Questions
Review Questions
What is the horizontal branch? Where is it located on an H-R diagram? How do stars on the horizontal branch differ from red giants or main-sequence stars?Horizontal-branch stars are sometimes referred to as “helium main-sequence stars.” In what sense is this true?
What is the asymptotic giant branch? Where is it located on an H-R diagram? How do asymptotic giant branch stars differ from red giants or main-sequence stars?
Is a carbon star a star that is made of carbon? Explain your answer.
What is the connection between dredge-ups in old stars and life on Earth?
What are thermal pulses in AGB stars? What causes them? What effect do they have on the luminosity of the star?
How is a planetary nebula formed?
How can an astronomer tell the difference between a planetary nebula and a planet?
What is the evidence that typical planetary nebulae are only a few thousand years old?
Why do we not observe planetary nebulae that are more than about 50,000 years old?
What is a white dwarf? Does it produce light in the same way as a star like the Sun?
What is nuclear density? Why is it significant when a star’s core reaches this density?
How does the radius of a white dwarf depend on its mass? How is this different from other types of stars?
What is the significance of the Chandrasekhar limit?
On an H-R diagram, sketch the evolutionary track that the Sun will follow from when it leaves the main sequence to when it becomes a white dwarf. Approximately how much mass will the Sun have when it becomes a white dwarf? Where will the rest of the mass go?
What prevents nuclear reactions from occurring at the center of a white dwarf? If no nuclear reactions are occurring in its core, why doesn’t the star collapse?
A white dwarf has a greater mass than either a red dwarf or a brown dwarf. Yet a white dwarf has a smaller radius than either a red dwarf or a brown dwarf. Explain why, in terms of the types of pressure that keep the different kinds of dwarfs from collapsing under their own gravity.
Why do you suppose that all the white dwarfs known to astronomers are relatively close to the Sun?
Why does the mass of a star play such an important role in determining the star’s evolution?
Why is the temperature in a star’s core so important in determining which nuclear reactions can occur there?
What is the difference between a red giant and a red supergiant?
Why does the evolutionary track of a high-mass star move from left to right and back again in the H-R diagram?
In what way does the structure of an aging supergiant resemble that of an onion?
Can stars fuse iron as nuclear fuel? How does this affect the core of a supergiant?
What happens if the iron core of a star exceeds the Chandrasekhar limit? About how large must the star be for this to occur?
Supernovae can produce uranium that, billions of years later, release nuclear energy through radioactive decay. In what form was this energy during the supernova event?
Why is SN 1987A so interesting to astronomers? In what ways was it not a typical supernova?
Why are neutrinos emitted by core-collapse supernovae? How can these neutrinos be detected? How can they be distinguished from solar neutrinos?
What causes a thermonuclear supernova? How does a thermonuclear supernova compare with a core-collapse supernova?
What are the differences among Type Ia, Type Ib, Type Ic, and Type II supernovae? Which type is most unlike the other three, and why?
How can a supernova continue to shine for many years after it explodes?
How do supernova remnants produce radiation at nonvisible wavelengths?
There may have been recent supernovae in our Galaxy that have not been observable even though they are incredibly luminous. How is it this possible?
Is our own Sun likely to become a supernova? Why or why not?
What are neutron stars? Where do the neutrons come from?
In what type of supernova can a neutron star form? Why?
What is degenerate neutron pressure? How is it related to degenerate electron pressure?
What does the radio emission from a pulsar look like?
During the weeks immediately following the discovery of the first pulsar, one suggested explanation was that the pulses might be signals from an extraterrestrial civilization. Why did astronomers soon discard this idea?
How are rotating neutron stars able to produce pulses of radiation as seen by an observer on Earth?
Why do neutron stars rotate so much more rapidly than ordinary stars? Why do they have such strong magnetic fields?
Is our Sun likely to end up as a neutron star? Why or why not?
Why does a neutron star need to have a mass above 1.4 M⊙? What effects contribute to the pressure as a neutron star approaches its maximum mass?
What are the similarities between a nova and a Type Ia supernova? What are the differences?
What are the similarities between novae and X-ray bursters? What are the differences?
Advanced Questions
Questions preceded by an asterisk (*) involve topics discussed in the Boxes in Chapter 1, Chapter 7, or Chapter 17.
Problem-solving tips and tools
The small-angle formula is given in Box 1-1. You may find it useful to review Box 17-4, which discusses stellar radii and their relationship to temperature and luminosity. Section 4-7 explains the formula for gravitational force, and Box 7-2 explains the concept of escape speed. Section 5-2 and Section 5-4 describe some key properties of light, especially blackbody radiation. We discussed the relationship among luminosity, apparent brightness, and distance in Box 17-2. The relationship among absolute magnitude, apparent magnitude, and distance was the topic of Box 17-3. Section 17-6 gives the formula relating a star’s luminosity, surface temperature, and radius (see Box 17-4 for worked examples). In our discussion of binary stars in Section 17-9 we saw how the masses of the stars, the orbital period, and the average distance between the two stars are all related. The volume of a sphere of radius r is 4πr3/3. Appendix 6 gives the conversion between seconds and years as well as the radius of the Sun.
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Some blue main-sequence stars in our region of the Galaxy have the same luminosity and surface temperature as the horizontal-branch stars in the globular cluster M55 (see Figure 20-3). How do we know that the horizontal-branch stars in M55 are not main-sequence stars?
Stellar winds from an AGB star can cause it to lose mass at a rate of up to 10−4 M⊙ per year. (a) Express this rate in metric tons per second. (One metric ton equals 1000 kilograms.) (b) At this rate, how long would it take an AGB star to eject an amount of mass equal to the mass of Earth? Express your answer in days.
The globular cluster M15 depicted in Figure 20-7a contains 30,000 old stars, but only one of these stars is presently in the planetary nebula stage of its evolution. Explain why planetary nebulae are not more prevalent in M15.
The central star in a newly formed planetary nebula has a luminosity of 1000 L⊙ and a surface temperature of 100,000 K. What is the star’s radius? Give your answer as a multiple of the Sun’s radius.
You want to determine the age of a planetary nebula. What observations should you make, and how would you use the resulting data?
Figure 20-7a shows the planetary nebula Abell 39. Use the information given in the figure caption to calculate the angular diameter of the nebula as seen from Earth.
*The Ring Nebula is a planetary nebula in the constellation Lyra. It has an angular size of 1.4 arcmin × 1.0 arcmin and is expanding at the rate of about 20 km/s. Approximately how long ago did the central star shed its outer layers? Assume that the nebula is 2,700 ly from Earth.
The accompanying image shows the planetary nebula IC 418 in the constellation Lepus (the Hare). (a) The image shows a small shell of glowing gas (shown in blue) within a larger glowing gas shell (shown in orange). Discuss how IC 418 could have acquired this pair of gas shells. (b) Explain why the outer shell looks thicker around the edges than near the middle.
R I V U X G(NASA and Hubble Heritage Team, STScI/AURA)(a) Calculate the wavelength of maximum emission of the white dwarf Sirius B. In what part of the electromagnetic spectrum does this wavelength lie? (b) In a visible-light photograph such as Figure 20-9, Sirius B appears much fainter than its primary star. But in an image made with an X-ray telescope, Sirius B is the brighter star. Explain the difference.
*Sirius is 2.63 pc from Earth. By making measurements on Figure 20-9, calculate the distance between the centers of Sirius A and Sirius B at the time that this image was made in October 2003. Give your answer in astronomical units (AU). (Note that your result is the true distance only if Sirius A and Sirius B were exactly the same distance from Earth at the time the image was made. If one of the stars was closer to us than the other, the actual distance between them is greater than what you calculate.)
(a) Find the average density of a 1-M⊙ white dwarf having the same diameter as Earth. (b) What speed is required to eject gas from the white dwarf’s surface? (This is also the speed with which interstellar gas falling from a great distance would strike the star’s surface.)
In the classic 1960s science-fiction comic book The Atom, a physicist discovers a basketball-sized meteorite (about 10 cm in radius) that is actually a fragment of a white dwarf star. With some difficulty, he manages to hand-carry the meteorite back to his laboratory. Estimate the mass of such a fragment, and discuss the plausibility of this scenario.
*(a) Use the information in the caption to Figure 20-12 to calculate the diameter of the nebula SMC N76. Express your answer in parsecs. (b) How does your answer to part (a) compare to the diameters of the planetary nebulae depicted in Figure 20-7? Explain how this is consistent with the observation that gases ejected from a supergiant travel faster than gases ejected from an AGB star.
*The supergiant star depicted in Figure 20-12 is actually one member of a binary star system. The masses of the two stars are 18 M⊙ and 34 M⊙, and the orbital period is 19.56 days. (a) What is the average separation between the two stars? Give your answer in AU. (b) Compare your answer in part (a) to the sizes of the orbits of Mercury, Venus, and Earth around the Sun.
(a) What kinds of stars would you monitor if you wished to observe a core-collapse supernova explosion from its very beginning? (b) Examine Appendices 4 and 5, which list the nearest and brightest stars, respectively. Which, if any, of these stars are possible supernova candidates? Explain your answer.
*Consider a high-mass star just prior to a supernova explosion, with a core of diameter 20 km and density 4 × 1017 kg/m3. (a) Calculate the mass of the core. Give your answer in kilograms and in solar masses. (b) Calculate the force of gravity on a 1-kg object at the surface of the core. How many times larger is this than the gravitational force on such an object at the surface of Earth, which is about 10 newtons? (c) Calculate the escape speed from the surface of the star’s core. Give your answer in meters per second and as a fraction of the speed of light. What does this tell you about how powerful a supernova explosion must be in order to blow material away from the star’s core?
The shock wave that traveled through the progenitor star of SN 1987A took 2.8 hours to reach the star’s surface (see Figure 20-15a). (a) Given the size of a blue supergiant star (see Section 20-7), estimate the speed with which the front-end of the shock wave traveled through the star’s outer layers. (The core of the progenitor star was very small, so you may consider the shock wave to have started at the very center of the star.) Give your answer in meters per second.
The neutrinos from SN 1987A arrived 3 hours before the visible light. While they were en route to Earth, what was the distance between the neutrinos and the first photons from SN 1987A? Assume that neutrinos are massless and thus travel at the speed of light. Give your answers in kilometers and in AU.
*Compared to SN 1987A (see Figure 20-16), a supernova observed in 1993 called SN 1993J had a maximum apparent brightness only 9.1 × 10-4 as great. SN 1993J was 3.6 Mpc away in the galaxy M81. Using the distances from Earth to each of these supernovae, determine the ratio of the maximum luminosity of SN 1993J to that of SN 1987A. Which of the two supernovae had the greater maximum luminosity?
*Suppose that the brightness of a star becoming a supernova increases by 20 magnitudes. Show that this corresponds to an increase of 108 in luminosity.
*Suppose that the red supergiant star Betelgeuse, which lies some 425 ly from Earth, becomes a Type II supernova. (a) At the height of the outburst, how bright would it appear in the sky? Give your answer as a fraction of the brightness of the Sun (b⊙). (b) How would it compare with the brightness of Venus (about 10−9 b⊙)?
*In July 1997, a supernova named SN 1997cw exploded in the galaxy NGC 105 in the constellation Cetus (the Whale). It reached an apparent magnitude of +16.5 at maximum brilliance, and its spectrum showed an absorption line of ionized silicon. Use this information to find the distance to NGC 105. (Hint: Inspect the light curves in Figure 20-20 to find the absolute magnitudes of typical supernovae at peak brightness.)
Figure 20-21 shows a portion of the Veil Nebula in Cygnus. Use the information given in the caption to find the average speed at which material has been moving away from the site of the supernova explosion over the past 15,000 years. Express your answer in km/s and as a fraction of the speed of light.
The images that open this chapter show two kinds of glowing gas clouds: a planetary nebula and a supernova remnant. (a) Explain what makes the planetary nebula glow and what makes the supernova remnant glow. (Hint: The explanations are different for the two kinds of gas clouds.) (b) Which of these two kinds of gas clouds continues to glow for a longer time? Why?
The planetary nebula and supernova remnant shown in the images that open this chapter are both about the same age. Both objects consist of glowing gases that have expanded away from a central star. Based on these images, in which of these objects have the gases expanded more rapidly? Explain your reasoning.
There are many more main-sequence stars of low mass (less than 8 M⊙) than of high mass (8 M⊙ or more). Use this fact to explain why white dwarf stars are far more common than neutron stars.
The distance to the Crab Nebula is about 2000 parsecs. In what year did the star actually explode? Explain your answer.
The Crab Nebula has an apparent size of about 5 arcmin, and this size is increasing at a rate of 0.23 arcsec per year. (a) Assume that the expansion rate has been constant over the entire history of the Crab Nebula. Based on this assumption, in what year would Earth observers have seen the supernova explosion that formed the nebula? (b) Does your answer to part (a) agree with the known year of the supernova, 1054 c.e? If not, can you point to assumptions you made in your computations that led to the discrepancies? Or do you think your calculations suggest additional physical effects are at work in the Crab Nebula, over and above a constant rate of expansion?
Emission lines in the spectrum of the Crab Nebula exhibit a Doppler shift, which indicates that gas in the part of the nebula closest to us is moving toward us at 1450 km/s. (a) Assume that the expanding gas has been moving at the same speed since the original supernova explosion, observed in 1054 c.e., and calculate what radius and what diameter (in light-years) we should observe the nebula to have today. (b) Compare your result in part (a) to the actual size of the nebula, given in the caption to Figure 20-26.
A neutron has a mass of about 1.7 × 10−27 kg and a radius of about 10−15 m. (a) Compare the density of matter in a neutron with the average density of a neutron star. (b) If the neutron star’s density is more than that of a neutron, the neutrons within the star are overlapping; if it is less, the neutrons are not overlapping. Which of these seems to be the case for average neutrons within the star? Which do you think is the case at the center of the neutron star, where densities are higher than average?
In an X-ray burster, the surface of a neutron star 10 km in radius is heated to a temperature of 3 × 107 K. (a) Determine the wavelength of maximum emission of the heated surface (which you may treat as a blackbody). In what part of the electromagnetic spectrum does this lie? (See Figure 5-7.) (b) Find the luminosity of the heated neutron star. Give your answer in watts and in terms of the luminosity of the Sun, given in Table 16-1. How does this compare with the peak luminosity of a nova? Of a Type Ia supernova?
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Discussion Questions
Suppose that you discover a small, glowing disk of light while searching the sky with a telescope. How would you decide if this object is a planetary nebula? Could your object be something else? Explain.
Suppose the convective zone in AGB stars did not reach all the way down into their carbon-rich cores. How might this have affected the origin and evolution of life on Earth?
Imagine that our Sun was somehow replaced by a 1-M⊙ white dwarf star, and that our Earth continued in an orbit of semimajor axis 1 AU around this star. Discuss what effects this would have on our planet. What would the white dwarf look like as seen from Earth? Could you look at it safely with the unaided eye? Would Earth’s surface temperature remain the same as it is now?
The similar names white dwarf, red dwarf, and brown dwarf describe three very different kinds of objects. Suggest better names for these three kinds of objects, and describe how your names more accurately describe the objects’ properties.
The major final product of silicon fusion is 56Fe, an isotope of iron with 26 protons and 30 neutrons. This is also the most common isotope of iron found on Earth. Discuss what this tells you about the origin of the solar system.
SN 1987A did not agree with the theoretical picture outlined in Section 20-6. Does this mean that the theory was wrong? Discuss.
Imagine that we are somehow able to stand (and survive) at one of the magnetic poles of the Crab pulsar. Describe what you would see. How would the stars appear to move in the sky? What would you see if you looked straight up? What factors make this location a very unhealthy place to visit?
When neutrons are very close to one another, they repel one another through the strong nuclear force. If this repulsion were made even stronger, what effect might this have on the maximum mass of a neutron star? Explain your answer.
Web/eBook Questions
It has been claimed that the Dogon tribe in western Africa has known for thousands of years that Sirius is a binary star. Search the World Wide Web for information about these claims. What is the basis of these claims? Why are scientists skeptical, and how do they refute these claims?
Search the World Wide Web for information about SN 1994I, a supernova that occurred in the galaxy M51 (NGC 5194). Why was this supernova unusual? Was it bright enough to have been seen by amateur astronomers?
Convection Inside a Giant Star. Access and view the animation “Convection Inside a Giant Star” in Chapter 20 of the Universe Web site or eBook. Describe the motion of material in the interior of the star. In what ways is this motion similar to convection within the present-day Sun (see Section 16-2)? In what ways is it different? Is a dredge-up taking place in this animation? How can you tell?
Types of Supernovae. Access and view the animations “In the Heart of a Core-Collapse (Type II, Ib, or Ic) Supernova” and “A ThermoNuclear (Type Ia) Supernova” in Chapter 20 of the Universe Web site or eBook. Describe how these two types of supernova are fundamentally different in their origin.Search the World Wide Web for information about the latest observations of the stellar remnant at the center of SN 1987A. Has a neutron star been detected? Has a pulsar been detected? Has the supernova’s debris thinned out enough to give a clear view of the neutron star?