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.)