Stars form when an interstellar cloud collapses under its own gravity and breaks up into pieces comparable in mass to our Sun. Heat, rotation, and magnetism all compete with gravity to influence the cloud's evolution. The evolution of the contracting cloud—the changes in its temperature and luminosity—can be conveniently represented as an evolutionary track on the Hertzsprung—Russell diagram. A cold interstellar cloud containing a few thousand solar masses of gas can fragment into tens or hundreds of smaller clumps of matter, from which stars eventually form.
As a collapsing prestellar fragment heats up and becomes denser it eventually becomes a protostar—a warm, very luminous object that emits radiation mainly in the infrared portion of the electromagnetic spectrum. At this stage of its evolution, the protostar is also known as a T Tauri star, after the first object of this type discovered.
Eventually, a protostar's central temperature becomes high enough for hydrogen fusion to begin, and the protostar becomes a star. For a star like the Sun, the whole formation process takes about 50 million years. More massive stars pass through similar stages, but much more rapidly. Stars less massive than the Sun take much longer to form. The zero-age main sequence is the region on the H—R diagram where stars lie when the formation process is over.
Mass is the key property for determining a star's characteristics and life span. The most massive stars have the shortest formation times and main-sequence lifetimes. At the other extreme, some low-mass fragments never reach the point of nuclear ignition. The universe may be populated with a vast number of brown dwarfs—objects that are not massive enough 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.
Protostellar winds encounter less resistance in the directions perpendicular to a protostar's disk. Thus they expel two jets of matter in the directions of the protostar's poles. As the protostellar wind gradually destroys the disk the jets widen until, with the disk gone, the wind flows away from the star equally in all directions.
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. Infrared observations have revealed young star clusters in several emission nebulae. Loosely bound groups of newborn stars are called stellar associations. Eventually, star clusters break up into individual stars, although the process may take billions of years to complete.
1. Given the typical temperatures found in interstellar space, a cloud containing as few as 1000 atoms has sufficient gravity for it to begin to collapse. (Hint)
2. Both rotation and magnetic fields act to accelerate the gravitational collapse of an interstellar cloud. (Hint)
3. The time a solar-type star spends forming is relatively short compared to the time it spends as a main-sequence star. (Hint)
4. Stars evolve along the main sequence. (Hint)
5. Most stars form as members of groups or clusters of stars. (Hint)
6. A stage 4 object has a luminosity about 1000 times that of the current Sun. (Hint)
7. As it evolves along the Hayashi track from stage 4 to stage 6, a prestellar object moves more or less horizontally across the H-R diagram. (Hint)
8. The rate of evolution of a stage 5 object is fast compared with the rates at previous stages. (Hint)
9. Brown dwarfs take a long time to form but will eventually arrive as stars on the lower main sequence. (Hint)
10. Stages 1 and 2 of star formation can be observed using optical telescopes. (Hint)
11. Shock waves produced from emission nebulae can initiate star formation in nearby molecular clouds. (Hint)
12. Shock waves for star formation can also be produced by large stars moving rapidly through the interstellar medium. (Hint)
13. In star formation, more G, K, and M stars form than O and B stars. (Hint)
14. The gas in an emission nebula eventually dissipates into space, leaving behind a star cluster. (Hint)
15. Star clusters eventually dissipate, leaving behind individual stars like the Sun. (Hint)
1. Atoms in an interstellar cloud have random motions, with an average velocity determined by the cloud's _____. (Hint)
2. A(n) _____ plots a star or protostar's changing location on the H-R diagram as the object evolves. (Hint)
3. In stage 1 of prestellar evolution, a typical interstellar cloud has the following properties: temperature _____ K, size _____ pc, mass _____ solar masses. (Hint)
4. In stage 2 of prestellar evolution, a contracting interstellar cloud _____ into smaller pieces. (Hint)
5. During stage 3 of prestellar evolution, as each piece of the original interstellar cloud continues to contract, its central density and temperature _____. (Hint)
6. At stage 4 of prestellar evolution, each piece of the interstellar cloud becomes a _____. (Hint)
7. A stage 4 object is plotted in the _____ (upper/lower) _____ (right/left) part of the H-R diagram. (Hint)
8. At stage 6 the central temperature of the object reaches _____ K. (Hint)
9. At this temperature, a stage 6 object begins to _____. (Hint)
10. At stage 7, the star has reached the _____. (Hint)
11. The T Tauri phase of a star occurs during stage _____. (Hint)
12. It takes a star like the Sun a total of about _____ million years to form. (Hint)
13. Stars much more massive than the Sun take about _____ years to form; very low mass stars may take over _____ years. (Hint)
14. Astronomers look for emissions at _____ wavelengths to identify interstellar clouds in stages 1 and 2. (Hint)
15. At stages 4, 5, and 6, objects emit a great deal of radiation in the _____ part of the electromagnetic spectrum. (Hint)
1. Briefly describe the basic chain of events leading to the formation of a star like the Sun. (Hint)
2. What is the role of heat in the process of stellar birth? (Hint)
3. What is the role of rotation in the process of stellar birth? (Hint)
4. What is the role of magnetism in the process of stellar birth? (Hint)
5. What is an evolutionary track? (Hint)
6. Why do stars tend to form in groups? (Hint)
7. At what point does a star-forming cloud become a protostar? When does it become a full-fledged star? (Hint)
8. What are brown dwarfs? (Hint)
9. What are T Tauri stars? (Hint)
10. Because stars live much longer than we do, how do astronomers test the accuracy of theories of star formation? (Hint)
11. At what evolutionary stages must astronomers use radio and infrared radiation to study prestellar objects? Why can't they use visible light? (Hint)
12. What is a shock wave? Of what significance are shock waves in star formation? (Hint)
13. Explain the usefulness of the Hertzsprung—Russell diagram in studying the evolution of stars. Why can't evolutionary stages 1—3 be plotted on the diagram? (Hint)
14. Compare the times necessary for the various stages in the formation of a star like the Sun. Why are some so short and others so long? (Hint)
15. In the formation of a star cluster with a wide range of stellar masses, is it possible for some stars to die out before others have finished forming? Do you think this will have any effect on the cluster's formation? (Hint)
1. In order for an interstellar gas cloud to contract, the average speed of its constituent atoms must be less than half the cloud's escape speed. Will a hydrogen cloud of mass 1000 solar masses, radius 10 pc, and temperature of 10 K begin to collapse? (See More Precisely 8-1.)
2. A certain interstellar cloud contains 1060 atoms. Hydrogen (mass per atom = 1.7 
10-27 kg) accounts for 90 percent of the atoms, and the remainder are helium (each atom having four times the mass of a hydrogen atom). What is the cloud's mass, in solar masses (2 1030 kg)? (Hint)
3. Use the radius—luminosity—temperature relation L 
R2 T4; (Hint) to explain how a protostar's luminosity changes as it moves from stage 4 (T = 3000 K, R = 2 108 km) to stage 6 (T = 4500 K, R = 106 km).
4. A protostar on the Hayashi track evolves from a temperature T = 3500 K and a luminosity of L = 5000 times that of the Sun to T = 5000 K and L = 3 solar units. What is its radius (a) at the start of the evolution? (b) At the end of the evolution? (c) When the luminosity is half the initial value? (Hint)
5. Through how many magnitudes does a 3—solar mass star decrease in brightness as it evolves from stage 4 to stage 6? (Hint)
6. 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)
7. 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 that of the Sun)? (Hint)
8. 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?
9. A typical open cluster has a diameter of 10 pc; its component stars have an average speed of 1 km/s. Estimate the number of times a typical star orbits the center of the cluster in the 1 billion years it takes for the cluster to dissolve in the Galactic tidal field.
10. 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 2000—solar mass star cluster—that is, the distance from the cluster center outside of which the Galactic tidal force overwhelms the cluster's gravity. (Hint)
1. The Trifid Nebula, otherwise known as M20, is a place where new stars are forming. It has been called a "dark night revelation, even in modest apertures." An 8- to 10-inch telescope is needed to see the triple-lobed structure of the nebula. Ordinary binoculars reveal the Trifid as a hazy patch located in the constellation Sagittarius. This nebula is set against the richest part of the Milky Way, the edgewise projection of our own Galaxy around the sky. It is one of many wonders in this region of the heavens. What are the dark lanes in M20? Why are other parts of the nebula bright? There have been reports of large-scale changes occurring in this nebula in the last century and a half. The reports are based on old drawings, which show M20 looking slightly different from how it appears today. Do you think it possible for a cloud in space to undergo a change in appearance on a time scale of years, decades, or centuries?
