11-5 Low-mass stars pulsate and eject planetary nebulae, leaving behind a white dwarf at the end of their life cycles

For a star that began with a moderately low mass (between about 0.4 M_⊙ and 4 M_⊙), the AGB stage in its evolution is a dramatic turning point. Before this stage, a star loses mass only gradually through steady stellar winds. But as it evolves during its AGB stage, a star divests itself completely of its outer layers. The aging star undergoes a series of bursts in luminosity, and in each burst it ejects a shell of material into space. Eventually, all that remains of a low-mass star is a fiercely hot, exposed core, surrounded by glowing shells of ejected gas. This late stage in the life of a star is called a planetary nebula. Figure 11-23 shows the wide variety observed in planetary nebula, often given names reflective of their shapes.

Figure 11-23: RIVUXG Collage of Four Planetary Nebula These four planetary nebulae imaged by the Hubble Space Telescope are all roughly 7000 ly away. Planetary nebulae show a wide variety of shapes, indicative of the complex processes that occur at the end of stellar life. Henize 2-47 (top left) is dubbed the “starfish,” because of its six lobes of gas and dust, which were created by separate ejections of material occurring in different directions. IC 4593 (top right) displays a prominent pair of jets ending in red knots of glowing nitrogen gas. NGC 5307 (bottom left) displays a spiral pattern, which may have been caused by the dying star’s wobbling. NGC 5315, the chaotic-looking nebula at bottom right, reveals an X-shaped structure suggesting that the dying star ejected material in two different outbursts in two distinct directions.

Making a Planetary Nebula

To understand how an AGB star can eject its outer layers in a sequence of spherical shells, consider the internal structure of such a star as shown in Figure 11-21. As the helium in the helium-fusing shell is used up, the pressure that holds up the dormant hydrogen-fusing shell decreases. Hence, the dormant hydrogen shell contracts and heats up, and hydrogen fusion begins anew. This revitalized hydrogen fusion creates helium, which rains downward onto the temporarily dormant helium-fusing shell. As the helium shell gains mass, it shrinks and heats up. When the temperature of the helium shell reaches a certain critical value, it reignites. The released energy pushes the hydrogen-fusing shell outward, making it cool off, so that hydrogen fusion ceases and this shell again becomes dormant. The process then starts over again.

When this momentary reignition of the helium shell occurs, the luminosity of an AGB star increases substantially in a relatively short-lived burst called a thermal pulse. Figure 11-24, which is based on a theoretical calculation of the evolution of a 1-M_⊙ star, shows that thermal pulses begin when the star is about 12.365 billion years old. The calculations predict that thermal pulses occur at ever-shorter intervals of about 100,000 years.

Figure 11-24: Further Stages in the Evolution of the Sun This diagram shows how the luminosity of the Sun (a 1-M_⊙ star) changes over time. We use different scales for the final stages because the evolution is so rapid. During the AGB stage there are brief periods of runaway helium fusion, causing spikes in luminosity called thermal pulses. All red giants exhibit a slow oscillation in brightness due to their rhythmic “breathing” in and out, and one-third of them are also affected by additional slower and mysterious changes in their luminosity.

During these thermal pulses, the dying star’s outer layers can separate completely from its carbon-oxygen core. As the ejected material expands into space, dust grains condense out of the cooling gases. Radiation pressure from the star’s hot, burned-out core acts on the specks of dust, propelling them further outward, and the star sheds its outer layers altogether. In this way an aging 1-M_⊙ star loses as much as 40% of its mass. More massive stars eject even greater fractions of their original masses.

As a dying star ejects its outer layers, the star’s hot core becomes exposed. With a surface temperature of about 100,000 K, this exposed core emits ultraviolet radiation intense enough to ionize and excite the expanding shell of ejected gases. These gases therefore glow and emit visible light through the process of fluorescence, producing planetary nebulae like those shown in Figure 11-25.

Figure 11-25: Planetary Nebulae (a) The pinkish blob is a planetary nebula surrounding a star in the globular cluster M15, about 33,000 ly from Earth in the constellation Pegasus. (b) The planetary nebula Abell 39 is about 7000 ly from Earth in the constellation Hercules. The almost perfectly spherical shell that constitutes the nebula is about 5 ly in diameter; the thickness of the shell is only about 0.3 ly. (c) This infrared image of the planetary nebula NGC 7027 suggests a more complex evolutionary history than that of Abell 39. NGC 7027 is about 900 pc (3000 ly) from Earth in the constellation Cygnus and is roughly 14,000 AU across.

The Properties of Planetary Nebulae

Planetary nebulae are quite common. Astronomers estimate that there are 20,000 to 50,000 planetary nebulae in our Galaxy alone. Many planetary nebulae, such as those in Figure 11-23, are more or less spherical in shape. This is a result of the symmetrical way in which the gases were ejected. But if the rate of expansion is not the same in all directions, the resulting nebula takes on an hourglass or dumbbell appearance (Figure 11-26).

Figure 11-26: Making an Elongated Planetary Nebula (a, b) These illustrations show one proposed explanation for why many planetary nebulae have an elongated shape. (c) The planetary nebula MyCn18, shown here in false color, may have acquired its elongated shape in this way. It lies some 8000 ly from Earth in the constellation Musca (the Fly).

Spectroscopic observations of planetary nebulae show emission lines of ionized hydrogen, oxygen, and nitrogen. From the Doppler shifts of these lines, astronomers have concluded that the expanding shell of gas moves outward from a dying star at speeds from about 20,000 mi/h to mi/h (10 km/s to 30 km/s). For a shell expanding at such speeds to have attained the typical diameter of a planetary nebula, about 1 light-year, it must have begun expanding about 10,000 years ago. Thus, by astronomical standards, the planetary nebulae we see today were created only very recently.

We do not observe planetary nebulae that are more than about 50,000 years old. After this length of time, the shell has spread out so far from the cooling central star that its gases cease to glow and simply fade from view. The nebula’s gases then mix with the surrounding interstellar medium.

Astronomers estimate that all the planetary nebulae in the Galaxy return a total of about 5 M_⊙ to the interstellar medium each year. This amounts to 15% of all the matter expelled by all the various sorts of stars in the Galaxy each year. Because this contribution is so significant, and because the ejected material includes heavier elements (metals) manufactured within a nebula’s central star, planetary nebulae play an important role in the chemical evolution of the Galaxy as a whole.

Formation of a White Dwarf

We have seen that after a moderately low-mass star (from about 0.4 solar masses to about 4 solar masses) consumes all the hydrogen in its core, it is able to ignite thermonuclear reactions that convert helium to carbon and oxygen. Given sufficiently high temperature and pressure, carbon and oxygen can also undergo fusion reactions that release energy. But for such a moderately low-mass star, the core temperature and pressure never reach the extremely high values needed for these reactions to take place. Instead, as we have seen, the process of mass ejection just strips away the star’s outer layers and leaves behind the hot carbon-oxygen core. With no thermonuclear reactions taking place, the core simply cools down like a dying ember. Such a burnt-out relic of a star’s former glory is called a white dwarf. Such white dwarfs prove to have exotic physical properties that are wholly unlike any object found on Earth.

Properties of White Dwarfs

You might think that without thermonuclear reactions to provide internal heat and pressure, a white dwarf should keep on shrinking under the influence of its own gravity as it cools. Actually, however, a cooling white dwarf maintains its size because the burnt-out stellar core is so dense that most of its electrons are so tightly packed they are classified as being degenerate. Thus, degenerate-electron pressure supports the star against further collapse. This pressure does not depend on temperature, so it continues to hold up the star even as the white dwarf cools and its temperature drops.

Many white dwarfs are found in our local solar neighborhood, but all are too faint to be seen with the naked eye. One of the first white dwarfs to be discovered is a companion to Sirius, the brightest star in the night sky. This companion, designated Sirius B (Figure 11-27), was first glimpsed in 1862 by the American astronomer Alvan Clark. Recent Hubble Space Telescope observations at ultraviolet wavelengths, where hot white dwarfs emit most of their light, show that the surface temperature of Sirius B is 25,200 K.

Figure 11-27: RIVUXG Sirius A and Its White-Dwarf Companion Sirius, the brightest-appearing star in the sky, is actually a binary star. The secondary star, called Sirius B, is a white dwarf. In this Hubble Space Telescope image, Sirius B is almost obscured by the glare of the overexposed primary star, Sirius A, which is about 104 times more luminous than Sirius B. The halo and rays around Sirius A are the result of optical effects within the telescope.

Observations of white dwarfs in binary systems like Sirius allow astronomers to determine the mass, radius, and density of these stars. Such observations show that the density of the degenerate matter in a white dwarf is typically 10⁹ kg/m³ (a million times denser than water). A teaspoonful of white dwarf matter brought to Earth would weigh nearly 5.5 tons—as much as an elephant!

Degenerate matter has a very different relationship between its pressure, density, and temperature than that of ordinary gases. Consequently, white-dwarf stars have an unusual mass-radius relation: The more massive a white-dwarf star, the smaller it is.

Figure 11-28 displays the mass-radius relation for white dwarfs. Note that the more degenerate matter you pile onto a white dwarf, the smaller it becomes. However, there is a limit to how much pressure degenerate electrons can produce. As a result, there is an upper limit to the mass that a white dwarf can have. This maximum mass is called the Chandrasekhar limit, after the Indian-American scientist Subrahmanyan Chandrasekhar, who pioneered theoretical studies of white dwarfs in the 1930s. The Chandrasekhar limit is equal to 1.4 M_⊙, meaning that all white dwarfs must have masses less than 1.4 M_⊙.

Figure 11-28: The Mass-Radius Relationship for White Dwarfs The more massive a white dwarf is, the smaller its radius. (The drawings of white dwarfs of different mass are drawn to the same scale as the image of Earth.) This unusual relationship is a result of the degenerate-electron pressure that supports the star. The maximum mass of a white dwarf, called the Chandrasekhar limit, is 1.4 M_⊙.

The material inside a white dwarf consists mostly of ionized carbon and oxygen atoms floating in a sea of degenerate electrons. As the dead star cools, the carbon and oxygen ions slow down, and electric forces between the ions begin to prevail over the random thermal motions. About 5 × 10⁹ years after the star first becomes a white dwarf, when its luminosity has dropped to about 10⁻⁴ L_⊙ and its surface temperature is a mere 4000 K, the ions no longer move freely. Instead, they arrange themselves in orderly rows, like an immense crystal lattice. From this time on, you could say that the star is “solid.” The degenerate electrons move around freely in this crystal material, just as electrons move freely through an electrically conducting metal like copper or silver. A diamond is also crystallized carbon, so a cool carbon-oxygen white dwarf can resemble an immense spherical diamond!

From Red Giant to Planetary Nebula to White Dwarf

Figure 11-29 shows the evolutionary tracks followed by three burned-out stellar cores as they pass through the planetary nebula stage and become white dwarfs. When these three stars were red giants, they had masses of 0.8 M_⊙, 1.5 M_⊙, and 3.0 M_⊙. Mass ejection strips these dying stars of up to 60% of their matter. During their final spasms, the luminosity and surface temperature of these stars change quite rapidly. The points representing these stars on an H-R diagram race along their evolutionary tracks, sometimes executing loops corresponding to thermal pulses (shown as Track B and Track C in Figure 11-29). Finally, as the ejected nebulae fade and the stellar cores cool, the evolutionary tracks of these dying stars take a sharp turn toward the white-dwarf region of the H-R diagram. As the table accompanying Figure 11-29 shows, the final white dwarf has only a fraction of the mass of the giant star from which it evolved.

Figure 11-29: Evolution from Giants to White Dwarfs This H-R diagram shows the evolutionary tracks of three low-mass giant stars as they eject planetary nebulae. The table gives the extent of mass loss in each case. The dots represent the central stars of planetary nebulae whose surface temperatures and luminosities have been determined; the crosses represent white dwarfs of known temperature and luminosity.

Although a white dwarf maintains the same size as it cools, its luminosity and surface temperature both decrease with time. Consequently, the evolutionary tracks of aging white dwarfs point toward the lower right corner of the H-R diagram. You can see this in Figure 11-29; Figure 11-30 shows it in more detail. The energy that the white dwarf radiates into space comes only from the star’s internal heat, which is a relic from the white dwarf’s past existence as a stellar core. Over billions of years, white dwarfs grow dimmer and dimmer as their surface temperatures drop toward absolute zero.

Figure 11-30: White-Dwarf “Cooling Curves” As white-dwarf stars radiate their internal energy into space, they become dimmer and cooler. The blue lines show the evolutionary tracks of four white dwarfs of different mass: The more massive a white dwarf, the smaller and hence fainter it is.

COSMIC CONNECTIONS: The Sun: The Next 8 Billion Years

The Sun is presently less than halfway through its lifetime as a main-sequence star. The H-R diagram and cross-sections on this page summarize the dramatic changes that will take place when the Sun’s main-sequence lifetime comes to an end.

After ejecting much of its mass into space, our own Sun will eventually evolve into a white-dwarf star about the size of Earth and with perhaps one-tenth of its present luminosity. It will become even dimmer as it cools. After 5 billion years as a white dwarf, the Sun will radiate with no more than one ten-thousandth of its present brilliance. With the passage of eons, our Sun will simply fade into obscurity. Cosmic Connections: The Sun: The Next 8 Billion Years summarizes the full evolutionary cycle of a 1-M_⊙ star like the Sun, from its birth to becoming a main-sequence star to its demise as a white dwarf.

This process describes the evolutionary process of the vast majority of stars in our Galaxy. Yet, the most dramatic and dynamic changes happen in the rarest of the largest aging stars, which we address in Chapter 12.