11.3 The Formation of Stars Like the Sun

Let us now turn our attention to the connection between the interstellar medium and the stars in our Galaxy. How do stars form? What factors determine their masses, luminosities, and spatial distribution? In short, what basic processes are responsible for the appearance of our night sky?

Gravity and Heat

Simply stated, star formation begins when part of the interstellar medium—one of the cold, dark clouds discussed in the previous section—collapses under its own weight. An interstellar cloud is maintained in equilibrium by a balance between two basic opposing influences: gravity (which is always directed inward) and heat (in the form of outwardly directed pressure). (More Precisely 5-2) However, if gravity somehow begins to dominate over heat, then the cloud can lose its equilibrium and start to contract.

Consider a small portion of a large interstellar cloud. Concentrate first on just a few atoms, as shown in Figure 11.13. Even though the cloud’s temperature is very low, each atom has some random motion. (More Precisely 2-1) Each atom is also influenced by the gravitational attraction of all its neighbors. The gravitational force is not large, however, because the mass of each atom is so small. When a few atoms accidentally cluster for an instant, as sketched in Figure 11.13(b), their combined gravity is insufficient to bind them into a lasting, distinct clump of matter. This accidental cluster disperses as quickly as it formed. The effect of heat—the random motion of the atoms—is much stronger than the effect of gravity.

As the number of atoms increases, their gravitational attraction increases too, and eventually the collective gravity of the clump is strong enough to prevent it from dispersing back into interstellar space How many atoms are required for this to be the case? The answer, for a typical cool (100 K) cloud, is about 1057—in other words, the clump must have mass comparable to that of the Sun. If our hypothetical clump is more massive than that, then it will not disperse. Instead, its gravity will cause it to contract, ultimately to form a star.

Of course, 1057 atoms don’t just clump together by random chance. Rather, star formation is triggered when a sufficiently massive pocket of gas is squeezed by some external event. Perhaps it is compressed by the pressure wave produced when a nearby O- or B-type star forms and heats its surroundings, or possibly part of a cloud simply cools below the temperature at which its internal pressure is no longer sufficient to support it against its own gravity. Whatever the cause, theory suggests that once the collapse begins, star formation inevitably follows.

Table 11.2 lists seven evolutionary stages that an interstellar cloud goes through before becoming a main-sequence star like our Sun. These stages are characterized by different 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 11.2 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 stars of other masses.

Stage 1—An Interstellar Cloud

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 to 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. 4.3)

Figure 11.13 Atomic Motions The motions of a few atoms within an interstellar cloud are influenced by gravity so slightly that the atoms’ paths are hardly changed (a) before, (b) during, and (c) after an accidental, random encounter.

The dark region outlined by the red and green radio contours in Figure 11.12 (not the emission nebula itself, where stars have already formed) probably represents a stage-1 cloud just starting to collapse. Doppler shifts of the observed formaldehyde lines indicate that it is contracting. Less than a light year across, this region has a total mass over 1000 times the mass of the Sun—considerably greater than the mass of M20 itself.

Figure 11.14 Cloud Fragmentation As an interstellar cloud contracts, gravitational instabilities cause it to fragment into smaller pieces. The pieces also contract and fragment, eventually forming many tens or hundreds of individual stars.

Once the collapse begins, theory indicates that fragmentation into smaller and smaller clumps of matter naturally follows. As illustrated in Figure 11.14, 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. 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 collection of hundreds of stars comparable to or smaller than our Sun. There is little evidence for stars born in isolation, one star from one cloud. Most stars—perhaps all stars—appear to originate as members of multiple systems.

The process of continuing fragmentation is eventually stopped by the increasing density within the shrinking cloud. As 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 stop. However, the contraction continues.

Stages 2 and 3—A Contracting Cloud Fragment

As it enters stage 2, a fragment destined to form a star like the Sun—the end product of the process sketched in Figure 11.14—contains between one and two solar masses of material. 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 about 1012 particles/m3.

Even though the fragment has shrunk substantially, its average temperature is not much different from that of its parent 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 anywhere within it easily escape without being reabsorbed, so virtually all the energy released in the contraction 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 might be as warm as 100 K by this stage. For the most part, however, the fragment stays cold as it shrinks.

Several tens of thousands of years after it first began contracting, the start of stage 3 occurs when a stage 2 fragment has shrunk to a gaseous sphere with a diameter roughly the size of our solar system (still 10,000 times the size of our Sun). The inner regions have become opaque to their own radiation and have started to heat up considerably, as noted in Table 11.2. The central temperature has reached about 10,000 K—hotter than the hottest steel furnace on Earth. However, the gas near the edge is still able to radiate its energy into space and so remains cool. The central density by this time is approximately 1018 particles/m3 (still only 10-9 kg/m3 or so).

Figure 11.15 Orion Nebula, Up Close (a) The constellation Orion, with the region around its famous emission nebula marked by a rectangle. The Orion Nebula is the middle "star" of Orion’s sword. (b) Enlargement of the framed region of part (a), suggesting how the nebula is partly surrounded by a vast molecular cloud. Various parts of this cloud are probably fragmenting and contracting, with even smaller sites forming protostars. (c) and (d) Some of the evidence for those protostars: (c) false-color radio image of some intensely emitting molecular sites, (d) real-color visible image of embedded nebular "knots" thought to harbor protostars, and (e) high-resolution image of several young stars surrounded by disks of gas and dust where planets might ultimately form. (J. Sanford/Astrostock-Sanford; AURA; Harvard-Smithsonian Center for Astrophysics; NASA; NASA)

Orion Nebula Mosaic

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 increases 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. By the end of 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 operational definition of surface we used for the Sun.) (Sec. 9.1) From here on, the surface temperatures listed in Table 11.2 refer to the photosphere and not to the edge of the collapsing fragment, where the temperature remains low.

Figure 11.15 shows a star-forming region in Orion. Lit from within by several O-type stars, the bright Orion Nebula is partly surrounded by a vast molecular cloud that extends well beyond the roughly 5 10 parsec region bounded by the photograph in Figure 11.15(b). The Orion complex harbors several smaller sites of intense radio emission from molecules deep within its core. Shown in Figure 11.15(c), they measure about 1010 km, about the diameter of our solar system. Their density is about 1015 particles/m3, much higher than the density of the surrounding cloud. Although the temperatures of these regions cannot be estimated reliably, many researchers regard the regions as objects between stages 2 and 3, on the threshold of becoming protostars. Figures 11.15(d) and (e) are visible-light images of part of the nebula showing other evidence for protostars.

Figure 11.16 Protostar on the H-R Diagram The red arrow indicates the approximate evolutionary track followed by an interstellar cloud fragment before becoming a stage-4 protostar. (The boldface numbers on this and subsequent H-R plots refer to the prestellar evolutionary stages listed in Table 11.2 and described in the text.) Recall from Chapter 10 that"R" means the radius of the Sun.
Stages 4 and 5—Protostellar Evolution

As the protostar evolves, it shrinks, its density increases, and its temperature rises, both in the core and at the photosphere. Some 100,000 years after the fragment formed, 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, but the temperature is still short of the 107 K needed to ignite the proton-proton nuclear reactions that fuse hydrogen into helium. Still much larger than the Sun, our gassy heap is now about the size of Mercury’s orbit. Its surface temperature has risen to a few thousand kelvins.

Knowing the protostar’s radius and surface temperature, we can calculate its luminosity using the radius-luminosity-temperature relationship. (Sec. 10.4) Remarkably, it turns out to be around 1000 times the luminosity of the Sun. Because nuclear reactions have not yet begun in the protostar’s core, 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 4) rains down on its surface. (Sec. 4.3)

By the time stage 4 is reached, our protostar’s physical properties can be plotted on a Hertzsprung-Russell (H-R) diagram. (Sec. 10.5) At each phase of a star’s evolution, its surface temperature and luminosity can be represented by a single point on the diagram. The motion of that point around the diagram as the star evolves is known as the star’s evolutionary track. It is a graphical representation of a star’s life. The red track on Figure 11.16 depicts the approximate path followed by our interstellar cloud fragment since it became a protostar at the end of stage 3 (which itself lies off the right-hand edge of the figure). Figure 11.17 is an artist’s sketch of an interstellar gas cloud proceeding along the evolutionary path outlined so far.

Figure 11.17 Interstellar Cloud Evolution Artist’s conception of the changes in an interstellar cloud during the early evolutionary stages outlined in Table 11.2. (Not drawn to scale.) The duration of each stage, in years, is 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 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 contraction slows, but it does not stop completely.

After stage 4, the protostar moves downward on the H-R diagram (toward lower luminosity) and slightly to the left (toward higher temperature), as shown in Figure 11.18. By stage 5, 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. The central temperature has risen to about 5,000,000 K. The gas is completely ionized by now, but the protons still do not have enough thermal energy for nuclear fusion to begin.

Figure 11.18 Newborn Star on the H-R Diagram The changes in a protostar’s observed properties are shown by the path of decreasing luminosity, from stage 4 to stage 6. At stage 7, the newborn star has arrived on the main sequence.
Protostars often exhibit violent surface activity during this phase of their evolution, resulting in extremely strong protostellar winds, much denser than that of our Sun. This portion of the evolutionary track is often called the T Tauri phase, after T Tauri, the first "star" (actually protostar) to be observed in this stage of prestellar development.

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. Its contraction is governed largely by the rate at which it can radiate its internal energy into space. As the luminosity decreases, so too does the contraction rate.

Until the Infrared Astronomy Satellite was launched in the early 1980s, astronomers were aware only of very massive stars forming in clouds far away. IRAS showed that stars are forming much closer to home, and some of these protostars have masses comparable to that of our Sun. Figure 11.19 shows a premier example of a solar-mass protostar—Barnard 5. Its infrared heat signature is that expected of a stage 5 object.

Stages 6 and 7—A Newborn Star

Some 10 million years after its first appearance, the protostar finally becomes a true star. By stage 6, when our roughly one-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 11.18, the star’s surface temperature at this point is about 4500 K, still a little cooler than the Sun. Even though the radius of the newly formed star is slightly larger than that of the Sun, its lower temperature means that its luminosity is slightly less than (actually, about two-thirds of) the present solar value.

Figure 11.19 Protostar, Imaged An infrared image of the nearby region containing the source Barnard 5 (indicated by the arrow). On the basis of its temperature and luminosity, Barnard 5 appears to be a protostar around stage 5 on the H-R diagram. (NASA)
Indirect evidence for stage-6 stars comes from infrared observations of objects that seem to be luminous hot stars hidden from optical view by surrounding dark clouds. Their radiation is mostly absorbed by a "cocoon" of dust, then reemitted by the dust as infrared radiation. Two considerations support the idea that the hot stars responsible for heating the clouds have only recently ignited: 1) dust cocoons are predicted to disperse quite rapidly once their central stars form, and 2) these objects are invariably found in the dense cores of molecular clouds, consistent with the star-formation sequence just outlined.

Over the next 30 million years or so, the stage-6 star contracts a little more. Its 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 40 to 50 million years. Although this is a long time by human standards, it is still less than one 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 almost unchanged for the next 10 billion years.

Concept Check

What distinguishes a collapsing cloud from a protostar and a protostar from a star?