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Chapter 20 - White Dwarfs, Neutron Stars, and Black Holes
CHAPTER 20
WHITE DWARFS, NEUTRON STARS, AND BLACK HOLES
CHAPTER OUTLINE AND LECTURE NOTES
1. White Dwarf Stars
The evolution of a star in the H-R diagram after it becomes a white dwarf can be simulated
by heating the end of a strip of stainless steel. (Stainless steel should be used because of its
low conductivity. This confines the heated region to the tip of the strip.) When the lights
are turned off and the strip is removed from the heat, the students can see that the heated
region grows dimmer and cooler (redder) simultaneously.
2. Neutron Stars
I find it worthwhile to show a model of a pulsar consisting of a rotating air table with a
flashlight strapped to it. Obviously, during every rotation, the flashlight beam sweeps past
the class. A couple of important points can be made using the model. First, careful timing,
which the class can help with, shows that the air table is slowing its rotation, increasing the
period of time between pulses. This is due to energy losses just as for a real pulsar.
Second, if the classroom is an amphitheater, so the students are at different heights above
the air table, then if the flashlight has a fairly tight beam, the students in the back of the
room can see little or no light from the flashlight as it sweeps past. It is likely that pulsars
are tightly enough beamed that there are many of them for which we aren’t in the right
direction to see pulses.
3. Black Holes
The demonstration discussed in connection with Figure 20.28 is a pretty powerful way to
relate spatial curvature and the invention of nonexistent forces. The key is for the students
to be able to look at the television picture of what is going on and realize that they would
probably have had to invent some kind of force if they hadn’t been able to see that the
rubber material was curved.
KEY TERMS
black hole — A region of space from which no matter or radiation can escape. A black hole is
a result of the extreme curvature of space by a massive compact body.
Chandrasekhar limit — The maximum mass, about 1.4 solar masses, that a white dwarf star
can have.
event horizon — The boundary of a black hole. No matter or radiation can escape from within
the event horizon.
gamma ray burst — A brief blast of gamma rays that originates in a distant galaxy.
geodesic — The path in spacetime followed by a light beam or a freely moving object.
gravitational redshift — The increase in the wavelength of electromagnetic radiation that
occurs when the radiation travels outward through the gravitational field of a body.
magnetar — A highly magnetized neutron star that emits bursts of gamma rays.
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Chapter 20 - White Dwarfs, Neutron Stars, and Black Holes
neutron star — A star composed primarily of neutrons and supported by the degenerate
pressure of the neutrons.
neutronization — A process by which, during the collapse of the core of a star, protons and
electrons are forced together to make neutrons.
pulsar — A rotating neutron star with beams of radiation emerging from its magnetic poles.
When the beams sweep past the Earth, we see “pulses” of radiation.
Schwarzschild radius — The radius of the event horizon of a black hole.
spacelike trip — A path in spacetime that would require motion at a speed faster than the speed
of light.
spacetime — The combination of three spatial and one time coordinate that we use to locate an
event.
spacetime diagram — A diagram showing one spatial coordinate against time in which the
paths of bodies and beams of light can be plotted.
supernova — An explosion in which a star’s brightness temporarily increases by as much as a
billion times. Type Ia supernovae are caused by the rapid fusion of carbon and oxygen
within a white dwarf. Other Type I and Type II supernovae are produced by the collapse of
the core of a star.
supernova remnant — The luminous, expanding region of gas driven outward by a
supernova explosion.
synchrotron emission — Electromagnetic radiation, usually observed in the radio region of the
spectrum, produced by energetic electrons spiraling about magnetic field lines.
timelike trip — A path in spacetime that can be followed by a body moving slower than the
speed of light.
type II supernova — An extremely energetic explosion that occurs when the core of a massive
star collapses, probably producing a neutron star or black hole.
white dwarf star — A small, dense star that is supported against gravity by the degenerate
pressure of its electrons.
ANSWERS TO QUESTIONS AND PROBLEMS
Conceptual Questions
1. For main sequence stars, radius increases as mass increases. For white dwarf stars, radius
decreases as mass increases.
2. The Chandrasekhar limit, the maximum mass a white dwarf can have, is 1.4 solar masses.
3. The more massive white dwarf is dimmer because it is smaller and has less surface to
radiate energy.
4. The star becomes fainter and dimmer as time passes. Its size remains constant.
5. The rest of the star’s mass is blown into space as a cool wind while the star is an
asymptotic giant branch star.
6. Most, if not all, white dwarf stars evolve directly from the central stars of planetary
nebulae.
7. There would be fewer white dwarf stars, because stars originally more massive than 1.4
solar masses couldn’t become white dwarfs.
8. Type II supernovae show hydrogen lines in their spectra, Type I supernovae do not.
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Chapter 20 - White Dwarfs, Neutron Stars, and Black Holes
9. The iron in the core of an AGB star was produced by a long series of nuclear reactions.
The shells surrounding the iron core represent the products of earlier series of reactions.
The earliest nuclear products are farthest from the core.
10. Neutronization, in which a proton and electron combine to produce a neutron, reduces the
number of degenerate electrons in the star.
11. Infalling material rebounds from the neutron core of the star. Also, and more important,
neutrinos are absorbed by the outward moving gas. The energy from the absorbed
neutrinos pushes material outward.
12. The energy is derived from the gravitational collapse of the core of the star.
13. Observations have identified faint, distant galaxies at the locations of a number of gammaray bursts.
14. Both gamma ray bursts and supernovae are thought to occur when the core of a massive
star collapses.
15. Most of the energy is released in the form of neutrinos.
16. The bright radio emission is produced by synchrotron radiation from large numbers of
energetic electrons spiraling around magnetic field lines.
17. The expansion is slowed by sweeping up surrounding interstellar gas.
18. They enrich interstellar gas in heavy elements.
19. In both cases, as mass increases radius decreases. For a given mass, a neutron star is much
smaller than a white dwarf.
20. As a star shrinks to become a neutron star, conservation of angular momentum causes the
rotation rate of the star to increase greatly.
21. A white dwarf rotating as fast as a pulsar would break up. A pulsating white dwarf can’t
pulsate as fast as the fastest pulsars. A pulsating neutron star can’t pulsate as slowly as the
slowest pulsars.
22. The magnetic poles, from which the beams of radiation are emitted would always point in
the same directions and couldn’t sweep past the direction to the Earth.
23. The rotation rate slows as time passes.
24. The pulse-producing mechanism turns off when the period of the pulsar reaches a few
seconds.
25. Pulsars “live” much longer than supernova remnants, so the remnants that once surrounded
most pulsars can’t be seen.
26. Four, three spatial and one temporal.
27. The object maintains the same location in space (represented horizontally) but changes its
vertical position as time passes.
28. Horizontal motion would require instantaneous movement, in violation of the limitation
that nothing moves faster than the speed of light.
29. Spacelike trips require faster than light motion and are impossible. Timelike trips require
speeds slower than the speed of light and are possible.
30. One way would be to use geodesics to make a large triangle and measure the sum of the
angles in the triangle. If the sum is 180°, space is flat. If the sum is different than 180°,
space is curved.
31. The difference between 180° and the sum of the angles in a triangle in curved space
increases as the size of the triangle increases. Only if the triangle is reasonably large can
the difference be measured accurately enough to provide a real test of curvature.
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Chapter 20 - White Dwarfs, Neutron Stars, and Black Holes
32. Objects and light follow geodesics in spacetime. Because we can’t see the curvature of
spacetime, we believe the objects and light follow curved paths and invent a mythical force,
gravity, to explain their motion.
33. Her pulse rate remains constant because to measure her pulse she compares her biological
clock to a mechanical clock. All clocks run more slowly in highly curved regions of
spacetime, so both her clocks slow at the same rate and her pulse rate remains constant.
34. Light emerging from highly curved regions of spacetime is redshifted.
35. The red shifts of white dwarf spectra are mostly gravitational redshifts rather than Doppler
shifts.
36. We would see the motion of the object slow as it approaches the event horizon. It would
appear to hover just above the event horizon, but would quickly become redder and dimmer
and disappear.
37. All we can measure are the mass, electric charge, and angular momentum of the material
within a black hole.
38. The length of the year would remain the same.
Problems
1. 8 solar masses
2. 1 cm
3. –37.4, 42 magnitudes brighter than the sun
Figure-based Questions
1. 1.0 Earth radii
2. 1.25 solar masses
3. 1.2 solar masses
4. 5%
5. 14 km
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