Late in the Life of the Sun:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
the mass of a star determines its life cycle. Very low-mass blobs of gas become objects like Jupiter; a blob the mass of the sun will live out a sun-like life; more massive stars will evolve much more rapidly and end their lives in spectacular fashion, with supernova explosions and other fireworks
for all stars, the main sequence lifetime is the longest stable period because the hydrogen fuel is abundant and high quality (i.e. it releases the most energy in its nuclear reactions). Once the star's core contains heavier elements -- the products of nuclear fusion -- subsequent reactions depend on lower-grade fuel, which means that their lifetimes will be limited
the outer parts of stars do not get 'stirred down' into the core, which means that not all of the raw hydrogen fuel gets used. This means that stars do not live as long as they could, in principle
the lack of 'stirring' means that stars become stratified, with progressively heavier elements being created in the deep interior where it is hot enough to do so. Note that the stratification is not the result of the settling of dense material to the core
the sun's core will eventually be pure helium, and the reactions will go out. The core will contract and heat until helium fusion reactions begin, releasing more energy and preventing futher contraction. So we expect the sun to get more compact and hot late in its life
once begun, the helium burning reactions convert helium nuclei to carbon nuclei, in a process called the 'triple-alpha' process
the problem is that this happens deep inside the stellar envelope, so it is not obvious that we will see this at all. It depends what the outer parts of the star do while all that action is going on in the core
while the core contracts and heats ups, leading to the onset of helium burning, the outer parts of the sun indeed do something remarkably different: they expand and cool down, turning the sun into a red giant
ideally, we would test this proposition by watching a one-solar mass star go through its aging process, or by looking at a variety of one-solar-mass stars of different ages. Neither of these approaches works in practice. The lifetimes of stars are so long that we would see no significant changes over many centuries or millennia. Moreover, for single stars sitting in empty space, we have no good way of estimating the ages. There is no easy way of identifying single stars that have been around for ten billion years and are running out of fuel
nor do we want to rely on 'what the astrophysics theorists tell us'. We really need to refer to observational evidence
the solution is to study star clusters. A cluster contains stars of varied masses, so we can see what different evoltuionary stages they have reached in comparison to one another. Moreover, we can identify star clusters of different ages, and see how they compare
Associated Readings from the Text.Please look at: Chapter 16, page 535 Chapter 17, pages 551-554 in particularThe Importance of Mass.At various times, I have pointed out that essentially every part of a star's life (including the rates of formation and evolution, as well as its eventual fate) is completely determined by the mass of that star. The more massive stars form (`fall together') more quickly under the stronger self-gravity which they experience, and become hotter as a result. This extra heat supports the star against continued gravitational contraction, but at a price: the higher temperatures make the nuclear reactions run more rapidly, and the fuel within the star is used up more quickly. Thus the more massive stars reach their demise long before the low-mass stars. It is a matter of subjective judgement, of course, but I think it is also safe to say that the more massive stars also end up in more interesting ways (as neutron stars, pulsars, supernovae, or black holes) than do the low-mass stars. In the next few lectures, we will explore stellar evolution for (i) lower-mass stars (like the sun and smaller) and (ii) more massive stars - those with spectacular deaths ahead of them! On the figure below, I show some of this in schematic form. Across the bottom of the figure, you will see numbers which indicate the masses of various blobs of gas, in units of the mass of the sun. Now look upwards, along the direction of the pointing arrows, to see how these blobs change as time passes. (The time in years is shown on the axis at the left of the figure.) Notice that the very smallest gas blob plotted, one with a mass of only one one-thousandth (0.001) that of sun, will never become a star. It will contract under the influence of its own gravity, gradually becoming warmer and emitting infrared radiation, only to wind up as a planet. (This is indeed what Jupiter is like.) It will never get hot enough in its core to ignite nuclear reactions. Stars with a mass of a tenth (0.1) of that of the sun become main sequence stars of type M, taking almost one billion (10**9) years to form but then lasting a very long time. After their demise, they turn into white dwarfs, about which we will learn more later. A star of exactly one solar mass becomes a main sequence star of G spectral type. Notice that such a star takes about one hundred million years to form (10**8 years), but that it then lasts about ten billion years - one hundred times as long. (This is analogous to human life, in some senses: we spend about nine months in utero, before birth, and then live for about one hundred times as long, which is 75 years.) The sun, too, will eventually become a white dwarf `cinder.' A somewhat more massive star, like Sirius (with a mass a few times that of the sun), will live a considerably shorter life, and may become a pulsar or a neutron star. But considerably more massive stars, ten times the mass of the sun, will form very quickly and then live out their whole lives within a few million years. Their deaths are spectacular, marked by supernova explosions and the formation of black holes.Why These Lifetimes?Remember that the nuclear energy generation in the core of a star is what keeps the star hot and supports it against further gravitational contraction. A little thought reveals that there are two reasons for the great longevity of a star like the sun during the time that it is on the main sequence, converting its hydrogen to helium. The first and most obvious point is that the stars are largely made of hydrogen, so there is plenty of that particular fuel. Moreover, each individual hydrogen reaction yields quite a lot of energy. (Remember the shape of the binding energy curve!) This means that, in its quest to keep its interior hot enough to resist further gravitational contraction, the sun needs to call on only a modest number of fusion reactions per second. Suppose instead that you had a hypothetical star made of helium. How would it behave? Well, in a star made of helium, lots and lots of reactions would be needed (since each one provides only a modest amount of energy) to provide enough energy to keep the star hot enough to support itself against further gravitational contraction. As a consequence, the helium fuel would get used up very quickly. It is clear, therefore, that a helium star (with no hydrogen fuel) would have only a short potential life - it is like a `gas guzzler' car, using up its fuel very rapidly. Moreover, we can anticipate later developments by noting that fusing together still heavier elements will yield very much less. Are there helium stars? The answer must be "yes": it does not take great insight to realise that the sun will itself eventually be just like a `helium star' (at least in its central regions, which is where the action is). After it reaches that stage, its days will be numbered.Slow Changes in the Core of the Star.In its very center, where the temperatures are high enough, the sun is slowly converting hydrogen to helium. Recall that it started with about a uniform composition which was nearly two-thirds hydrogen and one-third helium (plus trace amounts of other things). As time passes, the amount of helium in the core builds up as an `ash' which cannot be burnt. Eventually the core will be nearly pure helium, so the deep interior parts are like the `helium star' we just considered. Meanwhile, however, the outer parts of the sun remain as they are now: there are no nuclear reactions happening out there in the cooler regions, and the composition does not change. An important point: In general, the outer parts of stars do not get `stirred down' into the central regions. Thus the raw fuel (the hydrogen) in the outer parts of a star never gets subjected to the extreme temperatures of the core of the star, and so will not get burned up. This limits the potential life of the star. I used an analogy in class. Imagine a campfire with long sticks of wood pointing in to the center. The fire will burn for a time, but eventually you will be left with ashes in the middle and unburned lengths of wood sticking out to the periphery. If you want to extend the life of the fire, of course, one simple way would be to slowly push the sticks in, bit by bit, as the fuel is consumed. In similar fashion, a star would be able to use more of its reserves of fuel, and last longer, if the outer layers could somehow be made to move down to the core - which means that the helium `ash' would have to move outwards, of course, to make room for the fresh fuel. In other words, what is wanted is a general circulation of material. Unfortunately, there is no such large-scale motion in stars like the sun, so only part of the fuel gets used. (The outermost ten or fifteen percent of the sun is in swirling convective motion, but those motions do not reach down into the nuclear furnaces at the core.) This has three very important consequences: A star does not have as much fuel available to it as you might think, given its total mass, because the outer parts never get used. When we study the absorption lines in the spectrum of a star to deduce the composition of the star, we are really only studying the star's outer parts, since that is where the light comes from and where the spectral absorption lines are formed. In other words, we are really determining the composition of the gas cloud out of which the star was born (since the outer parts of the star still have that composition). The deep inner parts may be quite different by now, but are mostly unobservable. For instance, the core of the sun is by now relatively rich in helium, the ashes produced by several billion years of nuclear reactions. But the light from the sun does not tell us anything directly about that. (We are able to test and confirm this hypothesis by using the GONG [helioseismology] results, however.) Stars become stratified as they age. The sun has a helium-rich core, but a deep outer envelope which is still, and always will be, two-thirds hydrogen, just as it was when the sun formed. Please note that the helium-rich core comes into existence because the extra helium was produced at the very center, where the temperatures were high enough to drive the nuclear reactions. It is most definitely not because the heavier helium settled to the middle, a very common misunderstanding. In studying the later stages of the evolution of more massive stars, we will encounter what are usually called `onion-skin' models of stars. (See the figure on page 562 of your text.) You can see that the progressively heavier elements in such stars are found nearer the center, but only because they were produced there, not because they settled there. To fuse two carbon nuclei to make magnesium, for example, takes extremely high temperatures, and magnesium can therefore only be produced right in the very heart of a massive, much-contracted star. No magnesium could ever be made in the cooler outer parts of a star.The Behaviour of a Hypothetical Helium Star.A few billion years from now, the sun will have used up all the hydrogen in its core, and will contain a central lump of helium surrounded by a deep envelope of the original material out of which it formed. What will happen? One way of understanding this is to ignore the stellar envelope for the moment, and just to imagine a pure helium star on its own. Indeed, we could carry this to a real extreme, and imagine a universe in which there was no such element as hydrogen at all. If the simplest and most abundant element was helium, would there still be stars? What would they be like? There would indeed still be stars. At various places in the universe, you might find a big blob of helium-rich gas which was massive and dense enough for gravity to dominate. The blob would start condensing under its own gravity to form a star. The process would parallel our previous discussion exactly, with the word `helium' replacing `hydrogen' everywhere. Thus: The particles would draw together under gravity, and the release of gravitational potential energy would heat them as they become more compressed and start to collide vigorously with each other. In other words, the gas would become hot. The heat would temporarily support the new star against continuing rapid collapse, but as the built-up heat is radiated away the pressure would fall and further slow contraction would follow (with a consequent release of energy and further heating). This is the Kelvin contraction which was once thought to explain the stability of the sun. For millions of years, the star would slowly condense, getting hotter as it did so. In this way, the star would contract and heat up until finally the critical central temperature is reached at which helium can burn. This parallels what happened in the sun (where we saw that reaching a temperature of about ten million degrees sets the hydrogen fusion going). As we realised above, helium requires a much higher temperature: remember that we have to force the particles together against the repulsion each nucleus feels from the other one, and they carry two positive charges. It can be determined that a temperature of about one hundred million degrees is needed, about six times the temperature in the centre of the sun at present. So a hypothetical star made of pure helium would have to contract far enough to reach such a temperature before the reactions could start. Such a star would be small, dense, and very hot.Back to the Sun Itself.The simple considerations of the preceding paragraphs lead to the conclusion that helium-burning stars will be very compact, dense, and extremely hot. This is how the central parts of the sun will behave once it has converted most of its central hydrogen fuel into helium. When it runs out of fuel, the energy source will disappear (i.e. no more hydrogen fusion). We will then have a large lump of helium, one in which no energy is being generated at all. It is effectively ash. The heat which is contained within it will slowly trickle out and be radiated away, so the temperature will drop somewhat and the pressure will fall. Since the core of sun will no longer be able to hold itself up against gravitation, there will be a steady contraction and heating of the core. In other words, the core of the sun will act just like our hypothetical pure helium star! Eventually the necessary temperature (100,000,000 K) will be reached and helium fusion will start, at which point the core will stop contracting since the energy release will maintain the temperature and the pressure. Once again we will have a stable star, with the energy generated in the core exactly matching that escaping to space from the surface. But such a star will not last for long, since the helium fuel provides less energy than the hydrogen fuel did, and will be consumed more quickly as a result. Unfortunately, however, this will all take place hidden from direct view, deep within the gaseous envelope of remaining pristine material out of which the sun formed four-and-a-half billion years ago. We thus have to consider the interesting question of the possible outward manifestations -- if any! -- of the goings-on in the core. Will the sun get perceptibly smaller and hotter as a whole when it runs out of its central fuel, or will the outer envelope of gas do something quite different and unpredictable? That is the question we will turn to next. What we can predict with confidence, however, is that the sun will not last in its new form for very long, whatever its outward appearance. Its death cannot be long forestalled.Defending the Fortress.As you now know, stars begin their lives when gravity causes a blob of material to condense and contract together into a denser object. The hydrogen-burning nuclear reactions, once ignited, stop the slow condensation for quite a long time, using the energy available from fusion to hold the star up; but this is merely a temporary respite. Eventually that fuel is exhausted, the core of the star becomes inert ashes, and the slow contraction begins again . At a later stage, helium may be ignited and converted to carbon, but once again this is a finite fuel reserve - indeed, a smaller reserve than the hydrogen represented, since less energy comes from each fusion event, as the binding energy curve shows. At each stage, gravity can outlast the finite fuel supply and start to dominate again. Unless something else happens, then, the star is in a situation analogous to that of defenders of a besieged fortress of old. Cannon fire from the ramparts will hold the attacking army at bay for a long time, but once the ammunition is gone the enemy can approach the foot of the walls. The defenders now resort to less effective weaponry - arrows and spears, perhaps - until these too are gone. As the attackers swarm up the ladders, the defenders throw bricks and stones at them. And eventually they meet in hand-to-hand combat, kicking and scratching if necessary to fight off inevitable defeat and death. What an unpleasant metaphor! A less disturbing analogy might be that of a fire in a pot-bellied stove in your house. If you misjudge the amount of fuel you need for the winter months, your woodpile of seasoned maple will be all consumed by the end of February. You will start to feed in low-grade poplar in an effort to keep your house warm, but it does not produce much heat, so is quickly all consumed in turn. You go out and scavenge fallen branches and dead limbs, and then resort to throwing in old newspapers and bits of cardboard to keep the cold at bay. Gravity is the attacking army, and the fortress is bound to be overwhelmed. The various sources of nuclear fuel merely postpone the inevitable, less and less efectively as each energy source is tapped. As we will see later, however, not all hope is lost. Stars like the sun have a surprise in store for us - a surprise which lies outside the realm of `classical' physics.What Does Helium Turn Into? The Triple-Alpha Process.Once helium-burning reactions begin in the sun, what happens to the helium? What is it turned into? Well, I hope that you will remember that the hydrogen burning in the sun involves a complex set of reactions. It is not simply a case of four protons colliding simultaneously to form a nucleus of helium. Similarly here: one has to think about all the possible steps and by-products. Once again, I am not interested in the details of the reactions expect to point out to you that the net effect, in stars like the sun, is that helium is converted to carbon through a series of reactions called the triple-alpha process. The name comes from the fact that three helium nuclei (which used to be called `alpha particles') combine to form one carbon nucleus. This is shown in schematic form on page 554 of your text (where not all the various possible reaction steps are shown).How Will the Sun Look Late in Its Life?Since the core of the sun has to shrink considerably to reach the enormous temperature required to support helium burning, your expectation might be that the sun would, overall, be very hot, and rather small. This raises an interesting question: If you come back five billion years from now, will the Earth be orbiting a tiny, hot blue pearl of a star rather than the larger yellow present-day sun? The answer, alas, is no. Things are never as simple as one hopes! Despite what is happening in the core, the sun will actually become a red giant for a time - a star which is enormous in radius and volume, much bigger (though no more massive) than the present sun. Although it will be rather cool at the surface, it will be a very bright star because of its huge radiating area. It is as though Nature set out intentionally to mislead us! -- at the very time that the middle of the star is contracting and heating, the outer parts become puffier and more distended, and cool off. In a sense, the envelope (the outer parts) of the star act like a mirror image of what is going on in the middle - as the core falls in, the outer parts move out; as the core heats, the outer parts cool. Why does this happen? Well, when the core of the sun contracts, a lot of gravitational potential energy is released: some of it goes into heating the core, but some of it goes into `puffing up' the outer parts into a big distended envelope of low-density gas. (To do so takes a fantastic amount of energy, by the way. Trillions of tons of material have to be lifted some tens of millions of kilometers away from the compact central core of the sun, fighting the sun's gravity. Imagine how hard you would have to work to lift millions of tons of rock high up above the Earth! Some mornings, even walking up a flight of stairs is exhausting enough.) The material is then kept up there by the gas pressure of the star as a whole, just as the upper parts of the Earth's atmosphere are supported by the pressure of the lower levels. The bottom line is that red giants are deceptive : they are very large, and cool at the surface, but have deep within them a very dense, hot core.How Do We Know This? The Difficulty.How do we know any of this with any confidence? Perhaps you think that we astronomers and astrophysicists rely entirely on our computer models (the calculations which tell us how the structure and nature of a star will change as its various bits of fuel are slowly used up). Indeed, we have quite a lot of confidence in the fundamental correctness of our theoretical modelling, so there is some truth to this. But the statement must be understood in the right context: we inevitably have to relate models to the observable universe! Consider: if we had only computer models to go on -- if, for instance, we had never seen a star -- how would we ever know whether or not we had made some simple mistake? Would you have any confidence in a prediction based only on such modelling, or would you prefer also to know what ``really happens'' in the universe? Clearly the latter! We need real observations. Then, if our computer models predict something other than what is seen, we will know there is something wrong with them, and reconsider the assumptions we have made (or simply fiddle around!) until they work right! In other words, the stars themselves provide the evidence of what happens late in their lives. We just have to know how to interpret what we see. Well, then, how do we know what the sun will look like after another five billion years? There are two possible answers to this question, easily understood with a simple analogy. To know what you will look like when you are ninety years old, you might choose simply to wait and see . Alternatively, you could examine a bunch of people who are already ninety years old. From their general appearance, you might confidently predict that you will have white hair, to be less fit and limber than you are at present, and so on. Now apply that thinking to the stars. The most straightforward thing to do would be to sit and watch a star progress through its lifetime until it runs out of fuel. Unfortunately, of course, this cannot be done - it will take thousands of times longer than a single human life for appreciable changes to show up in even the most massive stars (those which are using up their fuel most rapidly), so we have to rely on something else. (Anyway, if any star were to change its appearance overnight, we would still have a problem of interpretation unless we knew how old the star was already! Has it been around for a billion years, or was it just formed a few thousand years ago? Does this change mark the onset of the star's death throes, or is this an adolescent `growing pain'?) More sensibly, then, you might try to work out what the sun will look like in the distant future by examining a bunch of very old stars, each of which contains exactly one solar mass of material. In other words, find a one-solar-mass star which was formed ten billion years ago (rather than 4.6 billion years ago, as the sun itself was), and see if it is now a red giant, or slowly swelling up to become one. That is the ideal, but there is a problem. It is almost impossible to figure out the age of a single star sitting in the middle of empty space. (People are not a problem: you can always ask a person's age! The stars are silent.) There are some sensible limits you can deduce. A massive star like Rigel, for example, cannot be ten billion years old: it would have long since used up all its fuel. But how can we guess at the age of Sirius? Was it formed a million years ago, or a billion? Since individual stars change almost imperceptibly during their time on the main sequence, there is no reliable evidence. Until recently, even the age of the sun was known only because of what we learn from the study of lunar rocks and meteors. (Helioseismology -- the 'GONG' experiment -- now gives us an independent estimate, which agrees well.) But even at the middle age of 4.6 billion years, the sun looks very much as it did shortly after its birth. (Imagine humans who, having attained full growth and adulthood, did not change in appearance one bit until just before their deaths, so that every ninety-year-old looked just like a twenty-year-old! In a sense, that is exactly what the sun does.)How Do We Know This? The Answer.Here is a simple thought experiment. Imagine creating a pair of stars side-by-side in space, at exactly the same moment, out of exactly the same material. This means that the stars will be then and forever of equal age (i.e. formed at the same time) and of the same composition (at least to start with, until they change deep within their cores). Moreover, since they are at the same distance from us, any differences in their appearance will be real differences. That is, if one star looks brighter than the other, it is not a trick of perspective because it is relatively close to us, but rather an indication of a real difference between the stars. Given enough time, we could watch the two stars and see if the more massive one is indeed the first to become a red giant (and indeed see if stars become red giants at all). We cannot do this artificially, of course, but nature does it for us by providing us with star clusters. Previous chapter:Next chapter0: 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: Part 1:Part 2:Part 3: |
(Wednesday, 22 April, 2026.)
