Chapter 20

(Background, above) These frames are the conceptions of noted space artist Dana Berry. The ten frames depict a sequence of the birth, evolution, and death of a binary-star system. The sequence starts with the large rendering of a 1 M star and a 4 M star in the process of formation and then proceeds clockwise from top left.

(Inset A) The binary stars spend most of their lives as a yellow, 1 M star much like our Sun and a blue 4 M star.

(Inset B) Nearing the end of its life, the 4 M star swells, spilling gas onto its companion and forming an accretion disk around it.

(Inset C) Continuing to flood its companion with loose gas, the accretion disk thickens, causing the two stars to resemble a dumbell.

(Inset D) The common envelope surrounding the two stars has swollen to what appears as a single, red-giant star.

(Inset E) The red giant has now reached the point where the gravity of the original two stars cannot contain the gas. The result is a gentle expulsion--not really an explosion--forming a planetary nebula rich in oxygen gas (hence the green color).

(Inset F) Zooming in on the white dot at the center of the previous frame, E, we find our original binary stars. Now they are both dwarf stars--a red dwarf on the right overheated by a white dwarf on the left.

(Inset G) An accretion bridge again joins the two stars, forming a disk of hot gas around the white-dwarf star.

(Inset H) When the white dwarf can no longer contain the infalling plasma, a violent outburst results--a nova. This mild explosion can occur many times as members of the system continue to orbit one another.

(Inset I) The likely end point of the system is two white dwarfs of roughly equal mass circling each other until long after their energy is exhausted.

LEARNING GOALS

Studying this chapter will enable you to:

Explain why stars evolve off the Main Sequence.

Outline the events that occur after a Sun-like star exhausts the supply of hydrogen in its core.

Summarize the stages in the death of a typical low-mass star, and describe the resulting remnant.

Contrast the evolutionary histories of high-mass and low-mass stars.

Discuss the observations that help verify the theory of stellar evolution.

Explain how the evolution of stars in binary systems may differ from that of isolated stars.

The process of star formation produces great changes in the physical properties of a prestellar object. After reaching the main sequence, a newborn star is destined to change very little in outward appearance for more than 90 percent of its entire stellar lifetime. At the end of this period, as the star begins to run out of fuel and die, its properties once again change greatly. Aging stars travel along evolutionary tracks that take them far from the main sequence as they head toward death. In this and the next two chapters, we will study the evolution of stars during and after their main-sequence burning stages. We will find that the ultimate fate of a star depends primarily on its mass, although interactions with other stars can also play a decisive role, and that the final states of stars can be strange indeed. By continually comparing theoretical calculations with detailed observations of stars of all types, astronomers have refined the theory of stellar evolution into a precise and powerful tool for understanding the universe.

Back The main sequence of the H-R diagram is the evolutionary stage in which most stars spend most of their lives. For example, a star such as the Sun, after spending a few tens of millions of years in formation, is expected to reside on or near the main sequence for 10 billion years before evolving into something else. That "something else" is the main topic of this chapter. As we will see, once a star leaves the main sequence, its days are numbered. Evolving off the main sequence represents the beginning of the end for any star.

Virtually all the low-mass stars that have ever formed still exist as stars. M-type dwarfs burn their fuel so slowly that not one of them has yet left the main sequence. Some of them will burn steadily for a trillion years or more. Conversely, the most massive O- and B-type stars evolve away from the main sequence after only a few tens of millions of years of burning. Most of the massive stars that have ever existed perished long ago. Between these two extremes, many stars are observed in advanced stages of stellar evolution, their properties quite different from when they first arrived on the main sequence.

All theoretical models suggest that the final stages of stellar evolution depend critically on the mass of the star. As a rule of thumb, low-mass stars die gently, and high-mass stars die catastrophically. Depending on which astronomer you ask, the dividing line between "low mass" and "high mass" is anywhere from 5 to 10 times the mass of the Sun. In this text, we will consider stars of 8 solar masses or more to be high-mass stars.

We begin by considering the evolution of a fairly low-mass star like the Sun. The stages described in the next few sections will pertain to the Sun as it nears the end of its fusion cycle 5 billion years from now. In fact, most of the qualitative features of the discussion apply to any low-mass star, although the exact numbers vary considerably. Later, we will broaden our discussion to include all stars, large and small.

MAIN-SEQUENCE EQUILIBRIUM

Gravity is always present wherever matter exists. Only some counteracting phenomenon prevents an astronomical object from completely collapsing under its own weight. In the case of stars, that competing phenomenon is gas pressure, caused by the heat of the raging inferno at the stellar core. Figure 20.1 depicts the equilibrium in which gravity's inward pull balances pressure's outward push. Keep this simple picture in mind while you study the various stages of stellar evolution described in this chapter. Also bear in mind a simple maxim that summarizes the eventual outcome of the struggle between gravity and heat in almost every phase of a star's life: Sooner or later, gravity wins.

Figure 20.1 In a steadily burning star on the main sequence, the outward pressure of hot gas balances the inward pull of gravity. This is true at every point within the star, guaranteeing its stability.

Provided that a star remains in this equilibrium state, nothing spectacular happens to it. While the star is a resident of the main sequence, its hydrogen fuel slowly fuses into helium in the core. This process is called core hydrogen burning. In Chapter 16, we saw how the proton-proton fusion chain powers the Sun. The More Precisely feature below describes another sequence of nuclear reactions, of great importance in stars more massive than the Sun, that accomplishes the same basic result as the proton-proton chain, but in a very different way.

A main-sequence star's surface occasionally erupts in flares and spots, and its atmosphere ejects copious amounts of particles and photons, but for the most part the star does not experience sudden, large-scale changes in its properties. Its average temperature and luminosity remain fairly constant. (The luminosity actually increases very slowly--the Sun is now some 30 percent brighter than it was 5 billion years ago). The star might release energy indefinitely if nothing drastic occurred. But eventually something drastic does occur.

DEPLETION OF HYDROGEN IN THE CORE

After approximately 10 billion years of steady core hydrogen burning, a Sun-like star begins to run out of fuel. Hydrogen becomes depleted, at least in a small central region about 1/100 of the star's full size. The depletion of hydrogen is slow and steady, but the consequences are severe. It is a little like an automobile cruising effortlessly along a highway at a constant speed of 55 mph for many hours, only to have the engine cough and sputter as the gas gauge reaches empty. Unlike automobiles, though, stars are not easy to refuel.

As the nuclear burning proceeds, the composition of the star's interior changes. FigureS 20.2 illustrates the increase in helium abundance and the corresponding decrease in hydrogen 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. Helium 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.

After about 10 billion years, a serious problem arises. While hydrogen burning continues in the outer core, the lack of burning at the center leads to an unstable situation. The gas pressure weakens in the helium inner core, but the inward pull of gravity does not. Gravity never lets up. Once the outward push against gravity is relaxed--even a little--structural changes in the star become inevitable.

CONTRACTION OF THE HELIUM CORE

If more heat could be generated, the star might possibly return to equilibrium. For example, were helium in the core to begin fusing into some heavier element such as carbon, all would be well once again. Energy would be created as a by-product of helium burning, and the necessary gas pressure could be reestablished. But the helium there cannot burn--not yet, anyway. Despite its high temperature, the core is far too cold to fuse helium into anything heavier.

Recall that a temperature of at least 107 K is needed to burn hydrogen into helium. Above that temperature, colliding hydrogen nuclei--that is, protons--have enough speed to overwhelm the repulsive electromagnetic force between them. With helium, however, even 107 K is insufficient for fusion. Each helium nucleus, composed of two protons and two neutrons, has a net positive charge twice that of the hydrogen nucleus. As a result, the repulsive electromagnetic force between two helium nuclei is also larger, and more violent collisions are needed to fuse helium. Tremendously high temperatures are required--about 108 K.

A core composed of helium at 107 K thus cannot generate energy through fusion. As soon as the hydrogen fuel becomes substantially depleted, the helium core begins to contract because the pressure there--without nuclear burning--is too low to counteract gravity. Just as in earlier phases of stellar evolution, this shrinkage releases gravitational energy, driving up the central temperature.

The increasingly hot core heats the overlying layers. The higher temperatures--now well over 107 K--cause hydrogen nuclei to fuse even more rapidly than before. Figure 20.3 depicts this situation, in which hydrogen is burning at a fantastic rate in a shell surrounding the nonburning helium "ash" in the center. This phase is usually known as the hydrogen-shell-burning stage. The hydrogen shell generates energy faster than the original main-sequence star's hydrogen-burning core, and its energy production continues to grow. Strange as it may seem, the star's response to the disappearance of the fire at its center is to get brighter!

Formation of Helix Nebula

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 once characterized it as a main-sequence object. The helium core is unbalanced and shrinking, on its way to becoming hot enough for helium fusion. The rest of the core is also unbalanced, fusing hydrogen into helium at a growing rate. The gas pressure exerted by this enhanced hydrogen burning increases, forcing the intermediate layers and especially the outermost layers of the star to expand. Not even gravity can stop them. Even while the core is shrinking, the overlying layers are expanding! The star, aged and unbalanced, is on its way to becoming a red giant.

Consider the observational consequences of all this. An outside observer would see the star swell, eventually becoming nearly 100 times larger than a main-sequence star of the same spectral type. Analysis of the star's Planck curve would show that the surface was about 2000 K cooler than before. This is not to say that the period of ballooning and cooling of an aged star could be observed directly. The change from a normal main-sequence star to an elderly red giant takes about 100 million years to complete.

We can trace these large-scale changes on the H-R diagram. Figure 20.4 shows the path away from the main sequence, stage 7. (Recall from Chapter 19 that stage 7 corresponds to the star's arrival on the main sequence.) The luminosity of the giant at the point marked 8 on the figure is about 10L (Remember that L is the Sun's luminosity.) It exceeds 100L at point 9. 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.

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 star. 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.

Given the rising luminosity and the falling surface temperature, it follows that the star's radius must increase, and it does so to about 20R (R is the Sun's radius) at stage 8 and eventually to about 70R at stage 9. The roughly constant-luminosity path from stage 7 (the main sequence) to stage 8 is often called the subgiant branch. 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.

RED GIANTS

Figure 20.5 compares the relative sizes of our Sun and a stage-9 red-giant star. It also indicates the evolutionary stages through which the Sun will evolve. The red giant is huge, having swollen to about 70 times its main-sequence size--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 it just a few times larger than the Earth.

Evolution of a 1-Solar Mass Star

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 density in the core is now enormous. Continued shrinkage of the red giant's core has compacted its helium gas to approximately 108 kg/m3. Contrast this with the 10-3 kg/m3 in the outermost layers of the red giant, with the 5000 kg/m3 average density of the 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 17.9). Despite its great distance from Earth (about 150 pc), its enormous luminosity of 104L makes it one of the brightest stars in the night sky.

HR Diagram Tracks Stellar Evolution

Back 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 does not 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, the temperature in the core has reached the 108 K needed for helium fusion. Helium nuclei then collide with one another, fusing into carbon nuclei and igniting the central fires once again. 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 s. 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 108K 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.

THE HELIUM FLASH

For low-mass stars, there is a major complication in the helium-burning process. 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 of 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.

Given the conditions 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 a 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.

The importance of electron degeneracy to the onset of helium burning in the core of a red giant is this: Under normal ("nondegenerate") circumstances, the core can react to and accommodate the onset of helium burning, but in its degenerate state the burning becomes unstable, with explosive consequences. In a normal star, 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 degenerate case, 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 pressure remains more or less unchanged while the nuclear reaction rates increase and the temperature continues to rise. The temperature increases rapidly in a runaway explosion called the helium flash.

For a period of a few hours, the helium burns ferociously, like an uncontrolled bomb. Despite its brevity, this period of uncontrolled fusion releases a flood of new energy, enough to expand the core, lowering its density and ultimately returning it to a stable, nondegenerate state. This expansive adjustment of the core halts its gravitational collapse, returning it to equilibrium--an equilibrium reached once again between the inward pull of gravity and the outward push of gas pressure. 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, at this stage the surface temperature is higher than it was on the red-giant branch, whereas 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--a "helium main sequence" of sorts, 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.

Death of the Sun Part I

Death of the Sun Part II

THE CARBON CORE

The nuclear reactions in a 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 million years after the initial flash.

As the helium burns, a new inner core of carbon ash forms, and phenomena familiar to us from the earlier buildup of helium ash begin to occur. Now helium becomes depleted at the very center, and eventually fusion ceases there. In response, the carbon core shrinks and heats up a little 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 in the first red-giant stage; at stage 11 the star becomes 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 the star'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.

COMPARING THEORY WITH REALITY

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. The numbers refer to the evolutionary stages noted in the figures and discussed in the text. Table 19-1 ended with stage 7, a main-sequence object fusing hydrogen into helium. Table 20-1 begins at that point and then moves on to stage 8 on the subgiant branch, as the star evolves away from the main sequence and into the red-giant phase. Stage 9 is the helium flash, at the tip of the red-giant branch. Stage 10 describes an established horizontal-branch star stably fusing helium into carbon at its core, whereas stage 11 is the asymptotic giant branch, the star's final burning phase. The remaining stages (12-14) listed in the table represent the death of a low-mass star, which we will discuss in a moment.

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 theory with reality. Figure 20.9 shows a real H-R diagram, drawn using the stars of the old globular cluster M3. The evolutionary stages discussed in the text and summarized in Figure 20.8 are marked. The similarity between theory and observation is very 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 here because observa-tional limitations make it difficult to determine the apparent brightness of low-luminosity stars in the cluster. (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 is a few parsecs across.

New Insights into Planetary Nebulae

THE FIRES GO OUT

Back As our red supergiant ascends the asymptotic giant branch, its envelope swells while its core, too cool for further nuclear burning, continues to contract. If the core temperature could become high enough for the fusion of carbon nuclei, or even a mixture of carbon and helium nuclei, still heavier products could be synthesized, and the newly generated energy would again support the star, restoring for a while the earlier equilibrium between gravity and heat. For the case of our solar-type star, however, this does not occur. The temperature never reaches the 600 million K needed for new nuclear reactions to occur. The red supergiant is now very close to the end of its nuclear-burning lifetime.

Before the carbon core can attain the incredibly high temperatures needed for carbon ignition, its density reaches a point beyond which it cannot be compressed further. At about 1010 kg/m3, the electrons in the core once again become degenerate, the contraction of the core ceases, and its temperature stops rising. This stage represents the maximum compression that the star can achieve--there is simply not enough matter in the overlying layers to bear down any harder.

This is an extraordinarily high density. A single cubic centimeter of core matter would weigh 1000 kg on the Earth--a ton of matter compressed into a volume about the size of a grape. Yet despite the extreme compression of the core, the central temperature is "only" about 300 million K. Collisions among nuclei are neither frequent nor violent enough to fuse carbon into any of the heavier elements. Consequently, silicon, iron, gold, uranium, and the many other heavy elements are not synthesized in low-mass stars. The central fires go out when carbon has formed.

PLANETARY NEBULAE

Our aged star is now in quite a predicament. Its inner carbon core is, for all practical purposes, dead. The outer-core shells continue to burn hydrogen and helium and, as more and more of the inner core reaches its final, high-density state, the zone of nuclear burning increases in intensity. Meanwhile, the outermost layers of the star continue to expand.

Around this time, the burning becomes very unstable. The helium-burning shell is subject to a series of explosive helium-shell flashes. These flashes are caused by the enormous pressure there and the extreme sensitivity of the triple-alpha burning rate to small changes in temperature. The flashes produce large fluctuations in the intensity of the radiation reaching the star's outermost layers, causing them to pulsate more and more violently.

Compounding the star's problems, its surface layers are also becoming unstable. As the temperature drops to the point at which electrons can recombine with nuclei to form atoms, each recombination produces additional photons, which tend to push the outer envelope to greater and greater distances from the core. As shown in Figure 20.10, the radius of the star oscillates more and more violently. In less than a few million years, the star's outer envelope is ejected into space at a speed of a few tens of kilometers per second.

Figure 20.10 Buffeted by helium-shell flashes from within and subject to the destabilizing influence of recombination, the outer layers of a red giant become unstable and enter into a series of growing pulsations. Eventually, the envelope is ejected and forms a planetary nebula.

In time, a rather unusual-looking object results. We say unusual because the "star" now has two distinct parts, both of which constitute stage 12 of Table 20-1. At the center, there is a small well-defined core of mostly carbon ash. Hot and dense, only the outermost part of this core still burns helium into carbon. Well beyond the core, there is a spherical shell of cooler and thinner matter--the ejected envelope of the giant--spread over a volume roughly the size of our solar system. Such an object is called a planetary nebula. Some well-known examples are shown in Figures 20.11 and 20.12. In all, some 1000 planetary nebulae are known in our Galaxy.

Formation of Knots in Helix Nebula

Figure 20.11 A planetary nebula is an object with a small dense core (central blue-white star) surrounded by an extended shell (or shells) of glowing matter. (a) The Ring Nebula in the constellation Lyra, a classic example of a planetary nebula, is about 1500 pc from us. It is about 0.2 pc in diameter--much larger than our solar system--but because of its great distance, its apparent size is only about 1/100 that of the full Moon, and it is too dim to see well with the naked eye. (See also the images on p. 52.) (b) The appearance of the planetary nebula can be explained once we realize that the shell of glowing gas around the central core is actually quite thin. There is very little gas along the line of sight between the observer and the central star (path A), so that part of the shell is invisible. Near the edge of the shell, however, there is more gas along the line of sight (paths B and C), so the observer sees a glowing ring. (c) The Helix Nebula appears to the eye as a small star with a halo around it. About 140 pc from the Earth and 0.6 pc across, its apparent size in the sky is roughly half that of the full Moon. (All the other stars visible in the photo are foreground or background objects, unrelated to the planetary nebula.)

Figure 20.12 (a) The Dumbell Nebula more clearly shows the shell-like structure of the expanding gases that make up a planetary nebula. (b) The Cat's Eye Nebula is an example of a much more complex planetary nebula. Intricate structures, including concentric gas shells, jets of high-speed gas, and shock-induced knots of gas are all visible. As usual, red indicates the presence of excited hydrogen. The nebula is about 1000 pc away, in the constellation Draco. It may have been produced by a pair of binary stars (unresolved at the center) that have both shed planetary nebulae.

The term planetary here is very misleading, for these objects have no association with planets. The name originated in the eighteenth century, when optical astronomers could barely distinguish between the myriad faint, fuzzy patches of light in the nighttime sky. With poor resolution, some of these patches did not appear as points, like stars, but instead looked more like disks--in other words, like planets. However, later observations have clearly demonstrated that the planetary nebula's fuzzy circular shape results from a shell of warm, glowing gas.

The term nebula is also a little confusing, because it suggests kinship with the various gaseous nebulae studied in Chapter 18. Although in some ways planetary nebulae resemble some emission nebulae, and both undergo similar ionization-recombination processes, these two types of objects are very different. Not only are planetary nebulae much smaller than emission nebulae, they are also associated with much older stars. Emission nebulae are the signposts of recent stellar birth. Planetary nebulae indicate impending stellar death.

The "ring" of the planetary nebula is really a three-dimensional shell completely surrounding the core. Its halo-shaped appearance is only an illusion. The shell is a complete envelope that has been expelled from around the core. However, we can see it only at the edges, where the emitting matter has accumulated along our line of sight. As shown in Figure 20.11, the shell is virtually invisible in the direction of the core. Few planetary nebulae are quite as regular as this simple picture might suggest, however. Figure 20.12 shows two systems in which the details of the gas-ejection process and interactions with the surrounding interstellar medium have apparently played important roles in determining a planetary nebula's shape and appearance.

WHITE DWARFS

The expanding envelope of a planetary nebula continues to spread out with time, becoming more diffuse and cooler, gradually merging with interstellar space. This is one way in which interstellar space becomes enriched with additional helium atoms and possibly some carbon atoms as well. These atoms are dredged up from the depths of the core into the envelope by convection during the star's final years.

The carbon core, the stellar remnant at the center of the planetary nebula, continues to evolve. Formerly concealed by the atmosphere of the red-giant star, the core appears as the envelope recedes. The core is very small. By the time the envelope is ejected as a planetary nebula, it has shrunk to about the size of Earth. In some cases, it may be even smaller than our planet. Shining only by stored heat, not by nuclear reactions, this small star has a white-hot surface when it first becomes visible, although it appears rather dim because of its small size. The core's heat and size give rise to its new name--white dwarf. This is stage 13 of Table 20-1. The approximate path followed by the star on the H-R diagram as it evolves from stage-11 red supergiant to stage-13 white dwarf is shown in Figure 20.13.

Figure 20.13 A star's passage from the horizontal branch (stage 10) to the white-dwarf stage (stage 13) by way of the asymptotic giant branch creates an evolutionary path that cuts across the entire H-R diagram.

Not all white-dwarf stars are found as the cores of planetary nebulae. Several hundred have been discovered "naked" in our Galaxy, their envelopes expelled to invisibility (or stripped away by a binary companion--as discussed shortly) long ago. Figure 20.14 shows an example of a white dwarf, Sirius B, that is particularly close to Earth; it is the faint binary companion of the much brighter and better-known Sirius A. Detailed observations show it to have the properties listed in Table 20-2. Our planet, with a radius of 0.009 R, is actually larger than this star! With more than the mass of the Sun packed into a volume smaller than the Earth, Sirius B's density is about a million times greater than anything familiar to us in the solar system.

Figure 20.14 Sirius B (the speck of light at right) is a white-dwarf star, a companion to the much larger and brighter star Sirius A. (The "spikes" on the image of Sirius A are not real; they are artifacts caused by the support struts of the telescope.)

BLACK DWARFS

Several tens of thousands of years are needed for the white dwarf to appear from behind the veil of expanding gas. Once a star becomes a white dwarf, its evolution, for all practical purposes, is over. It continues to cool and dim with time, following the dashed line near the bottom of the H-R diagram of Figure 20.13, finally becoming a black dwarf--a cold, dense, burned-out ember in space. This is stage 14 of Table 20-1, the graveyard of stars.

The cooling dwarf does not shrink much as it fades away, however. Even though its heat is leaking away into space, gravity does not compress it further. Why not? Because at the enormously high densities in the star (from the white-dwarf stage on), the resistance of electrons to being squeezed together--the same electron degeneracy that prevailed in the red-giant core around the time of the helium flash--holds the star up, even as its temperature drops almost to absolute zero. As the dwarf cools, it remains about the size of the Earth.

Back High-mass stars evolve much faster than their low-mass counterparts. The more massive a star, the more ravenous is its fuel consumption and the shorter its main-sequence lifetime. The Sun will spend a total of some 10 billion years on the main sequence, but a 5-solar-mass B-type star will remain there for only a few hundred million years. A 10-solar-mass O-type star will depart in only 20 million years or so. This trend toward much faster evolution for more massive stars continues even after the main sequence. All evolutionary changes happen much more rapidly for high-mass stars because their larger mass and stronger gravity generate more heat, which speeds up all phases of stellar evolution.

Stars leave the main sequence for one basic reason: They run out of hydrogen in their cores. As a result, the early stages of stellar evolution beyond the main sequence are qualitatively the same in all cases: Main-sequence hydrogen burning in the core eventually gives way to the formation of a nonburning, collapsing helium core surrounded by a hydrogen-burning shell. A high-mass star leaves the main sequence on its journey toward the red-giant region with an internal structure quite similar to that of its low-mass cousin.

After the main sequence, two major divergences between low-mass and high-mass stars occur. First, when a high-mass star reaches the point at which helium begins to burn, its central density is so low that the core is nondegenerate when helium fusion starts. As a result, the burning begins smoothly and stably, not explosively. There is no helium flash. The red giant remains a red giant as helium fuses into carbon. Second, the core is subsequently able to attain the 600 million K needed to burn carbon, so the evolution does not end with a carbon white dwarf. (Recall that, the heavier the nucleus, the greater its charge and the higher the temperature needed for it to fuse.) Instead, evolution continues smoothly as the star creates heavier and heavier elements, burning ever faster as it goes.

Figure 20.15 compares evolutionary tracks for several stars of different masses, from the point at which they leave the main sequence to their arrival in the red-giant region. Whereas low-mass stars ascend the giant branch almost vertically, high-mass stars move nearly horizontally across the H-R diagram after leaving the upper main sequence. Their luminosities stay roughly constant as their radii increase and their surface temperatures drop.

Figure 20.15 Evolutionary tracks for stars of 1, 5, and 15 solar masses (shown only up to the point of the helium flash in the low-mass cases). Low-mass stars ascend the giant branch almost vertically, whereas high-mass stars move roughly horizontally across the H-R diagram from the main sequence into the red-giant region. The most massive stars experience smooth transitions into each new burning stage. No helium flash occurs for stars more massive than about 4 solar masses. The loops in the tracks generally indicate the point at which a new burning stage begins. Some points are labeled with the element that has just started to fuse in the inner core.

The sudden "loops," or changes in direction of a star's motion, in Figure 20.15 are associated with the onset of new burning stages in the core. With no helium flash in a high-mass star, there is no sudden jump to the horizontal branch and no subsequent reascent of the asymptotic giant branch. Instead, the star simply loops back and forth at the top of the H-R diagram at roughly constant luminosity, creating heavier and heavier nuclear ash in its core. Some of the burning stages are marked on the figure. Notice that the most massive stars (those more massive than about 15 M) don't even reach the red-giant region before they start to fuse helium in their cores. They achieve a central temperature of 108 K while still quite close to the main sequence, and their evolutionary track continues smoothly across the H-R diagram, apparently unaffected by each successive phase of burning.

With heavier and heavier elements forming at an ever-increasing rate, the high-mass stars shown in Figure 20.15 are very close to the ends of their lives. We will discuss their fate in more detail in the next chapter, but suffice it to say here that they are destined to die in a violent explosion soon after carbon and oxygen begin to fuse in their cores. These stars evolve so rapidly that we are unlikely ever to "catch one in the act" of leaving the main sequence and traversing the H-R diagram. For most practical observational purposes, high-mass stars explode and die as soon as they leave the main sequence.

White Dwarfs in Globular Cluster

Back Star clusters provide excellent test sites for the theory of stellar evolution. Every star in a given cluster formed at the same time, from the same interstellar cloud, with virtually the same composition. Only the mass varies from one star to another. This allows us to check the accuracy of our theoretical models in a very straightforward way. Having studied in some detail the evolutionary tracks of individual stars, we now consider how their collective appearance changes in time.

In Chapter 17, we saw how astronomers estimate the ages of star clusters by determining which of their stars have already left the main sequence. In fact, the main-sequence lifetimes that go into those age measurements represent only a tiny fraction of the data obtained from theoretical models of stellar evolution. Using the information presented in the preceding sections and starting from the zero-age main sequence, we can predict exactly how a newborn cluster should look at any later time. Ever since high-speed computers began to become available in the 1960s, this is precisely what astronomers have done. Although they cannot see into the interiors of stars to test their models, they can compare stars' outward appearances with theoretical predictions. The agreement--in detail--between theory and observation is remarkably good.

To illustrate this point, let us consider the evolution of a hypothetical star cluster somewhere in the Galaxy. We begin our study shortly after the cluster's formation, with the upper main sequence already fully formed and burning steadily, and lower-mass stars just beginning to arrive on the main sequence, as shown in Figure 20.16(a). The appearance of the cluster at this early stage is dominated by its most massive stars--the bright blue supergiants. Using the evolutionary tracks described above, let us follow the cluster forward in time and ask how its H-R diagram evolves.

Figure 20.16 The changing H-R diagram of a hypothetical star cluster. (a) Initially, stars on the upper main sequence are already burning steadily while the lower main sequence is still forming. (b) At 107 years, O-type stars have already left the main sequence, and a few red giants are visible. (c) By 108 years, stars of spectral type B have evolved off the main sequence. More red giants are visible, and the lower main sequence is almost fully formed. (d) At 109 years, the main sequence is cut off at about spectral type A. The subgiant and red-giant branches are just becoming evident, and the formation of the lower main sequence is complete. A few white dwarfs may be present. (e) At 1010 years, only stars less massive than the Sun still remain on the main sequence. The cluster's subgiant, red-giant, horizontal, and asymptotic giant branches are all discernible. Many white dwarfs have now formed.

Figure 20.16(b) shows the appearance of our cluster's H-R diagram after 10 million years. The most massive O-type stars have evolved off the main sequence. Most have already exploded and vanished, as just discussed, but one or two may still be visible as red giants. The remaining cluster stars are largely unchanged in appearance--their evolution is slow enough that little happens to them in 107 years. The cluster's H-R diagram shows the main sequence slightly cut off, along with a rather poorly defined red-giant region. Figure 20.17 shows the twin open clusters h and (the Greek letter chi) Persei, along with their combined H-R diagram. Comparing Figure 20.17(b) with such diagrams as those in Figure 20.16, astronomers estimate the age of this pair of clusters to be about 10 million years.

Figure 20.17 (a) The "double cluster" h and Persei.
(b) The H-R diagram of the pair indicates that the stars are very young--probably only about 10 million years old.

At any time during the evolution, the cluster's original main sequence is intact up to some well-defined stellar mass, corresponding to the stars that are just leaving the main sequence at that instant. We can imagine the main sequence being "peeled away" from the top down, with fainter and fainter stars turning off and heading for the giant branch as time goes on. Astronomers refer to the high-luminosity end of the observed main sequence as the main-sequence turnoff. The mass of the star that is just evolving off the main sequence at any moment is known as the turnoff mass.

After 100 million years (Figure 20.16c), stars brighter than type B5 or so (about 4-5M) have left the main sequence, and a few more red supergiants are visible. By this time, most of the cluster's low-mass stars have finally arrived on the main sequence, although the dimmest M stars may still be in their contraction phase. The appearance of the cluster is now dominated by bright B stars and brighter red giants.

At 1 billion years, the main-sequence turnoff mass is around 2M, corresponding roughly to spectral type A2. The subgiant and giant branches associated with the evolution of low-mass stars are just becoming visible, as indicated in Figure 20.16(d). The formation of the lower main sequence is now complete. In addition, the first white dwarfs have just appeared, although they are generally too faint to be observed at the distances of most clusters. Figure 20.18 shows the Hyades open cluster, with its H-R diagram. The H-R diagram appears to lie between Figures 20.16(c) and 20.16(d), suggesting that the cluster's age is about 5 ×108 years.

Figure 20.18 (a) The Hyades cluster, a relatively young group of stars visible to the naked eye. (b) The H-R diagram for this cluster is cut off at about spectral type A, implying an age of about 500 million years.

At 10 billion years, the turnoff point has reached solar-mass stars, of spectral type G2. The subgiant and giant branches are now clearly discernible (see Figure 20.16e), and the horizontal and asymptotic giant branches appear as distinct regions in the H-R diagram. Many white dwarfs are also present in the cluster. Although stars in all these evolutionary stages are also present in the 1-billion-year-old cluster shown in Figure 20.16(d), they are few in number--typically only a few percent of the total number of stars in the cluster. Also, because they evolve so rapidly, they spend very little time in these regions. Low-mass stars are much more numerous and evolve more slowly, so their evolutionary tracks are more easily detected.

Figure 20.19 shows the globular cluster 47 Tucanae. By carefully adjusting their theoretical models until the cluster's main sequence, subgiant, red-giant, and horizontal branches are all well matched, astronomers have determined its age to be roughly 14 billion years, a little older than our hypothetical cluster in Figure 20.16(e). In fact, as mentioned in Chapter 17, globular cluster ages determined this way show a remarkably small spread. All the globular clusters in our Galaxy appear to have formed between about 12 and 15 billion years ago.

Figure 20.19 (a) The southern globular cluster 47 Tucanae. (b) Fitting its main-sequence turnoff and its giant and horizontal branches to theoretical models gives 47 Tucanae an age of about 14 billion years, making it one of the oldest known objects in the Milky Way Galaxy. The inset is a high-resolution ultraviolet image of 47 Tucanae's core region, taken with the Hubble Space Telescope and showing many "blue stragglers"--massive stars lying on the main sequence above the turnoff point, resulting perhaps from the merging of binary star systems.

Stellar evolution is one of the great success stories of astrophysics. Like all good scientific theories, it makes definite testable predictions about the universe, at the same time remaining flexible enough to incorporate new discoveries as they occur. Theory and observation have advanced hand in hand. At the start of the twentieth century, many scientists despaired of ever knowing even the compositions of the stars, let alone why they shine and how they change. Today, the theory of stellar evolution is a cornerstone of modern astronomy.

Back We have noted that most stars in our Galaxy are not isolated objects, but are actually members of binary-star systems. However, our discussion of stellar evolution has so far focused exclusively on isolated stars. This prompts us to ask, "How does membership in a binary-star system change the evolutionary tracks we have just described?" Because nuclear burning occurs deep in the core, does the presence of a stellar companion have any significant effect? Perhaps not surprisingly, the answer depends on the distance between the two stars in question.

For a binary system whose component stars are very widely separated--that is, the distance between the stars is greater than perhaps a thousand stellar radii--the answer is that the two stars evolve more or less independently of one another, each following the track for an isolated star of its particular mass. However, if the two stars are closer, the gravitational pull of one may strongly influence the envelope of the other. In that case, the physical properties of both may deviate greatly from those calculated for isolated single stars.

As an example, consider the star Algol (Beta Persei, the second brightest star in the constellation Perseus). By studying its spectrum and the variation in its light intensity, astronomers have determined that Algol is actually a binary (in fact, an eclipsing double-lined spectroscopic binary, as described in Chapter 17), and they have measured its properties very accurately. Algol consists of a 3.7M main-sequence star of spectral type B8 (a blue giant) with a 0.8M red subgiant companion moving in a circular orbit around it. The stars are 4 million km apart, with an orbital period of about 3 days.

A moment's thought reveals that there is something odd about these findings. On the basis of our earlier discussion, the more massive main-sequence star should have evolved faster than the less massive component. If the two stars formed at the same time (as is assumed to be the case), there should be no way that the 0.8M star could be approaching the giant stage first. Either our theory of stellar evolution is seriously in error or something has modified the evolution of the Algol system. Fortunately for theorists, the latter is the case.

To understand Algol, we must consider binary systems in a little more detail. As sketched in Figure 20.20, each star is surrounded by its own teardrop-shaped "zone of influence," inside of which its gravitational pull dominates the effects of both the other star and the overall rotation of the binary. Any matter within that region "belongs" to the star. It cannot easily flow onto the other component or out of the system. Outside the two regions, it is possible for gas to flow toward either star relatively easily. The two teardrop-shaped regions are usually called Roche lobes, after Edouard Roche, the French mathematician who first studied the binary-system problem in the nineteenth century and whose work we have already encountered in the context of planetary rings. The Roche lobes of the two stars meet at a point on the line joining them--the inner Lagrange point (L1), which we discussed in Chapter 14 when discussing asteroid motions in the solar system. This Lagrange point is a place where the gravitational pulls of the two stars exactly balance the rotation of the binary system. The greater the mass of one component, the larger is its Roche lobe and the farther from its center (and the closer to the other star) is the Lagrange point.

Figure 20.20 Each star in a binary system can be pictured as being surrounded by a "zone of influence," or Roche lobe, inside of which matter may be thought of as being "part" of that star. The two teardrop-shaped Roche lobes meet at the Lagrange point between the two stars. Outside the Roche lobes, matter may flow onto either star with relative ease.

Normally, both stars lie well within their respective Roche lobes, and such a binary system is said to be detached, as in Figure 20.21(a). However, as a star evolves off the main sequence and moves toward the giant branch, it is possible for its radius to become so large that it overflows its Roche lobe. Its gas begins to flow onto the companion through the Lagrange point. The binary in this case is said to be semidetached (Figure 20.21b). Because matter is flowing from one star onto the other, semidetached binaries are also known as mass-transfer binaries. If, for some reason, the other star also overflows its Roche lobe (either because of stellar evolution or because so much extra material is dumped onto it), the surfaces of the two stars merge, and a new configuration results. The binary system then consists of two nuclear-burning stellar cores surrounded by a single continuous common envelope--a contact binary, shown in Figure 20.21(c).

Figure 20.21 (a) In a detached binary, each star lies within its respective Roche lobe. (b) In a semidetached binary, one of the stars fills its Roche lobe and transfers matter onto the other, which still lies within its own Roche lobe. (c) In a contact or common-envelope binary, both stars have overflowed their Roche lobes, and a single star with two distinct nuclear-burning cores results.

In a binary system in which the two stars are very close together, neither star has to evolve far off the main sequence before it overflows its Roche lobe and mass transfer begins. In a wide binary, both stars may evolve all the way up the giant branch without either surface ever reaching the Lagrange point, and they evolve just as though they were isolated. Depending on the stars involved and their orbital separations, there are many different possibilities for the eventual outcome of the evolution. Let's make these ideas more definite by returning to the question of how the binary star Algol may have reached its present state.

Astronomers believe that Algol started off as a detached binary. For reference, let us label the component that is now the 0.8M subgiant as star 1 and the 3.7M main-sequence star as star 2. Initially, star 1 was the more massive of the two--perhaps 3M or so. It thus evolved off the main sequence first. Star 2 was originally a less massive star, perhaps comparable in mass to the Sun. As star 1 ascended the giant branch, it overflowed its Roche lobe, and gas began to flow onto star 2. This had the effect of reducing the mass of star 1 and increasing that of star 2, which in turn caused the Roche lobe of star 1 to shrink as its gravity decreased. As a result, the rate at which star 1 overflowed its Roche lobe increased, and a period of unstable rapid mass transfer ensued, transporting most of star 1's envelope onto star 2. Eventually, the mass of star 1 became less than that of star 2. Detailed calculations show that the rate of mass transfer dropped sharply at that point, and the stars entered the relatively stable state we see today. These changes in Algol's components are illustrated in Figure 20.22.

Figure 20.22 The evolution of the binary star Algol. (a) Initially, Algol was probably a detached binary made up of two main-sequence stars --a relatively massive blue giant and a less massive companion similar to the Sun. (b) As the more massive component (star 1) evolved off the main sequence, it expanded to fill and eventually overflow its Roche lobe, transferring large amounts of matter onto its smaller companion (star 2). (c) Today, star 2 is the more massive of the two, but it is on the main sequence. Star 1 is still in the subgiant phase and fills its Roche lobe, causing a steady stream of matter to pour onto its companion.

Being part of a binary system has radically altered the evolution of both stars in the Algol system. The original high-mass star 1 is now a low-mass subgiant, whereas the roughly solar-type star 2 is now a massive blue main-sequence star. The removal of mass from the envelope of star 1 may prevent it from ever reaching the helium flash. Instead, its naked core may eventually be left behind as a helium white dwarf. In a few tens of millions of years, star 2 will itself begin to ascend the giant branch and fill its own Roche lobe. If star 1 is still a subgiant or a giant at that time, a contact binary system will result. If, instead, star 1 has by then become a white dwarf, a new mass-transferring period--with matter streaming from star 2 back onto star 1--will begin. In that case (as we will see), Algol may have a very active and violent future in store.

Just as molecules exhibit few of the physical or chemical properties of their constituent atoms, binaries can display types of behavior that are quite different from either of their component stars. The Algol system is a fairly simple example of binary evolution, yet it gives us an idea of the sorts of complications that can arise when two stars evolve interdependently. A substantial fraction of all the binary stars in the Galaxy will pass through some sort of mass-transfer or common-envelope phase. In this chapter, we have seen one possible result of mass transfer involving main-sequence stars. We will return to this subject in the next two chapters, when we continue our discussion of stellar evolution and the strange states of matter that may result.