A nova is a star that suddenly increases greatly in brightness, then slowly fades back to its normal appearance over a period of months. It results when a white dwarf in a binary system draws hydrogen-rich material from its companion. The gas builds up on the white dwarf’s surface, eventually becoming hot and dense enough for the hydrogen to burn explosively, temporarily causing a large increase in the dwarf’s luminosity. The matter flowing from the companion star does not fall directly onto the surface of the dwarf. Instead, it goes into orbit around it, forming an accretion disk. Friction within the disk causes the gas to spiral slowly inward, heating up and glowing brightly as it nears the dwarf’s surface.
Stars more massive than about 8 solar masses are able to attain high enough central temperatures to burn carbon and heavier nuclei. As they burn, their cores form a layered structure consisting of burning shells of successively heavier elements. A nonburning core of iron builds up at the center. Iron is special in that its nuclei can neither be fused together nor split apart to produce energy. As a result, stellar nuclear burning stops at iron. As a star’s iron core grows in mass it eventually becomes unable to support itself against gravity and begins to collapse. At the enormous densities and temperatures produced during the collapse, iron nuclei are broken down into their constituent particles—protons and neutrons. The protons combine with electrons to form more neutrons. Eventually, when the core has become so dense that the neutrons are effectively brought into physical contact with one another, their resistance to further squeezing stops the collapse and the core rebounds, sending a violent shock wave out through the rest of the star. The star is blown to pieces in a core-collapse supernova.
Astronomers classify supernovae into two broad categories: Type I and Type II. These classes differ by their light curves and by their composition. Type I supernovae are hydrogen- poor and have a light curve similar in shape to that of a nova. Type II supernovae are hydrogen-rich and have a characteristic bump in the light curve a few months after maximum. A Type II supernova is a core-collapse supernova. A Type I supernova occurs when a carbon-oxygen white dwarf in a binary system exceeds about 1.4 solar masses (the Chandrasekhar mass)—the maximum mass that can be supported against gravity by electron degeneracy pressure. The star collapses and explodes as its carbon ignites. This type of supernova is called a carbon-detonation supernova.
Theory predicts that a supernova visible from Earth should occur within our Galaxy about once a century, although none has been observed in the last 400 years. We can see evidence of a past supernova in the form of a supernova remnant, a shell of exploded debris surrounding the site of the explosion and expanding into space at thousands of kilometers per second.
All elements heavier than helium formed by stellar nucleosynthesis—the production of new elements by nuclear reactions in the cores of evolved stars. Elements beyond carbon tend to form by helium capture rather than by the fusion of two heavy nuclei. Therefore, nuclei whose masses are a multiple of the mass of a helium nucleus tend to be more common than others. At high enough core temperatures, photodisintegration breaks apart some heavy nuclei, providing helium-4 nuclei for the synthesis of even more massive elements, leading to a buildup of iron-56 in the core. Elements beyond iron form by neutron capture in the cores of evolved stars. With no repulsive electromagnetic barrier to overcome, neutrons can easily combine with nuclei. During a supernova explosion, rapid neutron capture occurs, producing the heaviest nuclei of all. Comparisons between theoretical predictions of element production and observations of element abundances in stars and supernovae provide strong support for the theory of stellar nucleosynthesis.
The processes of star formation, evolution, and explosion form a cycle that constantly enriches the interstellar medium with heavy elements and sows the seeds of new generations of stars. Without the elements produced in supernovae, life on Earth would be impossible.
|PROBLEMS||Algorithmic versions of these questions are available in the Practice Problems Module of the Companion Website.|
The number of squares preceding each problem indicates the approximate level of difficulty.
1. Estimate how close an 0.5-solar-mass white dwarf must come to the center of a 2-solar-mass subgiant of radius 10 times that of the Sun in order for the white dwarf’s tidal field to strip matter from the companion’s surface. (Hint: The tidal force approximation given in More Precisely 7-3 won’t work here. Go back to the definition of the tidal force as a difference between two gravitational forces.) HINT
2. Calculate the orbital speed of matter in an accretion disk just above the surface of 0.6-solar-mass, 15,000-km-diameter white dwarf. HINT
3. A certain telescope could just detect the Sun at a distance of 10,000 pc. What is the apparent magnitude of the Sun at this distance? (For convenience, take the Sun’s absolute magnitude to be 5.) What is the maximum distance at which it could detect a nova having a peak luminosity of 105 solar luminosities? HINT
4. Repeat the previous calculation for a supernova having a peak luminosity 1010 times that of the Sun. What would be the apparent magnitude of the explosion if it occurred at a distance of 10,000 Mpc? Would it be detectable by any existing telescope? HINT
5. At what distance would a supernova of absolute magnitude -20 look as bright as the Sun? As the Moon? Would you expect a supernova to occur that close to us? HINT
6. A (hypothetical) supernova at a distance of 150 pc has an absolute magnitude of -20. Compare its apparent magnitude with that of (a) the full Moon; and (b) Venus at its brightest. (See Figure 17.7.) Would you expect a supernova to occur this close to us? HINT
7. A supernova’s energy is often compared to the total energy output of the Sun over its lifetime. Using the Sun’s current energy output, calculate its total energy output, assuming it has a 1010 year main-sequence lifetime. How does this compare with the energy released by a supernova? HINT
8. The Hubble Space Telescope is observing a distant Type I supernova of peak apparent magnitude 24. Using the light curve in Figure 21.8, estimate how long after the peak brightness the supernova will become too faint to be seen. HINT
9. The Crab Nebula is now about 1 pc in radius. If it was observed to explode in A.D. 1054, roughly how fast is it expanding? (Assume a constant expansion rate. Is that a reasonable assumption?) HINT
10. If stars form in our Galaxy at an average rate of 10 per year and all stars greater than 8 solar masses explode as supernovae, use Figure 17.23 to estimate the rate of Type II supernovae in our Galaxy. HINT
11. Assuming an interstellar extinction of 2 mag/kpc, calculate the maximum distance at which we could see (with the naked eye, limiting magnitude 6) a Galactic supernova of absolute magnitude -19. (See Chapter 18, problem 9 for more on how to go about solving the equation you obtain here.) HINT
12. Repeat the previous question, but for a survey telescope of limiting magnitude 18. HINT
13. As we will see in Chapter 23, the star-forming portion of our Galaxy consists of a highly flattened circular disk about 30 kpc (30,000 pc) in diameter. Interstellar extinction limits our view to within a radius of about 5 kpc of the Sun. If supernovae occur in the Galaxy roughly once every 30 years, on average, and are uniformly spread throughout the disk, calculate how often we should expect to see a supernova. HINT
14. Assuming the data in the previous question, taking all supernovae, for simplicity, to have absolute magnitude -20, and ignoring interstellar extinction for such nearby events, calculate how often we should expect to observe a supernova brighter than the full Moon (apparent magnitude -12.5). HINT
15. Based on the data in Table 21.1, estimate the fraction by mass of “iron-group” elements and the total mass of all elements in the Sun. Compare this with Earth’s mass. HINT
1. Supernova Brightness. Each group member should select a different star listed in Appendix 3: Table 4—The Twenty Brightest Stars—and determine what its new apparent visual magnitude would be if it became a supernova and increased in brightness by a factor of 10,000.
RESEARCHING ON THE WEB
To complete the following exercises, go to the online Destinations Module for Chapter 21 on the Companion Website for Astronomy Today 4/e.
1. Access the "Supernova Remnants" page and describe the Cygnus loop in terms of what object it is a part of and where it is found in the sky.
1. In 1758, the French comet hunter Charles Messier discovered the sky’s most legendary supernova remnant, now called M1, or the Crab Nebula. It is located northwest of Zeta Tauri, the star that marks the southern tip of the horns of Taurus the Bull. Try to find it—an 8-inch telescope reveals the Crab’s oval shape, but it will appear faint; a 10-inch or larger telescope reveals some of its famous filamentary structure.
2. In the Handbook of Chemistry and Physics, available in the library reference section, look up the table of isotopes. Pick one or more isotopes and follow their decay into a final stable isotope. For example, choose cobalt-59, formed in the s-process. Note how the isotope decays, what is emitted, and the half-life of the decays. Try this exercise for uranium-235, uranium-238, and plutonium-239.
|SKYCHART III PROJECTS||The SkyChart III Student Version planetarium program on which these exercises are based is included as a separately executable program on the CD in the back of this text.|
1. The Crab Nebula in Taurus, also known as M1, is a famous diffuse nebula that is not particularly easy to discern under poor seeing conditions. Use SkyChart III to find the location of M1. The easiest way to locate it with the software is with VIEW/Center Object/Crab Nebula. Set VIEW/5° FIELD so you can see which object is M1. Then zoom out to a field of about 45° so you can see where it is in relation to Pleiades, M45, Orion, and Gemini.
In addition to the Practice Problems and Destinations modules, the Companion Website at http://www.prenhall.com/chaisson
provides for each chapter an additional true-false, multiple choice,
and labeling quiz, as well as additional annotated images, animations,
and links to related Websites.