Chapter 23 The Death of Stars
23.9 Questions and Exercises
1: How does a white dwarf differ from a neutron star? How does each form? What keeps each from collapsing under its own weight?
2: Describe the evolution of a star with a mass like that of the Sun, from the main-sequence phase of its evolution until it becomes a white dwarf.
3: Describe the evolution of a massive star (say, 20 times the mass of the Sun) up to the point at which it becomes a supernova. How does the evolution of a massive star differ from that of the Sun? Why?
4: How do the two types of supernovae discussed in this chapter differ? What kind of star gives rise to each type?
5: A star begins its life with a mass of 5 MSun but ends its life as a white dwarf with a mass of 0.8 MSun. List the stages in the star’s life during which it most likely lost some of the mass it started with. How did mass loss occur in each stage?
6: If the formation of a neutron star leads to a supernova explosion, explain why only three of the hundreds of known pulsars are found in supernova remnants.
7: How can the Crab Nebula shine with the energy of something like 100,000 Suns when the star that formed the nebula exploded almost 1000 years ago? Who “pays the bills” for much of the radiation we see coming from the nebula?
8: How is a nova different from a type Ia supernova? How does it differ from a type II supernova?
9: Apart from the masses, how are binary systems with a neutron star different from binary systems with a white dwarf?
10: What observations from SN 1987A helped confirm theories about supernovae?
11: Describe the evolution of a white dwarf over time, in particular how the luminosity, temperature, and radius change.
12: Describe the evolution of a pulsar over time, in particular how the rotation and pulse signal changes over time.
13: How would a white dwarf that formed from a star that had an initial mass of 1 MSun be different from a white dwarf that formed from a star that had an initial mass of 9 MSun?
14: What do astronomers think are the causes of longer-duration gamma-ray bursts and shorter-duration gamma-ray bursts?
15: How did astronomers finally solve the mystery of what gamma-ray bursts were? What instruments were required to find the solution?
16: Arrange the following stars in order of their evolution:
- A star with no nuclear reactions going on in the core, which is made primarily of carbon and oxygen.
- A star of uniform composition from center to surface; it contains hydrogen but has no nuclear reactions going on in the core.
- A star that is fusing hydrogen to form helium in its core.
- A star that is fusing helium to carbon in the core and hydrogen to helium in a shell around the core.
- A star that has no nuclear reactions going on in the core but is fusing hydrogen to form helium in a shell around the core.
17: Would you expect to find any white dwarfs in the Orion Nebula? (See The Birth of Stars and the Discovery of Planets outside the Solar System to remind yourself of its characteristics.) Why or why not?
18: Suppose no stars more massive than about 2 MSun had ever formed. Would life as we know it have been able to develop? Why or why not?
19: Would you be more likely to observe a type II supernova (the explosion of a massive star) in a globular cluster or in an open cluster? Why?
20: Astronomers believe there are something like 100 million neutron stars in the Galaxy, yet we have only found about 2000 pulsars in the Milky Way. Give several reasons these numbers are so different. Explain each reason.
21: Would you expect to observe every supernova in our own Galaxy? Why or why not?
22: The Large Magellanic Cloud has about one-tenth the number of stars found in our own Galaxy. Suppose the mix of high- and low-mass stars is exactly the same in both galaxies. Approximately how often does a supernova occur in the Large Magellanic Cloud?
23: Look at the list of the nearest stars in Appendix I. Would you expect any of these to become supernovae? Why or why not?
24: If most stars become white dwarfs at the ends of their lives and the formation of white dwarfs is accompanied by the production of a planetary nebula, why are there more white dwarfs than planetary nebulae in the Galaxy?
25: If a 3 and 8 MSun star formed together in a binary system, which star would:
- Evolve off the main sequence first?
- Form a carbon- and oxygen-rich white dwarf?
- Be the location for a nova explosion?
26: You have discovered two star clusters. The first cluster contains mainly main-sequence stars, along with some red giant stars and a few white dwarfs. The second cluster also contains mainly main-sequence stars, along with some red giant stars, and a few neutron stars—but no white dwarf stars. What are the relative ages of the clusters? How did you determine your answer?
27: A supernova remnant was recently discovered and found to be approximately 150 years old. Provide possible reasons that this supernova explosion escaped detection.
28: Based upon the evolution of stars, place the following elements in order of least to most common in the Galaxy: gold, carbon, neon. What aspects of stellar evolution formed the basis for how you ordered the elements?
29: What observations or types of telescopes would you use to distinguish a binary system that includes a main-sequence star and a white dwarf star from one containing a main-sequence star and a neutron star?
30: How would the spectra of a type II supernova be different from a type Ia supernova? Hint: Consider the characteristics of the objects that are their source.
Figuring for Yourself
31: The ring around SN 1987A (Figure 23.12) initially became illuminated when energetic photons from the supernova interacted with the material in the ring. The radius of the ring is approximately 0.75 light-year from the supernova location. How long after the supernova did the ring become illuminated?
32: What is the acceleration of gravity (g) at the surface of the Sun? (See Appendix E for the Sun’s key characteristics.) How much greater is this than g at the surface of Earth? Calculate what you would weigh on the surface of the Sun. Your weight would be your Earth weight multiplied by the ratio of the acceleration of gravity on the Sun to the acceleration of gravity on Earth. (Okay, we know that the Sun does not have a solid surface to stand on and that you would be vaporized if you were at the Sun’s photosphere. Humor us for the sake of doing these calculations.)
33: What is the escape velocity from the Sun? How much greater is it than the escape velocity from Earth?
34: What is the average density of the Sun? How does it compare to the average density of Earth?
35: Say that a particular white dwarf has the mass of the Sun but the radius of Earth. What is the acceleration of gravity at the surface of the white dwarf? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the white dwarf (again granting us the dubious notion that you could survive there)?
36: What is the escape velocity from the white dwarf in Exercise 23.35? How much greater is it than the escape velocity from Earth?
37: What is the average density of the white dwarf in Exercise 23.35? How does it compare to the average density of Earth?
38: Now take a neutron star that has twice the mass of the Sun but a radius of 10 km. What is the acceleration of gravity at the surface of the neutron star? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the neutron star (provided you could somehow not become a puddle of protoplasm)?
39: What is the escape velocity from the neutron star in Exercise 23.38? How much greater is it than the escape velocity from Earth?
40: What is the average density of the neutron star in Exercise 23.38? How does it compare to the average density of Earth?
41: One way to calculate the radius of a star is to use its luminosity and temperature and assume that the star radiates approximately like a blackbody. Astronomers have measured the characteristics of central stars of planetary nebulae and have found that a typical central star is 16 times as luminous and 20 times as hot (about 110,000 K) as the Sun. Find the radius in terms of the Sun’s. How does this radius compare with that of a typical white dwarf?
42: a) According to a model described in the text, a neutron star has a radius of about 10 km. Assume that the pulses occur once per rotation. According to Einstein’s theory of relatively, nothing can move faster than the speed of light. Check to make sure that this pulsar model does not violate relativity. b) Then calculate the rotation speed of the Crab Nebula pulsar at its equator, given its period of 0.033 s. (Remember that distance equals velocity × time and that the circumference of a circle is given by 2πR).
43: Do the same calculations as above but for a pulsar that rotates at 1000 times per second. That would give a period of 1/1000 seconds. Remember as it said above, according to a model described in the text, a neutron star has a radius of about 10 km.
44: If the Sun were replaced by a white dwarf with a surface temperature of 10,000 K and a radius equal to Earth’s, how would its luminosity compare to that of the Sun?
45: A supernova can eject material at a velocity of 10,000 km/s. How long would it take a supernova remnant to expand to a radius of 1 AU? How long would it take to expand to a radius of 1 light-years? Assume that the expansion velocity remains constant and use the relationship:
46: A supernova remnant was observed in 2007 to be expanding at a velocity of 14,000 km/s and had a radius of 6.5 light-years. Assuming a constant expansion velocity, in what year did this supernova occur?
47: The ring around SN 1987A (Figure 23.12) started interacting with material propelled by the shockwave from the supernova beginning in 1997 (10 years after the explosion). The radius of the ring is approximately 0.75 light-year from the supernova location. How fast is the supernova material moving, assume a constant rate of motion in km/s?
48: Before the star that became SN 1987A exploded, it evolved from a red supergiant to a blue supergiant while remaining at the same luminosity. As a red supergiant, its surface temperature would have been approximately 4000 K, while as a blue supergiant, its surface temperature was 16,000 K. How much did the radius change as it evolved from a red to a blue supergiant?
49: What is the radius of the progenitor star that became SN 1987A? Its luminosity was 100,000 times that of the Sun, and it had a surface temperature of 16,000 K.
50: What is the acceleration of gravity at the surface of the star that became SN 1987A? How does this g compare to that at the surface of Earth? The mass was 20 times that of the Sun and the radius was 41 times that of the Sun.
51: What was the escape velocity from the surface of the SN 1987A progenitor star? How much greater is it than the escape velocity from Earth? The mass was 20 times that of the Sun and the radius was 41 times that of the Sun.
52: What was the average density of the star that became SN 1987A? How does it compare to the average density of Earth? The mass was 20 times that of the Sun and the radius was 41 times that of the Sun.
53: If the pulsar shown in Figure 23.16 is rotating 100 times per second, how many pulses would be detected in one minute? The two beams are located along the pulsar’s equator, which is aligned with Earth.