminute angular resolution of thenaked eye [Section 5.3]. For increasingly distant stars, the parallax anglesquickly become too small to measure even with our highest-resolution tele-scopes. As of 2010, we have accurate parallax measurements only for starswithin a few hundred light-years—not much farther than what we call ourlocal solar neighborhood in the vast, 100,000-light-year-diameter Milky WayGalaxy. The European Gaia mission, scheduled for launch in 2012, is de-signed to measure parallax for stars up to about 10,000 light-years away.

By definition, the distance to an object with a parallax angle of 1 arc-second is 1 parsec (pc), which is equivalent to 3.26 light-years. (The wordparsec comes from combining the words parallax and arcsecond.) With a bitof geometry, we can find a simple formula for a star’s distance: If we mea-sure the parallax angle p in arcseconds, the star’s distance d in parsecs is

; we just multiply by 3.26 to convert from parsecs to light-years. Ford = 1p

We can measure the distance to a nearbystar by observing how its apparentlocation shifts as Earth orbits the Sun.

example, a star with a parallax angle arcsecond is 10 parsecs away,p = 110

or 10 � 3.26 � 32.6 light-years. You’ll often hear astronomers statedistances in parsecs, kiloparsecs (1000 parsecs), or megaparsecs (1 millionparsecs), but in this book we’ll stick to giving distances in light-years.

Suppose Star A has a parallax angle of 0.2 arcsecond andStar B has a parallax angle of 0.4 arcsecond. How does the

distance of Star A from Earth compare to that of Star B?

312 Part IV Stars

Parallax was the first reliable technique for measuring distances tostars, and it remains the only technique that tells us stellar distanceswithout any assumptions about the nature of stars. If we know a star’sdistance from parallax, we can calculate its luminosity with the inversesquare law for light. We now have parallax measurements for thou-sands of stars, which means that astronomers have been able to calcu-late the luminosities of all these stars. By discovering patterns amongthe stars with known luminosities, astronomers learned how to esti-mate luminosities for many more stars, even without first knowingtheir distances.

The Luminosity Range of Stars Now that we have discussedhow we determine stellar luminosities, it’s time to take a quick look atthe results. We usually state stellar luminosities in comparison to theSun’s luminosity, which we write as LSun for short. For example,Proxima Centauri, the nearest of the three stars in the Alpha Centaurisystem and the nearest star besides our Sun, is only about 0.0006times as luminous as the Sun, or 0.0006LSun. Betelgeuse, the brightleft-shoulder star of Orion, has a luminosity of 38,000LSun, meaningthat it is 38,000 times as luminous as the Sun. Overall, studies of theluminosities of many stars have taught us two particularly importantlessons:

• Stars come in a wide range of luminosities, with our Sun some-where in the middle. The dimmest stars have luminosities times that of the Sun (10-4LSun) while the brightest stars are about 1 million times as luminous as the Sun (106LSun).

• Dim stars are far more common than bright stars. For example,even though our Sun is roughly in the middle of the overall rangeof stellar luminosities, it is brighter than the vast majority of starsin our galaxy.

The Magnitude System If you study astronomy further, you’ll findthat many amateur and professional astronomers describe the apparentbrightnesses and luminosities of stars in an alternative way: Instead ofapparent brightness they quote apparent magnitude, and instead ofluminosity they quote absolute magnitude. Although comparisonsbetween stars are much easier when we think in terms of luminosity, themagnitude system is used often enough that it’s worth understandinghow it works.

The magnitude system was originally devised by the Greek astrono-mer Hipparchus (c. 190–120 B.C.). He gave the brightest stars the desig-nation “first magnitude,” the next brightest “second magnitude,” andso on. The faintest visible stars were magnitude 6. Today we call thesedescriptions apparent magnitudes because they compare how bright dif-ferent stars appear in the sky. Notice that the magnitude scale runs“backward”: A larger apparent magnitude means a dimmer apparentbrightness. For example, a star of magnitude 4 is dimmer than a star ofmagnitude 1.

In modern times, the magnitude system has been extended andmore precisely defined: Each difference of five magnitudes is defined torepresent a factor of exactly 100 in brightness. For example, a magnitude1 star is 100 times as bright as a magnitude 6 star, and a magnitude 3 staris 100 times as bright as a magnitude 8 star. As a result of this precisedefinition, stars can have fractional apparent magnitudes and a fewbright stars have apparent magnitudes less than 1—which means brighter

110,000

commonMisconceptions

Photos of Stars

Photographs of stars, star clusters, and galaxies convey a great deal ofinformation, but they also contain a few artifacts that are not real. Forexample, different stars seem to have different sizes in photographssuch as that in Figure 11.4, but stars are so far away that they shouldall appear as mere points of light. The sizes are an artifact of how ourinstruments record light. Bright stars tend to be overexposed in pho-tographs, making them appear larger than dimmer stars. Overexposurealso explains why the centers of globular clusters and galaxies usuallylook like big blobs in photographs: The central regions of these objectscontain many more stars than the outskirts, and the combined light ofso many stars tends to get overexposed, making a big blotch of light.

Spikes around bright stars in photographs, often making the patternof a cross with a star at the center, are another such artifact. You cansee these spikes around many of the brightest stars in Figure 11.4.These spikes are not real but rather are created by the interaction ofstarlight with the supports holding the secondary mirror in the telescope[Section 5.3]. The spikes generally occur only with point sources oflight like stars, and not with larger objects like galaxies. When you lookat a photograph showing many galaxies (for example, Figure 15.1), youcan tell which objects are stars by looking for the spikes.


than magnitude 1. For example, the brightest star in the night sky, Sirius,has an apparent magnitude of

The modern magnitude system also defines a star’s absolute magnitudeas the apparent magnitude it would have if it were at a distance of 10parsecs (32.6 light-years) from Earth. For example, the Sun’s absolutemagnitude is about 4.8, meaning that the Sun would have an apparentmagnitude of 4.8 if it were 10 parsecs away from us—bright enough to bevisible but not conspicuous on a dark night.

� How do we measure stellar temperatures?

A second fundamental property of a star is its surface temperature. Youmight wonder why we emphasize surface temperature rather than interiortemperature. The answer is that only surface temperature is directly mea-surable; interior temperatures are inferred from mathematical models ofstellar interiors [Section 10.2]. Whenever you hear astronomers speak ofthe “temperature” of a star, you can be pretty sure they mean surfacetemperature unless they state otherwise.

Measuring a star’s surface temperature is somewhat easier thanmeasuring its luminosity, because the star’s distance doesn’t affect themeasurement. Instead, we determine surface temperature directly fromeither the star’s color or its spectrum.

Color and Temperature Take a careful look at Figure 11.4. Noticethat stars come in almost every color of the rainbow. Simply looking atthe colors tells us something about the surface temperatures of the stars.For example, a red star is cooler than a blue star.

Stars come in different colors because they emit thermal radiation[Section 5.2]. Recall that a thermal radiation spectrum depends only onthe (surface) temperature of the object that emits it (see Figure 5.11). Forexample, the Sun’s 5800 K surface temperature causes it to emit moststrongly in the middle of the visible portion of the spectrum, which is whythe Sun looks yellow or white in color. A cooler star, such as Betelgeuse(surface temperature 3400 K), looks red because it emits much more redlight than blue light. A hotter star, such as Sirius (surface temperature9400 K), emits a little more blue light than red light and therefore has aslightly blue color to it.

Astronomers can measure surface temperature fairly preciselyby comparing a star’s apparent brightness in two different colors oflight. For example, by comparing the amount of blue light and redlight coming from Sirius, astronomers can measure how much moreblue light it emits than red light. Because thermal radiation spectrahave a very distinctive shape (again, see Figure 5.11), this differencein blue and red light output allows astronomers to calculate a surfacetemperature.

Spectral Type and Temperature A star’s spectral lines provide asecond way to measure its surface temperature. Moreover, becauseinterstellar dust can affect the apparent colors of stars, temperaturesdetermined from spectral lines are generally more accurate than temper-atures determined from colors alone. Stars displaying spectral lines ofhighly ionized elements must be fairly hot, because it takes a high tem-perature to ionize atoms. Stars displaying spectral lines of molecules mustbe relatively cool, because molecules break apart into individual atomsunless they are at relatively cool temperatures. The types of spectral lines

-1.46.

Figure 11.4

This Hubble Space Telescope photo shows a wide variety ofstars that differ in color and brightness. Most of the stars in thisphoto are at roughly the same distance, about 2000 light-years,from the center of our galaxy. Clouds of gas and dust obscureour view of visible light from most of our galaxy’s centralregions, but a gap in the clouds allows us to see the starsin this photo.

VIS

Each spectral type is subdividedinto numbered subcategories (e.g.,B0, B1, . . . , B9). The larger thenumber, the cooler the star. For ex-ample, the Sun is designated spec-tral type G2, which means it is

slightly hotter than a G3 star but cooler than a G1 star.The range of surface temperatures for stars is much narrower than the

range of luminosities. The coolest stars, of spectral type M, have surfacetemperatures as low as 3000 K. The hottest stars, of spectral type O, have

314 Part IV Stars

present in a star’s spectrum therefore provide a direct measure of thestar’s surface temperature.

Astronomers classify stars according to surface temperature byassigning a spectral type determined from the spectral lines presentin a star’s spectrum. The hottest stars, with the bluest colors, are calledspectral type O, followed in order of declining surface temperature byspectral types B, A, F, G, K, and M. The traditional mnemonic for re-membering this sequence, OBAFGKM, is “Oh Be A Fine Girl/Guy,Kiss Me!” Table 11.1 summarizes the characteristics of each spectraltype. (The sequence of spectral types has recently been extendedbeyond type M to include spectral types L and T, representing starlikeobjects—usually brown dwarfs [Section 12.1]—even cooler than starsof spectral type M.)

Spectra of stars show that their surfacetemperatures range from more than40,000 K to less than 3000 K, corre-sponding to the sequence of spectraltypes OBAFGKM.

Table 11.1 The Spectral Sequence

SpectralType Example(s)

Temperature Range

Key Absorption Line Features

Brightest Wavelength (color)

Typical Spectrum

O Stars of Orion’s Belt

>30,000 K Lines of ionized helium, weak hydrogen lines

>97 nm (ultraviolet)*

B Rigel 30,000 K–10,000 K

Lines of neutral helium, moderate hydrogen lines

97–290 nm (ultraviolet)*

A Sirius 10,000 K– 7500 K

Very strong hydrogen lines

290–390 nm (violet)*

F Polaris 7500 K– 6000 K

Moderate hydrogen lines, moderate lines of ionized calcium

390–480 nm (blue)*

G Sun, Alpha Centauri A

6000 K– 5000 K

Weak hydrogen lines, strong lines of ionized calcium

480–580 nm (yellow)

K Arcturus 5000 K– 3500 K

Lines of neutral and singly ionized metals, some molecules

580–830 nm (red)

M Betelgeuse, Proxima Centauri

<3500 K Strong molecular lines

> 830 nm (infrared)

*All stars above 6000 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

ionizedcalcium

titaniumoxide

titaniumoxide

M


Invent your own mnemonic for the OBAFGKM sequence.To help get you thinking, here are two examples: (1) Only

Bungling Astronomers Forget Generally Known Mnemonics and (2) Only BusinessActs For Good, Karl Marx.

History of the Spectral Sequence You may wonder why the spectraltypes follow the peculiar order of OBAFGKM. The answer lies in thehistory of stellar spectroscopy.

Our current system of stellar classification began at Harvard CollegeObservatory. The observatory director, Edward Pickering (1846–1919),had numerous assistants, whom he called “computers.” Most of Pickering’scomputers were women who had studied physics or astronomy atwomen’s colleges such as Wellesley and Radcliffe. Pickering’s interest instudying and classifying stellar spectra provided plenty of work and oppor-tunity for his computers, and many of the Harvard Observatory womenended up among the most prominent astronomers of the late 1800s andearly 1900s.

One of the first computers was Williamina Fleming (1857–1911),who classified stellar spectra according to the strength of their hydrogenlines: type A for the strongest hydrogen lines, type B for slightly weakerhydrogen lines, and so on, to type O, for stars with the weakest hydrogenlines. Pickering published Fleming’s classifications of more than 10,000stars in 1890.

As more stellar spectra were obtained and the spectra were studiedin greater detail, it became clear that a classification scheme basedsolely on hydrogen lines was inadequate. Ultimately, the task of findinga better classification scheme fell to Annie Jump Cannon (1863–1941),who joined Pickering’s team in 1896 (Figure 11.5). Building on thework of Fleming and another of Pickering’s computers, Antonia Maury(1866–1952), Cannon soon realized that the spectral classes fell into anatural order—but not the alphabetical order determined by hydrogenlines alone. Moreover, she found that some of the original classes over-lapped others and could be eliminated. Cannon discovered that thenatural sequence consisted of just a few of Pickering’s original classes inthe order OBAFGKM, and she also added the subdivisions by number.

The astronomical community adopted Cannon’s system of stellarclassification in 1910. However, no one at that time knew why spectrafollowed the OBAFGKM sequence. Many astronomers guessed, incor-rectly, that the different sets of spectral lines indicated different composi-tions for the stars. The correct answer—that all stars are made primarilyof hydrogen and helium and that a star’s surface temperature determinesthe strength of its spectral lines—was discovered at Harvard Observatoryin 1925 by Cecilia Payne-Gaposchkin (1900–1979). Relying on insightsfrom what was then the newly developing science of quantum mechan-ics, Payne-Gaposchkin showed that the differences in spectral lines fromstar to star merely reflected changes in the ionization level of the emit-ting atoms. For example, O stars have weak hydrogen lines because, attheir high surface temperatures, nearly all their hydrogen is ionized.Without an electron to “jump” between energy levels, ionized hydrogencan neither emit nor absorb its usual specific wavelengths of light. At theother end of the spectral sequence, M stars are cool enough for some

surface temperatures that can exceed 40,000 K. However, cool, red starsturn out to be much more common than hot, blue stars.

Figure 11.5

Edward Pickering and his “computers” pose at HarvardCollege Observatory in 1913. Annie Jump Cannon is fifthfrom the left in the back row.

316 Part IV Stars

particularly stable molecules to form, explaining their strong molecularabsorption lines.

� How do we measure stellar masses?

Mass is generally more difficult to measure than surface temperatureor luminosity. The most dependable method for “weighing” a starrelies on Newton’s version of Kepler’s third law [Section 4.4] Recallthat this law can be applied only when we can observe one objectorbiting another, and it requires that we measure both the orbitalperiod and the average orbital distance of the orbiting object. Forstars, these requirements generally mean that we can apply the law tomeasure masses only in binary star systems—systems in which twostars continually orbit one another. Before we consider how we deter-mine the orbital periods and distances needed to use Newton’s versionof Kepler’s third law, let’s look briefly at the different types of binarystar systems that we can observe.

Types of Binary Star Systems Surveys show that about half of allstars orbit a companion star of some kind and thus are members of binarystar systems. These star systems fall into three classes:

• A visual binary is a pair of stars that we can see distinctly (with atelescope) as the stars orbit each other. Sometimes we observe a starslowly shifting position in the sky as if it were a member of a visualbinary, but its companion is too dim to be seen. For example, slowshifts in the position of Sirius, the brightest star in the sky, revealedit to be a binary star long before its companion was discovered(Figure 11.6).

• An eclipsing binary is a pair of stars that orbit in the plane of our lineof sight (Figure 11.7). When neither star is eclipsed, we see thecombined light of both stars. When one star eclipses the other, theapparent brightness of the system drops because some of the light isblocked from our view. A light curve, or graph of apparent brightnessagainst time, reveals the pattern of the eclipses. The most famousexample of an eclipsing binary is Algol, the “demon star” in the con-stellation Perseus (algol is Arabic for “the ghoul”). Algol’s brightnessdrops to only a third of its usual level for a few hours about everythree days as the brighter of its two stars is eclipsed by its dimmercompanion.

• If a binary system is neither visual nor eclipsing, we may be ableto detect its binary nature by observing Doppler shifts in its spec-tral lines [Section 5.2]. Such a system is called a spectroscopic binary.If one star is orbiting another, it periodically moves toward us andaway from us in its orbit. Its spectral lines show blueshifts andredshifts as a result of this motion (Figure 11.8). Sometimes wesee two sets of lines shifting back and forth—one set from each of

A

B

1900 1910 1920 1930 1940 1950 1960 1970

Figure 11.6

In this series of images, each frame represents the relativepositions of Sirius A and Sirius B at 10-year intervals from 1900 to 1970. The back-and-forth “wobble” of Sirius A allowedastronomers to infer the existence of Sirius B even before thetwo stars could be resolved in telescopic photos. The averageorbital separation of the binary system is about 20 AU.

We see lightfrom both

stars A and B.

app

aren

t brig

htne

ss

time

AA

A A

BB

B

We see lightfrom all of B,some of A.

We see lightfrom both A and B.

We see lightonly from A(B is hidden).

Figure 11.7

The apparent brightness of an eclipsing binary system dropswhen one star eclipses the other.

Determining the average sepa-ration of the stars in a binary systemis usually much more difficult. Inrare cases we can measure the sepa-ration directly; otherwise we can

calculate the separation only if we know the actual orbital speeds of thestars from their Doppler shifts. Unfortunately, a Doppler shift tells us onlythe portion of a star’s velocity that is directed toward us or away from us(see Figure 5.15). Because orbiting stars generally do not move directlyalong our line of sight, their actual velocities can be significantly greaterthan those we measure through the Doppler effect.

The exceptions are eclipsing binary stars. Because these stars orbitin the plane of our line of sight, their Doppler shifts can tell us theirtrue orbital velocities. Eclipsing binaries are therefore particularlyimportant to the study of stellar masses. As an added bonus, eclipsingbinaries allow us to measure stellar radii directly. Because we knowhow fast the stars are moving across our line of sight as one eclipsesthe other, we can determine their radii by timing how long eacheclipse lasts.

Through careful observations of eclipsing binaries and otherbinary star systems, astronomers have established the masses of manydifferent kinds of stars. The overall range extends from as little as 0.08times the mass of the Sun (0.08MSun) to about 150 times the mass ofthe Sun (150MSun). We’ll discuss the reasons for this mass range inChapter 12.

The Hertzsprung-Russell Diagram Tutorial, Lessons 1–3

11.2 Patterns Among StarsWe have seen that stars come in a wide range of luminosities, surfacetemperatures, and masses. But are these characteristics randomly distrib-uted among stars, or can we find patterns that might tell us somethingabout stellar lives?

Before reading any further, take another look at Figure 11.4 and thinkabout how you would classify these stars. Almost all of them are at nearlythe same distance from Earth, so we can compare their true luminosities


the two stars in the system (a double-lined spectroscopic binary).Other times we see a set of shifting lines from only one starbecause its companion is too dim to be detected (a single-linedspectroscopic binary).

Some star systems combine two or more of these binary types. Forexample, telescopic observations reveal Mizar (the second star in thehandle of the Big Dipper) to be a visual binary. Spectroscopy then showsthat each of the two stars in the visual binary is itself a spectroscopicbinary (Figure 11.9).

Measuring Masses in Binary Systems Even for a binary system,we can apply Newton’s version of Kepler’s third law only if we canmeasure both the orbital period and the separation of the two stars.Measuring orbital period is fairly easy. In a visual binary, we simplyobserve how long each orbit takes. In an eclipsing binary, we measurethe time between eclipses. In a spectroscopic binary, we measure thetime it takes the spectral lines to shift back and forth.

A

B

B

to Earth

On one side of its orbit, star Bis approaching us . . . . . . so its spectrum is blueshifted.

On the other side of its orbit,star B is receding from us . . . . . . so its spectrum is redshifted.

Figure 11.8

The spectral lines of a star in a binary system are periodicallyblueshifted as it moves toward us in its orbit and redshifted asit moves away from us.

Mizar A

Mizar B

Alcor

Mizar

Mizar is a visual binary . . .

. . . and spectroscopy shows that eachof the visual “stars” is itself binary.

Figure 11.9

Mizar looks like one star to the naked eye but is actually a system of four stars. Through a telescope, Mizar appears tobe a visual binary made up of two stars, Mizar A and Mizar B,that gradually change positions, indicating that they orbit eachother every few thousand years. Moreover, each of these two“stars” is itself a spectroscopic binary, for a total of four stars.(The ring around Mizar A is an artifact of the photographicprocess, not a real feature.)

We can determine the masses of stars inbinary systems if we can measure boththeir orbital period and the separationbetween them.

Each location on the H-R diagram represents a unique combinationof spectral type and luminosity. For example, the dot representing theSun in Figure 11.10 corresponds to the Sun’s spectral type, G2, and its

luminosity, 1LSun. Because luminosityincreases upward on the diagram andsurface temperature increases leftward,stars near the upper left are hot and

luminous. Similarly, stars near the upper right are cool and luminous,stars near the lower right are cool and dim, and stars near the lower leftare hot and dim.

318 Part IV Stars

by looking at their apparent brightnesses in the photograph. If you lookclosely, you might notice a couple of important patterns:

• Most of the very brightest stars are reddish in color.

• If you ignore those relatively few bright red stars, there’s a generaltrend to the luminosities and colors among all the rest of the stars:The brighter ones are white with a little bit of blue tint, the moremodest ones are similar to our Sun in color with a yellowish whitetint, and the dimmest ones are barely visible specks of red.

Keeping in mind that colors tell us about surface temperature—blue ishotter and red is cooler—we can see how these patterns tell us aboutrelationships between surface temperature and luminosity.

Danish astronomer Ejnar Hertzsprung and American astronomerHenry Norris Russell discovered these relationships in the first decade ofthe 20th century. Building upon the work of Annie Jump Cannon andothers, Hertzsprung and Russell independently decided to make graphs of stellar properties by plotting stellar luminosities on one axis and spec-tral types on the other. These graphs revealed previously unsuspected patterns among the properties of stars and ultimately unlocked the se-crets of stellar life cycles.

� What is a Hertzsprung-Russell diagram?

Graphs of the type first made by Hertzsprung and Russell are now calledHertzsprung-Russell (H-R) diagrams. These diagrams quickly be-came one of the most important tools in astronomical research, and theyremain central to the study of stars.

Basics of the H-R Diagram Figure 11.10 on pages 320–321 showsan H-R diagram and how we construct it. As Step 1 in the figure shows,you can plot any star on an H-R diagram, as long as you know its spectraltype and luminosity.

• The horizontal axis represents stellar surface temperature, which, aswe’ve discussed, corresponds to spectral type. Temperature decreasesfrom left to right because Hertzsprung and Russell based their dia-grams on the spectral sequence OBAFGKM.

• The vertical axis represents stellar luminosity, in units of the Sun’sluminosity (LSun). Stellar luminosities span a wide range, so we keepthe graph compact by making each tick mark represent a luminosity10 times as large as the prior tick mark.

An H-R diagram plots the surfacetemperatures of stars against theirluminosities.

Explain how the colors of the stars in Figure 11.10 helpindicate stellar surface temperature. Do these colors tell

us anything about interior temperatures? Why or why not?

We use both spectral type andluminosity class to fully classify astar. For example, the completeclassification of our Sun is G2 V.

The G2 spectral type means it is yellow-white in color, and theluminosity class V means it is a main-sequence star undergoing hy-drogen fusion in its core. Betelgeuse is M2 I, making it a red


The H-R diagram also provides direct information about stellarradii, because a star’s luminosity depends on both its surface tempera-ture and its surface area or radius. If two stars have the same surfacetemperature, one can be more luminous than the other only if it islarger in size. Stellar radii therefore must increase as we go from thehigh-temperature, low-luminosity corner on the lower left of the H-Rdiagram to the low-temperature, high-luminosity corner on the upperright. Notice the diagonal lines that represent different stellar radii inFigure 11.10.

Patterns in the H-R Diagram Stars do not fall randomly throughoutan H-R diagram like Figure 11.10 but instead cluster into four major groups:

• Most stars fall somewhere along the main sequence, the prominentstreak running from the upper left to the lower right on the H-Rdiagram. Notice that our Sun is one of these main-sequence stars.

• The stars in the upper right are called supergiants because they arevery large in addition to being very bright.

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

• The stars near the lower left are small in radius and appear white incolor because of their high temperatures. We call these stars whitedwarfs.

Luminosity Classes In addition to the four major groups we’ve justlisted, stars sometimes fall into “in-between” categories. For more precisework, astronomers therefore assign each star to a luminosity class,designated with a Roman numeral from I to V. The luminosity classdescribes the region of the H-R diagram in which the star falls; so despitethe name, a star’s luminosity class is more closely related to its size thanto its luminosity. The basic luminosity classes are I for supergiants, III forgiants, and V for main-sequence stars. Luminosity classes II and IV areintermediate to the others. For example, luminosity class IV representsstars with radii larger than those of main-sequence stars but not quitelarge enough to qualify them as giants. Table 11.2 summarizes the lumi-nosity classes. White dwarfs fall outside this classification system andinstead are often assigned the luminosity class “wd.”

Complete Stellar Classification We have now described two differ-ent ways of categorizing stars:

• A star’s spectral type, designated by one of the letters OBAFGKM, tellsus its surface temperature and color. O stars are the hottest andbluest, while M stars are the coolest and reddest.

• A star’s luminosity class, designated by a Roman numeral, is basedon its luminosity but also tells us about the star’s radius. Luminosityclass I stars have the largest radii, with radii decreasing to lumino-sity class V.

The full classification of a star includesboth a spectral type (OBAFGKM) and a luminosity class.

Table 11.2 Stellar Luminosity Classes

Class Description

I Supergiants

II Bright giants

III Giants

IV Subgiants

V Main-sequence stars

cosmicCalculations 11.2

Radius of a Star

Almost all stars are too distant for us to measure their radiidirectly. So how do we know that some are small and someare supergiants? We can calculate a star’s radius from itsluminosity and surface temperature. Recall from CosmicCalculations 5.1 that the amount of thermal radiationemitted per unit area by a star of temperature T is T 4,where the constant � 5.7 � 10-8 watt/(m2 � Kelvin4).The star’s total luminosity L is equal to this power per unitarea times the star’s surface area, which is 4πr2 for a starof radius r:

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

Example: The star Betelgeuse has a surface temperatureof about 3400 K and a luminosity of 1.4 � 1031 watts,which is 38,000 times that of the Sun. What is its radius?

Solution: We use the formula given above with L � 1.4 � 1031 watts and T � 3400 K:

The radius of Betelgeuse is about 380 billion meters, whichis the same as 380 million kilometers—more than twice theEarth–Sun distance of about 150 million kilometers. That iswhy we call it a supergiant.

= 3.8 * 1011 m

=

R1.4 * 1031 watts

4p * ¢5.7 * 10-8 watt

m2 * K4 ≤ * 13400 K24r = A L

4psT 4

r = A L

4psT4

L = 4pr2 * sT4

s

s

1

10 2

102

103

104

Sun

105

106

0.1

1

10

surface temperature (Kelvin)30,000 10,000 6000 3000

10 3

10 4

10 5

lum

inos

ity (

sola

r un

its)

O B A F G K M

1 LSun

5800 K

10 2

102

103

104

Sun

105

106

0.1

10


10 3

10 4

10 5lu

min

osity

(so

lar

units

)O B A F G K M

main sequence

10 2

102

103

104

Sun

105

106

0.1

1

10


10 3

10 4

10 5

lum

inos

ity (

sola

r un

its)

O B A F G K M

main sequence

SUPERGIANTS

GIANTS

SUPERGIANTS

GIANTS

10 2

102

103

104

Sun

105

106

0.1

1

10


10 3

10 4

10 5

lum

inos

ity (

sola

r un

its)

O B A F G K M

main sequence

W H I T E D W A R F S

Hertzsprung-Russell (H-R) diagrams are very important tools in astronomy because they reveal key relationships among the properties of stars. An H-R diagram is made by plotting stars according to their surface temperatures and luminosities. This figure shows a step-by-step approach to building an H-R diagram.

1 An H-R Diagram Is a Graph: A star’s position along the horizontal axis indicates its surface temperature, which is closely related to its color and spectral type. Its position along the vertical axis indicates its luminosity.

2 Main Sequence: Our Sun falls along the main sequence, a line of stars extending from the upper left of the diagram to the lower right. Most stars are main-sequence stars, which shine by fusing hydrogen into helium in their cores.

3 Giants and Supergiants: Stars in the upper right of an H–R diagram are more luminous than main-sequence stars of the same surface temperature. They must therefore be very large in radius, which is why they are known as giants and supergiants.

4 White Dwarfs: Stars in the lower left have high surface temperatures, dim luminosities, and small radii. These stars are known as white dwarfs.

Temperature runs backward on the horizontal axis, with hot blue stars on the left and cool red stars on the right.

Each step up the luminosity axis corresponds to a luminosity ten times as great as the previous step.

The Sun’s position in the H-R diagram is determined by its luminosity and surface temperature.

Figure 11.10. Reading an H-R DiagramcosmicContext

Ceti EridaniCentauri B

Centauri A

Centauri

decreasing temperatureincreasing temperature

Lifetime109 yrs

Lifetime1010 yrs

Lifetime1011 yrs

Lifetime107 yrs

Lifetime108 yrs

Proxima Centauri

Barnard’s Star

Altair

Procyon

Sirius

Vega

Arcturus

Canopus

Pollux

Aldebaran

DX Cancri

Wolf 359Ross 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

60MSun

30MSun

10MSun

6MSun

3MSun

0.3MSun

0.1MSun

1.5MSun

1MSun

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 S10 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 2

102

103

104

105

106

0.1

10

10 3

10 4

10 5

lum

inos

ity (

sola

r un

its)

1

5 Masses on the Main Sequence: Stellar masses (purple labels) decrease from the upper left to the lower right on the main sequence.

6 Lifetimes on the Main Sequence: Stellar lifetimes (green labels) increase from the upper left to lower right on the main sequence: High-mass stars live shorter lives because their high luminosities mean they exhaust their nuclear fuel more quickly.

Stars along each of these diagonal lines all have the same radius. Note that radius increases from the lower left to the upper right of the H–R diagram.

The orderly arrangement of stellarmasses along the main sequence tellsus that mass is the most importantattribute of a hydrogen-fusing star.

This is because mass determines the balancing point at which energyreleased by hydrogen fusion in the core equals the energy lost from thestar’s surface. The great range of stellar luminosities on the H-R diagramshows that the point of energy balance is very sensitive to mass. Forexample, a main-sequence star 10 times as massive as the Sun (10MSun) isabout 10,000 times as luminous.

The relationship between mass and surface temperature is a littlemore subtle. In general, a very luminous star must be very large orhave a very high surface temperature, or some combination of both.The most massive main-sequence stars are many thousands of timesmore luminous than the Sun but only about 10 times the size of theSun in radius. Their surfaces must be significantly hotter than the Sun’ssurface to account for their high luminosities. Main-sequence starsmore massive than the Sun therefore have higher surface temperaturesthan the Sun, and those less massive than the Sun have lower surface

322 Part IV Stars

By studying Figure 11.10, determine the approximatespectral type, luminosity class, and radius of the following

stars: Bellatrix, Vega, Antares, Pollux, and Proxima Centauri.

supergiant. Proxima Centauri is M5 V—similar in color and surfacetemperature to Betelgeuse, but far dimmer because of its muchsmaller size.

O B K MA F G

Sun


lum

inos

ity (

sola

r un

its)

10–2

102

103

104

105

106

0.1

1

10

10–3

10–4

10–5

Lifetime109 yrs

Lifetime1010 yrs

Lifetime1011 yrs

Lifetime107 yrs

Lifetime108 yrs

60MSun30MSun

10MSun

6MSun

3MSun

1.5MSun

1MSun

0.3MSun

0.1MSun

Figure 11.11

The main sequence from Figure 11.10 is isolated here sothat you can more easily see how masses and lifetimes varyalong it. Notice that more massive hydrogen-fusing stars arebrighter and hotter than less massive ones, but have shorterlifetimes. (Stellar masses are given in units of solar masses:1Msun � 2 � 1030 kg.)

� What is the significance

of the main sequence?

Most of the stars we observe, including our Sun, have properties thatplace them on the main sequence of the H-R diagram. You can see inFigure 11.10 that high-luminosity main-sequence stars have hot surfacesand low-luminosity main-sequence stars have cooler surfaces. The signif-icance of this relationship between luminosity and surface temperaturebecame clear when astronomers started measuring the masses of main-sequence stars in binary star systems. These measurements showed that astar’s position along the main sequence is closely related to its mass. Wenow know that all stars along the main sequence are fusing hydrogeninto helium in their cores, just like the Sun, and the relationship betweensurface temperature and luminosity arises because the rate of hydrogenfusion depends strongly on a star’s mass.

Masses Along the Main Sequence If you look along the main se-quence in Figure 11.10, you’ll notice purple labels indicating stellar massesand green labels indicating stellar lifetimes. To make them easier to see,Figure 11.11 repeats the same data but shows only the main sequencerather than the entire H-R diagram.

Let’s focus first on mass: Notice that stellar masses decrease downwardalong the main sequence. At the upper end of the main sequence, the hot,luminous O stars can have masses as high as 300 times that of the Sun(300MSun). On the lower end, cool, dim M stars may have as little as 0.08times the mass of the Sun (0.08MSun). Many more stars fall on the lowerend of the main sequence than on the upper end, which tells us that low-mass stars are much more common than high-mass stars.

A main-sequence star’s mass deter-mines both its luminosity and itssurface temperature.


temperatures. That is why the main sequence slices diagonally from theupper left to the lower right on the H-R diagram.

The fact that mass, surface temperature, and luminosity are all relatedmeans that we can estimate a main-sequence star’s mass just by knowingits spectral type. For example, any hydrogen-fusing, main-sequence starthat has the same spectral type as the Sun (G2) must have about the samemass and luminosity as the Sun. Similarly, any main-sequence star ofspectral type B1 must have about the same mass and luminosity as Spica(see Figure 11.10). Note that only main-sequence stars follow this simplerelationship between mass, temperature, and luminosity; it does not applyto giants or supergiants.

Lifetimes Along the Main Sequence A star is born with a limitedsupply of core hydrogen and therefore can remain as a hydrogen-fusing,main-sequence star for only a limited time—the star’s main-sequencelifetime. Because stars spend the vast majority of their lives as main-sequence stars, we sometimes refer to the main-sequence lifetime assimply the “lifetime.” Like masses, stellar lifetimes vary in an orderly wayas we move up the main sequence: Massive stars near the upper end ofthe main sequence have shorter lives than less massive stars near the lowerend (see Figure 11.11).

Why do more massive stars have shorter lives? A star’s lifetimedepends on both its mass and its luminosity. Its mass determines howmuch hydrogen fuel the star initially contains in its core. Its luminositydetermines how rapidly the star uses up its fuel. Massive stars start theirlives with a larger supply of hydrogen, but they fuse this hydrogeninto helium so rapidly that they end up with shorter lives. For example, a

10-solar-mass star (10MSun) is bornwith 10 times as much hydrogen asthe Sun. However, its luminosity of10,000LSun means that it uses up this

hydrogen at a rate 10,000 times as fast as the rate in the Sun. Because a10-solar-mass star has only 10 times as much hydrogen and consumes it10,000 times faster, its lifetime is only as long as the Sun’s lifetime.Since the Sun’s core hydrogen-fusion lifetime is about 10 billion years, a10-solar-mass star must have a lifetime of only about 10 million years.(Its actual lifetime is a little longer than this, because it can use more of itscore hydrogen for fusion than the Sun can.)

11000

More massive stars live much shorterlives because they fuse hydrogen at amuch greater rate.

On the other end of the scale, a 0.3-solar-mass main-sequence staremits a luminosity just 0.01 times that of the Sun and consequently livesroughly as long as the Sun, or some 300 billion years. Ina universe that is now about 14 billion years old, even the most ancientof these small, dim, red stars of spectral type M still survive and willcontinue to shine faintly for hundreds of billions of years to come.

Mass: A Star’s Most Fundamental Property Astronomers beganclassifying stars by their spectral type and luminosity class before theyunderstood why stars vary in these properties. As we have seen, the pat-terns they discovered revealed that the most fundamental property ofany star is its mass (Figure 11.12). A star’s mass determines both its surfacetemperature and its luminosity throughout the main-sequence portionof its life, and these properties in turn explain why higher-mass stars haveshorter lifetimes.

0.30.01 = 30 times

M5.5 VProximaCentauri 0.12MSun

G2 V

Sun 1MSun

Lifetime 1012 yrs

A1 V

Sirius 2MSun

Lifetime 109 yrs

B1 V

Spica 11MSun

Lifetime 107 yrs

Lifetime 1010 yrs

Figure 11.12

Four main-sequence stars shown to scale. The mass of a main-sequence star determines its fundamental properties of lumi-nosity, surface temperature, radius, and lifetime. More massivemain-sequence stars are hotter and brighter than less massiveones, but have shorter lifetimes.

Which star shown in Figure 11.10 has the longest lifetime?Explain.

As we’ll discuss in Chapter 12,we now know that giants andsupergiants are stars nearing the

ends of their lives. They have already exhausted the supply of hydro-gen fuel in their central cores and are in essence facing an energy crisisas they try to stave off the inevitable crushing force of gravity. Thiscrisis causes these stars to release fusion energy at a furious rate, whichexplains their high luminosities, while the need to radiate away thishuge amount of energy causes them to expand to enormous size(Figure 11.13). For example, Arcturus and Aldebaran (the eye of thebull in the constellation Taurus) are giant stars more than 10 times aslarge in radius as our Sun. Betelgeuse, the left shoulder in theconstellation Orion, is an enormous supergiant with a radius roughly500 times that of the Sun, equivalent to more than twice theEarth–Sun distance.

324 Part IV Stars

� What are giants, supergiants,

and white dwarfs?

Stars that are fusing hydrogen into helium in their cores all fall on themain sequence, but what about the other classes of stars on the H-Rdiagram? These other classes all represent stars that have exhaustedthe supply of hydrogen in their central cores, so that they can nolonger generate energy in the same way as our Sun.

Giants and Supergiants The bright red stars you observed inFigure 11.4 are giants and supergiants whose properties place them tothe upper right of the main sequence in an H-R diagram. The fact thatthese stars are cooler but much more luminous than the Sun tells usthat they must be much larger in radius than the Sun. Remember that astar’s surface temperature determines the amount of light it emits perunit surface area [Section 5.2]: Hotter stars emit much more light perunit surface area than cooler stars. For example, a blue star would emitfar more total light than a red star of the same size. A star that is redand cool can be bright only if it has a very large surface area, whichmeans it must be enormous in size.

Giants and supergiants are stars that arenearing the ends of their lives.

Aldebarangiant star

K5 III, 4500 K,350LSun,

30 solar radii

Sunmain-sequence star

G2 V, 5800 K,1LSun,

1 solar radius

Relative Sizes of Stars from Supergiants to White Dwarfs

Betelgeusesupergiant star

M2 I, 3400 K,38,000LSun,

500 solar radii

Procyon Bwhite dwarf

0.01 solar radius

Earth(for comparison)

or

bit of Venus orbit of M

ercury

x10x10

x5

orb

it of Mercury

Figure 11.13

The relative sizes of stars. A supergiant like Betelgeuse wouldfill the inner solar system. A giant like Aldebaran would fill theinner third of Mercury’s orbit. The Sun is a hundred timeslarger in radius than a white dwarf, which is roughly the samesize as Earth.

White dwarfs are hot becausethey are essentially exposed stellarcores, but they are dim becausethey lack an energy source and

radiate only their leftover heat into space. A typical white dwarf is nolarger in size than Earth, although it may have a mass as great as that ofour Sun. Clearly, white dwarfs must be made of matter compressed to anextremely high density, unlike anything found on Earth. We’ll discussthe nature of white dwarfs and other stellar corpses in Chapter 13.

Stellar Evolution Tutorial, Lessons 1, 4

11.3 Star ClustersAll stars are born from giant clouds of gas. Because a single interstellarcloud can contain enough material to form many stars, stars usually formin groups. In our snapshot of the heavens, many stars still congregate inthe groups in which they formed.

These groups are known as star clusters, and they are extremely usefulto astronomers for two key reasons:

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

2. All the stars in a cluster formed at about the same time (within a fewmillion years of one another).

Astronomers can therefore use star clusters to compare the proper-ties of stars that all have similar ages, and we shall see that these featuresof star clusters also enable us to use them as cosmic clocks.

� What are the two types of star clusters?

Star clusters come in two basic types: modest-size open clusters anddensely packed globular clusters. The two types differ not only inhow densely they are packed with stars, but also in their locationsand ages.

Recall that most of the stars, gas, and dust in the Milky Way Galaxy,including our Sun, lie in the relatively flat galactic disk; the region aboveand below the disk is called the halo of the galaxy (see Figure 1.14).Open clusters are always found in the disk of the galaxy, and their starstend to be quite young. They can contain up to several thousand starsand typically are about 30 light-years across. The most famous opencluster, the Pleiades (Figure 11.14), is often called the Seven Sisters,although only six of the cluster’s several thousand stars are easily visible


Because giants and supergiants are so bright, we can see themeven if they are not especially close to us. Many of the brightest starsin our sky are giants or supergiants, often identifiable by their reddishcolors. Overall, however, giants and supergiants are considerably rarerthan main sequence stars. In our snapshot of the heavens, most starsare fusing hydrogen into helium in their cores and relatively few are ina later stage of life.

White Dwarfs Giants and supergiants eventually run out of fuelentirely. A giant with a mass similar to that of our Sun ultimatelyejects its outer layers, leaving behind a “dead” core in which allnuclear fusion has ceased. White dwarfs are these remaining embersof former giants.

White dwarf stars are the cooling embersof stars that have exhausted their fuel fornuclear fusion.

326 Part IV Stars

to the naked eye. Other cultures have other names for this beautifulgroup of stars. In Japanese, it is called Subaru, which is why the logo forSubaru automobiles is a diagram of the Pleiades.

In contrast, most globular clusters are found in the halo, and theirstars are among the oldest in the universe. A globular cluster can containmore than a million stars concentrated in a ball typically 60 to 150 light-years across. Its central region can have 10,000 stars packed into a spacejust a few light-years across (Figure 11.15). The view from a planet in aglobular cluster would be marvelous, with thousands of stars lying closerto that planet than Alpha Centauri is to the Sun.

� How do we measure the age

of a star cluster?

We can use clusters as clocks, because we can determine their ages byplotting their stars in an H-R diagram. To understand how the processworks, look at Figure 11.16, which shows an H-R diagram for the Plei-ades. Most of the stars in the Pleiades fall along the main sequence, withone important exception: The Pleiades’ stars trail away to the right ofthe main sequence at the upper end. That is, the hot, short-lived stars ofspectral type O are missing from the main sequence. Apparently, thePleiades cluster is old enough for its main-sequence O stars to have fin-ished with core hydrogen fusion. At the same time, the cluster is youngenough that some of its stars of spectral type B still survive as hydrogen-fusing stars on the main sequence.

The precise point on the H-R diagram at which the Pleiades’ mainsequence diverges from the standard main sequence is called its main-sequence turnoff point. In this cluster, it occurs around spectral typeB6. 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 the Pleiades that was

Figure 11.15

The globular cluster M80 is more than 12 billion years old. Theprominent reddish stars in this Hubble Space Telescope photoare red giant stars nearing the ends of their lives. The centralregion pictured here is about 15 light-years across.

Lifetimes of stars at this point on the main sequence are about 100 million years.

O B K MA F G

10 2 Solar Radii

10 3 Solar Radii

0.1 Solar Radius

1 Solar Radius

10 Solar Radii

surface temperature (Kelvin)

30,000 10,000 6000 3000

lum

inos

ity (

sola

r un

its)

10–2

102

103

104

105

106

0.1

1

10

10–3

10–4

10–5

Figure 11.16

An H-R diagram for the Pleiades. Triangles represent individualstars. The Pleiades cluster is missing its upper main-sequencestars, indicating that these stars have already finished fusinghydrogen in their cores. The main-sequence turnoff point atabout spectral type B6 tells us that the Pleiades are about100 million years old.

VIS

Figure 11.14

A photo of the Pleiades, a nearby open cluster of stars in theconstellation Taurus. The most prominent stars in this opencluster are of spectral type B, indicating that the Pleiades areno more than 100 million years old—relatively young for a starcluster. The region shown is about 11 light-years across.

VIS

Comparing the H-R diagrams ofother open clusters makes this ef-fect more apparent (Figure 11.17).In each case, the age of the cluster isequal to the lifetime of stars at its main-

sequence turnoff point. Stars in a particular cluster that once resided abovethe turnoff point on the main sequence have already exhausted their coresupply of hydrogen, while stars below the turnoff point remain on themain sequence.


The age of a star cluster approximatelyequals the hydrogen core-fusion lifetimeof the most massive main-sequence starsremaining within it.

O B K MA F G

0.1 Solar Radius

1 Solar Radius

10 Solar Radii

NGC 188 – 7 billion years

Hyades – 650 million years

Pleiades – 100 million years

h + χ Persei – 14 million years


30,000 10,000 6000 3000

lum

inos

ity (

sola

r un

its)

10–2

102

103

104

105

106

0.1

1

10

10–3

10–4

10–5

10 2 Solar Radii

10 3 Solar Radii

Lifetime107 yrs

Lifetime108 yrs

Lifetime109 yrs

Lifetime1010 yrs

Lifetime1011 yrs

Figure 11.17

This H-R diagram shows stars from four clusters. Their differ-ing main-sequence turnoff points indicate very different ages.

O B K MA F G

0.1 Solar Radius

1 Solar Radius

10 Solar Radii

10 –2 Solar Radius

Sun


30,000 10,000 6000 3000

lum

inos

ity (

sola

r un

its)

10–2

102

103

104

105

106

0.1

1

10

10–3

10–4

10–5

10 2 Solar Radii

10 3 Solar Radii

Lifetime1010 yrs

Figure 11.18

This H-R diagram shows stars from the globular cluster M4.The main-sequence turnoff point is in the vicinity of stars likeour Sun, indicating an age for this cluster of around 10 billionyears. A more technical analysis of this cluster places its age at around 13 billion years.

The technique of identifying main-sequence turnoff points is our mostpowerful tool for evaluating the ages of star clusters. We’ve learned thatmost open clusters are relatively young, with very few older than about5 billion years. In contrast, the stars at the main-sequence turnoff points inglobular clusters are usually less massive than our Sun (Figure 11.18).Because stars like our Sun have a lifetime of about 10 billion years andthese stars have already died in globular clusters, we conclude that globu-lar cluster stars are older than 10 billion years.

More precise studies of the turnoff points in globular clusters, cou-pled with theoretical calculations of stellar lifetimes, place the ages ofthese clusters at about 13 billion years, making them the oldest knownobjects in the galaxy. In fact, globular clusters place a constraint on thepossible age of the universe: If stars in globular clusters are 13 billionyears old, then the universe must be at least this old. Recent observationssuggesting that the universe is about 14 billion years old therefore fit wellwith the ages of these stars and tell us that the first stars began to form bythe time the universe was a billion years old.

Suppose a star cluster is precisely 10 billion years old. Wherewould you expect to find its main-sequence turnoff point?

Would you expect this cluster to have any main-sequence stars of spectral type A?Would you expect it to have main-sequence stars of spectral type K? Explain.(Hint: What is the lifetime of our Sun?)

We have classified the diverse families of stars visible in the night sky.Much of what we know about stars, galaxies, and the universe itself isbased on the fundamental properties of stars introduced in this chapter.Make sure you understand the following “big picture” ideas:

• All stars are made primarily of hydrogen and helium, at least at thetime they form. The differences between stars are primarily due todifferences in mass and stage of life.

• Stars spend most of their lives as main-sequence stars that fusehydrogen into helium in their cores. The most massive stars, whichare also the hottest and most luminous, live only a few million

the big picturePutting Chapter 11

into Perspective

born with a main-sequence spectral type hotter than B6 had a lifetimeshorter than 100 million years and hence is no longer found on themain sequence. Stars with lifetimes longer than 100 million years arestill fusing hydrogen and hence remain as main-sequence stars. Over thenext few billion years, the B stars in the Pleiades will die out, followedby the A stars and the F stars. If we could make an H-R diagram for thePleiades every few million years, we would find that the main sequencegradually becomes shorter with time.

328 Part IV Stars

years. The least massive stars, which are coolest and dimmest, willsurvive until the universe is many times its present age.

• The key to recognizing these patterns among stars was the H-R dia-gram, which shows stellar surface temperatures on the horizontalaxis and luminosities on the vertical axis. The H-R diagram is one ofthe most important tools of modern astronomy.

• Much of what we know about the universe comes from studies ofstar clusters. For example, we can measure a star cluster’s age byplotting its stars in an H-R diagram and determining the corehydrogen-fusion lifetime of the brightest and most massive starsstill on the main sequence.

11.1 Properties of Stars

� How do we measure stellar luminosities?

The apparent brightness of a starin our sky depends on both itsluminosity—the total amount oflight it emits into space—and its dis-tance from Earth, as expressed by theinverse square law for light. We cantherefore calculate a star’s luminosityfrom its apparent brightness and its dis-tance, which we can measure throughstellar parallax.

� How do we measure stellar temperatures?

We measure a star’s surface tempera-ture from its color or spectrum, and weclassify stars according to the sequenceof spectral types OBAFGKM, whichruns from hottest to coolest. Cool, redstars of spectral type M are much more

common than hot, blue stars of spectral type O.

� How do we measure stellar masses?

We can measure the masses of stars in binary star systemsusing Newton’s version of Kepler’s third law if we know theorbital period and separation of the two stars.

11.2 Patterns Among Stars

� What is a Hertzsprung-Russell diagram?

An H-R diagram plots stars accord-ing to their surface temperatures (orspectral types) and luminosities. Starsspend most of their lives fusing hydro-gen into helium in their cores, and starsin this stage of life are found in the H-Rdiagram in a narrow band known asthe main sequence. Giants andsupergiants are to the upper right of

the main sequence and white dwarfs are to the lower left.

� What is the significance of the main sequence?

Stars on the main sequence are all fusing hydrogen intohelium in their cores, and a star’s position along the mainsequence depends on its mass. High-mass stars are at theupper left end of the main sequence, and the masses of starsbecome smaller as we move toward the lower right end.Lifetimes vary in the opposite way, because high-mass starslive shorter lives.

� What are giants, supergiants, and white dwarfs?

Giants and supergiants are stars that have exhausted their cen-tral core supplies of hydrogen for fusion and are undergoingother forms of fusion at a prodigious rate as they near the endsof their lives. White dwarfs are the exposed cores of stars thathave already died, meaning they have no further means ofgenerating energy through fusion.

11.3 Star Clusters

� What are the two types of star clusters?

Open clusters contain up to severalthousand stars and are found in thedisk of the galaxy. Globular clusterscontain hundreds of thousands of stars,

all closely packed together. They are found mainly in the haloof the galaxy.

� How do we measure the age of a star cluster?

Because all of a cluster’s stars wereborn at the same time, we can mea-sure a cluster’s age by finding themain-sequence turnoff point of itsstars on an H-R diagram. The cluster’sage is equal to the core hydrogen-fusion lifetime of the hottest, mostluminous stars that remain on themain sequence. Open clusters are

much younger than globular clusters, which can be as oldas about 13 billion years.

summary of key concepts

1 AU 2 AU 3 AU

O

B

A

F

G

K

M

surface temperature (Kelvin) decreasing temperatureincreasing temperature

30,000 10,000 6000 3000

W H I T E

G I A N T S

S U P E R G I A N T S

D W A R F S

lum

inos

ity (

sola

r un

its)

10–2

102

103

104

105

106

0.1

1

10

10–3

10–4

10–5


30,000 10,000 6000 3000

Lifetime108 yrs

Lifetime107 yrs

Lifetime109 yrs

Lifetime1010 yrs

Lifetime1011 yrs

lum

inos

ity (

sola

r un

its)

10–2

102

103

104

105

106

0.1

1

10

10–3

10–4

10–5


Use the following questions to check your understanding of some of the many types of visual information usedin astronomy. Answers are provided in Appendix J. For additional practice, try the Chapter 11 Visual Quiz atwww.masteringastronomy.com.

The figure above, similar to Figure 11.13, uses zoom-ins to compare thesizes of giant and supergiant stars to the sizes of Earth and the Sun.

The H-R diagram above is identical to Figure 11.11. Answer the followingquestions based on the information given in the figure.

4. What are the approximate luminosity and lifetime of a starwhose mass is 10 times that of the Sun?

5. What are the approximate luminosity and lifetime of a starwhose mass is 3 times that of the Sun?

6. What are the approximate luminosity and lifetime of a starwhose mass is twice that of the Sun?

visual skills check

orbit of Mercury

Aldebaran

Sun

Betelgeuse

Procyon B

orb i

t of Venu

s o

rbit of M

ercury

x5

x10x10

Earth

10�2

102

103

104

105

106

0.1

1

10

10�3

10�4

10�5

lum

inos

ity (

sola

r un

its)

O B K MA F G

Sun


Lifetime108 yrs

Lifetime107 yrs

Lifetime109 yrs

Lifetime1010 yrs

Lifetime1011 yrs

60MSun30MSun

10MSun

3MSun

1.5MSun

1MSun

0.3MSun

0.1MSun

6MSun

1. Suppose we wanted to represent all of these objects on the 1-to-10-billion scale from Chapter 1, on which the Sun is aboutthe size of a grapefruit. Approximately how large in diameterwould the star Aldebaran be on this scale?a. 40 centimeters (the size of a typical beach ball)b. 4 meters (roughly the size of a dorm room)c. 15 meters (roughly the size of a typical house)d. 70 meters (slightly smaller than a football field)

2. Approximately how large in diameter would the star Betelgeusebe on this same scale?a. 40 centimeters (the size of a typical beach ball)b. 4 meters (roughly the size of a dorm room)c. 70 meters (slightly smaller than a football field)d. 3 kilometers (the size of a small town)

3. Approximately how large in diameter would the star Procyon Bbe on this same scale?a. 10 centimeters (the size of a large grapefruit)b. 1 centimeter (the size of a grape)c. 1 millimeter (the size of a grape seed)d. 0.1 millimeter (roughly the width of a human hair)

exercises and problems

Review Questions

1. Briefly explain how we can learn about the lives of stars eventhough their lives are far longer than human lives.

2. In what ways are all stars similar? In what ways can stars differ?3. How is a star’s apparent brightness related to its luminosity? Explain

by describing the inverse square law for light.4. Briefly explain how we use stellar parallax to determine a star’s

distance. Once we know a star’s distance, how can we determineits luminosity?

5. What do we mean by a star’s spectral type? How is a star’s spectral type related to its surface temperature and color? Whichtypes of stars are hottest and coolest in the spectral sequenceOBAFGKM?

For instructor-assigned homework go to www.masteringastronomy.com.

6. What are the three basic types of binary star systems? Why areeclipsing binaries so important for measuring masses of stars?

7. What is the defining characteristic of a main-sequence star? How issurface temperature related to luminosity for main-sequence stars?

8. How do we know that giants and supergiants are large in radius?How big are they? How do they differ from main-sequence stars?

9. What are white dwarfs?10. What do we mean by a star’s luminosity class? What does the

luminosity class tell us about the star? Briefly explain how weclassify stars by spectral type and luminosity class.

11. Briefly explain why massive main-sequence stars are moreluminous and have hotter surfaces than less massive ones.

12. Which stars have longer lifetimes: massive stars or less massivestars? Explain why.

www.masteringastronomy.com

www.masteringastronomy.com

330 Part IV Stars

13. Draw a sketch of a basic Hertzsprung-Russell (H-R) diagram.Label the main sequence, giants, supergiants, and white dwarfs.Where on this diagram do we find stars that are cool and dim?Cool and luminous? Hot and dim? Hot and luminous?

14. Describe in general terms how open clusters and globular clustersdiffer in their numbers of stars, ages, and locations in a galaxy.

15. Explain why H-R diagrams look different for star clusters ofdifferent ages. How does the location of the main-sequenceturnoff point tell us the age of the star cluster?

Test Your Understanding

Does It Make Sense?

Decide whether the statement makes sense (or is clearly true) or doesnot make sense (or is clearly false). Explain clearly; not all of these havedefinitive answers, so your explanation is more important than yourchosen answer.

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

17. Two stars that have the same apparent brightness in the skymust also have the same luminosity.

18. Sirius looks brighter than Alpha Centauri, but we know thatAlpha Centauri is closer because its apparent position in the skyshifts by a larger amount as Earth orbits the Sun.

19. Stars that look red-hot have hotter surfaces than stars that look blue.20. Some of the stars on the main sequence of the H-R diagram are

not converting hydrogen into helium.21. The smallest, hottest stars are plotted in the lower left portion of

the H-R diagram.22. Stars that begin their lives with the most mass live longer than

less massive stars because they have so much more hydrogen fuel.23. Star clusters with lots of bright, blue stars of spectral type O and B

are generally younger than clusters that don’t have any such stars.24. All giants, supergiants, and white dwarfs were once main-

sequence stars.25. Most of the stars in the sky are more massive than the Sun.

Quick Quiz

Choose the best answer to each of the following. Explain your reasoningwith one or more complete sentences.

26. If the star Alpha Centauri were moved to a distance 10 timesfarther from Earth than it is now, its parallax angle would (a) getlarger. (b) get smaller. (c) stay the same.

27. What do we need to measure in order to determine a star’s lumi-nosity? (a) apparent brightness and mass (b) apparent brightnessand temperature (c) apparent brightness and distance

28. What two pieces of information would you need in order to mea-sure the masses of stars in an eclipsing binary system? (a) the timebetween eclipses and the average distance between the stars (b) theperiod of the binary system and its distance from the Sun (c) thevelocities of the stars and the Doppler shifts of their absorption lines

29. Which of these stars has the coolest surface temperature? (a) anA star (b) an F star (c) a K star

30. Which of these stars is the most massive? (a) a main-sequenceA star (b) a main-sequence G star (c) a main-sequence M star

31. Which of these stars has the longest lifetime? (a) a main-sequenceA star (b) a main-sequence G star (c) a main-sequence M star

32. Which of these stars has the largest radius? (a) a supergiantA star (b) a giant K star (c) a supergiant M star

33. Which of these stars has the greatest surface temperature? (a) a main-sequence star (b) a supergiant A star (c) a giant K star

34. Which of these star clusters is youngest? (a) a cluster whosebrightest main-sequence stars are white (b) a cluster whosebrightest stars are red (c) a cluster containing stars of all colors

35. Which of these star clusters is oldest? (a) a cluster whose brightestmain-sequence stars are white (b) a cluster whose brightest main-sequence stars are yellow (c) a cluster containing stars of all colors

Process of Science

36. Classification. As discussed in the text, Annie Jump Cannon andher colleagues developed our modern system of stellar classifica-tion. Why do you think rapid advances in our understanding ofstars followed so quickly on the heels of this effort? In whatother areas of science have huge advances in understandingfollowed an improved system of classification?

37. Life Spans of Stars. Scientists estimate the life span of a star bydividing the total amount of energy available for fusion by the rateat which the star radiates energy into space. Such calculationspredict that the life spans of high-mass stars are shorter than thoseof low-mass stars. Describe one type of observation that can testthis prediction and verify that it is correct.

Group Work Exercise

38. Comparing Stellar Properties. For this exercise, your group will breakup into two pairs to analyze two different data tables. Pair 1 willstudy Table F.1 in Appendix F, and Pair 2 will study Table F.2.Before you begin, assign the following roles to the people in yourgroup: Analyst 1 (analyzes data in Table F.1), Scribe 1 (records resultsand conclusions about Table F.1), Analyst 2 (analyzes data in TableF.2), Scribe 2 (records results and conclusions about Table F.2).a. Count and record the number of stars of each spectral type

(OBAFGKM) for both tables.b. Count and record the number of stars of each luminosity class

(I, II, III, IV, V) for both tables.c. Compare the counts of spectral types in the two tables. Discuss

any differences you find and develop a hypothesis that couldexplain them.

d. Compare the counts of luminosity classes in the two tables.Discuss any differences you find and develop a hypothesisthat could explain them.

e. Write down the nearest star of each spectral type; if it cannotbe determined, explain why.

f. Determine whether there could be an O star within 200 light-years of the Sun based on the data in the tables, and explainyour reasoning.

Investigate Further

Short-Answer/Essay Questions

39. Stellar Data. Consider the following data table for several brightstars. Mv is absolute magnitude, and mv is apparent magnitude.(Hint: Remember that the magnitude scale runs backward, sothat brighter stars have smaller or more negative magnitudes.)Answer each of the following questions, and include 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 fusing hydrogen in their cores?k. Among the main-sequence stars listed, which one is the most

massive?l. Among the main-sequence stars listed, which one has the

longest lifetime?40. Data Tables. Study the spectral types listed in Appendix F for the

20 brightest stars and for the stars within 12 light-years of Earth.Why do you think the two lists are so different? Explain.

41. Interpreting the H-R Diagram. Using the information in Figure11.10, describe how Proxima Centauri differs from Sirius.

42. Parallax from Jupiter. Suppose you could travel to Jupiter andobserve changes in positions of nearby stars during one orbit ofJupiter around the Sun. Describe how those changes would dif-fer from what we would measure from Earth. How would yourability to measure the distances to stars from the vantage pointof Jupiter be different?

43. An Expanding Star. Describe what would happen to the surfacetemperature of a star if its radius doubled in size with no changein luminosity.

44. Colors of Eclipsing Binaries. Figure 11.7 shows an eclipsing binarysystem consisting of a small blue star and a larger red star. Ex-plain why the decrease in apparent brightness of the combinedsystem is greater when the blue star is eclipsed than when thered star is eclipsed.

45. Visual and Spectroscopic Binaries. Suppose you are observing twobinary star systems at the same distance from Earth. Both arespectroscopic binaries consisting of similar types of stars, butonly one of the binary systems is a visual binary. Which of thesestar systems would you expect to have the greater Doppler shiftsin its spectra? Explain your reasoning.

46. Life of a Star Cluster. Imagine you could watch a star cluster fromthe time of its birth to an age of 13 billion years. Describe in one ortwo paragraphs what you would see happening during that time.

Quantitative Problems

Be sure to show all calculations clearly and state your final answers incomplete sentences.

47. The Inverse Square Law for Light. Earth is about 150 million km fromthe Sun, and the apparent brightness of the Sun in our sky is about1300 watts/m2. Using these two facts and the inverse square lawfor light, determine the apparent brightness that we would mea-sure for the Sun if we were located at the following positions.a. Half Earth’s distance from the Sunb. Twice Earth’s distance from the Sunc. Five times Earth’s distance from the Sun

48. The Luminosity of Alpha Centauri A. Alpha Centauri A lies at a dis-tance of 4.4 light-years and has an apparent brightness in our nightsky of 2.7 � 10-8 watt/m2. Recall that 1 light-year � 9.5 � 1015 m.a. Use the inverse square law for light to calculate the luminos-

ity of Alpha Centauri A.b. Suppose you have a light bulb that emits 100 watts of visible

light. (Note: This is not the case for a standard 100-watt lightbulb, in which most of the 100 watts goes to heat and onlyabout 10–15 watt is emitted as visible light.) How far awaywould you have to put the light bulb for it to have the sameapparent brightness as Alpha Centauri A in our sky? (Hint:Use 100 watts as L in the inverse square law for light, and usethe apparent brightness given above for Alpha Centauri A.Then solve for the distance.)

49. More Practice with the Inverse Square Law for Light. Use the inversesquare law for light to answer each of the following 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. Whatis its apparent brightness?

b. Suppose a star has the same apparent brightness as AlphaCentauri A (2.7 � 10-8 watt/m2) but is located at a distanceof 200 light-years. What is its luminosity?

c. Suppose a star has a luminosity of 8 � 1026 and an apparentbrightness of 3.5 � 10-12 watt/m2. How far away is it? Giveyour answer in both kilometers and light-years.

d. Suppose a star has a luminosity of 5 � 1029 and an apparentbrightness of 9 � 10-15 watt/m2. How far away is it? Giveyour answer in both kilometers and light-years.

50. Parallax and Distance. Use the parallax formula to calculate thedistance to each of the following stars. Give your answers inboth parsecs and light-years.a. Alpha Centauri: parallax angle of 0.7420 arcsecondb. Procyon: parallax angle of 0.2860 arcsecond

51. Radius of a Star. Sirius A has a luminosity of 26LSun and a surfacetemperature of about 9400 K. What is its radius? (Hint: See Cos-mic Calculations 11.2.)

Discussion Question

52. Snapshot of the Heavens. The beginning of the chapter likened theproblem of studying the lives of stars to learning about humanbeings from a 1-minute glance at human life. What could youlearn about human life by looking at a single snapshot of a largefamily, including babies, parents, and grandparents? How is thestudy of such a snapshot similar to what scientists do when theystudy the lives of stars? How is it different?

Web Projects

53. Women in Astronomy. Until fairly recently, men greatly outnumberedwomen in professional astronomy. Nevertheless, many womenmade crucial discoveries in astronomy throughout history—includ-ing the discovery of the spectral sequence for stars. Do some re-search about the life and discoveries of one female astronomer fromany time period and write a two- to three-page scientific biography.

54. Parallax Missions. The European Space Agency’s Hipparcos space-craft made precise parallax measurements for more than 40,000stars from 1989 to 1993, and the agency’s Gaia mission, slatedfor launch in 2012, will measure parallax for many more stars.Learn about how these satellites can measure much smallerparallax angles than is possible from the ground and how thosemeasurements affect our knowledge of the universe. Write aone- to two-page report on your findings.

Star Mv mv

Spectral Type

LuminosityClass

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

surveying the stars - weeblyjasysci.weebly.com/uploads/1/6/3/8/1638942/chapter_11.pdfchapter 11...

Documents