imate level of difficulty.
1. In order for an interstellar gas cloud to contract, the average speed of its constituent particles must be less than half the cloud’s escape speed. Will a (spherical) molecular hydrogen cloud of mass 1000 solar masses, radius 10 pc, and temperature of 10 K begin to collapse? Why or why not? (See More Precisely 8-1.) HINT
2. Under the same assumptions as in Problem 1, estimate the minimum mass needed to cause a 1000 K, 1 pc cloud to collapse. HINT
3. Use the radius–luminosity–temperature relation to explain how a protostar’s luminosity changes as it moves from stage 4 (temperature 3000 K, radius 2 108 km) to stage 6 (temperature 4500 K, radius 106 km). What is the change in absolute magnitude (Sec. 17.5) HINT
4. A protostar on the Hayashi track evolves from a temperature of 3500 K and a luminosity 5000 times that of the Sun to a temperature of 5000 K and a luminosity of 3 solar units. What is its radius (a) at the start, and (b) at the end of the evolution? HINT
5. What is the (approximate) absolute magnitude of a stage-5 protostar? (See Figure 19.7.) HINT
6. Use the H–R diagrams in this chapter to estimate by what factor a 1000-solar luminosity, 3000 K protostar is larger than a main-sequence star of the same luminosity. HINT
7. By how many magnitudes does a 3-solar-mass star decrease in brightness as it evolves from stage 4 to stage 6? (See Figure 19.8.) HINT
8. As a simple model of the final stage of star formation, imagine that between stages 6 and 7 a star’s surface temperature increases with time at a constant rate while the luminosity remains constant at the stage 7 level. The stage 7 radius is equal to the solar value. Using the temperatures given in Table 19.1, calculate the star’s radius at a time exactly halfway between these two stages. HINT
9. What is the luminosity, in solar units, of a brown dwarf whose radius is 0.1 solar radii and whose surface temperature is 600 K (0.1 times that of the Sun)? HINT
10. What is the maximum distance at which the brown dwarf in the previous problem could be observed by a telescope of limiting apparent magnitude (a) 18, (b) 30? HINT
11. A shock wave from a supernova explosion moves at a speed of about 5000 km/s. How long will such a disturbance take to cross a molecular cloud 20 pc in diameter? HINT
12. The luminosity of a hypothetical star-forming region is dominated by five bright O-type stars, each of absolute magnitude 28. What is the net absolute magnitude of the region? HINT
13. If the star-forming region in Problem 12 is in a galaxy 10 Mpc (1 megaparsec = 1,000,000 pc) from Earth, calculate its apparent magnitude. HINT
14. An open cluster has a diameter of 5 pc and a mass 1000 times the mass of the Sun. (a) Estimate the typical speed of its component stars. (b) Based on this speed, estimate the number of times a typical star orbits the center of the cluster in the 500 million years it takes for the cluster to dissolve in the galactic tidal field. HINT
15. Approximating the gravitational field of our Galaxy as a mass of 1011 solar masses at a distance of 8000 pc (see Chapter 23), estimate the “tidal radius” of a 20,000-solar-mass open-star cluster—that is, the distance from the cluster’s center, outside of which the galactic tidal force overwhelms the cluster’s own gravity. HINT
1. Prestellar Evolution. As a group, create a large pie chart showing the amount of time spent in each of the stages 1 through 6 listed in Table 19.1 for a solar-type star over a total period of 30 million years. Each group member should label one or two of the stages and clearly describe the characteristics of each.
RESEARCHING ON THE WEB
To complete the following exercises, go to the online Destinations Module for Chapter 19 on the Companion Website for Astronomy Today 4/e.
1. Access the "Hertzsprung–Russell Diagram" page and describe the current evolutionary stage of 80 percent of the stars in our galaxy.
2. Access the "All Star Line Up" page and describe how Alpha Centauri relates to our Sun in terms of size, brightness, and spectral class.
3. Access the "What i