ASTR 103 - Text Supplement

Post-Main Sequence Evolution


Latest Modification: November 23, 1998

Table of Contents


In preceding chapter we discussed the hydrogen-burning, or main-sequence, phase that follows the birth of stars. After stars have exhausted their hydrogen fuel, they are unable to support the weight of the overlying layers with their internal gas pressure. This crisis means that they must renew the battle against gravitational compression through a sequence of contracting, heating, and igniting new sources of nuclear fuel in order to survive. This chapter discusses these advanced stages of stellar evolution, which ultimately lead to the death of stars.


End of Main-Sequence Life

Hydrogen Exhaustion

Throughout hydrogen burning the cores of stars contract very slowly as stars try to maintain hydrostatic equilibrium. This contraction converts gravitational potential energy into thermal energy, raising the core temperature and the star's luminosity. As the star brightens, it moves up from the zero-age main sequence in the H-R diagram, moving toward the point on the diagram which represents the time when the star has exhausted its hydrogen fuel.

The main sequence consists of a broad avenue of stars of different ages that are evolving away from the zero-age main sequence to their respective hydrogen-exhaustion points (Figure 18.1). Unlike what happens in pre-main-sequence contraction, a star's overall radius does not decrease but rather increases. And since the H-R diagram records increases in luminosity and temperature at a star's surface, the diagram does not reflect the core's slow contraction. For a star like the Sun, the radius will roughly double during its main-sequence life as about 12 percent of its hydrogen is depleted.

As hydrogen burning ends, hydrostatic equilibrium shifts in favor of gravity, and the core contracts more rapidly. The contraction releases substantial amounts of gravitational potential energy, further heating the interior. The layers just outside the former energy-generating core are now hot enough to initiate hydrogen burning in a relatively thin shell surrounding an inactive helium-rich core. Although the core continues to contract and heat, it is the burning of hydrogen in the surrounding shell that is responsible for supplying the star's luminosity. Evolution now carries stars along tracks leading to the red-giant region in the H-R diagram.

The red-giant branch in Figure 18.1 is the portion of the evolutionary track that extends steeply upward at the extreme right. When the contracting helium-rich core reaches about 120 million K (Table 18.1), the second major thermonuclear reaction, helium burning, begins. In this reaction, three helium (He4) nuclei fuse to form a carbon (C12) nucleus and two gamma-ray photons. Stars burn helium (and hydrogen in a shell about the helium-burning core) for about 5 to 20 percent of the time they spent burning core hydrogen as main-sequence stars.

Thermonuclear Burning and Electron Degeneracy
Thermonuclear
Process
Mass on
Main Sequence
Needed to Burn
(MSun)
Ignition
Temperature
(K)
Approximate
Density
(g/cm3)
Electrons
Degenerate
at Densities
Greater Than
Hydrogen burning
H->He
0.1 4 x 106 101-102 ~103
Helium burning
He->C, O
0.4 120 x 106 103-106 ~105
Carbon burning
C->Ne, Na, Mg, O
4.0 600 x 106 105-108 ~107
Oxygen, neon, and
silicon burning
Ne-->O,Mg
O-->S,Si,P
Si-->Ni-->Fe
8.0 1 x 109 to 3 x 109 >107 ~109

When helium burning commences, rapid contraction in the core ends. And just as hydrogen burning led to a slow contraction of the energy-generating core, helium burning also causes a slow contraction. While part of the main-sequence, a star's core is some 20 percent of its radius, but when helium burning starts, the star's core is more like 0.1 percent of its radius. The star's structure has thus changed dramatically from what it was as a main-sequence star.

When will contraction raise the core temperature to 120 million K so that helium begins thermonuclear fusion? This event is determined by a star's main-sequence mass. To discuss this point, we must divide stars into two groups for their approach to helium burning and subsequent evolution: low-mass stars, whose masses are less than about 2MSun, and high-mass stars, whose masses are greater than 2MSun.

X-Rays from Stars]

X-rays emitted by celestial objects do not reach the surface of the Earth. Instead, they are absorbed in the atmosphere above the about 30 km. Therefore, in order to study celestial X-rays, we must fly rockets or balloons above the absorbing layers.

In 1949, the Sun was demonstrated to be a source of X-rays, by a group of scientists at the U.S. Naval Research Laboratory. They flew a captured German V-2 rocket outfitted with a device to detect X-rays from a large area of the sky. The fact that the quantity of X-rays that the detector saw was largest when it was pointed toward the sun clearly indicated a solar origin for the radiation. During the decade that followed, improved systems were sent into space to continue studying the Sun's X-ray emission. The steady X-ray emission from the Sun has been found to come from the plasma in its 2 million K corona. In addition, solar flares were found to be transient sources of X-rays.

The researchers soon realized that if they could build sensitive enough detectors, they might be able to measure X-rays from other stars, as well. In 1962, the first celestial X-ray source outside the Solar System was discovered by scientists at the American Science and Engineering Company, and was quickly verified by other groups of scientists. The source was dubbed Sco X-1, since it was the first and strongest X-ray source in the constellation Scorpius. Subsequent studies of Sco X-1 have shown it to be a type of object known as a low-mass, X-ray binary system. These systems, of which a number of examples are now known, consist of a pair of stars one of which is a main sequence star and the other is a neutron star in close proximity. In a somewhat oversimplified picture, plasma flows from the larger star and accretes onto the tiny but massive neutron star. The accretion process causes the plasma to be compressed and heated to such high temperatures that it can emit X-rays.

X-ray astronomy continued through the 1960s with sounding rocket flights which took instruments above the bulk of the atmosphere for periods of five minutes or so, and with high-altitude balloon flights. A handful of sources of celestial X-rays were identified, and their positions on the sky were ascertained with some accuracy.

The first major satellite for X-ray astronomy was the Uhuru satellite, launched in late 1970. The satellite was launched from a platform off the coast of Kenya on that country's independence day, so it was dubbed Uhuru, the Swahili word for freedom. Over the next several years, a number of additional satellites were launched to study the X-ray sky, culminating in the High Energy Astronomy Observatory, HEAO-1, launched in 1977. Many of the X-ray emitting stars found by these observatories were, in fact, binary star systems where the X-rays were produced in an accretion process.

In 1978, HEAO-2, renamed the Einstein Observatory, was launched with the first true telescope for imaging X-rays from objects outside the Solar System. Its great sensitivity permitted it to observe an enormous array of hither to unknown X-ray emitting objects. The totality of X-ray sources observed since 1950 contain a variety of objects, including supernova remnants, active galaxies, and quasars. We will talk briefly about non-binary stars below.

The Sun has a hot corona because energy produced in its turbulent envelope is deposited in the corona through complex magnetic interactions and heats the plasma to the enormous temperature that is observed. The most common main-sequence stars, cooler than roughly 7000oK or spectral type F5, share the same type of structure, and should have coronae like the Sun. Observations from the Einstein Observatory have verified that stars with convective outer layers do in fact emit X-rays, and the strength of the X-ray emission is related to the strength of magnetic fields of the stars.

The Einstein Observatory found that hot young stars without convective outer regions also emit X-rays, but at a lesser rate than the cool stars. This observation remains something of a mystery. Some clues were found when the ultraviolet emissions from the stars was studied extensively using a satellite known as the International Ultraviolet Explorer. These stars turn out to have extensive stellar winds, in which mass pours out of the stars at a rate more than a million times larger than in the case of the Sun's wind. At least some of the X-ray emission may arise in plasma heated by processes such as shock waves in the wind. However, the fact that X-rays are also emitted by hot young stars with weak winds points to an additional, as yet unknown source as well. It remains for future generations of scientists using new, high-technology X-ray and ultraviolet observatories in space to sort out this enigma.


Red-Giant Evolution for Low-Mass Stars

Helium Flash

Continuing our discussion of evolution away from the main sequence, let us consider first the post-main-sequence evolution of low-mass stars. When hydrogen is exhausted, these stars begin an internal restructuring that eventually ends when they are red giants (Figure 18.2). The result of this action is, first, to decrease their surface temperature but to keep about the same luminosity (Figure 18.1). Second, before helium burning actually begins, these stars will brighten appreciably and follow an evolutionary track into the red-giant region that is basically upward in the H-R diagram. For the Sun, this change will take about 1 billion years; for less massive stars, the time will be even longer.

By the time a star like the Sun reaches the red-giant region, the helium-rich core (containing about 30 percent of the star's mass) has been compressed to a volume about twice that of the Earth, with a density of some 106 g/cm3. At this density, the gas no longer acts as a perfect gas, for the electrons have become degenerate (Section 17.1).

For low-mass stars the presence of degenerate electrons in their cores causes helium to ignite very differently from the way it would in a perfect gas. In a perfect gas, any rise in temperature is followed by an increase in pressure, and the contraction then underway is halted. Under perfect-gas conditions, therefore, the increase in pressure expands the core slightly, cools it, and reduces the thermonuclear burning rate until thermal equilibrium is restored.

But when the gas in a star's core is a degenerate-electron gas, it behaves more like a solid than a gas. The core does not expand with an increase in temperature, and if it cannot expand, it cannot cool. Since the rate of helium burning increases with temperature, it continues to rise as more energy is generated; in turn, this increases the rate at which energy is generated, which pushes the temperature still higher; and a runaway condition follows. In a few hours temperatures leap to hundreds of millions of degrees, causing the generation of as much energy as 100 billion stars of solar luminosity--about that of a whole galaxy. This explosive flash of energy is called a helium flash. Even as huge as this energy generation is, the helium flash is not enough to blow the star apart. Instead, all the energy goes into removing electron degeneracy, and this so alters the structure that the star may now burn helium in a core that acts as a perfect gas.

The helium flash just described is generated in computer models of stars--astronomers have not and never will see helium flashes in real stars. This is because a helium flash occurs deep inside a star, hidden by millions of kilometers of gas. Do we believe that such a process as the helium flash actual takes place just because our computers say so? Galileo long ago point science in the direction of discovering the mathematical laws that relate observable quantities in nature. When these laws are discovered and put together in the larger framework of a theory, they represent the boldest stroke of our imagination for understanding nature. Until such a means of pursuing understanding is shown to be incorrect, then science will continue to believe the predictions of its theories even though we may not be able to observationally validate each step, so long as we can relate to the observable world at some points along the quest.

Open-Cluster H-R Diagrams

Astronomers have found observational evidence in H-R diagrams for open clusters that supports the evolution of low-mass stars as just described. As individual stars in a cluster evolve, their rate of aging is determined by their luminosity, which in turn depends on their mass. The more massive ones age faster than do stars of lower mass, as illustrated in Figure 18.3. It is from the relative aging of a cluster's members that astronomers can find the age of the cluster. The critical time when a star reaches the point at which it exhausts its core hydrogen depends on its mass, which in turn is related to its luminosity and hence its age. From stellar models, ages can be placed along the vertical axis of an H-R diagram that correspond to the luminosity of the turnoff point for the least massive star that has reached hydrogen exhaustion, such as that shown in Figure 18.4.

In Figure 18.4, the youngest cluster is NGC 2362, whose age is estimated to be less than 2 million years, since none of its massive blue stars have yet crossed the Hertzsprung gap. In the next youngest cluster, h and Persei, some of the stars that were originally massive blue ones have evolved across the diagram and are now red giants. Next youngest is the Pleiades, followed, in order, by M41, M11, the Hyades, NGC 752, M67, and NGC 188. The difference between the two oldest clusters, M67 and NGC 188, is that in M67 subgiant and giant stars are more luminous than comparable ones in NGC 188. This is so because stars leaving M67's main sequence are more massive and therefore younger than those in NGC 188. Subgiant branches in M67 and NGC 188 strongly resemble evolutionary tracks for 1.25 and 1MSun stars, respectively. Estimated ages are 5 billion years for M67 and about 10 billion years for NGC 188.

Horizontal-Branch Stars

One conspicuous difference between an H-R diagram for open clusters and one for globular clusters is the horizontal branch in that for globular clusters (Figure 18.4). This region of stars runs almost horizontally across the diagram from the red-giant branch to the very blue stars at a visual absolute magnitude of about +1. What does the horizontal branch represent in the evolution of stars?

To answer that question, first remember that the helium flash in solar-mass stars reduces a stars' central temperature over a very short time interval, say, about 10,000 years. After the flash, the drop in core and the hydrogen-burning shell temperatures reduces the star's luminosity while its surface temperature increases. This causes the star to move down and to the left of its original position in the red-giant region and onto the horizontal branch. From stellar models we are led to believe that horizontal-branch stars are stars between about 1 and 0.5MSun that are burning helium.

The horizontal branch is a relatively stable phase in a star's life. Yet there is a period when such stars can become temporarily unstable and pulsate as RR Lyrae variables (Section 13.5). Even though the comparison in Figure 18.5 suggests reasonable agreement between H-R diagrams for stars in the globular cluster M92 and a theoretical cluster made up of stellar models of different masses, all aspects of horizontal-branch stars are still not known.

As the time approaches when helium will be exhausted at the low-mass star's center, the battle resumes between gravity and gas pressure. The conversion of helium to carbon causes a star's core to contract slowly and heat, and the star moves upward from the horizontal branch in the H-R diagram along a track that carries them into the giant region a second time. For these stars, the outer layers are bound so loosely by gravity that large amounts of matter may be expelled as a result of stellar winds (Section 16.1). As stated earlier, observations show that luminous red giants and supergiants are indeed losing significant amounts of matter. Most important for low-mass stars, however, is that mass loss reduces the compression of these stars, consequently, compression can not sufficiently heat the core to start carbon burning, the next possible stage in nuclear burning, as shown in Table 18.1. This end to the sequence of nuclear burning processes is the beginning of the end for low-mass stars.

In preceding chapter we discussed the hydrogen-burning, or main-sequence, phase that follows the birth of stars. After stars have exhausted their hydrogen fuel, they are unable to support the weight of the overlying layers with their internal gas pressure. This crisis means that they must renew the battle against gravitational compression through a sequence of contracting, heating, and igniting new sources of nuclear fuel in order to survive. This chapter discusses these advanced stages of stellar evolution, which ultimately lead to the death of stars.

Stars That Become Planetary Nebulae

While low-mass stars evolve toward the red-giant branch the second time after their horizontal-branch phase, burning helium and hydrogen in two separate shells, they pulsate slightly. Eventually their outer layers separate from the core and expand outward at several tens of kilometers per second to form the shell of a planetary nebula. The ejected shell holds most of the original outer layers that missed thermonuclear burning because they were never hot enough (Figure 18.6). Near the red-giant branch the luminosity and temperature of the star's original surface are what is plotted in the H-R diagram. But as the ejected shell expands, the former core is exposed so that its luminosity and temperature become the quantities to plot. Because the former core is hot, the star's position is now on the blue side of the diagram. Thus, after the outburst, the tracks in the H-R diagram along which the star evolves very rapidly cross the top of the diagram from the low-temperature to the high-temperature side. Later, by the time the central star moves into the white-dwarf region, the expanding nebula has mixed with the interstellar medium and is no longer recognizable.

It seems likely that the Sun will eject its outer layers as a planetary nebula some 6 billion years from now. And most, if not all, of the disk-population stars with main-sequence masses between 1 and 4MSun, as well as some low-mass spheroidal-population stars, also seem likely to become planetary nebulae after being red giants and before becoming white dwarfs.


Post-Main-Sequence Evolution for Massive Stars

Just as it does for low-mass stars, the day comes in the lives of high-mass stars (those greater than about 2MSun), such as Regulus (B7 V), when they also exhaust the hydrogen fuel in their cores. The evolutionary track in the H-R diagram followed by high-mass stars, such as Betelgeuse (M1 I) and Antares (M2 I), is described in this and the next section. Evolution for high-mass stars is very different in many respects from what we have just learned for low-mass stars.

Helium Burning In High-Mass Stars

With hydrogen gone in the cores of massive main-sequence stars, the core shrinks drastically, driving up the density and temperature and exaggerating the differences between a star's central regions and its outer layers.

For stars above 2MSun in Figure 18.1, evolution away from the main sequence is quite rapid, almost horizontal, across the H-R diagram toward the red-giant region. These stars expand their radii by a factor of about 10, which constitutes a hundredfold increase in their surface area. Still the temperature is reduced enough to keep the luminosity roughly constant. The region in the diagram across which these stars are evolving is the Hertzsprung gap. Very few stars have been found in this gap, so the transition across the gap must be rapid--occurring in 50 million years to less than 1 million years.

Just when will contraction raise the temperature in the core to 120 million K so that helium burning may begin? Again this is decided by the star's mass. For stars between 2 and 9MSun the time comes when the star has become a red giant. When helium burning begins (without a flash, as in low-mass stars, because the density is lower), the star's evolution upward along the red-giant branch stops. Following this, a star, still burning helium in its core and hydrogen in a concentric shell, first contracts its radius and moves to the high-temperature side of the red-giant branch and then back to the low-temperature side a second time, as shown in Figure 18.1.

The path these stars follow in the H-R diagram leads some across the Cepheid instability strip (Section 13.5 and Figure 18.1). A Cepheid variable pulsates only in its outermost layers, where small rhythmic expansions and contractions cause the cyclic variation in its brightness. Once pulsation begins, it continues for a brief time until evolution carries the star toward higher temperatures in the H-R diagram. Classical Cepheids appear to be a spiral-arm component of the stars in the disk of the Galaxy (whose masses range from 3 to 9MSun) and that are in their helium-burning phase.

Stars more massive than 9MSun begin and complete helium burning on the blue side of the H-R diagram before they cross the Hertzsprung gap leading to the red-giant branch.

Carbon Burning

After helium burning ceases, the parts of a star that have burned helium are rich in carbon and oxygen (Figure 18.10). The next step in thermonuclear evolution is carbon burning, which a star more massive than about 25MSun initiates even before crossing the Hertzsprung gap. Carbon burning, which takes place at temperatures above 600 million K, is the fusion of two carbon nuclei to produce primarily neon (Ne20), sodium (Na23), or magnesium (Mg24).

By the time helium is exhausted in the cores of 3 to 9MSun stars, they have returned to the red-giant branch a second time (Figure 18.1). The core is slowly contracting and heating. The increased density of an already-dense core squeezes electrons and ions closer together, imposing degeneracy on the electrons.

Once the central temperature in the core has reached about 600 million K, carbon nuclei initiate the thermonuclear fusion reactions of carbon burning. Carbon burning in an electron-degenerate gas can start explosively, just as helium burning does. Thus the core can experience a carbon flash, which removes the degeneracy and allows carbon burning to restore thermal equilibrium.

Stellar models suggest, however, that carbon burning in some stars may start so explosively as to blow the star completely apart and is one type of supernova outburst, as suggested in Table 18.3, where we summarize evolution of all masses of stars. Astronomers are not yet absolutely certain that this explosion actually occurs. This is so because extensive mass loss can apparently prevent these stars from ever reaching the carbon-burning phase and instead they end up as carbon-rich white dwarfs, such as those found in some clusters.

For stars with main-sequence masses greater than about 9MSun, carbon burning begins in a gaseous core that still obeys the perfect-gas law. This is so because the temperature is so high in these massive stars that radiation pressure is an important part of the total pressure, inhibiting the occurrence of electron degeneracy. Thus there is no carbon flash, just as there is no helium flash for any of the high-mass stars.

Oxygen, Neon, and Silicon Burning

In stars more massive than 9MSun further contraction after carbon burning makes their cores hot enough to initiate the next round of thermonuclear reactions, known as oxygen, neon, and silicon burning, which take place at 1 to 3 billion K (Table 18.1). Nuclear burning for these massive stars ends with the nuclear reactions that produce the nuclei near iron in the periodic table. Because iron and those elements near it are the nuclei most resistant to any type of structural change, thermonuclear burning beyond them does not release energy but takes up thermal energy from its surroundings. From here on a star cannot go through the alternate contracting, heating, and nuclear-burning sequence that has sustained it against gravity through most of its existence.

The evolution of very massive stars (15MSun and up) is the most difficult range of stellar mass about which to have confidence in our stellar models (Table 18.1). Nevertheless, several important conclusions can be made from these stellar models. First, stars more massive than 9MSun initiate helium burning as blue supergiants, and those more massive than 25MSun also burn carbon while located on the blue side of the H-R diagram. While most massive stars probably become red supergiants, the vigorous mass loss by the very rare 50 to 100MSun O stars may prevent them from ever crossing the H-R diagram and becoming red supergiants. That is their entire life span is spent as extremely hot, blue, luminous stars. This is a point that is still under investigation since it bears on our understanding of the most recent nearby supernova outburst, supernova 1987A in the Large Magellanic Cloud--a companion galaxy of our Galaxy that is visible only in the southern hemisphere skies.

Massive stars evolve through their nuclear-burning sequence to a structure in which they possess a very small, extremely dense core with shells like those of an onion that have different chemical compositions. In them the successive thermonuclear reactions are taking place simultaneously: silicon burning at the center with neon, oxygen, carbon, helium, and hydrogen burning in successive concentric shells outward, as depicted in Figure 18.11. Surrounding these shells is a highly distended hydrogen-rich envelope. The star is very large, very bright, and quite red or possibly it is distinctly blue depending on its mass. Thermonuclear burning is a viable energy source for shorter and shorter periods as synthesis proceeds toward heavier elements. This is true in part because energy carried away by neutrinos becomes an increasingly greater fraction of the total energy with each successive burning stage beyond carbon burning, thereby reducing the energy available to supply the luminosity. For example, a 25MSun star spends about 5 to 10 million years in hydrogen burning, 0.5 to 1.0 million years in helium burning, 500 to 1000 years in carbon burning, 6 to 12 months in oxygen burning, and a mere day or so in silicon burning.


Copyright 1995 J. C. Evans
Physics & Astronomy Department, George Mason University
Maintained by J. C. Evans; jevans@gmu.edu