Star clusters provide excellent test sites for the theory of stellar evolution. Every star in a given cluster formed at the same time, from the same interstellar cloud, with virtually the same composition. Only the mass varies from one star to another. This allows us to check the accuracy of our theoretical models in a very straightforward way. Having studied in some detail the evolutionary tracks of individual stars, let us now consider how their collective appearance changes in time.

In Chapter 17 we saw how astronomers estimate the ages of star clusters by determining which of their stars have already left the main sequence. (Sec. 17.10) In fact, the main-sequence lifetimes that go into those age measurements represent only a tiny fraction of the data obtained from theoretical models of stellar evolution. Starting from the zero-age main sequence, astronomers can predict exactly how a newborn cluster should look at any subsequent time. Although we cannot see into the interiors of stars to test our models, we can compare stars' outward appearances with theoretical predictions. The agreement—in detail—between theory and observation is remarkably good.

We begin our study shortly after the cluster's formation, with the upper main sequence already fully formed and burning steadily, and lower-mass stars just beginning to arrive on the main sequence, as shown in Figure 20.16(a). The appearance of the cluster at this early stage is dominated by its most massive stars—the bright blue supergiants. Now let's follow the cluster forward in time and see how its H—R diagram evolves.

Figure 20.16 The changing H—R diagram of a hypothetical star cluster. (a) Initially, stars on the upper main sequence are already burning steadily while the lower main sequence is still forming. (b) At 10⁷ years, O-type stars have already left the main sequence, and a few red giants are visible. (c) By 10⁸ years, stars of spectral type B have evolved off the main sequence. More red giants are visible, and the lower main sequence is almost fully formed. (d) At 10⁹ years, the main sequence is cut off at about spectral type A. The subgiant and red-giant branches are just becoming evident, and the formation of the lower main sequence is complete. A few white dwarfs may be present. (e) At 10¹⁰ years, only stars less massive than the Sun still remain on the main sequence. The cluster's subgiant, red-giant, horizontal, and asymptotic giant branches are all discernible. Many white dwarfs have now formed.

Figure 20.16(b) shows the appearance of our cluster's H—R diagram after 10 million years. The most massive O-type stars have evolved off the main sequence. Most have already exploded and vanished, as just discussed, but one or two may still be visible as red giants. The remaining cluster stars are largely unchanged in appearance—their evolution is slow enough that little happens to them in such a relatively short period of time. The cluster's H—R diagram shows the main sequence slightly cut off, along with a rather poorly defined red-giant region. Figure 20.17 shows the twin open clusters h and (the Greek letter chi) Persei, along with their combined H—R diagram. Comparing Figure 20.17(b) with such diagrams as those in Figure 20.16, astronomers estimate the age of this pair of clusters to be about 10 million years.

Figure 20.17 (a) The "double cluster" h and Persei. (b) The H—R diagram of the pair indicates that the stars are very young—probably only about 10 million years old.

After 100 million years (Figure 20.16c) stars brighter than type B5 or so (about 4—5 solar masses) have left the main sequence, and a few more red supergiants are visible. By this time most of the cluster's low-mass stars have finally arrived on the main sequence, although the dimmest M stars may still be in their contraction phase. The appearance of the cluster is now dominated by bright B stars and brighter red giants.

At any time during the evolution the cluster's original main sequence is intact up to some well-defined stellar mass, corresponding to the stars that are just leaving the main sequence at that instant. We can imagine the main sequence being "peeled away" from the top down, with fainter and fainter stars turning off and heading for the giant branch as time goes on. Astronomers refer to the high-luminosity end of the observed main sequence as the main-sequence turnoff. The mass of the star that is just evolving off the main sequence at any moment is known as the turnoff mass.

At 1 billion years, the main-sequence turnoff mass is around 2 solar masses, corresponding roughly to spectral type A2. The subgiant and giant branches associated with the evolution of low-mass stars are just becoming visible, as indicated in Figure 20.16(d). The formation of the lower main sequence is now complete. In addition, the first white dwarfs have just appeared, although they are often too faint to be observed at the distances of most clusters. Figure 20.18 shows the Hyades open cluster and its H—R diagram. The H—R diagram appears to lie between Figures 20.16(c) and 20.16(d), suggesting that the cluster's age is about 500 million years.

Figure 20.18 (a) The Hyades cluster, a relatively young group of stars visible to the naked eye. (b) The H—R diagram for this cluster is cut off at about spectral type A, implying an age of about 500 million years.

At 10 billion years, the turnoff point has reached solar-mass stars, of spectral type G2. The subgiant and giant branches are now clearly discernible (see Figure 20.16e), and the horizontal and asymptotic giant branches appear as distinct regions in the H—R diagram. Many white dwarfs are also present in the cluster. Although stars in all these evolutionary stages are also present in the 1-billion-year-old cluster shown in Figure 20.16(d), they are few in number—typically only a few percent of the total number of stars in the cluster. Also, because they evolve so rapidly, they spend very little time in these regions. Low-mass stars are much more numerous and evolve more slowly, so their evolutionary tracks are more easily detected.

Figure 20.19 shows the globular cluster 47 Tucanae. By carefully adjusting their theoretical models until the cluster's main sequence, subgiant, red-giant, and horizontal branches are all well matched, astronomers have determined its age to be roughly 11 billion years, a little older than our hypothetical cluster in Figure 20.16(e). In fact, globular cluster ages determined in this way show a remarkably small spread. All the globular clusters in our Galaxy appear to have formed between about 10 and 12 billion years ago.

Figure 20.19 (a) The southern globular cluster 47 Tucanae. (b) Fitting its main-sequence turnoff and its giant and horizontal branches to theoretical models gives 47 Tucanae an age of about 11 billion years, making it one of the oldest known objects in the Milky Way Galaxy. The inset is a high-resolution ultraviolet image of 47 Tucanae's core region, taken with the Hubble Space Telescope and showing many "blue stragglers"—massive stars lying on the main sequence above the turnoff point, resulting perhaps from the merging of binary star systems (see also Figure 20.9). The points representing white dwarfs, red dwarfs, and blue stragglers are for illustration only—they have been added to the original data set, based on Hubble observations of this and other clusters.

Recent Hubble observations of nearby globular clusters have also revealed for the first time the white dwarf sequences long predicted by theory but previously too faint to detect at such large distances. Figure 20.20 (b) shows a cluster called M4 on image of white dwarfs in HST lying 2100 pc from Earth. To illustrate our point, we have combined in Figure 20.19(b) both the newer white-dwarf data for M4 and the older main-sequence/red-giant data for 47 Tuc. The complete H-R diagram for a single cluster is expected to look qualitatively similar.

Figure 20.20 (a) The globular cluster M4, as seen through a large ground-based telescope on Kitt Peak Mountain. This is the closest globular cluster to us, at 2100 pc away; it spans some 16 pc. (b) A peek at M4's suburbs by the Hubble telescope shows nearly a hundred white dwarfs within a small 0.4-pc area, some of the brightest ones are circled in blue.

Stellar evolution is one of the great success stories of astrophysics. Like all good scientific theories, it makes definite testable predictions about the universe while remaining flexible enough to incorporate new discoveries as they occur. Theory and observation have advanced hand in hand. At the start of the twentieth century many scientists despaired of ever knowing even the compositions of the stars, let alone why they shine and how they change. Today, the theory of stellar evolution is a cornerstone of modern astronomy.