The Importance of Star Clusters in Understanding Stellar Evolution: A Point-Form Summary. This section of the course notes, and the associated PowerPoint presentation, makes the following critical points: star clusters provide groups of stars where the only important difference between individual stars is that they have different masses. They are alike in age, composition, and distance the reality of star clusters is unmistakeable, and can be confirmed both statistically and because the individual stars move in common directions and with similar speeds through space a star cluster forms from a distended cloud of gas, when gravity dominates and starts its collapse. Individual stars subsequently form here and there within it as they form, stars pass through a 'protostar' phase in which they are large and cool (but gradually heating up as they contract). This means that protostars are superficially rather like red giants. They can be distinguished, however within a cluster, we can readily measure the brightnesses and colours of the member stars, and plot an HR diagram. We do not need to know the distance of the cluster to do this, because all the stars are at the same distance and the differences in brightness are meaningful. (If the cluster was farther away, all the member stars would look fainter, but their distribution in the HR diagram would not change). a very young cluster, newly formed, would be expected to have a long main sequence, with stars of all colours in a somewhat older cluster, the brightest, hottest main sequence stars have used up their fuel. In clusters which lack these extremely hot blue stars, we find instead a number of red giants, which is the evidence we need to tell us that that is what the stars turn into some clusters have almost no stars left on the blue part of the main sequence, and must be billions of years old (since every star more massive than the sun has used up its fuel). In such clusters, there are very many red giants, again confirming our understanding that all stars turn into red giants when they run out of hydrogen fuel on the main sequence the 'turnoff' is the colour of the point on the main sequence beyond which (to the blue side) there are no main sequence stars left. The turnoff is an indicator of the age of the cluster. A young cluster still has some moderately massive stars, and a blueish turnoff colour; in an old cluster, only orange and red stars will still be found on the main sequence there are star clusters that span an enormous range of ages. Some clusters formed very recently (in astronomical terms); others are billions of years older than the sun and solar system we can use computer models to predict how stars will chew up their fuel and turn into red giants (and later remnants). These predictions can be compared to the observations and do remarkably well. We seem to understand stellar evolution well the sun is not in a cluster at present, but may have been formed in one five billion years ago. Individual clusters can disrupt and break apart either because they 'evaporate' or because of the tidal influences of other massive objects

Associated Readings from the Text.

Please look at: Chapter 16, especially pages 536-539. Chapter 17, pages 546-547, for a glimpse of star formation. (We will return to this topic in more detail later.)

The Use and Importance of Star Clusters.

A star cluster provides us with a region within which a whole bunch of stars - some massive ones, some smaller ones, and so on - formed at nearly the same time out of a big cloud of gas which was of pretty nearly uniform composition, so that all the stars in a particular cluster start out with the same mix of elements within them. Just as in our hypothetical experiment, a cluster provides stars which are: at the same distance from us. This means that differences in brightness and appearance tell us of true differences among the stars. In other words, if one star in the cluster looks brighter than another one, it really is . (This is not precisely correct, of course. Some of the stars will be on the `near side' of the cluster and some on the `far side'. Generally this difference is inconsequential, as it would be if you were ask about two friends living in Vancouver: one may be closer to Kingston than the other, but not by enough to really matter.) of the same initial composition; and of very nearly the same age. With respect to the ages of the stars, it must be admitted that the star formation process is not all that simple: big stars, with more gravity, may collapse together somewhat faster and form more quickly than little stars, for example. But after a few billion years, these small differences are no longer important, and it is reasonable to speak as though all the stars in a particular cluster are of the same age. Here is an analogy: if you meet a pair of twenty-year-old twins, and one is more mature in behaviour than the other, you don't claim that this is directly a consequence of the fact that she is older than the other by eight minutes. Small differences in the precise time of birth don't matter after such a long time.

Are Star Clusters Real?

You will recall that the existence of binary stars proved a life-saver when we needed to work out the masses of stars. (It is virtually impossible to work out the precise mass of a single star sitting alone in space.) Well, in working out the ages of stars, the clusters are likewise essential, as we will see. But when we see an apparent grouping of stars in the sky, are they really related at all? You may, for instance, remember that at the start of the year I pointed out that the separate stars in a constellation may be quite unrelated and at very different distances from the Earth. In class, I showed some pictures of star clusters. (See page 537 of the text. By the way, the Pleiades, one of the clusters shown on that page, can be seen in the winter months, high in the night sky. With sharp eyes, you can pick out six, seven, or eight stars - although perhaps not from downtown Kingston!) In the Milky Way galaxy, there are literally thousands of clusters of stars. But there are billions of stars, and there are bound to be many chance clumpings in which a few stars in the foreground appear to lie in the same direction as several more in the far distance, mimicking a real clustering. How do we know that most of the so-called 'clusters' are not just accidental superpositions of that sort? Fortunately, there are several ways to prove that the groupings are not just random: Statistically. If stars were distributed at random over the sky, what are the odds that, just by chance, you would see a clumping of the sort shown in the bottom panel on page 537? I don't think I need to persuade you that this is unlikely, but for some of the less rich clusters, there is sometimes some doubt about their reality. From the proper motions. When we talk about a `real cluster,' we mean a system of stars which are moving under the influence of one another's gravity and acting, in some sense, like a common group. Part of that definition, therefore, implies that the stars will be seen to move in a common direction in space, like a fleet of ships sailing together across the sea. Such behaviour is seen for many clusters. Several of the prominent stars in the Big Dipper, for instance, are part of the so-called Ursa Major (Great Bear) cluster, and move in the same direction in space. Notice, however, that not all the stars are members - that is the reason that that constellation will change in appearance as the centuries pass. From the radial velocities. In addition to watching the transverse (`sideways') motions of the stars, we can get their spectra and use the Doppler shift to work out how fast they are moving toward or away from us. As we will see later when we discuss the origin and structure of the Milky Way galaxy, some clusters have rather large radial velocities, and any star which does not share that velocity will definitely not be a member. In this way we can identify stars with closely similar speeds, likely to be members of the cluster. In these various ways, we can convince ourselves that the star clusters are really physical groupings of stars.

The Pace of Stellar Evolution.

We have noted before that the whole aging process for a star depends very strongly on that star's mass. Every stage of the life of a massive star is shorter than for a less-massive star - it forms more quickly, doesn't last as long on the main sequence before consuming all its fuel, and goes through its death throes more quickly. Thanks to our well-developed understanding of the nuclear reaction rates within stars and their physical properties, these remarks can be made quantitative. Before looking at some actual numbers, however, let us first consider the properties of not-yet-fully-formed stars, otherwise known as protostars. (We will come back to the topic of star formtion a bit more thoroughly later on.)

Remarks on Protostars.

When we discussed the formation of the solar system in Physics 015, we imagined starting with a hypothetical cloud of distended gas in interstellar space. For one reason or another, the cloud attained a stage at which it began to contract under the influence of its self-gravity. That is, the particles within the cloud attracted each other more strongly than could be resisted by the pressure of the random motions of the particles, and the material began to draw in on itself. The material in the cloud started at quite a low temperature, but as the collapse proceeded the collisions between particles led to it heating up. (Indeed, at a late stage of the collapse, when the cloud had condensed to quite small size, this heating became extreme and led to the onset of nuclear reactions.) At some intermediate stage, however, before the star itself is born, the cloud will be moderately dense, less enormous than it was (but still quite large), and warm enough to emit quite a lot of infrared radiation and red light. What will such an obect resemble? Well, protostars will look reddish but fairly bright (because they are so big that they have lots of radiating surface area and emit lots of light in total). Remarkably, then, stars in the process of formation start out looking rather like the red giants they are destined eventually to turn into once their main sequence lives are over. I should emphasise that this similarity is only qualitative: there are details and subtleties which allow us to readily discriminate between stars in formation and those ending their careers. But you need to understand this general behaviour in order to interpret what I am about to present.

Imagine a Cluster in Formation.

Suppose you start with an enormous cloud of gas and dust in interstellar space, one with enough material for perhaps a thousand stars. Suppose that this cloud of gas starts slowly to contract, and that here and there it breaks up into lumps of various mass - one or two lumps of very large mass, fifteen times as massive as the sun; a few dozen stars as massive as the sun itself; and hundreds of lumps of very small size, let us say. What will those lumps do, and in what order? From what we have learned already, you know that the various lumps, on their way to becoming stars, will be large and cool, so will look reddish and bright. If you were to plot them in one of our familiar HR diagrams, they will be plotted where one would put the red giants. But the stronger self-gravity of the bigger lumps means that they collapse very quickly to the point at which they `turn on' their nuclear reactions and become bright main sequence stars. In other words, they become stars long before the lower mass objects finish their more leisurely contraction. This is shown schematically on page 551 of your text. (Don't take the numbers too seriously, and certainly don't memorise them! The important point is the qualitative sense of the dependence.) You can see that a star which is fifteen times the mass of the sun starts as a cool (red) bright object, but within about 60,000 years has contracted to the stage where nuclear reactions are ticking away inside it, and it has become a bright blue star on the upper end of the main sequence. An object of the mass of the sun, by contrast, takes tens of millions of years to do so, and lower-mass objects take longer still. As noted, in their early stages all these protostars looked rather like red giants - cool (red) and bright. Their individual masses determine what kind of main sequence stars they become.

The Deaths of the Cluster Stars.

Once formed, the various stars burn and consume their fuels at rates which depend on their masses. This is shown in the figures on page 535 and 538. You can see that a star of 20 solar masses, after spending about ten million years as a main sequence star, will have run out of its central hydrogen fuel and will quickly become a red giant (i.e. its outer envelope will `puff up' and cool off, even as its inner core is contracting and getting hotter). Notice, therefore, that this star, having formed in less than one hundred thousand years, becomes a red giant within another ten million. It will have gone through its entire life before the one solar mass object has even become a main sequence star! You can see, in fact, that a star as massive as the sun takes tens of millions of years to become a main sequence star, spends about ten billion years on or near the main sequence (changing only a little in its properties), and then becomes a red giant within another billion years or so. Let us reconsider an imperfect analogy which I introduced in class. Stars are rather like humans in the sense that their gestation period (9 months) is about one percent of their potential healthy lives (say, 75 years). This is true for stars as well: they last about 100 times as long on the main sequence as they did in becoming stars. But I will now extend the analogy somewhat to point out that it is not uncommon for people to suffer a slow decline in health and vigour over the span of a decade or so late in their lives. So, too, the stars spend about 10 percent of their remaining time in the post-main-sequence stages which lead up to their `deaths.' The nature of the `dead star' - whether a white dwarf, neutron star, or black hole - depends on the mass of the original star, but that stage lasts essentially forever thereafter, just as human deaths are forever. These proportions, then, are readily remembered through the simple analogy. But the absolute timescales are different for different stars, and the important thing to remember is that the whole process happens fastest for the more massive stars.

Estimating Stellar Ages.

Look again at the picture of the Pleiades on page 537 of your text. What can you conclude from a study of this cluster? Your immediate inference, as an astronomer, is that this must be quite a young cluster of stars! The reason is that we see that there are some very bright hot (blue) stars in the cluster, and as you know such stars simply cannot last very long. They use their fuel up very rapidly, and are foredoomed to an early demise. (Our suspicion that the cluster is young may be somewhat supported by the observation that there is still a lot of gas and dust present. Perhaps this is left over from the material out of which the cluster stars recently formed. But you don't need such evidence: the very presence of hot bright blue stars tells us the whole story.) But can we generalize such thinking to all kinds of clusters, and deduce their ages? The answer is yes.

The Turnoff Age.

What would we see if we lived long enough to watch a star cluster form from a great cloud of interstellar gas and to monitor the full lives of all the stars within it? The qualitative answer, of course, is that we would see numbers of stars form, and that at various later times, depending on their individual masses, they would become conspicuous red giants. But let us consider it more quantitatively, with reference to a familiar plot. The most easily measured properties of the stars in a cluster are their brightnesses and their colours (or, equivalently, their temperatures). With very little effort, then, we can straightforwardly plot these measured attributes and construct an HR diagram for the cluster. For a very young (indeed newly-formed) cluster, we would expect to see something like what is shown in the figure on page 535 of the text. But the massive blue stars chew up their fuel rapidly, and are the first to become red giants. So here is what happens next (read pages 538-539): Look at Figure 16.16 on page 538, which shows the properties of the stars in the Pleiades. You will see that there are still some relatively hot blue stars on the main sequence but also some yet brighter stars plotted `above' the main sequence. These were formerly even hotter main sequence stars, but their properties are changing: they are 'moving' to the upper right. (There is no motion in the physical sense, of course; we mean simply that if you return, say, a million years from now, you will measure different properties and need to plot the data points in a different location. These stars, having exhausted their hydrogen fuel at the core, are becoming cooler at the surface and turning into bright red giants.) In Figure 16.17, on the same page, you will find a figure where the same sort of behaviour is shown for several clusters. Since the data are all plotted on the same figure, you may find this figure confusing. Focus on the pale brown symbols, which represent the stars in NGC 188, a cluster of fairly advanced age (in astronomical terms). In this cluster, all the relatively massive stars have long since finished their hydrogen-burning phases and have turned into red giants, as you can see. Finally, in Figure 16.18 on page 539, you will see the HR diagram for one the oldest star clusters known: a globular cluster known as Palomar 3. Thanks to the great passage of time, the main sequence has gotten shorter and shorter as the massive stars evolve away, one after another. There are now quite a number of red giants in the cluster, and there will also be a large number of white dwarfs to the lower left, although they are not plotted here. (The white dwarfs are the remnants which are left after the demise of the red giants, as we will learn next.) From this somewhat idealised exercise, you can see that the construction of an HR diagram for a cluster allows us to work out its age. If there are bright blue stars still on the main sequence, the cluster must be young. If there are only faint red stars on the main sequence, all other stars having already become red giants, the cluster must be old. The observed turnoff, as it is called, is therefore an immediate indication of the age of the cluster. It provides the clock we need.

Not Only Red Giants!

From what I have been saying, you might be excused for thinking that a cluster of, say, one thousand main-sequence stars would eventually turn into a cluster of one thousand bright red giants. That would be an impressive sight! -- but the story is not so simple. Although each star in turn becomes a red giant as it runs out of hydrogen fuel in its core, it does not last long as a red giant. The red giant phase is actually a rather brief one, representing only about ten percent of the star's entirely lifetime. Thereafter, the stars fairly quickly turn into faint, inconspicuous white dwarfs. Thus even a very big cluster may not have many red giants within it at any given time.

The Practical Realities.

In practice, of course, we cannot watch a single cluster evolve over time. But if we study as many clusters as possible, we discover that there are clusters in all of these various phases, and infer their ages. But how do we know for certain that we have the story the right way around? It would be good to have some extra independent evidence about the relative ages of the clusters. In fact, there are some useful indications. When stars or clusters form, not all the gas that was there in the first place ever gets into condensed into stars, and a young cluster may still be immersed in some of the material from which it formed. In fact, clusters whose HR diagrams look like that of the Pleiades are often found in such `gassy' locations, confirming our thinking and supporting the relative ages which we infer. In the end, however, it has to be conceded that the absolute ages - the actual ages in years - that we deduce for the clusters are contingent on the correctness of our theoretical models. We are sure of the main sense of stellar evolution (the massive stars evolve fastest; the main sequence stars turn into giants; and so on) but the precise times taken may still subject to some small amendments as our detailed understanding of the nuclear reactions (and other things) changes.

Some Real Clusters.

Just so we don't lose our way in a lot of HR figures, let us look again at a couple of photographs of real clusters and remind ourselves of our present understanding. The Pleiades: On page 537 of your text, you will see a photograph of the Pleiades. Its main sequence is shown in the composite figure on page 538. As you can see, the Pleiades has a fairly long main sequence, one on which there are still some fairly massive blue stars burning hydrogen in this cluster. (Indeed, they look nice and blue to the eye!) Astronomers have determined that this cluster has an age of about 100 million years. In other words, our entire solar system had been around for over four billion years before the Pleiades even formed! This is, astronomically speaking, quite a young star cluster. A globular cluster : By contrast, look at the beautiful picture on the bottom of page 538. The HR diagram of this cluster, which is known as M80, resembles that shown on page 539, and the inescapable inference is that this is a very old cluster, with an age of 10-15 billion years. It formed 5-10 billion years before the sun and the solar system, so it really is a fossil relic of the earliest days of star formation in our galaxy.

A Real Research Example.

In class, I elaborated on this theme a little. (You will see the relevant figures in the associated PowerPoint presentation.) A group of Canadian astronomers have studied a few selected regions of the bright globular cluster 47 Tuc, using a very sensitive electronic CCD detector. Using a 4-metre telescope in Chile, they took a series of direct images through various filters to allow the determination of star colours and brightnesses in this cluster. The scientific analysis they carried out is simple in principle. It consists of plotting the carefully measured brightnesses and colours of all the stars in these regions to form an HR diagram. This sounds very simple, but is not easily accomplished because of the great crowding of the images. The final figure they presented was rather like that shown schematically on page 539, although it attained a precision previously unmatched in this kind of work. Now comes the interesting part: a comparison with theory. In essence, we are asking the following question: what we would see if a huge blob of gas, a million times the mass of the sun, were to condense and form stars, then sit there evolving away for billions of years? The computer can handle all this and predict what sorts of stars we would see now. In class, I showed the results in the form of solid lines superimposed on the original data to show where you would expect to see the general distribution of data, if our theory is correct. I hope you agree that the agreement was remarkable! We really do seem to have a pretty good understanding of stellar evolution. It has to be admitted that applying our theoretical models to data from a real cluster is subject to certain assumptions (most of which are based on other observations): we need have independent knowledge of the distance of the cluster, details of the chemical composition of the gas out of which the cluster formed, and so forth. Most of these things are known pretty well, and the consistency of the exercise is quite reassuring. All together, this kind of study seems to suggest that this cluster has an age of about 13 billion years.

The Crowded Confines of a Star Cluster.

If you look at the photographs on page 537, you could certainly be excused for thinking that the stars within a globular cluster must be (figuratively) rubbing shoulders! It looks as though a rocket ship fired in the direction of the cluster would never be able to pass through it without hitting a star. Surprisingly, though, the crowding is not as bad as it appears: the stars are actually fairly well separated. Unfortunately, our photographs are subject to a now-familiar problem. The blurring caused by the Earth's atmosphere smears out the star images. As you might expect, if you were right inside a globular cluster you would see many bright stars in the night-time sky, but actual collisions between stars are very rare indeed, even in these close quarters. Recent images taken with the Hubble Space Telescope have shown that the stars in a nearby globular cluster are so well separated that we can see right through the clusters and discern remote galaxies in the extreme distance.

Is the Sun in a Cluster at Present?

If the sun were in a loose cluster, would we even know it? When we go out at night, we see a bunch of bright stars randomly scattered around the sky. Is this because we are near the center of a cluster, or is it simply because the stars really are more or less uniformly spread out at varied distances? You might think that if we were in a cluster the effects would be very dramatic, but of course that depends on how bright the stars are and how far apart they are on average. One way of checking this is to measure the motions of the stars near the Sun. If we find that the sun and many more stars are travelling through space in a common direction and with closely similar speeds, then we might tentatively consider this a cluster. (It would take a fairly detailed analysis to confirm whether or not the stars are in fact `gravitationally bound' - that is, whether they would keep moving together for a long time yet to come, held together by their mutual gravity, while other `field stars' pass us by in random directions.) The answer is that we can identify some examples of what are called `moving groups' of stars around us, as well as the more conspicuous clusters like the Pleiades, but that the sun itself has no obvious companions and is apparently not in a cluster at present.

Was the Sun Ever in a Cluster?

This is a very sensible question, because when we study star formation we discover that we almost never see single stars in the process of formation. Instead, we usually see enormous clouds of gas in great complexes within which stars are condensing here and there in large numbers. It may be that most or even all star formation happens this way, in which case it is logical to infer that the sun itself started in a cluster. But, if that is so, where is the cluster now? How could we ever have escaped its gravitational clutches? Remember that the cluster is a group of stars which are held together because each of them feels the gravitational attraction of all the others. A little thought and calculation shows that there are basically two ways in which a cluster can be disrupted: evaporation, or tidal influences. The Evaporation of Clusters: How does a pan of water evaporate? The individual water molecules in the pan are jiggling about rapidly (the water is warm), and random collisions occasionally speed one of them up to such an extent that it is knocked right out of the pan into the air. At the same time, randomly moving water molecules in the air can hit the pan. In an enclosed system (like a pan of water inside a big glass jar) an equilibrium is reached, with as many molecules arriving as are leaving. But if the air above the pan is dry, or if a breeze sweeps away any molecules that make it out, or if the water is heated up a bit so the molecules move more quickly, then the rate of evaporation increases and eventually all the water may disappear. Something similar can happen in star clusters, except that it is not direct collisions which knock the stars out of the cluster. Instead, they orbit around and about, at every instant feeling the gravitation of all the other stars and constantly changing direction and speed. (You may like to visualize a globular cluster as something like a swarm of luminous bees -- or fireflies, if you prefer! Please note that there is no dominant single massive object at the centre of a star cluster. The stars move in response to the collective gravity of all the other stars.) In these complex motions, every so often a particular star gets up enough speed to fly right out of the cluster and escape. For technical reasons, the cluster is then even less able to hang on to all its members (partly because the total gravity is reduced) and the evaporation speeds up. The cluster will dissipate. The Tidal Disruption of Clusters: As a star cluster moves through the galaxy, it occasionally comes close to other big objects - perhaps another large cluster, or a great cloud of gas, for instance. A star which is momentarily on the outskirts of its own `parent' cluster may then feel a gravitational pull from the nearby big object which is comparable to or even larger than that of its own cluster, and can be pulled right away from it. Because of the complex motions, the escaping star does not merely join the other object; instead, it winds up moving freely through space. Why Do Any Clusters Survive? For either of the reasons described above, a star cluster can dissipate completely. Thus it is entirely possible that the sun formed in a cluster 4-5 billion years ago, and that the cluster has long since ceased to be. Earlier, however, we saw that the globular clusters (some of them, anyway) may be 13 billion years old. Why have they not long since disappeared? Partly it is because they are so massive: they can hang onto their stars quite firmly with a strong gravitational grip. It is also because the way they move through the Galaxy means that they seldom encounter other big objects.

The Kinds of Clusters.

Generally speaking, astronomers speak of two main kinds of star clusters: open clusters are younger, lie in the flattened plane of the Galaxy, contain fewer stars (perhaps several hundred), were formed from gas which consisted of a few percent heavy elements, and are a bit irregular in appearance. An example is the Pleiades. globular clusters are older, are distributed all around the galaxy (not just in the plane of the Milky Way), were formed from gas which was almost pure hydrogen and helium, and are rich and regular in appearance. As we will learn later, these different properties stem from, and tell us about, the way in which the Milky Way Galaxy itself formed. Previous chapter:Next chapter

0: Physics 016: The Course Notes, spring 2005. 1: The Properties of the Sun: 2: What Is The Sun Doing? 3: An Introduction to Thermonuclear Fusion. 4: Probing the Deep Interior of the Sun. 5: The Sun in More Detail. 6: An Introduction to the Stars. 7: Stars and Their Distances: 8: The HR Diagram: 9: Questions Arising from the HR Diagram: 10: The Importance of Binary Stars: 11: Implications from Stellar Masses: 12: Late in the Life of the Sun: 13: The Importance of Star Clusters in Understanding Stellar Evolution: 14: The Chandrasekhar Limit: 15: Supernovae: The Deaths of Massive Stars, 16: Pulsars: 17: Novae: 18: An Introduction to Black Holes: 19: Gravity as Geometry: 20: Finishing Off Black Holes: 21: Star Formation: 22: Dust in the Interstellar Medium: 23: Gas in the ISM: 24: The Size and Shape of Our Galaxy: 25: The Discovery of External Galaxies: 26: Galaxies of All Kinds: 27: The Expanding Universe: 28: Quasars and Active Galaxies: 29: The Hot Big Bang: 30: The Geometry of the Universe: 31: Closing Thoughts:

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