Exercises

Star Death

1. We have maintained that the light of a planetary nebula results from energy supplied by the hot central star. But when we look at a planetary nebula, the nebula itself is much brighter than the central star. How is this so if the nebula is powered by the central star? Hint: what does the spectrum of the central star look like?

2. From the energy output of a supernova, we may estimate that if one were to occur within fifty light years of the Earth, we would be in considerable danger. Since core collapse supernovae occur in supergiant stars that are very bright and easily seen, we can be fairly confident that there are no candidates to become supernovae in the near future that close to Earth. But maybe we shouldn't rest so easy. Can you think of a reason why? Hint: Are core collapse (type II) supernovae the only kind?

3. In the section on white dwarfs there is a table listing properties of brighter white dwarfs. Which of these would be visible to the naked eye?

4. Why do you think that many of the known white dwarf stars are parts of multiple star systems?

5. Both low-mass stars (red dwarfs) and intermediate mass stars eventually become white dwarfs. How would you answer the cynical statement that "since they will both end up at the same place, there is little point to studying them separately"?

6. The timescales for advanced burning in stars depend on three primary factors: the amount of fuel available, the amount of energy per reaction that the fuel yields, and the luminosity, which governs how fast the reactions must run in the core for equilibrium to be maintained. Explain why each of these factors leads to shorter burning timescales once a star leaves the main sequence.

7. Use Wien's Law to estimate the wavelength and the energy of the most abundant photons for temperatures of about 3 x 10⁹ K that are characteristic of silicon burning conditions in supergiants or the core of a massive star just before it collapses in a type II supernova. Compare with the corresponding energies and wavelengths in the core of the Sun.

8. In the sequence of reactions that we call nuclear statistical equilibrium, the photodisintegration of silicon into magnesium and an alpha particle requires a photon having an energy of 9.98 million electron volts (MeV). What wavelength and frequency is this photon? In what part of the spectrum does it lie?

9. In the plot of elemental abundances in the Solar System, there is an enormous dip between mass 4 and mass 12. Explain.

10. Chemists call the elements with atomic numbers from 58 to 71 (which have mass numbers roughly in the range 140 to 180) the "rare earths". Why do you think they are called "rare"?

11. Would you expect it to be more likely to see a type II supernova in a distant spiral galaxy in its disk, or in its halo? Hint: in spiral galaxies, the disk contains rather young stars and the halo contains rather old stars.

12. Why does detection of spectral lines for the element technetium in the atmospheres of red giant stars prove that neutron capture reactions occur in stars?

13. In a red giant star, iron-56 can capture three neutrons sequentially in the slow capture process to form iron-59. Iron-59 has a beta decay half-life of about a month (actually 45 days, but we just want an estimate so we assume a month). If the average rate of neutron capture in a red giant is one per year (a typical rate, given free neutron densities there), estimate the relative probablility that iron-59 will beta decay to cobalt-59 before it can capture another neutron to become iron-60.

14. Sirius A is a main sequence star of spectral class A, but Sirius B is a white dwarf that has already finished its main sequence lifetime. The mass of Sirius B is approximately half that of Sirius A. We know that stellar lifetimes are shorter for higher mass stars and longer for lower mass stars. How do you explain the apparent discrepancy?

15. What might cause a star in a binary system to fill its Roche lobe?

16. Suppose the progenitor of Supernova 1987A had been located at the position of the Sun. Counting from the time that the core collapses, how long would it have taken the light from the supernova to reach the Earth? How long would it have taken the neutrinos? Could we have observed the supernova, given that the flux of neutrinos would have been instantly lethal?

17. The expanding debris of Supernova 1987A has a velocity of about 3000 km/s. How long does it take the remnant to expand by a distance comparable to the radius of the Solar System?

18. Eta Carinae is surrounded by two hot X-ray gas regions. The first is about two light years in diameter and is believed to have been emitted from the star about 1000 years ago. The second is only about three light months in diameter and is believed to be associated with an eruption of the star about 150 years ago. If these are correct assumptions, what is the average expansion velocity of the two X-ray emitting regions?

19. Planetary nebulae were so named because they often looked like blue or blue-green Uranus and Neptune through nineteenth-century telescopes. Planetary nebulae and planets obviously have nothing to do with each other. What about the colors, though? Is there a relation between why planetary nebulae and Uranus and Neptune might look similar in color?

20. In the image of two supernovae in the galaxy NGC 664 shown below, estimate the angular width of the galaxy assuming it to be a spiral of typical size at its distance to be 300 million light years.

21. Supernovae are typically named by the year of the outburst followed by a letter sequence used to distinguish one supernova from another in a given year, for example, Supernova 1987A or SN 1987A. Use a Web search engine (for example, Alta Vista) to find information on supernovae discovered in the current year. For example, in 1999 you could search for the string "Supernova 1999" or "SN 1999" or "SN1999", since all names for supernovae discovered in 1999 would start with this prefix. Make a list of supernovae discovered in the current year and any information that you can find about them.

SOLUTIONS