ugh to fuse hydrogen to helium in their interiors.
Many of the objects predicted by the theory of star formation have been observed in real astronomical objects. The dark interstellar regions near emission nebulae often provide evidence of cloud fragmentation and protostars. Radio telescopes are used for studying the early phases of cloud contraction and fragmentation; infrared observations allow us to see later stages of the process. Many well-known emission nebulae, lit by several O-type stars, are partially engulfed by molecular clouds, parts of which are probably fragmenting and contracting, with smaller sites forming protostars. Shock waves can compress other interstellar clouds and trigger star formation. Star birth and the production of shock waves are thought to produce a chain reaction of star formation in molecular cloud complexes.
A single collapsing and fragmenting cloud can give rise to hundreds or thousands of stars—a star cluster. The formation of the most massive stars may play an important role in suppressing further formation of lower-mass cluster members. Open clusters, with a few hundred to a few thousand stars, are found mostly in the plane of the Milky Way. They typically contain many bright blue stars, indicating that they formed relatively recently. Globular clusters are found mainly away from the Milky Way plane and may contain millions of stars. They include no main-sequence stars much more massive than the Sun, indicating that they formed long ago. Globular clusters are believed to date from the formation of our Galaxy. Loosely bound groups of newborn stars are called stellar associations. Infrared observations have revealed young star clusters or associations in several emission nebulae. Eventually, clusters break up into individual stars, although the process may take billions of years to complete.
|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. 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 previ