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| Neutron Stars and Black Holes |
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1. | Use the "rules of thumb" that white dwarfs are about the size of the Earth but with the mass of the Sun, and neutron stars are about the size of a city, but with the mass of the Sun to (1) make a sketch, to scale, of the relative sizes of the Sun, a white dwarf, and a neutron star and (2) estimate the densities in grams per cubic centimeter for these three objects. |
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2. | Neutron stars are very hot, something like a million K for a young one. Hot objects glow brightly, so why are neutron stars hard to see? |
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3. | Neutron stars can have surface temperatures of a million K. Why are they so hot, since they have no internal source of fusion energy? |
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4. | Use the Planck law to calculate the total luminosity expected at visible wavelengths for a white dwarf of radius 8000 km and surface temperature 40,000 K and a neutron star of radius 10 kilometers and surface temperature 1,000,000 K. |
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5. | Some of the fastest pulsars known (millisecond pulsars) are found in globular clusters. Would you normally expect to find fast pulsars in globular clusters? |
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6. | What are the two main reasons that not every neutron star corresponds to a pulsar? |
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7. | In movies and television, black holes are often depicted as ravenous monsters wandering through space looking for matter. Would you expect black holes to be any more efficient than a normal star in sucking up any matter found in their vicinity? |
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8. | How many revolutions does the Binary Pulsar make in a year? |
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9. | The size of the Binary Pulsar's orbit is shrinking by about 3 millimeters per revolution, according to the observed decrease in orbital period. At that rate, how long will it take for the two neutron stars to merge? |
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10. | Suppose you had two nonrotating, uncharged black holes of the same mass. How could you label them to tell one from the other? |
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11. | On April 1, your astronomy instructor asks you to calculate the Schwarzschild radius of a watermelon. A fellow astronomy student tells you that it is an April Fool's joke: a watermelon does not have a Schwarzchild radius because that is characteristic of a black hole and watermelons clearly are not black holes. Is she correct? |
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12. | Can you think of a plausible qualitative reason why type I and type II Cepheid variables should have different period-luminosity relations? (Hint: variability is associated with changes in opacity in internal layers.) |
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13. | Accretion disks around compact objects such as neutron stars are often strong sources of X-rays. Assuming the accretion disks to radiate as black bodies, what is the approximate temperature required for the peak radiation to come in the X-ray portion of the spectrum? |
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14. |
Black holes are solutions of the general theory of relativity and require
advanced mathematics for their understanding. However, some results from this
theory are very simple. One is the prediction for the radius
R of a spherically
symmetric black hole without rotation (the Schwartzchild solution):
where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light. What would be the radius of a black hole of (a) Earth's mass, (b) the Sun's mass, and (3) 1 billion solar masses? |
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15. | Compare the relative size of the Crab Nebula to the Crab Pulsar with the relative size of a 1 km diameter sphere to that of a hydrogen atom. |