Star formation begins when gravity begins to dominate over heat, causing a cloud to lose its equilibrium and start to contract. Only after the cloud has undergone radical changes in its internal structure is equilibrium finally restored.
Table 19.1 lists seven evolutionary stages that an interstellar cloud goes through prior to becoming a main-sequence star like the Sun. These stages are characterized by varying central temperatures, surface temperatures, central densities, and radii of the prestellar object. They trace its progress from a quiescent interstellar cloud to a genuine star. The numbers given in Table 19.1 and the following discussion are valid only for stars of approximately the same mass as the Sun. In the next section we will relax this restriction and consider the formation of other stars.
| TABLE 19.1 Prestellar Evolution of a Solar-Type Star | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
*For comparison, recall that the diameter of the Sun is 1.4 |
The first stage in the star-formation process is a dense interstellar cloud—the core of a dark dust cloud or perhaps a molecular cloud. These clouds are truly vast, sometimes spanning tens of parsecs (1014—1015 km) across. Typical temperatures are about 10 K throughout, with a density of perhaps 109 particles/m3. Stage 1 clouds contain thousands of times the mass of the Sun, mainly in the form of cold atomic and molecular gas. (The dust they contain is important for cooling the cloud as it contracts and also plays a crucial role in planet formation, but it constitutes a negligible fraction of the total mass.) 
(Sec. 15.2)
If such a cloud is to be the birthplace of stars, it must become unstable and eventually break up into smaller pieces. The initial collapse occurs when a pocket of gas becomes gravitationally unstable. Perhaps it is squeezed by some external event, such as the pressure wave produced when a nearby O- or B-type star forms and ionizes its surroundings, or perhaps its supporting magnetic field leaks away as charged particles slowly drift across the confining field lines. Whatever the cause, theory suggests that once the collapse begins, fragmentation into smaller and smaller clumps of matter naturally follows, as gravitational instabilities continue to operate in the gas. As illustrated in Figure 19.3, a typical cloud can break up into tens, hundreds, even thousands, of fragments, each imitating the shrinking behavior of the parent cloud and contracting ever faster. The whole process, from a single quiescent cloud to many collapsing fragments, takes a few million years.
Figure 19.3 As an interstellar cloud contracts, gravitational instabilities cause it to fragment into smaller pieces. The pieces themselves continue to collapse and fragment, eventually to form many tens or hundreds of separate stars.
In this way, depending on the precise conditions under which fragmentation takes place, an interstellar cloud can produce either a few dozen stars, each much larger than our Sun, or a whole cluster of hundreds of stars, each comparable to or smaller than our Sun. There is little evidence of stars born in isolation, one star from one cloud. Most stars—perhaps even all stars—appear to originate as members of multiple systems or star clusters. The Sun, which is now found alone and isolated in space, probably escaped from the multiple-star system where it formed, after an encounter with another star or some much larger object (such as a molecular cloud).
The second stage in our evolutionary scenario represents the physical conditions in just one of the many fragments that develop in a typical interstellar cloud. A fragment destined to form a star like the Sun contains between one and two solar masses of material at this stage. Estimated to span a few hundredths of a parsec across, this fuzzy, gaseous blob is still about 100 times the size of our solar system. Its central density is now some 1012 particles/m3.
Even though it has shrunk substantially in size, the fragment's average temperature is not much different from that of the original cloud. The reason is that the gas constantly radiates large amounts of energy into space. The material of the fragment is so thin that photons produced within it easily escape without being reabsorbed by the cloud, so virtually all the energy released in the collapse is radiated away and does not cause any significant increase in temperature. Only at the center, where the radiation must traverse the greatest amount of material in order to escape, is there any appreciable temperature increase. The gas there may be as warm as 100 K by this stage. For the most part, however, the fragment stays cold as it shrinks.
The process of continued fragmentation is eventually stopped by the increasing density within the shrinking cloud. As stage 2 fragments continue to contract, they eventually become so dense that radiation cannot get out easily. The trapped radiation causes the temperature to rise, the pressure to increase, and the fragmentation to cease.
Several tens of thousands of years after it first began contracting, a typical stage 2 fragment has shrunk by the start of stage 3 to roughly the size of our solar system (still 10,000 times the size of our Sun). The inner regions have just become opaque to their own radiation and so have started to heat up considerably, as noted in Table 19.1. The central temperature has reached about 10,000 K—hotter than the hottest steel furnace on Earth. However, the temperature at the fragment's periphery has not increased much. It is still able to radiate its energy into space and so remains cool. The density increases much faster in the core of the fragment than at its periphery, so the outer portions of the cloud are both cooler and thinner than the interior. The central density by this time is approximately 1018 particles/m3 (still only 10-9 kg/m3 or so).
For the first time, our fragment is beginning to resemble a star. The dense, opaque region at the center is called a protostar—an embryonic object perched at the dawn of star birth. Its mass grows as more and more material rains down on it from outside, although its radius continues to shrink because its pressure is still unable to overcome the relentless pull of gravity. After stage 3, we can distinguish a "surface" on the protostar—its photosphere. Inside the photosphere, the protostellar material is opaque to the radiation it emits. (Note that this is the same definition of "surface" that we used for the Sun in Chapter 16. (Sec. 16.1)) From here on, the surface temperatures listed in Table 19.1 refer to the photosphere and not to the "periphery" of the collapsing fragment, whose temperature remains low.
As the protostar evolves, it shrinks, its density grows, and its temperature rises, both in the core and at the photosphere. Some 100,000 years after the fragment began to form, it reaches stage 4, where its center seethes at about 1,000,000 K. The electrons and protons ripped from atoms whiz around at hundreds of kilometers per second, yet the temperature is still short of the 107 K needed to ignite the proton—proton nuclear reactions that fuse hydrogen into helium. (Sec. 16.5) Still much larger than the Sun, our gassy heap is now about the size of Mercury's orbit. Heated by the material falling on it from above, its surface temperature has risen to a few thousand kelvins.
Knowing the protostar's radius and surface temperature, we can calculate its luminosity. Surprisingly, it turns out to be several thousand times the luminosity of the Sun. Even though the protostar has a surface temperature only about half that of the Sun, it is hundreds of times larger, making its total luminosity very large indeed—in fact, much greater than the luminosity of most main-sequence stars. Because nuclear reactions have not yet begun, this luminosity is due entirely to the release of gravitational energy as the protostar continues to shrink, and material from the surrounding fragment (which we called the solar nebula back in Chapter 15) rains down on its surface.
By the time stage 4 is reached, our protostar's physical properties can be plotted on the Hertzsprung—Russell (H—R) diagram, as shown in Figure 19.4. Recall that an H—R diagram is a plot of two key stellar properties—surface temperature (increasing to the left) and luminosity (increasing upward). (Sec. 17.7) The luminosity scale in Figure 19.4 is expressed in terms of the solar luminosity (4 
1026 W). Our G2-type Sun is plotted at a temperature of 6000 K and a luminosity of 1 unit. As before, the dashed diagonal lines in the H—R diagrams represent stellar radius, allowing us to follow the changes in a star's size as it evolves. At each phase of a star's evolution, its surface temperature and luminosity can be represented by a point on this diagram. The motion of that point as the star evolves is known as the star's evolutionary track. It is a graphical representation of a star's life.
Figure 19.4 Diagram of the approximate evolutionary track followed by an interstellar cloud fragment prior to reaching the end of the Kelvin—Helmholtz contraction phase as a stage 4 protostar. (The circled numbers on this and subsequent plots refer to the prestellar evolutionary stages listed in Table 19.1 and described in the text.)
The red track on Figure 19.4 depicts the approximate path followed by our interstellar cloud fragment since it became a protostar at stage 3 (which itself lies off the right-hand edge of the figure). This early evolutionary track is known as the Kelvin—Helmholtz contraction phase, after two European physicists (Lord Kelvin and Hermann von Helmholtz) who first studied the subject. Figure 19.5 is an artist's sketch of an interstellar gas cloud proceeding along the evolutionary path outlined so far.
Figure 19.5 Artist's conception of the changes in an interstellar cloud during the early evolutionary stages outlined in Table 19.1. Shown are a stage 1 interstellar cloud; a stage 2 fragment; a smaller, hotter stage 3 fragment; and a stage 4/stage 5 protostar. (Not drawn to scale.) The duration of each stage, in years, is also indicated.
Our protostar is still not in equilibrium. Even though its temperature is now so high that outward-directed pressure has become a powerful countervailing influence against gravity's continued inward pull, the balance is not yet perfect. The protostar's internal heat gradually diffuses out from the hot center to the cooler surface, where it is radiated away into space. As a result, the overall contraction slows, but it does not stop completely. From our perspective on Earth, this is quite fortunate: if the heated gas were somehow able to counteract gravity completely before the star reached the temperature and density needed to start nuclear burning in its core, the protostar would simply radiate away its heat and never become a true star. The night sky would be abundant in faint protostars, but completely lacking in the genuine article. Of course, there would be no Sun either, so it is unlikely that we, or any other intelligent life form, would exist to appreciate these astronomical subtleties.
After stage 4, the protostar on the H—R diagram moves down (toward lower luminosity) and slightly to the left (toward higher temperature), as shown in Figure 19.6. Its surface temperature remains almost constant, and it becomes less luminous as it shrinks. This portion of our protostar's evolutionary path running from point 4 to point 6 in Figure 19.6 is often called the Hayashi track, after C. Hayashi, a twentieth-century Japanese researcher.
Figure 19.6 The changes in a protostar's observed properties are shown by the path of decreasing luminosity, from stage 4 to stage 6, often called the Hayashi track. At stage 7, the newborn star has arrived on the main sequence.
Protostars on the Hayashi track often exhibit violent surface activity during this phase of their evolution, resulting in extremely strong protostellar winds, much denser than that of our Sun. As mentioned earlier in Section 15.3, this portion of the evolutionary track is often called the T Tauri star, after T Tauri, the first "star" (actually protostar) to be observed in this stage of prestellar development.
By stage 5 on the Hayashi track, the protostar has shrunk to about 10 times the size of the Sun, its surface temperature is about 4000 K, and its luminosity has fallen to about 10 times the solar value. At this point, the central temperature has reached about 5,000,000 K. The gas is completely ionized by now, but the protons still do not have enough thermal energy to overwhelm their mutual electromagnetic repulsion and enter the realm of the nuclear binding force. The core is still too cool for nuclear burning to begin.
Events proceed more slowly as the protostar approaches the main sequence. The initial contraction and fragmentation of the interstellar cloud occurred quite rapidly, but by stage 5, as the protostar nears the status of a full-fledged star, its evolution slows. The cause of this slowdown is heat—even gravity must struggle to compress a hot object. The contraction is governed largely by the rate at which the protostar's internal energy can be radiated away into space. The greater this radiation of internal energy—that is, the more energy that moves through the star to escape from its surface, the faster the contraction occurs. As the luminosity decreases, so too does the contraction rate.
Some 10 million years after its first appearance, the protostar finally becomes a true star. By the bottom of the Hayashi track, at stage 6, when our roughly 1—solar mass object has shrunk to a radius of about 1,000,000 km, the contraction has raised the central temperature to 10,000,000 K, enough to ignite nuclear burning. Protons begin fusing into helium nuclei in the core, and a star is born. As shown in Figure 19.6, the star's surface temperature at this point is about 4500 K, still a little cooler than the Sun. Even though the newly formed star is slightly larger in radius than our Sun, its lower temperature means that its luminosity is somewhat less than (actually, about two-thirds of) the solar value.
Over the next 30 million years or so, the stage 6 star contracts a little more. In making this slight adjustment, the central density rises to about 1032 particles/m3 (more conveniently expressed as 105 kg/m3), the central temperature increases to 15,000,000 K, and the surface temperature reaches 6000 K. By stage 7, the star finally reaches the main sequence just about where our Sun now resides. Pressure and gravity are finally balanced, and the rate at which nuclear energy is generated in the core exactly matches the rate at which energy is radiated from the surface.
The evolutionary events just described occur over the course of some 40—50 million years. Although this is a long time by human standards, it is still less than 1 percent of the Sun's lifetime on the main sequence. Once an object begins fusing hydrogen and establishes a "gravity-in/pressure-out" equilibrium, it burns steadily for a very long time. The star's location on the H—R diagram will remain virtually unchanged for the next 10 billion years.
