The interior of a typical main sequence star is illustrated by the internal conditions of the Sun, with the highest density, pressure, energy generation rate, and temperature occurring at the very center. The temperature dependency of the proton‐proton cycle means that energy is produced over a fairly large volume in the stellar center, out to about 25 percent of the total stellar radius in a star like the Sun.
Within this core, the star's chemical composition slowly changes as hydrogen is converted to helium (see Figure ). In the 4.6 billion years since the Sun formed, it has used about one‐half of its hydrogen at the very center. This slow progressive conversion of light‐weight hydrogen to fewer nuclei of heavier hydrogen is accompanied by slow changes in other physical factors in the stellar interior and related slow changes in the star's surface conditions. In due course, when all hydrogen in the core is exhausted, a star must make more dramatic changes in its structure. To a biologist, changes that occur in the lifetime of a living organism are referred to as aging. Astronomers refer to the aging of a star as stellar evolution.
Representative stages in post–Main Sequence evolution. At left, the star's core has been converted to helium and is slowly shrinking. Exterior to the core is a shell‐like region in which hydrogen is converting to helium. The envelope of the star is still dominated by hydrogen and slowly expands as this star evolves into the red giant region. At right, central temperatures have reached the point where helium can convert into carbon and oxygen in the core. This is surrounded by a shell that is not hot enough for helium reactions. Surrounding this is a shell in which hydrogen is being converted to helium. The outermost layer is the hydrogen‐dominated envelope. (Sizes of regions are not drawn to scale.)
Zero-Age Main Sequence
Upon the onset of central thermonuclear reactions, a star's chemical composition is homogeneous throughout its interior. The equilibrium structure of such a star is one whose surface temperature is a bit warmer and whose luminosity is a bit smaller than a typical star in that portion of the main sequence. The locus of newly formed, chemically homogeneous zero‐age main sequence ( ZAMS) stars forms a boundary to the lower left of the main sequence. As a star ages, lightweight hydrogen is converted to fewer nuclei of heavier helium. To maintain sufficient central pressure to balance gravity, both the mass density must increase slowly as well as the central temperature. Mass density can increase only if the stellar core slowly contracts (such an equilibrium that slowly changes is called quasi‐static equilibrium). Although the fraction of hydrogen is decreasing, the higher temperature ensures a somewhat greater rate of energy production that means a higher surface luminosity. The increase in interior temperature is accompanied by an increase in temperature in layers outside of the core of the star. Here, in the deeper stellar envelope, the higher temperature produces a higher pressure that expands the outer part of the star. Near the surface, however, the expansion supported from below is accompanied by a decrease in temperature. In sum, as the hydrogen is consumed in the central core, the stellar photosphere cools slightly and the luminosity increases (in other words, the star drifts rightward and upward across the main sequence band in the HR diagram).
Stars that are at the point of exhausting hydrogen in their cores form a locus that bounds the main sequence band on the upper right. As these stars are at the end of their main sequence stage, they are termed terminal‐age main sequence (TAMS) stars. (See Figure 2).
Evolution across the main sequence and into the giant region; the zero‐age main sequence and terminal‐age main sequence configurations are marked. The asterisks mark the stages for low‐mass stars at which time helium explosively begins to convert to carbon in the stellar core, resulting in a quick change in the stars' luminosities and surface temperatures.
Main Sequence Lifetimes
The luminosity of a star is a measure of how fast a star is using its nuclear fuel. The mass of a star indicates how much fuel is available. The lifetime of a star in any given evolutionary stage is given by the amount of available fuel for that stage divided by the rate of consumption of that fuel; in other words, lifetime is proportional to the mass divided by the luminosity. Because the mass‐luminosity relation for main sequence stars shows that luminosity is proportional to mass 3.5, a star's lifetime is proportional to mass –2.5. Bright, massive main sequence stars must evolve faster than faint, low‐mass stars. Not only are these stars intrinsically rarer than lower‐mass stars, but they do not last as long. More quantitative main sequence lifetimes may be obtained from theoretical calculations as shown in Table 1
What happens when the core hydrogen is depleted in a main sequence star like the Sun? In such a star, energy is still flowing outward from the core. The only means of replacing this lost energy is through gravitational contraction of the core, with half the released energy going into heat, the other half moving outward in the star to be radiated away at the surface. Density, temperature, and pressure all increase at the center; but the outer envelope responds to changes in the core by expanding. The surface area increases as the surface temperature decreases, yielding a constant luminosity. In the HR diagram, the star appears on observation to be “moving” to the right of the main sequence.
Immediately outside the helium core, the stellar material is still hydrogen‐rich. As the layer just above the helium contracts, it becomes hotter and denser until a shell‐burning source in which thermonuclear reactions converting hydrogen to helium are established. The star can now be considered to have three distinct regions—a central spherical core that is made of helium, a thin layer above the core in which hydrogen is being converted to helium, and lastly the thick outer envelope of the star comprised of the proportion of hydrogen (about 74 percent) and helium (about 24 percent) with which the star formed. The core contraction continues, the hydrogen‐burning shell slowly moves outward, and the exterior of the star continues to expand and cool, but the stellar luminosity remains approximately constant. The star is now a sub‐giant star, on its way to becoming a red giant.
The whole outer envelope of the star experiences decreasing temperatures. Of specific interest to astronomers is the depth of the interior layer, which sets the transition from a radiative interior to the convective envelope. When the surface temperature drops to around 3,000 K, this transition layer begins to move into the interior of the star; thus the depth of the outer convective envelope increases. Convection, however, is a very efficient means of moving energy outward, whereas the movement of energy by the diffusion of photons is slow. The interior radiative zone seems to store the energy produced by the core of the star over the previous few million years, because it is trapped by the slow radiative process. As the convection moves into the interior, this stored energy is brought rapidly to the surface and the star begins to brighten rapidly, though the surface remains at a constant temperature. Observationally, the star is seen moving up the Hayashi track, named after the Japanese theoretician who first recognized this stage of stellar evolution. This stage is also called the red giant branch. The core in turn responds to this outer loss of energy by accelerating its contraction. At the same time, the shell burning accelerates and the size of the helium core grows in mass more quickly.
As long as the core temperature is below about 200 million K, the only source of energy to replace that which is flowing outward into the cooler envelope is gravitational contraction in the center and hydrogen fusion in a shell just outside the helium core. Thermonuclear reactions uniting two helium nuclei into one of beryllium do occur, but beryllium is unstable; as soon as a beryllium nucleus is produced, it immediately splits to give back two helium nuclei. As the central temperatures and density continue to rise, the reaction He 4 + He 4 → Be 8 proceeds at an ever fast rate, but so does the reverse reaction Be 8 → He 4 + He 4. But as these reactions occur faster, the ambient amount of short‐lived beryllium is growing larger. When the central temperature approaches 200,000,000 K, there is sufficient beryllium at any instance that the likelihood of a reaction with another helium nucleus becomes significant.
Because the production of stable carbon requires essentially a simultaneous collision of three helium nuclei (also known as alpha particles), this is termed the triple‐alpha process, also called helium burning. For a Sun‐like star, it has been about a billion years since the star left the main sequence to bring the core to a circumstance where a new source of thermonuclear energy can be established. But a new factor has also come into play as the helium core became denser and denser: When pushed together until they essentially touch each other, the electrons resist any further compression. Their resistance is an electron degeneracy pressure that adds to and actually becomes greater than normal gas pressure. Unlike normal gas pressure, degeneracy pressure does not depend on temperature. Because the helium core is degenerate, the onset of helium‐burning is not moderated. Under normal circumstances, energy from nuclear fusion would heat the material, the pressure would rise forcing an expansion, which then would damp down the reaction rate. But in degenerate material, the onset of helium‐burning is so rapid as to be virtually explosive, a helium flash. But the energy produced in the flash quickly expands the core region and removes the degeneracy (that is, normal gas pressure becomes dominant), allowing a stable fusion of helium to carbon to ensue. The whole structure of the star readjusts dramatically to this new condition. With thermonuclear energy production replacing gravitational energy in the core, the exterior of the star shrinks and gains in temperature. It becomes a smaller and hotter type of red giant star.
A second factor, mass loss, is important during the star's evolution on the Hayashi track. A one solar mass star likely loses between 10 percent and 60 percent of its mass through strong stellar winds. The explosive onset of helium burning may also produce shock waves that blow off additional mass at the surface. The properties of the resultant star depend greatly on how much mass the star has retained.
In its core helium‐burning phase, a 0.9 solar mass star has a luminosity about 40 times that of the present‐day Sun and a relatively cool surface temperature. A 0.4 solar mass star is smaller and hotter, but still has about the same luminosity. Because luminosity does not depend on the resultant mass, but surface temperature and radius do, these core helium‐burning stars are called horizontal branch stars—plotted in an HR diagram, they fall in a horizontal track across the diagram (see Figure 3).
Schematic globular cluster HR diagram with branches labeled.
Old globular clusters in the galaxy show low‐mass stars still in their main sequence stages, whereas slightly more massive stars are found at various stages along the evolutionary part to the red giant and horizontal branch states of evolution. This turnoff of the main sequence can be used to determine the age of the cluster, because the mass of the star at the turnoff determines how long it has been on the main sequence.
All nuclear reactions do not produce the same energy. The triple‐alpha process 3 He 4 → C 12 generates a relatively small amount of energy compared to hydrogen burning 4 H 1 → He 4. As the carbon content builds up in the core, oxygen is produced via
But this production contributes only a small amount of additional energy. As this stage of evolution is a reasonably bright giant star, the nucleus fuel must also be used more rapidly by the star. Hence the horizontal branch lifetime is relatively short, about 100 million years (or about 1 percent of the hydrogen‐burning main sequence lifetime for the same star).
When helium becomes depleted in the core, the star again reverts to gravitation as the source of energy to replace that flowing out of the core. Once again, the surface swells to become a larger, cooler red giant star that follows a luminosity‐temperature track in the HR‐diagram just above the red giant branch. (As their luminosity and temperature pass very close to the track of the pre‐horizontal branch red giants, they are known as asymptotic branch stars.) Immediately outside the inert carbon‐oxygen core, a shell in which helium converts to carbon and oxygen is established. Farther out in the star there is a shell in which helium is at too low a temperature to support thermonuclear reactions; above that, hydrogen reactions produce helium in another layer. These shells in a sense resemble the layers in the interior of an onion, and computer models designed to reproduce the conditions in real stars are referred to as onion‐shell models.
In these low‐mass stars, there is insufficient gravity to compress the core to even higher temperatures and densities that would allow thermonuclear reactions producing even heavy elements. Once again at some point the existence of the electrons becomes increasingly important. As the carbon‐oxygen core grows in size and continues its slow contraction, the electrons again begin to resist further compression and electron degeneracy pressure dominates the balance against gravity. The electrons eventually halt any further contraction of the star, leading to its final state.
The post‐horizontal branch evolution of a low‐mass star is complicated. The greater part of the star's luminosity is coming out of the slowly shrinking core, with additional contributions from the helium‐burning and hydrogen‐burning shells that are slowly moving their way outward into the material of the stellar envelope. Outer convection rapidly takes this energy to the surface, and the star moves up the Hayashi track to become an extremely luminous red supergiant star. The outward movement of the hydrogen‐burning shell is slower than that of the helium‐burning shell because helium‐burning produces so much less energy per unit mass — helium must be processed more quickly to supply the energy to maintain the inner stability of the star. But at some point, the helium‐burning shell must overtake from below the hydrogen‐burning shell. When this happens, the hydrogen thermonuclear reactions shut down, but then so do the helium reactions because there now is insufficient helium to support them.
This loss of energy to the outward flow of luminosity produces an immediate effect in the outer regions and at the surface of the star. The surface quickly shrinks and becomes hotter — in terms of where the star would be plotted in the HR diagram, it undergoes a very rapid excursion into the blue supergiant region. Readjustment of the outer part of the star allows the hydrogen‐burning shell to be reestablished and to produce a new shell of helium below it. The outer layers readjust, with the surface expanding and cooling once again to take the star back into the red supergiant region. Such an excursion across the HR diagram is very rapid, lasting no more than a few thousand years. As a consequence, stars undergoing this type of shell‐burning instability are rarely observed. (See Figure 4.)
HR diagram of post‐horizontal branch evolution; b) Cross‐sectional model of post‐horizontal branch star configuration. (Not drawn to scale.)
Within a few million years, the greater part of the stellar mass is now converted to carbon and oxygen. The hydrogen‐ and helium‐burning shells have now moved so far out into the exterior of the star that little material remains above these layers. In fact, at some point these energy‐producing regions heat the outer stellar material so much that the star's gravity is no longer able to retain the outermost layers. These layers now are simply shed, blowing outward in a stellar wind, sometimes forming a spherically symmetric nebulosity about the remaining star (the Ring Nebula is the most familiar example) and other times forming more complex patterns of nebulosity. At the centers of these planetary nebulae (so named because when originally discovered, astronomers erroneously assumed these nebulae were planetary systems in formation, not dying stars as they actually are) are located the very hot interior remnant of the original star. This, now bereft of thermonuclear reactions, rapidly shrinks and becomes much dimmer as it finally stabilizes into a white dwarf.
Large numbers of planetary nebulae are known, and each contains a very hot central star surrounded by a complex nebula. Initially, when the star is a red giant, a slow and dense wind blows outward, and is usually more or less spherical (though it can be significantly flattened). However, as the star loses mass, the hotter core is exposed, and a faster, less dense wind is blown. This catches up to and collides with the slower denser wind, shaping it into a variety of shapes, depending on the geometery of the winds and our viewing angle. These planetary nebulae can be shaped like barrels, spheres, or even butterfly shapes with two huge lobes looking like the wings of a butterfly. The famous Ring Nebula is actually a barrel‐shaped structure, and we happen to be peering almost directly down the long axis, making the nebula appear round. Typical diameters of the nebula are 20,000 to 100,000 AU in size, representing 0.1 to 0.2 solar masses of material, with expansion velocities usually 10 to 12 km/s, although higher velocities have been observed. Likely all stars less than a few solar masses in their main sequence stars ultimately go through the planetary nebula stage, by which time the star retains no more than about a solar mass of material. Such planetary nebulae stars are observed with temperatures of 50,000 to 200,000 K (measured for the object NGC 2440), but their sizes are much smaller than the Sun. The larger of these stars are associated with the smaller nebulae, and the smaller stars are found in the larger nebulae, clearly indicating that these stars are shrinking as the surrounding nebulae expand over time. The observable lifetime of this phenomenon may be only 20,000 years as these stars undergo their final restructuring into a white dwarf configuration. See Figure 5.