Teach with the richest interactive media package available for astronomy

Chaisson and McMillan’s Seventh Edition of Astronomy: A Beginner’s Guide to the Universe is now fully integrated with MasteringAstronomy®—an online homework, tutorial, and assessment system that delivers self-paced tutorials, provides individualized coaching, focuses on course objectives, and encourages interactivity for further exploration.

MasteringAstronomy® Icons in the Text

Icons throughout the text connect key book figures and related activities to dynamic versions of interactive media in MasteringAstronomy.

Visual Activity Tutorials in MasteringAstronomy

Tutorials based on Interactive Figures™ help students understand the visual nature of astronomy by engaging them in interpreting key information that can be mined from the artwork.

Activities 375

PROBLEMSThe number of squares preceding each problem indicates its approxi-mate level of difficulty.

1. The angular momentum of a spherical body is proportional to the body’s angular speed times the square of its radius.

(More Precisely 4-1) Using the law of conservation of angu-lar momentum, estimate how fast a collapsed stellar core would spin if its initial spin rate was one revolution per day and its ra-dius decreased from 10,000 km to 10 km.

2. What would your mass be if you were composed entirely of neutron star material of density 3 * 1017 kg/m3 (Assume that your average density is 1000 kg/m3.) Compare this with the mass of (a) the Moon; (b) a typical 1-km diameter asteroid.

3. Calculate the surface gravity (relative to Earth’s gravity of 9.8 m>s2) and the escape speed of a 1.4-solar-mass neutron star with a radius of 10 km. What would be the escape speed of a 1-solar-mass object with a radius of 3 km? (More Precisely 5-1)

4. Use the radius–luminosity–temperature relation to calculate the luminosity of a 10-km-radius neutron star for temperatures of 105 K, 107 K, and 109 K. What do you conclude about the vis-ibility of neutron stars? Could the coolest of them be plotted on our H–R diagram?

5. A gamma-ray detector of area 0.5 m2 observing a gamma-ray burst records photons having total energy 10-8 joules. If the burst occurred 1000 Mpc away, calculate the total amount of energy it re-leased (assuming that the energy was emitted equally in all direc-tions). How would this figure change if the burst occurred 10,000 pc away instead, in the halo of our Galaxy? What if it occurred within the Oort cloud of our own solar system, at a distance of 50,000 AU?

6. An unstable elementary particle is known to decay into other particles in 2 μs, as measured in a laboratory where the particle are at rest. A beam of such particles is accelerated to a speed of 99.99 percent of the speed of light. How long do the particles in the beam take to decay, in the laboratory frame of reference?

7. Supermassive black holes are thought to exist in the centers of some galaxies. What would be the Schwarzschild radii of black holes of 1 million and 1 billion solar masses? How does the first black hole compare in size with the Sun? How does the second compare in size with the solar system?

8. Calculate the tidal acceleration on a 2-m-tall human falling feet first into a 1-solar-mass black hole—that is, compute the difference in the accelerations (forces per unit mass) on his head and his feet just before his feet cross the event horizon. Repeat the calculation for a 1-million-solar-mass black hole and for a 1-billion-solar-mass black hole (see the previous question). Compare these accelera-tions with the acceleration due to gravity on Earth (9.8 m/s2).

9. Endurance tests suggest that the human body cannot with-stand stress greater than about 10 times the acceleration due to gravity on Earth’s surface. At what distance from a 1-solar-mass black hole would the human in the previous question be torn apart? Calculate the minimum mass of a black hole for which an infalling human could just reach the event horizon intact.

10. Using the data given in the text (assume the upper limit on the stated range for the black hole mass), calculate the orbital separation of Cygnus X-1 and its B-type stellar companion. (Sec. 1.4)

ACTiViTiESCollaborative 1. We can’t easily observe a black hole, or make one to study, but theo-

rists have lots to say about their properties! The text focuses on the simplest possible type of black hole—the uncharged, nonrotating Schwarzchild black hole—but there is a large body of literature on charged and spinning black holes, too. Charged black holes don’t figure much in astronomy—the universe is electrically neutral on macroscopic scales—but rotating Kerr black holes are in fact very important. Divide your group in two and research online the proper-ties of Schwarzchild and Kerr black holes. You’ll probably find more information on the simpler Schwarzchild case, but some persistence will yield a lot on the rotating Kerr case, too. Combine your research to make a joint presentation on the similarities and differences be-tween the two types. Focus on properties such as the event horizon, the singularity, and the orbits of light and matter near the hole. How fast can a black hole rotate? Which kind of black hole is thought to be most common in nature? A note on researching on the Web: try to stick to “authoritative” sites, such as NASA, ESO, university, and jour-nal pages. Wikipedia is probably trustworthy, but always check what you find. And stay away from blogs and other nonauthoritative sites!

individual 1. Find the ninth-magnitude companion to Cygnus X-1, the sky’s most

famous black hole candidate. Because none of us can see X-rays, no

sign of anything unusual can be seen. Still, it’s fun to gaze toward this region of the heavens and contemplate Cygnus X-1’s powerful energy emission and strange properties. Even without a telescope, it is easy to locate the region of the heavens where Cygnus X-1 resides. The constellation Cygnus contains a recognizable star pattern, or aster-ism, in the shape of a large cross. This asterism is called the Northern Cross. The star in the center of the crossbar is called Sadr. The star at the bottom of the cross is called Albireo. Approximately midway be-tween Sadr and Albireo lies the star Eta Cygni. Cygnus X-1 is located slightly less than 0.5° from this star. Whether or not you are using a telescope, sketch what you see. Create a demonstration of the densi-ties of various astronomical objects—an interstellar cloud, a star, a terrestrial planet, a white dwarf, and a neutron star. Select a common object that is easily held in your hand—an apple, for example. For the lowest densities, calculate how large a volume would contain the object’s equivalent mass. For high densities, calculate how many of the objects would have to fit into a standard volume, such as 1 cm3. (This volume is better for this project than 1 m3 because most people don’t appreciate just how large a volume 1 m3 is.) Present your dem-onstration to your class or to some other group of students. Tell them about each astronomical object and how it comes by its density.

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Chapter Review 373

LO1 A core-collapse supernova may leave behind an ultracompressed ball of material called a neu-tron star (p. 350). This is the remnant of the inner core that rebounded and blew the rest of the star apart. Neutron stars are extremely dense and, at formation, are predicted to be extremely hot, strongly magnetized, and rapidly rotating. They cool down, lose much of their magnetism, and slow down as they age.

LO2 According to the lighthouse model (p. 351), neutron stars, because they are magnetized and rotating, send regular bursts of electro-magnetic energy into space. The beams are produced by charged particles confined by the strong magnetic fields. When we can see the beams from Earth, we call the source neutron star a pulsar (p. 348). The pulse period is the rotation period of the neutron star.

LO3 A neutron star that is a member of a binary system can draw matter from its companion, forming an accretion disk, which is usually a strong source of X-rays. As gas builds up on the star’s surface, it eventually becomes hot enough to fuse hydrogen. When hy-drogen burning starts on a neutron star, it does so explosively, and an X-ray burster (p. 354) results. The rapid rotation of the inner part of the accretion disk causes the neutron star to spin faster as new gas ar-rives on its surface. The eventual result is a very rapidly rotating neutron star—a mil-lisecond pulsar (p. 354). Many millisecond pulsars are found in the hearts of old globular clusters. They cannot have formed recently, and must have been spun up by interactions with other stars. Care-ful analysis of the radiation received has shown that some millisec-ond pulsars are orbited by planet-sized objects.

LO4 Gamma-ray bursts (p. 356) are very ener-getic flashes of gamma rays that occur about once a day and are distributed uniformly over the entire sky. In some cases, their dis-tances have been measured, placing them at very large distances and implying that they are extremely luminous. The leading theo-retical models for these explosions involve the violent merger of neutron stars in a dis-tant binary system, or the recollapse and subsequent violent explosion following a “failed” supernova in a very massive star.

LO5 Einstein’s special theory of relativity deals with the behavior of particles moving at speeds comparable to the speed of light. It agrees with Newton’s theory at low velocities, but makes many very differ-ent predictions for high-speed motion. All of its predictions have been repeatedly verified by experiment. The modern replacement for Newtonian gravity is Einstein’s gen-eral theory of relativity (p. 361), which describes gravity in terms of the warping, or bending, of space by the presence of mass. The more mass, the greater the warping. All particles—including pho-tons—respond to that warping by moving along curved paths.

LO6 The upper limit on the mass of a neutron star is about three solar masses. Beyond that mass, the star can no longer support it-self against its own gravity, and it collapses to form a black hole (p. 361), a region of space from which nothing can escape. The most massive stars, after exploding in a su-pernova, form black holes rather than neutron stars. Conditions in and near black holes can only be described by general rela-tivity. The radius at which the escape speed from a collapsing star equals the speed of light is called the Schwarzschild radius (p. 362). The surface of an imaginary sphere centered on the collapsing star and having a radius equal to the star’s Schwar-zschild radius is called the event horizon (p. 362).

LO7 To a distant observer, light leaving a spaceship that is falling into a black hole would be subject to gravitational red-shift (p. 369) as the light climbed out of the hole’s intense gravitational field. At the same time, a clock on the spaceship would show time dilation (p. 369)—the clock would appear to slow down as the ship approached the event horizon. The observer would never see the ship reach the surface of the hole. Once within the event hori-zon, no known force can prevent a collapsing star from contract-ing all the way to a pointlike singularity (p. 370), at which point both the density and the gravitational field of the star become infi-nite. This prediction of relativity theory has yet to be proved. Sin-gularities are places where the known laws of physics break down.

LO8 Once matter falls into a black hole, it can no longer communicate with the out-side. However, on its way in, it can form an accretion disk and emit X-rays. The best place to look for a black hole is in

c h a P t e r r e V i e w

S u M M A R y

Supernova(case b only)

Relativisticoutflow

Magneticfield lines

Equatorialplane

Pulsarwind

Pulsarwind

Magneticaxis

Beam ofradiation

Beam ofradiation

Neutronstar

Rotationaxis

“Hotspots”

R I U X G

R I V U GX

V

(a)

(b)

Black hole

Eventhorizon

10 km

3 kmVisible

X ray

Ultraviolet

Visible

Infrared

Radio100 km

10,000 km

Robot probe

Black hole X-ray source

Accretion disk

Mass transfer stream

B-star companionHDE226868

7988_Chaisson_Ch13_pp348_375.indd 373 6/6/12 1:32 PM

Learning is promoted throughout the book with clear guideposts that begin with an engaging chapter opener and continue through the comprehensive chapter summary. Learning Outcomes appear at the beginning of the chapter to help structure the student’s reading and again at the end so students can test mastery of key concepts.

NEW! Learning Outcomes from the book are also tagged to content in MasteringAstronomy, allowing for automatic tracking of students’ performance against your targeted course learning outcomes.

Focus on student learning with clear guideposts and learning outcomes

Track and assess student performance with robust media tools

NEW! Learning Outcomes

Recast from the Learning Goals of the previous editions, Learning Outcomes in each chapter introduce clear expectations of the skills students should be able to demonstrate after successfully completing the chapter.

NEW! Individual and Collaborative Activities

Individual and collaborative activities have been added to the end of each chapter, enabling group work and hands-on learning. Helpful review and discussion questions also address the process of science, visual interpretations of information, and Learning Outcomes.

Learning Outcomes

Mastering gives you the tools to quantify students’ learning gains and to share those results quickly and easily.

• Add your own or use the publisher-provided learning outcomes to track student performance and report it to your administration.

Learning Outcomes Summary

Mastering provides quick and easy access to information on student performance relative to your course’s learning outcomes.

• View class and individual performance against specific learning outcomes.

• Effortlessly export results to a spreadsheet that you can further customize and/or share with your chair, dean, administrator, and/or accreditation board.

End-of-Chapter Summaries

The End-of-Chapter Summaries are organized by the Learning Outcomes established at the start of each chapter, with reinforcing number cues, key terms, and repeated mini-images from the text. Selected End-of-Chapter problems in MasteringAstronomy® also feature links to interactive media and the eText.

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Student-friendly art teaches tough topics

Vivid, dynamic, and current art keeps students informed and engaged.

Multi-part Art

Multi-part figures are used to convey the greatest amount of information in the most vivid way.

NEW! Annotated Art

Annotations integrate written information with the visual information in illustrations, enabling students to learn more effectively, as proven by educational research.

Revised Visual Analogies

Visual analogies use simple-to-understand art to explain complex astronomical concepts. Key figures are combined with images of familiar objects, and annotations help students make the connections between them.