Questions

Review Questions

1. How does the chemical composition of the present-day Sun’s core compare to the core’s composition when the Sun formed? What caused the change?

2. Which regions of the Sun are denser today than they were a billion years ago? Which regions are less/dense? What has caused these changes?

3. What is a red dwarf? How are thermonuclear reactions in the core of a red dwarf able to consume hydrogen from the star’s outer layers?

4. Why do high-mass main-sequence stars have shorter lifetimes than those of lower mass?

5. On what grounds are astronomers able to say that the Sun has about 7 × 10⁹ years remaining in its main-sequence stage?

6. What will happen inside the Sun 7 billion years from now, when it begins to mature into a red giant?

7. Explain why Earth is expected to become inhospitable to life long before the Sun becomes a red giant.

8. Explain how it is possible for the core of a red giant to contract at the same time that its outer layers expand.

9. Why does helium fusion require much higher temperatures than hydrogen fusion?

10. How is a degenerate gas different from ordinary gases?

11. What is the helium flash? Why does it happen in some stars but not in others?

12. Why does a star’s luminosity decrease after helium fusion begins in its core?

13. What does it mean when an astronomer says that a star “moves” from one place to another on an H-R diagram?

14. Explain why the majority of the stars visible through telescopes are main-sequence stars.

15. On an H-R diagram, main-sequence stars do not lie along a single narrow line but are spread out over a band (see Figure 19-9b). On the basis of how stars evolve during their main-sequence lifetimes, explain why this should be so.

16. Explain how and why the turnoff point on the H-R diagram of a cluster is related to the cluster’s age.

17. There is a good deal of evidence that our universe is about 13.7 billion years old. Explain why no main-sequence stars of spectral class M have yet evolved into red giant stars.

18. How do astronomers know that globular clusters are made of old stars?

19. Red giant stars appear more pronounced in composites of infrared images and visible-light images, like those in Figure 19-4b and Figure 19-12. Explain why.

20. The horizontal-branch stars in Figure 19-12 appear blue. (a) Explain why this is consistent with the color-magnitude diagram shown in Figure 19-13. (b) All horizontal-branch stars were once red giants. Explain what happened to these stars to change their color.

21. What is the difference between Population I and Population II stars? In what sense can the stars of one population be regarded as the “children” of the other population?

22. Both diamonds and graphite (the material used in pencils to make marks on paper) are crystalline forms of carbon. Most of the carbon atoms in these substances have nuclei with 6 protons and 6 neutrons (¹²C). Where did these nuclei come from?

23. Why do astronomers attribute the observed Doppler shifts of a Cepheid variable to pulsation, rather than to some other cause, such as orbital motion?

24. Why do Cepheid stars pulsate? Why are these stars important to astronomers who study galaxies beyond the Milky Way?

25. What is a Roche lobe? What is the inner Lagrangian point? Why are Roche lobes important in close binary star systems?

26. What is the difference between a detached binary, a semidetached binary, a contact binary, and an overcontact binary?

27. Massive main-sequence stars turn into red giants before less massive stars. Why, then, is the more massive star in Algol a main-sequence star and the less massive star a red giant?

Advanced Questions

Questions preceded by an asterisk (*) involve topics discussed in Box 7-2, the Boxes in Chapter 17, or the Boxes in this chapter.

28. The radius of the Sun has increased over the past several billion years. Over the same time period, the size of the Moon’s orbit around Earth has also increased. A few billion years ago, were annular eclipses of the Sun (see Figure 3-12) more or less common than they are today? Explain your answer.

29. The Sun has increased in radius by 6% over the past 4.56 billion years. Its present-day radius is 696,000 km. What was its radius 4.56 billion years ago? (Hint: The answer is not 654,000 km.)

30. *Calculate the escape speed from (a) the surface of the present-day Sun and (b) the surface of the Sun when it becomes a red giant, with essentially the same mass as today but with a radius that is 100 times larger. (c) Explain how your results show that a red giant star can lose mass more easily than a main-sequence star.

31. *Calculate the average speed of a hydrogen atom (mass 1.67 × 10^–27 kg) (a) in the atmosphere of the present-day Sun, with temperature 5800 K, and (b) in the atmosphere of a 1-M_⊙ red giant, with temperature 3500 K. (c) Compare your results with the escape speeds that you calculated in Question 30. Use this comparison to discuss how well the present-day Sun and a 1-M_⊙ red giant can retain hydrogen in their atmospheres.

32. Use the value of the Sun’s luminosity (3.90 × 10²⁶ watts, or 3.90 × 10²⁶ joules per second) to calculate what mass of hydrogen the Sun will convert into helium during its entire main-sequence lifetime of 1.2 × 10¹⁰ years. (Assume that the Sun’s luminosity remains nearly constant during the entire 1.2 × 10¹⁰ years.) What fraction does this represent of the total mass of hydrogen that was originally in the Sun?

33. (a) The main-sequence stars Sirius (spectral type A1), Vega (A0), Spica (B1), Fomalhaut (A3), and Regulus (B7) are among the 20 brightest stars in the sky. Explain how you can tell that all these stars are younger than the Sun. (b) The third-brightest star in the sky, although it can be seen only south of 29° north latitude, is α (alpha) Centauri A. It is a main-sequence star of spectral type G2, the same as the Sun. Can you tell from this whether α Centauri A is younger than the Sun, the same age, or older? Explain your reasoning.

34. Using the same horizontal and vertical scales as in Figure 19-9a, make points on an H-R diagram for each of the stars listed in Table 19-1. Label each point with the star’s mass and its main-sequence lifetime. Which of these stars will remain on the main sequence after 10⁹ years? After 10¹¹ years?

35. *Explain why the quantity f in Box 19-2 has a different value for stars with masses less than 0.4 M_⊙ than for stars with masses greater than 0.4 M_⊙. In which case does f have a greater value?

36. *Calculate the main-sequence lifetimes of (a) a 9-M_⊙ star and (b) a 0.25-M_⊙ star. Compare these lifetimes with that of the Sun.

37. *The earliest fossil records indicate that life appeared on Earth about a billion years after the formation of the solar system. What is the most mass that a star could have in order that its lifetime on the main sequence is long enough to permit life to form on one or more of its planets? Assume that the evolutionary processes would be similar to those that occurred on Earth.

38. As a red giant, the Sun’s luminosity will be about 2000 times greater than it is now, so the amount of solar energy falling on Earth will increase to 2000 times its present-day value. Hence, to maintain thermal equilibrium, each square meter of Earth’s surface will have to radiate 2000 times as much energy into space as it does now. Use the Stefan-Boltzmann law to determine what Earth’s surface temperature will be under these conditions. (Hint: The present-day Earth has an average surface temperature of 14°C.)

39. When the Sun becomes a red giant, its luminosity will be about 2000 times greater than it is today. Assuming that this luminosity is caused only by fusion of the Sun’s remaining hydrogen, calculate how long our star will be a red giant. (In fact, only a fraction of the remaining hydrogen will be consumed, and the luminosity will vary over time as shown in Figure 19-8.)

40. What observations would you make of a star to determine whether its primary source of energy is hydrogen fusion or helium fusion?

41. The star whose spectrum is shown in Figure 19-15a has a lower percentage of heavy elements than the Sun, whose spectrum is shown in Figure 19-15b. Hence, the star in Figure 19-15a has a higher percentage of hydrogen. Why, then, isn’t the H_δ absorption line of hydrogen noticeably darker for the star in Figure 19-15a?

42. Would you expect the color of a Cepheid variable star (consider Figure 19-18) to change during the star’s oscillation period? If not, why not? If so, describe why the color should change, and describe the color changes you would expect to see during an oscillation period.

43. The brightness of a certain Cepheid variable star changes from maximum brightness to minimum brightness in 26 days. In 4 more days, the star returns to maximum brightness. (a) What is this star’s period? (b) What is this star’s approximate luminosity?

44. The star X Arietis is an RR Lyrae variable. Its apparent brightness varies between 2.0 × 10^–15 and 4.9 × 10^–15 that of the Sun with a period of 0.65 day. Interstellar extinction dims the star by 37%. Approximately how far away is the star?

45. The apparent brightness of δ Cephei (a Cepheid variable star) varies with a period of 5.4 days. Its average apparent brightness is 5.1 × 10^–13 that of the Sun. Approximately how far away is δ Cephei? (Ignore interstellar extinction.)

46. Suppose you find a binary star system in which the more massive star is a red giant and the less massive star is a main-sequence star. Would you expect that mass transfer between the stars has played an important role in the evolution of these stars? Explain your reasoning.

47. The larger star in the Algol binary system (see Figure 19-22a) is of spectral class K, while the smaller star is of spectral class B. Discuss how the color of Algol changes as seen through a small telescope (through which Algol appears as a single star). What is the color during a deep eclipse, when the large star eclipses the small one? What is the color when the small star eclipses the large one?

48. Suppose the detached star in β Lyrae (Figure 19-22b) did not have an accretion disk. Would the deeper dips in the light curve be deeper, shallower, or about the same? What about the shallower dip? Explain your answers.

49. The two stars that make up the overcontact binary W Ursae Majoris (Figure 19-22c) have estimated masses of 0.99 M_⊙ and 0.62 M_⊙. (a) Find the average separation between the two stars. Give your answer in kilometers. (b) The radii of the two stars are estimated to be 1.14 R_⊙ and 0.83 R_⊙. Show that these values and your result in part (a) are consistent with the statement that this is an overcontact binary.

50. The stars that make up the binary system W Ursae Majoris (see Figure 19-22c) have particularly strong magnetic fields. Explain how astronomers could have discovered this. (Hint: See Section 16-9.)

51. Consult recent issues of Sky & Telescope and Astronomy to find out when Mira will next reach maximum brightness. Look up the star’s location in the sky using the Starry Night™ program if you have access. (Use the Find… command in the Edit menu to search for Omicron Ceti.) Why is it unlikely that you will be able to observe Mira at maximum brightness?

Discussion Questions

52. Eventually the Sun’s luminosity will increase to the point where Earth can no longer sustain life. Discuss what measures a future civilization might take to preserve itself from such a calamity.

53. The half-life of the ⁸Be nucleus, 2.6 × 10^–16 second, is the average time that elapses before this unstable nucleus decays into two alpha particles. How would the universe be different if instead the ⁸Be half-life were zero? How would the universe be different if the ⁸Be nucleus were stable and did not decay?

54. Discuss how H-R diagrams of star clusters could be used to set limits on the age of the universe. Could they be used to set lower limits on the age? Could they be used to set upper limits? Explain your reasoning.

Web/eBook Questions

55. Suppose that an oxygen nucleus (¹⁶O) were fused with a helium nucleus (⁴He). What element would be formed? Look up the relative abundance of this element in, for example, the Handbook of Chemistry and Physics or on the World Wide Web. Based on the abundance, comment on whether such a process is likely. (Hint: See Figure 8-4.)

56. Although Polaris, the North Star, is a Cepheid variable, it pulsates in a somewhat different way than other Cepheids. Search the World Wide Web for information about this star’s pulsations and how they have been measured by astronomers at the U.S. Naval Observatory. How does Polaris pulsate? How does this differ from other Cepheids?

57. Observing Stellar Evolution. Step through the animation “The Hertzsprung-Russell Diagram and Stellar Evolution” in Chapter 19 of the Universe Web site or eBook. Use this animation to answer the following questions. (a) How does a 1-M_⊙ star move on the H-R diagram during its first 4.56 billion (4560 million) years of existence? Compare this with the discussion in Section 19-1 of how the Sun has evolved over the past 4.56 billion years. (b) What is the zero-age spectral class of a 2-M_⊙ star? At what age does such a star evolve into a red giant of spectral class K? (c) What is the approximate zero-age luminosity of a 1.3-M_⊙ star? What is its approximate luminosity when it becomes a red giant? (d) Suppose a star cluster has no main-sequence stars of spectral classes O or B. What is the approximate age of the cluster? (e) Approximately how long do the most massive stars of spectral class B live before leaving the main sequence? What about the most massive stars of spectral class F?