Supernovae: The Deaths of Massive Stars,
A Point-Form Summary
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
as a massive star uses up its fuel, it becomes progressively more stratified in structure, with heavier elements (up to iron) nearest the core. This stratification is because the heavy elements were created in the hottest central regions, not because they settled there
each set of fusion reactions produces an 'ash' which in turn becomes the fuel in the next sequence of reactions. But each new fuel is of 'lower quality' (produces less energy per reaction) than the one before, thanks to the binding energy curve. There is, moreover, less fuel available at each stage
the consequence is that the later fuels are consumed progressively more quickly and the star is doomed
the very first reactions in stars 'pair up' hydrogen protons to form helium. Later reactions predominantly fuse helium and subsequent species to form even heavier elements, but the consequence is a relative overabundance of elements with even numbers of protons. The 'odd-even' cosmic distribution of the elements reminds us that they were made in stars!
iron is at the peak of the binding energy curve, and once it is formed at the core of the star, no further energy can be extracted by nuclear reactions. Thereafter, gravity dominates, and the stellar core collapses inwards
the collapse may not be total (i.e. to a black hole), however, since there exists a phenomenon called neutron degeneracy which is comparable to the electron degeneracy which supports white dwarfs against further collapse. Neutron degeneracy was recognized in the 1930s, and it was hypothesised that neutron stars could exist, spheres of essentially pure neutrons only a few km across but with the mass of a star --- at a density a trillion times that of water!
when a massive star collapses, gravitational potential energy is converted to heat, and the radiant energy rips apart many heavier nuclei (those built up over the star's lifetime!) to neutrons and protons. The protons are 'squashed together' with electrons to form yet more neutrons. So the core of the inward-collapsing star is converted to a ball of neutrons.
when the neutrons collapse to a very dense configuration, the degeneracy pressure becomes important and the collapse is abruptly brought to a halt. A neutron star is formed
other material (from the outer parts of the star) falls onto the dense neutron star moments later, and rebounds to be blasted off into space. This is a supernova: an outrushing shell of hot gas, growing in size (and emitting lots of light). For a time, a supernova can outshine the whole galaxy to which it belongs
the process of forming neutrons during the collapse also releases neutrinos in huge numbers. Indeed, most of the energy of a supernova is in this form (invisible to us)
the late stages of the star's life, and the supernova event itself, provide the energy needed to fuse small amounts of the heaviest elements (those more massive than iron)
the most recent supernova near us was a mere 150,000 light years away, in a satellite galaxy of the Milky Way. When it was observed, so too were eleven neutrinos coming from that direction -- proof that they are created in huge numbers in supernova explosions
when a star goes supernova, it collapses down to neutron star size, and should spin much more rapidly because of the conservation of angular momentum. Its magnetic field also becomes much more concentrated, and it could have been predicted that any neutron star formed in a supernovae might be rapidly rotating and highly magnetized. This turns out to be the key to their discovery as pulsars
Associated Readings from the Text.Please look at: Chapter 17, pages 558-566.A Quick Review of the Low-Mass Stars.At a late stage in the life of a low-mass star, the core has been turned to carbon, the product of helium fusion. Surrounding that is a shell in which the somewhat lower temperature has led to somewhat lower reaction rates, with the result that not all the helium fuel has yet been consumed. In this region, therefore, nuclear reactions continue to convert helium to carbon. A little farther out, there is another shell at yet lower temperature, one in which not even all the hydrogen has yet been consumed. In this shell, therefore, continued reactions are slowly converting hydrogen to helium. And in the outermost shell of all, there is still some of the unprocessed material out of which the star was originally made. Things to remember: The star is layered, or stratified, but not because heavier elements settled toward the core. It is simply that the heavier elements were made there. The reason, of course, is that only in the central regions were the temperatures ever high enough to drive the nuclear reactions. The life of the low-mass star ends here (except for the details of how the outer shell of material is `puffed off'), leaving a dense carbon-rich white dwarf supported by electron degeneracy. This means that the star does not contract any more, so never gets hot enough to burn carbon into heavier elements. There is an upper limit to the mass of such a cinder, the Chandrasekhar mass (about 1.4 times the mass of the sun).More Massive Stars: Onion-Skin Models.Studies of the Interstellar Medium (ISM) show us that there is lots of gas between the stars, that here and there it is forming stars, and that many of the stars being formed are much more massive than the Chandrasekhar mass. What will happen to them? Well, analysis reveals that: Such stars will also become stratified, in a way which is shown in the figure on page 562 of your text. The reason, which I will explain in more detail in a moment, is exactly as for the lower-mass stars: when one fuel is used up in the center, the core contracts and heats up to the stage that a subsequent fuel supply can be used in the innermost parts. The stratification is a consequence of where the new elements were made, not because they migrated or settled to these locations. (This is in dramatic constrast to the way in which the Earth and the other terrestrial planets developed their stratified strucutres. In them, much of the iron simply settled towards the core. That is not what happens in the stars.) Each successive source of nuclear energy is less productive than the one before it, and can support the star only briefly. There are two reasons for this. The first comes from a consideration of the binding energy curve. When two moderately heavy nuclei fuse together, only a little energy is released. To keep the core hot enough to support the star against gravity requires lots of energy, so there must be lots of these low-productivity reactions per second, and the fuel is quickly exhausted. (By contrast, fusing hydrogen to helium released much more energy, and the fuel could be used sparingly.) Even if there was lots of carbon fuel, therefore, it could not support the star for long because of the limited amount of energy released. The second point is that not much of the available fuel ever gets used! To understand why this is so, consider the fate of all the hydrogen originally in the star. The hydrogen at and near the center is slowly converted to helium because it is hot enough for thermonuclear reactions to take place there, but farther out, where the material is so much cooler, the hydrogen remains as it was. A similar analysis holds at every stage of the star's life, no matter what fuel you are considering! For instance, once the star forms a ball of helium `ash' at the core, it will contract and heat up, but only near the very center of that ball does helium get converted to heavier elements. The outer part of the helium ball is somewhat cooler, and does not undergo nuclear reactions. This naturally leads to a carbon core within a helium shell which is itself within a bigger hydrogen shell -- and so on. This consideration explains, of course, why the star becomes stratified, but it also makes the critical point that the fuel supply is limited by two factors. In summary, and in very non-technical terms, you can consider that the fuel used at later evolutionary stages is poor in quality: the reactions do not deliver much energy. limited in quantity: not all of the fuel ever gets used.The Odd-Even Effect Explained.Several lectures ago, I pointed out that the cosmic abundance of the elements - not just in stars, but in meteors, Earth rocks, lunar rocks, cosmic rays, and so on - shows a pronounced `odd-even' effect. (See the figure on page 564 of your text.) The reason for this is now fairly obvious: most of the fusion reactions which occur late in the life of a star consist of helium nuclei combining with other heavier nuclei, or of two heavy nuclei themselves fusing together. (Examples of both processes are shown on page 561 of your text.) Carbon itself is built up from the fusing together of three helium nuclei, and in essence all the heavier elements produced in such reactions are 'merged helium nuclei.' If you remember that helium nuclei contain two protons, you can see successive nuclear reactions automatically create elements within which there are even numbers of protons! Here is a really simple analogy. Suppose you have a large crowd of pioneers who are going to be sent out to set up small villages and towns in some new territory. Rightly or wrongly, the government may insist that only married couples be allowed to go (to provide some stability and encourage the bearing of children in due course.) Since the first thing that happens is that all of the men and women in the crowd form into inseparable pairs, then the sub-groups you send out in various directions will automatically have even numbers of people! There might be, say, eighteen of them (nine couples) canoeing up the river; fifty-six more (twenty-eight couples) taking a wagon train across the prairie; forty-two (twenty-one couples) establishing a small town; and so on. In a sense, this is what the star does: it `pairs up' the hydrogen nuclei (the protons) into helium nuclei before permitting them to participate in subsequent nuclear reactions. Given that consideration, you might wonder why there are any elements with an odd number of protons. Why is there any nitrogen, for instance, with its seven protons? The answer is that the nuclear reactions are not as simple as described here, with a steady build-up taking place only because of the addition of helium nuclei. Perhaps you will remember the various branches I described in my discussion of the proton-proton cycle; and in explaining the CNO cycle I described what could loosely be called `catalysed' reactions. Similar complexities happen here. More to the point, the nuclear reactions do not take place in a mixture of pure helium. Even after helium burning begins, there will still be some unused hydrogen left (some free protons moving around), and they can combine with heavier nuclei to create odd-numbered elements. At any given time, there may be a range of reactions happening at different rates and with different efficiencies in a complex mix of elemental particles. The amazing thing, however, is that we can understand the presence and relative abundance of the elements around us as a natural consequence of the nuclear reactions which have taken place within the stars! Of course, this only explains the universe at large if the material produced within the stars somehow gets thrown out into space for the subsequent formation of planets and people. But before we see how that works, we consider one more implication from the binding energy curve.Iron Stars: The End of It All.Reconsider the binding energy curve. It peaks at the element which has an atomic number of 26: iron. What does this mean? The answer is that once iron nuclei are formed in the very core of the star, it has no defences left against gravity. The nuclear reactions which created iron released a little energy, keeping the core of the star hot and supporting it against the inward pull of gravity. But once the iron is made, no further reactions can help. To add to the iron, to convert it to something heavier, would take energy, not release it - that is what is meant by the shape of the binding energy curve, the fact that it now slopes back down as we consider more massive elements. Likewise, to break the iron into smaller pieces would take energy, not release it. (Remember that breaking uranium into smaller pieces does release energy, as in the atomic bomb. This is not so for iron, because it is at the peak of the curve.) So the star is doomed. The very central parts, which are still very hot because of the long history of contraction and thermonuclear reactions, consist of iron nuclei. Some of the heat will trickle outwards, the temperature will fall ever so slightly, the sustaining pressure falls as well, and an inward collapse begins. As the particles come closer together, the gravitational forces become ever stronger, and the collapse accelerates.What Now? Some Thoughts.Can the star be saved from collapse? Or will it dwindle down to immeasurably small size under the growing effects of gravity? To answer that question requires a very deep understanding of the behaviour of matter at extremely high density. As the particles within the stellar core get pushed closer and closer together, how will they behave? One of the problems with learning the answer to this question is that we are limited in our experimental capabilities. It is not easy, or even possible, to test material in every imaginable form. How could we, for instance, ever hope to compress ordinary material to a density a trillion times greater than that of water? So some of the early work in the subject was pure theory, not easily testable. On the other hand, similar things could be said about the study of white dwarfs. Chandrasekhar's work was almost entirely theoretical, based on the new sciences of relativity theory and quantum mechanics. What made it believeable was the existence of white dwarfs whose properties needed some explaining. (We knew, for instance, that the companion of Sirius is a million times as dense as water.) Should we look for something equivalent, some bizarre object which might be the remnant of the death of a massive star? Can we hope to find the corpses of massive stars?Neutron Degeneracy: Neutron Stars Predicted.Remember that a white dwarf is supported by electron degeneracy, and will continue to be so even if it cools down completely. Following Chandrasekhar's lead, and with a growing understanding of nuclear physics, it was realised in the 1930's that there could be an analogous state of neutron-rich matter. If, for instance, you had a ball of neutrons about 10 km in diameter (about the size of the city of Kingston), with a mass 2-3 times that of the sun, at a density a trillion times that of water, it could support itself against the inward pull of gravity thanks to the sustaining pressure of degenerate neutrons. (Once again, the sense of this is that the neutrons resist further compression to a degree which could not have been foretold on the basis of classical physics.) The pressure is independent of the temperature of the lump, so any `neutron star' formed in this way could stay intact forever, even if it cooled off to absolute zero temperature. This prediction, however, seemed irrelevant! Consider the following. The white dwarf companion to Sirius is about the size of the Earth - call it 10,000 km in diameter. A neutron star, with a diameter of 10 km, has only one millionth of the surface area of the white dwarf, and will look a million times fainter (if they are the same temperature). Moreover, a neutron star is so small that it would quickly radiate away any heat left over from its formation, so would quickly become a cool cinder. The implication seems to be that neutron stars in space would emit so little light as to be essentially invisible. You could, of course, still hope to detect them by virtue of their gravitational influence - if one is in a binary star system, for instance, the other star would orbit around in response to the neutron star's gravity. But direct detection of a single neutron star sitting in empty space seemed out of the question. This pessimistic view turns out to be wrong.Forming Neutron Stars.Before asking how we might detect neutron stars, let us ask how Nature might make them. As noted, theory says that such things could exist. But will Nature ever oblige us? If so, what are the details of the formation process? Let us go back to the stage at which we left the massive star - an iron core starting its collapse. I encourage you to read the graphic descriptions in the textbook (pages 563-564), but will quickly summarise the process as follows: As the collapse takes place, the inrushing nuclei collide with one another as gravitational potential energy is converted to random collisions and thermal energy. In other words, the core gets fantastically hot. (But the heat is not enough to support the star against collapse! Gravity is now dominant.) The extreme heat means that there are photons of extremely high energy rushing about in the core of the star. These photons are so energetic, in fact, that they tear apart many (but not all) of the heavy nuclei which have been so painstakingly built up over millions of preceding years. All that work is undone in a flash! The nuclei are ripped into protons and neutrons. In addition, there are of course lots of free electrons moving around (after all, the star is electrically neutral, with as many negative charges as positive). As the density increases, the electrons and protons are `squashed together' and merge to form neutrons. (Each such reaction also produces a neutrino, with consequences which we will explore in a bit.) Fairly promptly, then, the star's core is converted to a composition which is almost pure neutrons - all of them falling inward at high speed under the pull of gravity. Suddenly the density reaches the critical stage at which neutron degeneracy says ``Whoa!'' The neutrons cannot be compressed together any more tightly, and the collapse stops abruptly. The neutron star is born.Perfect Billiard Balls.In Physics 016, I described how the gravity of the Earth limits the size of any mountains which it can support. Similar considerations for Mars, where the gravity is weaker, explained why we are not surprised to see a huge mountain like Olympus Mons on its surface. Well, a similar consideration holds for a neutron star. The gravity at the surface is so enormous - you are, after all, only a few kilometers away from every speck of matter in an object more massive than the sun - that no big mountains could be raised at all. Indeed, the surface of a neutron star could have no features larger than a few millimeters in size! It would be as near-spherical as the most finely-polished billiard ball imaginable. The intense gravitational field has a related consequence: that of tides. The point is made on page 586, with reference to the near surroundings of a black hole (but similar arguments pertain to neutron stars). If you were to fall towards a neutron star with your feet leading the way, the atoms in your feet would feel a gravitational force so much stronger than that felt by the atoms in your head that you would be torn to bits long before you ever reached the surface.Supernovae: The Fireworks That Go With Neutron Star Birth.At this stage, you could be forgiven for thinking that the inward collapse of a massive star might lead to the formation of a neutron star sitting quietly by itself in empty space, perhaps containing all or most of the material in the original star. The situation is not that simple, however. First of all, think about the material which was originally near the outer edge of the star. When the core suddenly collapses under the influence of gravity, the matter out there responds just as you would if a trapdoor had been suddenly opened under your feet. The pressure support from beneath is gone, and all the particles start to fall in towards the middle. The problem is that these particles are considerably farther away from the center of the star than the iron nuclei were. This has two consequences: They feel a somewhat weaker gravitational force than do the atoms nearer the centre, so do not fall as quickly downward. Moreover, they have a longer distance to fall, so get there a little bit later. In short, the outer parts of the star fall onto the core a short time after the neutron star has itself formed. Indeed, there is more to it than just this. When the neutron star forms, the material collapsing inward falls a bit beyond its final equilibrium position, becoming a little bit too dense, and then `bounces' a bit outwards again before coming to rest. This outward `bounce' happens just as the rest of the star is hurtling downwards and falling onto it. The net effect is to blast the late-arriving material completely off the star (just as a swinging baseball bat can drive a pitched ball back over the pitcher and the center-field fence). You can demonstrate this effect quite dramatically by dropping a ping-pong ball and a well-pumped-up basketball together (with the ping-pong ball just above the basketball). The basketball hits the floor first and is already moving back upwards when it meets the downward-moving ping-pong ball. The effect of this is to launch the lighter ping-pong ball to a considerable height - many feet over your head. This is the fundamental cause of the supernova event which marks the death of a massive star. A large fraction of the mass of a star may be blown out into interstellar space at speeds of 10,000-20,000 km/sec. Since the shell of material is hot, it emits a lot of light. Moreover, it grows in size as the shell expands, so its radiating area increases dramatically, and it becomes very bright. In fact, a supernova may, almost instantaneously, become as bright as the entire galaxy of one hundred billion stars to which it belongs. As the material cools and slows down, the supernova slowly dwindles in brightness, over a timespan of months.Other Components of the Supernova.When we see a supernova, what captures our attention is the great brightness at visible wavelengths. But there is a lot of energy tied up in the actual motion of the outrushing gases (the kinetic energy of the material). As we saw, the formation of a neutron star also leads to the release of neutrinos as a by-product of the merging of electrons and protons, and there is even more energy tied up in neutrinos than in other forms. In fact: the kinetic energy of the moving material is about 100 x as much as the energy given off as visible light and the neutrinos in turn carry about 100 x as much energy as the kinetic energy of the matter! In other words, although the visible light is dramatic, the flood of neutrinos represents about 10,000 times as much energy in total! Of course, they go largely undetected.Forming Even Heavier Elements: Enriching the ISM.From what I have said, you might be excused for thinking that nuclear reactions within stars produce all the elements up to the mass of iron, but nothing heavier. Moreover, it appears that the collapse to the neutron star state leads to the tearing apart of all of these carefully built-up heavy nuclei, reducing them back to neutrons and protons. If so, where do the heavy elements come from? Well, the short answer (again!) is that the situation is not that simple! Here are some of the considerations: When the core collapse takes place, not absolutely every nucleus gets reduced to neutrons and protons. Some heavy elements, especially those not right in the very central parts, survive to be blasted off into space in the supernova shell. Elements even heavier than iron can be built up through the slow capture of neutrons earlier in the star's existence (before the core collapse). For instance, neutrons can merge with ordinary iron to form heavier isoptopes of iron which are radioactive; these decay to form cobalt. There is no need for high temperatures to make such reactions happen: the neutrons carry no charge and don't have to be moving fast to enter the heavy nucleus since they are not repelled. In this way, in what is called the s-process (slow process), some quite heavy elements are built up near the end of the star's life. Finally, the very heaviest elements of all are created during the supernova itself, at a time when neutrons are flying around in great numbers. This happens in what is known as the r (rapid) process, and nuclei in the outrushing gas can be converted to uranium and other such things in small quantities. The net result of all this is the build-up of the elements we see all around us, in the proportions described before. The supernova, of course, casts these all out into space. Thereafter, new stars may form from gas which now contains enough heavier elements to permit the formation of grains, stones, planets, and asteroids - and people.A Case Study of a Supernova: 1987A.Supernovae can be routinely detected in other galaxies, often by small automated telescopes which simply measure the brightness of one galaxy after another to see if something has flared up since the galaxy was last examined. (Remember that a supernova can be as bright as a whole galaxy.) In this way, many supernovae can be detected and studied. One problem, however, is that they are all seen after the fact, and are typically very far away. Within a big galaxy like the Milky Way, supernovae probably occur at a rate of about one per century. The ones most recently seen in our own Milky Way date from the time of Tycho and Kepler, so we are in a sense 'overdue' for one. But the best-studied one in modern times took place in 1987, in a small satellite galaxy called the Large Magellanic Cloud (LMC). (Dramatic before-and-after pictures are shown on pages 565 of your text.) It is particularly important in the following respects: The LMC is only 150,000 light years away, very close by astronomical standards. This allowed us to study the supernova in great detail. The star which became the supernova had already been studied from the Earth as part of a general investigation of the LMC. For the first time, we were able to consider the nature of the progenitor star. The blast of neutrinos from the supernova passed through the Earth, and through all of us, at about the same time as the light reached us. The Kamiokande neutrino observatory in Japan (an experimental facility rather like the SNO Observatory now used in Sudbury) detected eleven neutrinos in quick succession, all of them coming from the direction of the LMC. This provides direct evidence that there is indeed an enormous blast of neutrinos released in the supernova event. The supernova was discovered by Ian Shelton, a Canadian working in Chile. His discovery is a good example of the rewards for careful work. Ian was taking a series of photographs of the LMC, and followed the excellent policy of developing and examining every plate as he finished. In this way, he was able to recognize the presence of a very bright star where none had been the night before. I can testify from experience that this sort of thoroughness is unusual! It is very tempting, at the end of a long cold night, simply to put the exposed plate into a light-proof box and to develop it later the next day, when you feel more rested. If Ian had done that, he would have been `scooped' since the supernova was independently discovered in Australia and South Africa later the same day.The Detectability of Neutron Stars.As I noted above, the theoretical prediction of the possible existence of neutron stars seemed irrelevant. It seemed a certainty that they would be far too faint ever to be detected! But in retrospect there were a couple of extra considerations which might have been foreseen. A star like the sun rotates (spins on its axis) about once a month, and is about 1,000,000 km across. If it were to shrink down to a ball 10 km across (100,000 times smaller), it should spin 100,000 times faster, simply because of the conservation of angular momentum. In other words, it would then be spinning about once every 25 seconds. Many of the more massive stars spin faster than the sun, so any remnants they might leave behind would be spinning correspondingly faster as well. The sun has a magnetic field rather like that of the Earth; so too do other stars. For reasons I will not go into in detail, any shrinking of the sun would lead to the magnetic field being more `concentrated' and stronger by a factor of about ten billion or more. (The field strength goes up by the square of the factor by which the sun shrinks.) So, from these very simple physical considerations, a neutron star created in the inward collapse of a massive star might be predicted to be rapidly spinning; and very strongly magnetized This might have led astrophysicists to predict how neutron stars could have been looked for (although the technology to do the search did not exist at the time). Although those predictions were not made, when the objects were found serendipitously (in ways I will describe in the next section) they were almost instantly explained in terms of the considerations we have just discussed. Pulsars are rapidly-rotating neutron stars with enormous magnetic fields! 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.)
