Download SUMMARY White dwarfs, neutron stars, and black holes are the

SUMMARY
White dwarfs, neutron stars, and black holes are the remnants of dead stars. A white dwarf forms when a
low­mass star expels its outer layers to form a planetary nebula shell and leaves its hot core exposed. The
radius of a white dwarf is about the same as the radius of the Earth. Its matter is degenerate, and its mass
must be less than the Chandrasekhar limit or it collapses. Having no fuel supply, a white dwarf gradually
cools and dims. If a white dwarf is in a binary system, it may accrete mass from its neighbor and explode
either as a nova or as a type Ia supernova.
A neutron star forms when a massive star's iron core collapses and triggers a supernova explosion. The
collapse compresses the core's protons and electrons together to make neutrons, forming a ball of
neutrons with a radius of a mere 10 kilometers that may contain up to about 2 to 3 solar masses.
Conservation of angular momentum during its collapse accelerates its rotation rate to about 1000 times
per second. This spin and the star's magnetic field generate beams of radiation that sweep across space,
making the spinning neutron star a pulsar.
If the massive star's iron core contains more than about 3 M⊙, a black hole, rather than a neutron star, is
born. Gravity overwhelms the pressure forces of the core, crushing it and bending space around it so that
light cannot escape. The black hole lies invisibly inside its Schwarzschild radius. If it has a companion
star, however, we may be able to see X rays from an accretion disk as gas from the neighbor falls toward
the hole.
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QUESTIONS FOR REVIEW
1. (15.1) What are the approximate mass and radius of a white dwarf compared with those of the Sun?
2. (15.1) How does a white dwarf form?
3. (15.1) What keeps a white dwarf hot?
4. (15.1) Can a white dwarf have a mass of 10 solar masses? Why? What happens if a white dwarf
increases in mass?
5. (15.1–15.22) What is meant by degeneracy pressure? How is it related to white dwarfs and neutron
stars?
6. (15.1) Explain what makes a nova occur.
7. (15.2) What is a neutron star?
8. (15.2) What are the mass and radius of a typical neutron star compared with those of the Sun? Can a
neutron star have a mass of 10 solar masses?
9. (15.2) How does a neutron star form?
10. (15.2) How do we observe neutron stars?
11. (15.2) What is a pulsar? Does it pulsate?
12. (15.2) Are all neutron stars pulsars? Are all pulsars neutron stars?
13. (15.2) What creates the beams of radiation seen in pulsars?
14. (15.2) What is nonthermal radiation?
15. (15.2) What happens when a gravitational wave moves? What does it affect? Compare this to how
light waves move.
16. (15.3) What is a black hole? Are they truly “black”? What properties can they have?
17. (15.3) What is the Schwarzschild radius?
18. (15.3) Why might the distance to the event horizon of a black hole vary depending on which
direction you measure from the center?
19. (15.3) Can astronomers see black holes? Explain.
20. (15.3) What is Hawking radiation?
THOUGHT QUESTIONS
1. (15.1) Some astronomers have suggested that cooled white dwarfs are made of diamond. Why might
it be impractical to mine them?
2. (15.1) Is a white dwarf significantly different from the core of a low­mass main­sequence star?
Thinking about how the speed of stellar evolution relates to the mass of the stars, and about what
happens when novas occur, can you explain how you might have a binary system with an 8­solar­
mass blue main­sequence star and a 1­solar­mass white dwarf?
3. (15.2) Is it surprising that a pulsar is not seen in every supernova remnant? Why?
4. (15.2) The period of a star is equal to its circumference divided by its rotational velocity. If a star
collapses to 1/X of its previous radius, how many times shorter is the period?
5. (14.5/15.2) Explain how neutron star “pulses” are different from the “pulsing” of variable stars. Are
neutron stars variable stars?
6. (15.1–15.3) White dwarfs, neutron stars, and black holes can be found in binary star systems with
normal or giant companion stars. What happens in each of these systems?
7. (2.8/15.1–15.3) A 1­solar­mass black hole would be smaller than a 1­solar­mass neutron star, which
in turn would be smaller than a 1­solar­mass white dwarf. If the Sun were replaced by each of these
objects, what would be the impact on the Earth's orbit? Compare the conditions close to the surface
or event horizon of these objects.
8. (15.3) How would you explain to an 8­year­old child that black holes may exist?
9. (15.3) Suppose you jumped into a black hole feet first. What would happen to you as your feet
approached its Schwarzschild radius? Hint: Think about tides on the Earth created by the Moon
10. (15.3) What would be different if you were orbiting a 16­solar­mass black hole or a 16­solar­mass
star at a distance of 5 AU?
PROBLEMS
1. (15.1) Calculate the density of a white dwarf star of 1 solar mass that has a radius of 104kilometers.
2. (15.1–15.2) Calculate the escape velocity from a white dwarf and a neutron star. Assume that each is
1 solar mass. Let the white dwarf's radius be 104kilometers and the neutron star's radius be 10
kilometers.
3. (15.2) A neutron star has a radius of about 10 km. What is the circumference of the equator of a
neutron star? If you could stand on it, it would be a very visibly curved surface. Imagine walking
along the neutron star's equator. How many kilometers along the circumference would correspond to
moving 7° around the star? How far is 7° along the surface of the Earth (radius of 6400 km)? Seven
degrees was the difference in angle Eratosthenes measured when he determined the circumference of
the Earth in ancient times, a task that would be a little faster to do on a neutron star (if you could
survive the high temperature and gravity!)
4. (15.2) The mass of a neutron is about 1.7 × 10−27kg. Suppose the mass of a neutron star is about 3.4
× 1030kg. How many neutrons does such a star contain?
5. (15.2) The volume of a neutron is about 10−45cubic meters. Suppose you packed the number of
neutrons you found for problem 4 (above) into a cube so that the neutrons touched edge to edge.
How big would the volume of the cube be? How big across would the cube be? Hint: The volume of
a cube with sides of length X is X3. How does the cube's size compare to the size of a neutron star?
What can you conclude about the spacing of neutrons in a neutron star?
6. (15.2) Very approximately, the core of a high­mass star about to collapse to form a neutron star in a
type II supernova might be as large as 104km and have a rotational period of around a half a day. If
the core collapsed to a radius of 10 km, what would be the period of the resulting neutron star? (Use
the answer to Thought Question 4). How does this compare to the periods of the pulsars discussed in
the chapter?
7.
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(15.3) Calculate the Schwarzschild radius of the Sun
8. (15.3) Calculate your Schwarzschild radius. How does that compare to the size of an atom? How
does it compare to the size of a proton?
9. (4.2/13.2/15.3) Use Wien's law to determine the wavelength of light generated by 10 million K gas
in an accretion disk. What type of photons have this wavelength?
10. (15.1–15.3) You observe a main sequence K0­type star that moves as if it is in a binary system, but
no companion is visible. If the period of the system is 34 days and the semimajor axis is 0.5 AU,
what is the mass of the system (remember to convert 34 days to years to use Kepler's law as
discussed in section 13.4)? What is the mass of the companion (you can look up the mass of a K0
star in the appendix, table 9)? What kind of compact star do you think the companion is? What other
observational evidence would you look for to confirm this hypothesis?
11. (15.1–15.3) You observe a main sequence B5­type star that moves as if it is in a binary system, but
no companion is visible. If the period of the system is 8.4 years and the semimajor axis is 8 AU,
what is the mass of the system? What is the mass of the companion (you can look up the mass of a
B5 star in the appendix, table 10)? What kind of compact star do you think the companion is? What
other observational evidence could you look for to confirm this hypothesis?
12. (15.1–15.3) You observe a main­sequence A0­type star that moves as if it is in a binary system, but
no companion is visible. If the period of the system is 4 years and the semimajor axis is 4 AU, what
is the mass of the system? What is the mass of the companion (you can look up the mass of an A0
star in the appendix, table 10)? What kind of compact star do you think the companion is? What
other observational evidence could you look for to confirm this hypothesis?
TEST YOURSELF
1. (15.1) If a quantity of hydrogen is added to a white dwarf, then: (select all that apply)
(a) Its radius increases.
(b) Its radius decreases.
(c) Its density increases.
(d) It may exceed the Chandrasekhar limit and collapse.
(e) The hydrogen may explosively fuse to helium.
answer
2. (15.1–15.3) For a white dwarf or a neutron star to shrink,
(a) it must emit Hawking radiation.
(b) some of the electrons or neutrons must gain higher energies.
(c) material must be removed from the star through a burst event.
(d) a black hole must develop inside the white dwarf or neutron star.
(e) it must be losing material to a companion star.
answer
3. (15.1–15.2) The spectrum of a supernova shows lots of iron and nickel, but no hydrogen. This is
probably because
(a) the explosion was of a white dwarf pushed over the Chandrasekhar limit.
(b) the explosion was of an old star that had used up all its hydrogen.
(c) the hydrogen was fused into heavier elements in the explosion.
(d) the explosion was the result of core­collapse of a massive star.
(e) the shock of the explosion pushed all the hydrogen far away from the exploding stellar remnant.
answer
4. (15.2) Which of the following has a radius (linear size) closest to that of a neutron star?
(a) The Sun
(b) The Earth
(c) A basketball
(d) A small city
(e) A gymnasium
answer
5. (15.2) What causes the radio pulses of a pulsar?
(a) The star vibrates.
(b) As the star spins, beams of radio radiation from it sweep through space. If one of these beams
points toward the Earth, we observe a pulse.
(c) The star undergoes nuclear explosions that generate radio?emission.
(d) The star's dark orbiting companion periodically eclipses the radio waves emitted by the main
star.
(e) A black hole near the star absorbs energy from it and re­emits it as radio pulses.
answer
6. (15.2) In binary systems, accreting material that falls on a neutron star produces an X­ray burst while
material that falls on a white dwarf produces a visible­light nova burst because
(a) the acceleration of gravity is stronger near the surface of a neutron star.
(b) neutron stars are hotter than white dwarfs.
(c) the accreting material comes from a hotter source in an X­ray binary.
(d) in a nova, the accreting matter is hydrogen, but in an X­ray burst it is iron.
(e) neutron stars rotate much faster than white dwarfs.
answer
7. (15.3) What evidence leads astronomers to believe that they have detected black holes?
(a) They have seen tiny dark spots drift across the face of some distant stars.
(b) They have detected pulses of ultraviolet radiation coming from within black holes.
(c) They have seen X rays, perhaps from gas around a black hole, suddenly disappear as a
companion star eclipses the hole.
(d)
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They have seen a star suddenly disappear as it was swallowed by a black hole.
(e) They have looked inside a black hole with X­ray telescopes.
answer
8. (15.3) The Schwarzschild radius of a body is
(a) the distance from its center at which nuclear fusion ceases.
(b) the distance from its surface at which an orbiting companion will be broken apart.
(c) the maximum radius a white dwarf can have before it collapses.
(d) the maximum radius a neutron star can have before it collapses.
(e) the radius of a body at which its escape velocity equals the speed of light.
answer
9. (15.1/15.3) Spectral lines emitted by material close to the event horizon of a black hole appear
redshifted to us because
(a) blue light cannot escape from a black hole.
(b) there is always a strong Doppler effect near the black hole.
(c) the photons lose energy in the strong gravitational field.
(d) accreting material is heated and glows red.
answer
10. (15.1–15.3) The Sun will ultimately
(a) suffer core collapse and explode in a type II supernova and become a neutron star.
(b) collapse without exploding and become a black hole.
(c) eject its outer layers and leave behind its core as a white dwarf.
(d) suffer core collapse and explode in a type II supernova and become a black hole.
(e) explode as a type Ia supernova.
answer
KEY TERMS
accretion disk, 401
black hole, 403
Chandrasekhar limit, 393
compact star, 391
conservation of angular momentum, 398
core­collapse supernova, 396
curvature of space, 402
degeneracy pressure, 393
escape velocity, 403
event horizon, 405
exclusion principle, 393
glitches, 400
gravitational redshift, 394
gravitational waves, 402
Hawking radiation, 408
neutron star, 396
nonthermal radiation, 399
nova, 395
pulsar, 397
Schwarzschild radius, 403
synchrotron radiation, 400
type Ia supernova, 395
type II supernova, 396
white dwarf, 392
X­ray binary, 401
Q FIGURE QUESTION ANSWERS
WHAT IS THIS? (chapter opening): This image shows a Hubble Space Telescope image of an unusual
nova, an exploding star. Most of what is visible in the image is from the “light echo” of the flash lighting
up material expelled in the late stages of the star's life.
FIGURE 15.7: Count the peaks in a time interval of, say, 1 or 2 seconds. Then divide the number of
peaks by the time interval. The one in the upper graph spins 9 times per second. The one in the lower
graph spins 3 times in 2 seconds for a spin rate of 1.5 times per second. If pulses were visible from both
poles, the number of peaks should be first divided by 2.
PROJECTS
Modeling Curved Space: You can get a bit of insight into distorted space by building a model like the
waterbed example in the book. The model will be of a two­dimensional universe (why?). To make a
stretchy two dimensional space­time, you will need about a square yard of a stretchy fabric. Attach this
with clothespins, staples or other means across the top of a large, sturdy cardboard box at least two feet
per side (tuck the flaps inside to make it sturdy). Be careful not to start any rips in the fabric. You could
also mount the fabric on a large, old picture frame or on a hula hoop, but you'll need a way to hold up the
frame or hoop sturdily. The flat fabric represents a two­dimensional universe with no mass—space is
perfectly flat. Try rolling a marble across the fabric from one side to the other—does it travel more or
less in a straight line? If we add an object with mass, space will stretch around the object. Create a circle
with a piece of string, and compare the radius measured across it with what you get dividing the
circumference by 2π. Now place an orange or apple on the fabric. Try rolling the marble across at
different distances from the orange. How is its path affected? Try setting the marble in motion around the
orange. Can you create elliptical orbits? Can you get the marble going in a circular orbit? Friction with
the fabric will slow the marble. Pick up the orange and place the end of a fabric tape measure or a string
under the center of the orange and run it straight out along the surface. Using another piece of string,
measure the circumference of a circle about an inch or so from the orange (somewhere where the fabric
appears stretched). If you divide this circumference by 2π, is the apparent radius of the circle the same as
how far it is from the end of the tape measure to where your circle intersects it? Space has been stretched
—made longer—in the direction toward the mass. Replace the orange with a heavier object (you can put
something heavy in a bowl) and try the experiments again.