The surface of a main-sequence star like the Sun occasionally erupts in flares and spots, but for the most part the star does not experience sudden, large-scale changes in its properties. Its average temperature remains fairly constant while its luminosity increases very slowly with time. The Sun has roughly the same surface temperatureas it had when it formed nearly 5 billion years ago, and is some 30 percent brighter than it was at that time.
This stable state of affairs cannot continue indefinitely. Eventually, drastic changes occur in the star's interior structure. After approximately 10 billion years of steady core hydrogen burning, a Sun-like star begins to run out of fuel. The situation is a little like that of an automobile cruising effortlessly along a highway at a constant speed of 55 mph for many hours, only to have the engine suddenly cough and sputter as the gas gauge reaches empty. Unlike automobiles, though, stars are not easy to refuel.
As nuclear burning proceeds, the composition of the star's interior changes. Figure 20.2 illustrates the increase in helium abundance and the corresponding decrease in hydrogen abundance that take place in the stellar core as the star ages. Three cases are shown: (a) the chemical composition of the original core, (b) the composition after 5 billion years, and (c) the composition after 10 billion years. Case (b) represents approximately the present state of our Sun.
Figure 20.2 Theoretical estimates of the changes in a Sun-like star's composition. Hydrogen (yellow) and helium (orange) abundances are shown (a) at birth, on the zero-age main sequence; (b) after 5 billion years; and (c) after 10 billion years. At stage (b) only about 5 percent of the star's total mass has been converted from hydrogen into helium. This change speeds up as the nuclear burning rate increases with time.
The star's helium content increases fastest at the center, where temperatures are highest and the burning is fastest. The helium content also increases near the edge of the core, but more slowly because the burning rate is less rapid there. The inner, helium-rich region becomes larger and more hydrogen deficient as the star continues to shine. Eventually, hydrogen becomes completely depleted at the center, the nuclear fires there cease, and the location of principal burning moves to higher layers in the core. An inner core of nonburning pure helium starts to grow.
Without nuclear burning to maintain it, the outward-pushing gas pressure weakens in the helium inner core; however, the inward pull of gravity does not. Once the outward push against gravity is relaxed—even a little—structural changes in the star become inevitable. As soon as hydrogen becomes substantially depleted, about 10 billion years after the star arrived on the main sequence (Figure 20.2c), the helium core begins to contract.
If more heat could be generated, then the core might possibly return to equilibrium. For example, if helium in the core were to begin fusing into some heavier element, then all would be well once again. Energy would be created as a by-product of helium burning, and the necessary outward-pushing gas pressure would be reestablished. But the helium at the center cannot burn—not yet, anyway. Despite its high temperature, the core is far too cold to fuse helium into anything heavier.
Recall from Chapter 16 that a minimun temperature of about 107 K is needed to fuse hydrogen into helium. Only above that temperature do colliding hydrogen nuclei (that is, protons) have enough speed to overwhelm the repulsive electromagnetic force between them. 
(Sec. 16.5) Because helium nuclei, with two protons each, carry a greater positive charge, their electromagnetic repulsion is larger, and even higher temperatures are needed to cause them to fuse—at least 108 K. A core composed of helium at 107 K thus cannot generate energy through fusion.
The shrinkage of the helium core releases gravitational energy, driving up the central temperature and heating the overlying layers. The higher temperatures—now well over 107 K (but still less than 108 K)—cause hydrogen nuclei to fuse even more rapidly than before. Figure 20.3 depicts this situation, in which hydrogen is burning at a furious rate in a shell surrounding the nonburning inner core of helium "ash" in the center. This phase is usually known as the hydrogen-shell-burning stage. The hydrogen shell generates energy faster than did the original main-sequence star's hydrogen-e of helium "ash" in the center. This phase is usually known as the hydrogen-shell-burning stage. The hydrogen shell generates energy faster than did the original main-sequence star's hydrogen-burning core, and the shell's energy production continues to increase as the helium core continues to shrink. Strange as it may seem, the star's response to the disappearance of the fire at its center is to get brighter!
Figure 20.3 As a star's core loses more and more of its hydrogen the hydrogen in the shell surrounding the nonburning helium ash burns ever more violently.
Conditions in the aging star have clearly changed from the equilibrium that characterized it as a main-sequence object. The helium core is unbalanced and shrinking. The rest of the core is also unbalanced, fusing hydrogen into helium at an ever-increasing rate. The gas pressure exerted by this enhanced hydrogen burning increases, forcing the star's nonburning outer layers to increase in radius. Not even gravity can stop them. While the core is shrinking and heating up, the overlying layers are expanding and cooling. The star is on its way to becoming a red giant. The change from normal main-sequence star to elderly red giant takes about 100 million years.
We can trace these large-scale changes on the H—R diagram. Figure 20.4 shows the path away from the main sequence, labeled as stage 7. The star first evolves to the right on the diagram, its surface temperature dropping while its luminosity increases only slightly. The star's roughly horizontal path from its main-sequence location (stage 7) to stage 8 on the figure is called the subgiant branch. By stage 8, the star's radius has increased to about three times the radius of the Sun.
Figure 20.4 As the core of helium ash shrinks and the intermediate stellar layers expand, the star leaves the main sequence (stage 7). At stage 8 the star is on its way to becoming a red giant. The star continues to brighten and grow as it ascends the red-giant branch to stage 9, the top of the red-giant branch. As in Chapter 19, the diagonal lines correspond to stars of constant radius, allowing us to gauge the changes in the size of our star.
The surface temperature at stage 8 has fallen to the point at which much of the interior is opaque to the radiation from within. Beyond this point, convection carries the core's enormous energy output to the surface. One consequence is that the star's surface temperature remains nearly constant between stages 8 and 9. The nearly vertical path followed by the star between stages 8 and 9 is known as the red-giant branch of the H—R diagram. By stage 9, the giant's luminosity is many hundreds of times the solar value, and its radius is around 100 solar radii.
Figure 20.5 compares the relative sizes of a G star like our Sun and a stage 9 red giant. It also indicates the stages through which the star will evolve. The red giant is huge—about the size of Mercury's orbit. In contrast, its helium core is surprisingly small—only about 1/1000 the size of the entire star, making the core just a few times larger than Earth.
Figure 20.5 Diagram of the relative sizes and colors of a normal G-type star (such as our Sun) in its formative stages, on the main sequence, and while passing through the red-giant and white-dwarf stages. At maximum swelling, the red giant is approximately 70 times the size of its main-sequence parent; the core of the giant is about 1/15 the main-sequence size and would be barely discernible if this figure were drawn to scale. The length of time spent in the various stages—protostar, main-sequence star, red giant, and white dwarf—is roughly proportional to the length of this imaginary trek through space. The star's brief stay on the horizontal branch is not shown here.
|
|
|
The density at the center of a red giant is enormous. Continued shrinkage of the red giant's core has compacted its helium gas to approximately 108 kg/m3. Contrast this value with the 10-3 kg/m3 in the giant's outermost layers, with the 5000 kg/m3 average density of Earth, and with the 150,000 kg/m3 in the present core of the Sun. About 25 percent of the mass of the entire star is packed into its planet-sized core. Perhaps the most famous red giant is the naked-eye star Betelgeuse in the constellation Orion (shown in Figure 17.10). Despite its great distance from Earth (about 150 pc), its enormous luminosity, 104 times that of the Sun, makes it one of the brightest stars in the night sky.
Should the unbalanced state of a red-giant star continue, the core would eventually collapse, and the rest of the star would slowly drift into space. The forces and pressures at work inside a red giant would literally pull it apart. However, this simultaneous shrinking and expanding cannot continue indefinitely. A few hundred million years after a solar-mass star leaves the main sequence, something else happens—helium begins to burn in the core. By the time the central density has risen to about 108 kg/m3 (at stage 9), the temperature has reached the 108 K needed for helium to fuse into carbon, and the central fires reignite.
The reaction that transforms helium into carbon occurs in two steps. First, two helium nuclei come together to form a nucleus of beryllium-8 ( 8Be). Beryllium-8 is a very unstable isotope that would normally break up into two helium nuclei in about 10-12. However, at the densities in the core of a red giant, it is very likely that the beryllium-8 nucleus will encounter another helium nucleus before this occurs, fusing with it to form carbon-12 (12C). This is the second step of the helium-burning reaction. In part, it is because of the electrostatic repulsion between beryllium-8 (containing four protons) and helium-4 (containing two) that the temperature must rise to 108 K before this reaction can take place.
Symbolically, we can represent this next stage of stellar fusion as follows:
Helium-4 nuclei are traditionally known as alpha particles. The term dates from the early days of nuclear physics, when the true nature of these particles was unknown. Because three alpha particles are required to get from helium-4 to carbon-12, the foregoing reaction is usually called the triple-alpha process.
For stars comparable in mass to the Sun, there is a major complication when helium fusion begins. At the high densities found in the core, the gas has entered a new state of matter whose properties are governed by the laws of quantum mechanics rather than by those of classical physics. Up to now we have been concerned primarily with the nuclei—protons, alpha particles, and so on—that make up virtually all the star's mass and participate in the reactions that generate its energy. However, the star contains another important constituent—a vast sea of electrons stripped from their parent nuclei by the ferocious heat in the stellar interior. At this stage in our story, these electrons play a critical role in determining the star's evolution.
Under the conditions found in the stage 9 red giant core, a rule of quantum mechanics known as the Pauli exclusion principle (after Wolfgang Pauli, one of the founding fathers of quantum physics) prohibits the electrons in the core from being squeezed too close together. In effect, the exclusion principle tells us that we can think of the electrons as tiny rigid spheres that can be squeezed relatively easily up to the point of contact but become virtually incompressible thereafter. This condition is known (for historical reasons) as electron degeneracy, and the pressure associated with the contact of the tiny electron spheres is called electron degeneracy pressure. It has nothing to do with the thermal pressure (due to the star's heat) that we have been studying up to now. In our red-giant core, the pressure resisting the force of gravity is supplied almost entirely by degenerate electrons. Hardly any of the core's support results from "normal" thermal pressure, and this has dramatic consequences once the helium begins to burn.
Under normal ("nondegenerate") circumstances, the core could react to and accommodate the onset of helium burning, but in its degenerate state the burning becomes unstable, with explosive consequences. In a star supported by thermal pressure, the increase in temperature produced by the onset of helium fusion would lead to an increase in pressure. The gas would then expand and cool, reducing the burning rate and reestablishing equilibrium. In the electron-supported core of a solar-mass red giant, however, the pressure is largely independent of the temperature. When burning starts and the temperature increases, there is no corresponding rise in pressure, no expansion of the gas, no drop in the temperature, and no stabilization of the core. Instead, the core is unable to respond to the rapidly changing conditions within it. The pressure remains more or less unchanged as the nuclear reaction rates increase, and the temperature rises rapidly in a runaway explosion called the helium flash.
For a few hours, the helium burns ferociously, like an uncontrolled bomb. Eventually, the flood of energy released by this period of runaway fusion heats the core to the point at which normal thermal pressure once again dominates. Finally able to react to the energy dumped into it by helium burning, the core expands, its density drops, and equilibrium is restored as the inward pull of gravity and the outward push of gas pressure come back into balance. The core, now stable, begins to burn helium into carbon at temperatures well above 108 K.
The helium flash terminates the giant star's ascent on the red-giant branch of the H—R diagram. Yet despite the explosive detonation of helium in the core, the flash does not increase the star's luminosity. On the contrary, the helium flash produces a rearrangement of the core that ultimately results in a reduction in the energy output. On the H—R diagram, the star jumps from stage 9 to stage 10, a stable state with steady helium burning in the core. As indicated in Figure 20.6, the surface temperature is now higher than it was on the red-giant branch, but the luminosity is considerably less than at the helium flash. This adjustment in the star's properties occurs quite quickly—in about 100,000 years.
Figure 20.6 After its large increase in luminosity while ascending the red-giant branch is terminated by the helium flash, our star settles down into another equilibrium state at stage 10, on the horizontal branch.
At stage 10 our star is now stably burning helium in its core and fusing hydrogen in a shell surrounding it. It resides in a well-defined region of the H—R diagram known as the horizontal branch, where core-helium-burning stars remain for a time before resuming their journey around the H—R diagram. The star's specific position within this region is determined mostly by its mass—not its original mass, but whatever mass remains after its ascent of the red-giant branch. The two masses differ because during the red-giant stage strong stellar winds eject large amounts of matter from a star's surface (see Interlude 20-1). As much as 20—30 percent of the original stellar mass may escape during this period. It so happens that more massive stars have lower surface temperatures at this stage, but all stars have roughly the same luminosity after the helium flash. As a result, stage 10 stars tend to lie along a horizontal line on the H—R diagram, with more massive stars to the right, less massive ones to the left.
The nuclear reactions in our star's helium core burn on, but not for long. Whatever helium exists in the core is rapidly consumed. The triple-alpha helium-to-carbon fusion reaction—like the proton—proton and CNO-cycle hydrogen-to-helium reactions before it—proceeds at a rate that increases very rapidly with temperature. At the extremely high temperatures found in the horizontal-branch core, the helium fuel doesn't last long—no more than a few tens of millions of years after the initial flash.
As helium fuses to carbon a new inner core of carbon ash forms, and phenomena similar to the earlier buildup of helium ash begin to occur. Now helium becomes depleted at the very center of the star, and eventually fusion ceases there. In response, the nonburning carbon core shrinks and heats as gravity pulls it inward, causing the hydrogen- and helium-burning rates in the overlying layers of the core to increase. The star now contains a shrinking carbon core surrounded by a helium-burning shell, which is in turn surrounded by a hydrogen-burning shell. The outer envelope of the star—the nonburning layers surrounding the core—expands, much as it did earlier during the first red-giant stage. By the time it reaches stage 11, the star has become a swollen red giant for a second time. Figure 20.7 depicts the star's interior structure during this time.
Figure 20.7 Within a few million years after the onset of helium burning, carbon ash accumulates in the inner core of a star, above which hydrogen and helium are still burning in concentric shells.
The star's second ascent of the giant branch is shown in Figure 20.8. To distinguish this second track from the first red-giant stage, this phase is sometimes known as the asymptotic giant branch. The burning rates at the center are much fiercer this time around, and g's radius and luminosity increase to values even greater than those reached at the helium flash on the first ascent. Our star is now a red supergiant. The carbon core continues to shrink, driving the hydrogen-burning and helium-burning shells to higher and higher temperatures and luminosities.
Figure 20.8 A carbon-core star reascends the giant branch of the H—R diagram—this time on a track called the asymptotic giant branch—for the same reason it evolved there the first time around: lack of nuclear burning at the core causes contraction of the core and expansion of the overlying layers.
Table 20.1 summarizes the key stages through which a solar-mass star evolves. It is a continuation of Table 19.1, except that the density units have been changed from particles per cubic meter to the more convenient kilograms per cubic meter, and we now express sizes as radii rather than diameters. The numbers in the "Stage" column refer to the evolutionary stages noted in the figures and discussed in the text.
All the H—R diagrams and evolutionary tracks presented so far are theoretical constructs based largely on computer models of the interior workings of stars. Before continuing our study of stellar evolution, let's take a moment to compare models with actual observations. Figure 20.9 shows a real H—R diagram, drawn using the stars of the old globular cluster M3. The similarity between theory and observation is striking—stars in each of the evolutionary stages 7—11 can be seen, in numbers consistent with the theoretical models. (The points in Figure 20.9 are "shifted" a little to the left relative to Figure 20.8 because of composition differences between stars such as the Sun and stars in globular clusters—globular cluster stars tend to be slightly hotter than solar-type stars of the same mass.) Astronomers place great confidence in the theory of stellar evolution precisely because its predictions are so often found to be in excellent agreement with plots of real stars.
Figure 20.9 The various evolutionary stages predicted by theory and depicted schematically in Figure 20.8 are clearly visible in this H—R diagram (a) of an old star cluster—the globular cluster M3. The faintest main-sequence stars are not shown in this diagram, which was constructed using ground-based observations, because observational limitations make it difficult to determine the apparent brightness of low-luminosity stars in the cluster. These difficulties also manifest themselves in the thickness of the main sequence, which is due almost entirely to observational error. (b) Wide-angle photograph showing M3 as it appears in the night sky. The inset is a more detailed view of the cluster itself; its field of view is a few parsecs across.
