20.3 The Death of a Low-Mass Star


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 central temperature could become high enough for carbon fusion to occur, still heavier products could be synthesized, and the newly generated energy might again support the star, restoring for a time the equilibrium between gravity and heat. For solar-mass stars, however, this does not occur. The temperature never reaches the 600 million K needed for a new round of 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 (stage 12 in Table 20.1) represents the maximum compression that the star can achieve—there is simply not enough matter in the overlying layers to bear down any harder.

 TABLE 20.1  Evolution of a Sun-like Star
(km) (solar radii)
7 1010 15 6000 105 7105 1 Main-sequence star
8 108 50 4000 107 2106 3 Subgiant branch
9 105 100 4000 108 7107 100 Helium flash
10 5107 200 5000 107 7106 10 Horizontal branch
11 104 250 4000 108 4108 500 Asymptotic giant branch
12 105 300 100,000 1010 104 0.01 Carbon core
    3000 10-17 7108 1000 Planetary nebula*
13 100 50,000 1010 104 0.01 White dwarf
14 Close to 0 Close to 0 1010 104 0.01 Black dwarf

*Values refer to the envelope.

The core density at this stage is extraordinarily high. A single cubic centimeter of core matter would weigh 1000 kg on 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. Some oxygen is formed via reactions between carbon and helium at the inner edge of the helium-burning shell:


but collisions among nuclei are neither frequent nor violent enough to create any heavier elements. For all practical purposes, the central fires go out once carbon has formed.



Our aged stage 12 star is now in quite a predicament. Its inner carbon core no longer generates energy. 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 envelope continues to expand and cool.

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 is a small, well-defined core of mostly carbon ash. Hot and dense, only the outermost layers of this core still fuse helium into carbon and oxygen. Well beyond the core lies 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.

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. (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 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.)

Formation of Helix Nebula
Formation of Knots in Helix Nebula


The term planetary here is very misleading, for these objects have no association with planets. The name originated in the eighteenth century when, viewed at poor resolution through small telescopes, these shells of gas looked to some astronomers like the circular disks of planets in our solar system. The term nebula is also a little confusing, as it suggests kinship with the emission nebulae studied in Chapter 18. (Sec. 18.2) Although in some ways planetary nebulae do 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 a planetary nebula is in reality a three-dimensional shell of warm, glowing gas 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, but we can see it only at the edges, where emitting matter accumulates along our line of sight. As illustrated in Figure 20.11(b), 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 have evidently played an important role in determining the planetary nebula's shape and appearance.

Figure 20.12 (a) The NGC6826 Nebula more clearly shows the shell-like structure of the expanding gases that make up a planetary nebula. It resides some 700 pc away in the constellation Cygnus. (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.

Bipolar Planetary Nebula

The planetary nebula continues to spread out with time, becoming more diffuse and cooler, gradually dispersing into interstellar space. In doing so, it enriches the interstellar medium with atoms of helium, carbon, and oxygen dredged up by convection from the depths of the core into the envelope 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 becomes visible as the envelope recedes. Several tens of thousands of years are needed for the core to appear from behind the veil of expanding gas. 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). Its mass is about half the mass of the Sun. 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 dim because of its small size. The core's temperature 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.


H—R Diagram Tracks Stellar Evolution

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 perhaps stripped away by a binary companion—as discussed shortly) long ago. Figure 20.14 shows an example of a white dwarf, Sirius B, that happens to lie particularly close to Earth; it is the faint binary companion of the much brighter and better-known Sirius A. (Sec. 17.3) Some properties of Sirius B are listed in Table 20.2. With more than the mass of the Sun packed into a volume smaller than Earth, Sirius B's density is about a million times greater than anything familiar to us in the solar system. (In fact, Sirius B has an unusually high mass for a white dwarf—it is believed to be the evolutionary product of a star roughly four times the mass of the Sun. Interlude 20-2 discusses another possible peculiarity of Sirius B's evolution.)

 TABLE 20.2 Sirius B—A Nearby White Dwarf
Mass 1.1 solar masses
Radius 0.008 solar radii (5500 km)
Luminosity (total) 0.04 solar luminosities (1.6 1025 W)
Surface temperature 24,000 K
Average density 3 109 kg/m3

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.)

Once an isolated star becomes a white dwarf, its evolution is over. (As we will see in Chapter 21, white dwarfs in binary systems may have further activity in store.) It continues to cool and dim with time, following the white-yellow-red track near the bottom of the H—R diagram of Figure 20.13, eventually 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. 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 Earth.