1.5 Star clusters and stellar evolution
Detailed observations of star clusters suggest that they occur because the stars in them form at about the same time. Moreover, the compositions of the stars are similar. Isolated stars (including isolated binary stars) result from the later partial or complete dispersal of a cluster.
The crucial points for us here are that all the stars in a cluster formed at about the same time, and all have similar compositions.
Why are these the crucial points?
If the stars in a cluster have different masses, then we can discover the relative rates of evolution of stars that differ only in their mass.
These relative rates are conveniently revealed by plotting the H-R diagram of a cluster. Figure 10 shows two contrasting cases: the Pleiades, and a cluster that has only a catalogue number, M67 (the 67th object in a catalogue of nebulae that may be confused with comets, produced by French comet hunter Charles Messier (1730-1817)). In the case of the Pleiades, almost all the stars are on the main sequence, suggesting that this cluster is not old enough for many stars to have reached the end of this phase. The most luminous stars visible on this diagram appear to be moving away from the main sequence. The upper end of the main sequence, where the most massive stars are expected to lie (Figure 8), is unpopulated in this cluster. For the Pleiades, the most massive stars have already left the main sequence and therefore must have shorter main sequence lifetimes. In fact, the point at which this depopulation occurs, called the main sequence turn-off, is used as an indicator of the ages of clusters. The case of M67 (Figure 11) is the subject of Question 4.
We have come a long way in constructing a plausible model of stellar evolution, and it is summarized in Figure 12. We have described some of the observational basis of this model; further observations not only support it, but fill in some of the missing details. However, the time has now come to move away from pure observations as the sole basis for model building, and to involve a powerful body of physical theory in the modelling process. In the following sections we thus continue to develop the story of the stars, and of their evolution, but with considerable reliance on physical theory. This will necessarily involve us in modelling not only external events, but also stellar interiors.
Figure 10b shows the H-R diagram of the star cluster M67. (a) Discuss whether this is consistent with the model of stellar evolution in Figure 12. (b) Why is it reasonable to conclude that M67 is older than the Pleiades?
(a) The H-R diagram of M67 in Figure 10b is notable for the absence from the main sequence of all but the low-mass stars (Figure 8), and the presence of considerable numbers of stars between the main sequence and the red giant region, which could represent the higher masses missing from the main sequence. This suggests that the more massive a star, the sooner it leaves the main sequence, and that most stars that have left the main sequence go on to become red giants. Supergiants are absent in M67, and this could be because massive main sequence stars, which are their precursors, are rare. Also, if, as it seems, massive stars evolve rapidly, then any supergiants could have become Type II supernovae, and have thus vanished from the H-R diagram. The absence of white dwarfs is presumably because they are too faint to detect. Thus, the H-R diagram for M67 is consistent with the model of stellar evolution in Figure 12.
(b) Assuming the model is right, we can conclude that M67 is older than the Pleiades, because in the Pleiades the main sequence is populated to higher stellar masses than the main sequence in M67 (Figure 10). This occurs because the more massive the star the sooner it leaves the main sequence. In M67 there has been enough time for all but the low mass stars to leave the main sequence, whereas the Pleiades is too young for this to have happened.