Pulsars:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
pulsars were discovered serendipitously, by Jocelyn Bell, while she was a graduate student in Cambridge. They were seen as regular rapid pulses in radio signals, like a series of rapid 'beeps' at a rate of about one per second
the first interpretation was that it was local electrical interference, because no one could visualise an astronomical source that could vary so quickly. After that was ruled out, there was brief speculation that they were signals from extra-terrestrials. Many were soon discovered, and it became clear that an astronomical explanation was required
the modern understanding (rapidly rotating highly magnetized compact stars) was very quickly developed and has not materially changed over the years, except in detail
Jocelyn Bell's supervisor won the Nobel Prize, but she did not share it -- a great injustice, to my mind. Jocelyn herself is quite forgiving
pulsars act as lighthouses, sending out beams of light in two different directions. We only see them intermittently because the spin of the neutron star means that the beam sweeps across our field once every rotation
the light that is emitted is not caused by hot glowing material. It is said to be 'non-thermal' in origin, and is called synchrotron emission
the name comes from the way a synchroton operates. It is a machine sometimes colloquially called an 'atom-smasher' or a 'particle accelerator'. In such a machine, electrons (or other particles) are accelerated around and around in big circles through the combined effects of electric and magnetic fields. They can be sped up to very nearly the speed of light, and are then allowed to collide with other atoms to see what happens!
charged particles moving at these relativistic velocities -- near the speed of light -- give off radiation in the forward direction. That is what is happening in the pulsar, where fast-moving electrons have to race to keep up with the intense magnetic fields which are rotating with the rapidly-spinning neutron star
pulsars are known which range in period from milliseconds (that is, they spin thousands of times a second) to a few seconds. Most of them emit radiation at long wavelngths, detectable by radio telescopes. Only a few are seen to emit higher energy photons - visible light and even X-rays
since the pulsars are emitting radiation, they are losing energy. This comes from the rate of rotation, which can be seen gradually to slow down: the pulses come gradually farther apart
occasionally, some pulsars suffer an abrupt decrease in period, so that the pulses come with higher frequency -- in other words, the neutron star is now spinning faster. This seems to violate the conservation of angular momentum. The explanation for a 'glitch' of this sort is that the star has abruptly shrunk a little, and sped up as a result. Such 'starquakes' allow us to interpret the likely interior structure of neutron stars
in 1054 AD, a bright supernova occurred in our own Galaxy, and has left behind the 'Crab' nebula, an expanding cloud of gas. At the core is a pulsar which we see to flash thirty times a second. The link between pulsars and supernovae is manifest
Associated Readings from the Text.Please look at: Chapter 18, pages 579-583.The Discovery of Pulsars.The serendipitous discovery was made by a graduate student names Jocelyn Bell, working in Cambridge, England. She recognized that some of the radio signals which she was detecting were surprisingly regular (like `beeps' from a beacon - but please do not confuse these detected signals with sound. She was detecting electromagnetic radiation, at long radio wavelengths). These signals appeared to coming from somewhere in the sky, but no astronomical source was known which could provide such regular, clock-like emission. The explanations thought of, in order, were: Earth-based electrical interference. This is a very common problem at radio observatories, and can be caused by effects as mundane as a faulty generator in a car. But it was soon realized that the source was outside the Earth's atmosphere, because it was being detected four minutes earlier every day. This is a sure sign that it is up in the sky `where the stars are' - remember the difference between civil time and sidereal time. Once the extra-terrestrial nature of the source was recognized, the first thought was that it was caused by what was facetiously called LGM: Little Green Men. (The name is jokey, but the thinking was quite serious. Indeed, Sir Martin Ryle, a senior radio astronomer, argued that the news of the discovery should be kept secret to prevent panic!) That is, the possibility was seriously entertained for some time that Jocelyn Bell might have picked up signals from some extraterrestrial intelligence. Mostly this was because the very first pulsar detected had a period of about 1 second, and no one could immediately think of any natural phenomenon which could give rise to such emissions. (No ordinary star, and not even a white dwarf, can vibrate or spin that rapidly without tearing itself to pieces). Within a few weeks, however, more pulses were detected from other sources, and it was thought unlikely that there would be many races sending us signals all at once. Moreover, the explanation in terms of neutron stars came quickly to the fore (and in fact has not changed very dramatically since then, only in detail). At present, literally hundreds of pulsars are known, with periods which range from a few seconds down to a few thousandths of a second.A Sad Corollary.Jocelyn Bell did not win the Nobel Prize for her important discovery - but her supervisor (Tony Hewish) did! This has been a source of continuing controversy ever since, although Jocelyn herself has always been gracious enough to say that the decision was the right one. Interestingly, another Nobel Prize was awarded a few years ago for the work of Messrs Hulse and Taylor, two astronomers who studied a pulsar in a binary star system (and were thereby able to confirm much of Einstein's Theory of General Relativity). That partnership was between established scientist Taylor and his then-graduate-student Hulse, so the Nobel Prize Committee seems to have learned something from their earlier omission.Pulsars as Lighthouses.In the previous section, I pointed out that the formation of a neutron star would result in a small (10-km diameter) object. Even if this were terribly hot, it would not produce much radiant energy, so it sounds like it would be hard to detect. But then I pointed out that the pulsars discovered by Jocelyn Bell are thought to be exactly such objects. How do they radiate energy? Why do we see them at all? The answer is that a pulsar is acting like a lighthouse, the beam of which sweeps our direction every so often as the neutron star itself spins. To develop this notion further, let us consider just how a lighthouse works. When you are out at sea and see a flashing light on the mainland, possibly a light which is intended to warn you of dangerous rocks, how is it producing its signals? There are various possibilities: Perhaps there is a constantly-illuminated lamp inside some sort of housing, with a shutter which opens and closes rapidly to let the light shine forth. This is exactly what is done on the decks of ships at sea when they signal back and forth to each other with flashing lights while maintaining `radio silence.' In this way, for instance, ships in a wartime convoy could send Morse code signals back and forth over small distances with no danger that their radio emissions could be picked up by the enemy. The shutter on such lamps was controlled by hand, and the flashes could be varied in duration to make the dashes and dots of the Morse code. Perhaps there is a lamp which shines out in all directions, but one which is periodically turned on and off so that it is seen to flash. Many lighthouses are indeed built on this design, because this permits the signal to be modulated in some way. (For instance, there might be one long flash followed by three short ones.) This modulation is unique to each lighthouse along a stretch of coast, so the ships at sea can easily identify which one they are close to. This helps them navigate. Finally, it could be that the lamp is on all the time, but that it shines in only one direction, with a narrow beam like that of a searchlight. If, in addition, the lamp were turning, the ships at sea would see regular periodic flashes. (An example of this is the sort of searchlight you will find at Kingston Airport.) As I said, the pulsar is like the third of these - the rotating seachlight. But it differs from all the Earthbound lighthouses in one important way. All of them emit light because they contain a hot filament, a piece of incandescent wire through which electricity is flowing. In a pulsar, the overall temperature of the neutron star is irrelevant to what is going on. A pulsar's light is non-thermal in origin. To explain further, I must digress to tell you something about machines which are commonly known as atom-smashers. The connection will become clear in a bit.Cyclotrons.A cyclotron is a machine which is designed to make electrons (or other charged particles) move very fast, so that they can be smashed into other atoms and nuclei to see what happens. The philosophy here is a bit unusual. We learn about the internal workings of atoms and nuclei by smashing them to bits, to see what pieces fly out! It is rather like throwing a watch against the wall and noticing what pieces come out - a spring, a counterweight, etc. From this information we have to work out how the watch operates! Remember that an electron is electrically charged, and quite low in mass. It is fairly straightforward, therefore, to get it moving quickly. Merely put it into a strong electric field, and it will rush towards the positively-charged part of the apparatus. (This is how we get electrons whizzing through a fluorescent lamp, for instance, from one end to the other. Similarly, your television set works because a negatively-charged `electron gun' at the back of the set emits and repels electrons, spraying them in controlled fashion at the screen, which glows wherever it is struck by a flying electron.) A cyclotron takes this to the limit, being specially designed to allow us to accelerate electrons faster and faster by giving them regular repeated pushes, almost as one might push a child on a swing. To visualise how this works, imagine the following: Take a pair of `deep-dish' metal pie pans and glue them together, face to face, to make something shaped like a hollow metal flying saucer. Cut this construction in half across the middle to make two hollow `D-shaped' pieces, which are in fact called dees. Attach wires to make one dee negatively charged and the other positively charged. Put an electron into the negatively-charged dee: it will of course accelerate rapidly towards the other dee. As the electron enters the other dee, let us now instantly reverse the wires (or equvalently throw a switch of some sort) so that the dee which had been attracting the electron now repels it, and vice versa. The electron will now feel a force pushing it back the way it came. Of course, this is not particularly useful because it will simply bring the electron to a complete halt and then send it back, accomplishing not very much. Here is where a magnetic field helps. Let us now add a magnetic field which runs perpendicularly through each `dee' - from the face of one pie pan to the other, at right angles to the direction of the electron's motion. For reasons I will not go into, a charged particle moves in a curved trajectory as it passes through a magnetic field. Consequently: when the electric field is first turned on, the electron rushes from one dee to the other as it enters the second dee, the magnetic field causes it to move in a curved trajectory at the same time, the switching of electric charges on the dees accelerates the electron back towards the dee it came from. That's it! By repeating this process, cycle after cycle, we can get the electron really racing along. The motion is rather like that of a stone whirling in a sling around your head, except that the electron is in a spiral path: as it builds up speed, its circular orbit gets gradually larger and larger. Eventually, when the electron is fairly whizzing along, it is redirected so that it hurtles headlong into the atomic target, with interesting consequences.A Complication: The Synchrotron.As you can appreciate from the discussion of the cyclotron, it is important to switch the electric charges on the dees at just the right moment if you want to get the electron moving really fast. If you get out of step, you actually slow it down rather than speed it up. (Think about pushing a child on a swing, for instance. You have to push the swing at just the right instant if you want the effects to accumulate properly. If you push as the swing is coming towards you, you slow it down rather than speed it up. You have to get into the right rhythm, and time your pushes correctly.) Unfortunately, cyclotrons don't work as well as you might think. You might suppose that as we pump more and more energy into the machine, the electron would go faster and faster, without any limit to the speed. In fact, however, no matter how much energy we pour into it, the electron never gets going as fast as the speed of light, which seems to be an `ultimate speed limit.' This is a consquence of Einstein's Theory of Relativity, but why does it happen? In a sense, it is because the faster the electron moves, the more resistant it becomes to being pushed. At first, a small force is all that is required to get the electron moving quickly, because an electron is very light. But if it already moving very fast, it is very difficult to increase its speed even a little bit. It develops an enormous extra inertia (resistance to being accelerated) beyond what it ordinarily has. Relativity theory tells us, in fact, that no material object can be accelerated to or beyond the speed of light . One of the problems with the increased `sluggishness' of the electron is that it doesn't move quite so quickly inside the cyclotron as a straightforward calculation suggests it should, and the `pushes' provided by the regularly-changing electric polarities of the cyclotron start to get out of step. As the pushes become more out of phase, the machine doesn't speed up the electron any more; instead, it slows it down. A cyclotron has a fairly low practical speed limit, considerably less than the speed of light, as a result of this limitation. We see a distinct improvement if we switch the electric fields back and forth at a progressively changing rate to take into account this extra sluggishness. Doing this synchronization is what led to the name synchrotron (originally synchrocyclotron - quite a mouthful!) for such a machine. With such technology, we can get the electron moving yet faster, although still never beyond the speed of light, of course. This important point is worth noting! No matter how much power we pour into the machine - even if we use all the hydro-electric energy generated in North America, plus all the nuclear power plants in the world - we can never get that little tiny electron to go at the speed of light, although we can get up to 99.99999% of that speed! Needless to say, this experimental limtiation is very strong evidence in favour of Einstein's theory, which has some very counter-intuitive aspects.Synchrotron Radiation.When real synchrotrons are put into operation, with electrons whirling around inside their works, light of a particular kind is produced. Its nature is a little surprising, in a way which is best understood by considering an everyday analogy where we do not see the effects. Visualise a stone in a sling being whirled around your head. You would be surprised if the stone began to glow like a small lamp, although you might be willing to ascribe that to friction with the air, but you would be doubly surprised to see the stone send out a small beam of light aimed in some direction. (You would be completely astonished to discover that the effect persisted even if you were to swing the stone around and around in a vacuum chamber, thereby eliminating air resistance as a source of the light.) I emphasize that stones in slings don't behave in this fashion, but a fast-moving electron in a synchrotron does exactly this. In fact, it creates a beam of light which is pointing straight ahead, in the direction that the electron is moving at any given instant. This only happens if the electrons are moving at nearly the speed of light; they are said to be moving at relativistic speed. In a pulsar, this is the fundamental mechanism. But there is still a problem. How can this mechanism explain a single big searchlight beam coming from the neutron star? After all, if you had a great cloud of millions of very fast-moving electrons, all moving independently, you would see light coming off in all directions, with no preferred sense. (Each electron would be shining in a different `forward' direction.) There would be no beam. To get a well-defined beam of light from a pulsar, we need a second ingredient. We must have a great host of electrons all moving at high speed and in the same direction. The electrons have to be controlled and restricted in the paths they follow, rather than just wandering around at random. This is the role of the intense magnetic field of the neutron star.The Oblique Rotator.The ingredients for a pulsar (the `oblique rotator model') are shown in a figure on page 581 of your text. The essential parts are: the very strong magnetic field the rapid spin of the neutron star the fact that the magnetic field is tipped (i.e. not along the rotation axis of the star) so that we see different aspects at different times. (This is why the model refers to an `oblique' rotator.) multitudes of electrons which are spiralling along the magnetic field lines at high speed in some coherent way. (By `coherent', we mean that there must be many at once, all moving in nearly the same direction) You already know of one oblique rotator: the Earth itself. The spin axis of the Earth points straight up and down through the North and South geographical poles of the Earth (this is how those poles are defined!). The magnetic field is tipped, with the result that the North magnetic pole is located at some different place, in the high Arctic regions of Canada. This is also seen for Jupiter (see the figures on pages 343-344). The pulsar's magnetic `field lines,' shown in the textbook on page 581, are merely representations of the direction a small compass would point if it were to be placed in a particular position. These field lines form a pattern which looks like `Mickey Mouse ears' in cross-section, as you can see. But how does the magnetic field control the motions of all the electrons? The important point is that charged particles moving in a magnetic field tend to curve around the magnetic field lines. (This was instrumental in making our cyclotron work.) There is an interesting consequence on the Earth: the charged particles which spiral around the Earth's magnetic field lines can be trapped in the so-called van Allen belts high in the Earth's atmosphere. (See page 308.) These particles collide with the gases in the atmosphere at high latitudes, near the magnetic north pole in the Arctic, which is why we see Northern Lights. The same sort of behaviour takes place in the magnetic field of the pulsar. If the neutron star were not spinning, this would be uninteresting. The electrons would travel only a small distance, following the field lines from one pole of the neutron star to the other. (Remember that it is only a few kilometers across.) But the rapid rotation of the whole star carries the pattern of `Mickey Mouse ears' around with it, and the electrons have to move at very high speed to keep up with the moving magnetic field. (Imagine trying to jump onto a merry-go-round turning at high speed. You would have to run fast to keep up with it!) You can demonstrate this yourself with a bead on the end of a long string, held loosely in your hand. As you twirl your hand around, not really having to move it very much, you can make the bead move very rapidly through the air above and around your head. In fact, electrons near the outer parts of the `Mickey Mouse ears' have to travel at relativistic speed to keep up with the magnetic field - just the recipe for the production of synchrotron radiation. By the way, we have independent proof that the pulsar radiation is indeed synchrotron. For one thing, it is strongly polarized, which is a direct consequence of its method of production. (I will not go into the reasons.) Although some of the precise details are still uncertain, the general model of a pulsar is quite well understood. As the star spins, the rapidly-moving electrons, which are all travelling in the same direction because of the magnetic field, emit synchrotron radiation in the `forward' direction. Because of the misalignment between the magnetic axis and the spin axis, our perspective is constantly changing, and we see a beam of light which sweeps across us every time the star spins. In fact, with emission coming from both poles of the star, we might expect to see either one or two flashes, perhaps of different intensity, with every rotation.Pulsars: The Beacon Observed.On the bottom of page 580, you can see the sort of signals we get from a pulsar - the first one found, in fact. The scale across the bottom shows the time in seconds, so you can see that the whole flash lasts less than a second. This behaviour is actually rather slow, by pulsar standards; some flash a thousand times a second. On the other hand, Jocelyn Bell's equipment would not have recorded such rapid pulses, any more than your eye notices the flickering of the light bulbs as they turn on and off 60 times a second thanks to the alternating current we use. (If only millisecond pulsars existed, they might yet be undiscovered!) There are a few things to note: The signals are not all exactly the same: there is a sort of irregular scruffiness about them. This is largely due to the fact that we are detecting a signal which has passed through a lot of intervening gas in the interstellar medium, a circumstance which produces something analogous to the twinkling of the stars. The figure on page 580 shows the signal detected by a radio telescope, but that is almost unavoidable: with only a couple of exceptions, most pulsars are detected only at radio wavelengths. There are clear examples of pulsars in which we see two beams of slightly different intensities. The visible light pulsar in the Crab Nebula, which is also detected at radio wavelengths, is one such: its behaviour is shown on page 581.Pulsar Slowdown.Pulsars are emitting radiation, which of course means that they are releasing energy into surrounding space. In other words, there is a net output of energy in the form of photons. But energy cannot just magically appear out of nothing: remember the conservation laws! We can conclude that energy in some other form must be disappearing - or rather, being converted to radiant energy - even as we watch. Does this sort of thinking lead to any useful insights? Well, without describing the details, I can tell you that the fundamental source of the energy is the rapid rotation of the neutron star. Electrons are accelerated to high speed because they are forced to move with the rapidly-spinning `Mickey-Mouse ears' of the star's magnetic field. But this comes at a cost. To get uncountable numbers of electrons orbiting at high speed, the star itself has to give up some of its speed of rotation so that the total angular momentum is conserved. (As the massive star spins a little slower, the light electrons get moving a lot faster.) The fast-moving electrons then have enough energy to emit synchrotron radiation, and the energy winds up as photons streaming off into space. There is an obvious implication which follows from this. Over the passage of time, many photons are emitted, and lots of energy flows out into space. Since this comes at the cost of rotational energy, the neutron star will gradually spin a little more slowly and pulses should be detected a little less frequently than they once were. In other words, the pulsar's period should gradually lengthen. This sort of behaviour is indeed seen. In fact, it can be calculated that the total radiant energy being emitted from a pulsar is just about the same as rate at which a slowing neutron star would lose rotational energy. This is strong support for our model. There is a further corollary. Since all the rapidly-rotating neutron stars we see will gradually slow down and stop spinning, pulsars must have limited lifetimes. The pulsars we see around us at present (several hundred are known) must only be a fraction of all those which have ever existed in our galaxy. Moreover, we can not see every one which is out there now: their beams may not sweep in our direction, and they will be unobserved by us.Pulsar Spin-up.Pulsars undergo a progressive slow-down (their spin periods slowly lengthen) in the way I have just been discussing: After the passage of some years, the pulses arrive a little less frequently than they used to. But we occasionally detect a behavioural oddity called a `glitch', a moment in which the pulsar speeds up so that its period suddenly decreases abruptly. To visualise what is happening, imagine throwing a switch on your record player so that the turntable, which had been going around at 33 rpm to allow you to play an Long-Playing (LP) record, is now spinning faster, at 45 rpm, so that you can play a hit single. (This terminology is sadly dated since the coming of CDs, I realize!) But what can make a pulsar do this? We can easily understand why it slows down -- it is losing energy -- but what can make it speed up? There are a couple of obvious possibilities: 1 One possibility is that something bumps into it, perhaps a big asteroid or a planet, in such a way as to make it spin faster. (In class I gave the example of a basketball player spinning a basketball on the end of his or her fingertip. To keep the ball spinning fast, he or she must hit it on the side from time to time to compensate for frictional losses.) This can't explain the pulsar's behaviour, because about half the time one would expect to see glitches which abruptly slow the pulsar down (since the asteroids could come in from any direction). All the glitches we see are in the sense of speeding the pulsar up. 2 The second (correct) explanation is that the neutron star is suffering a `starquake', an abrupt redistribution of its material. The interior of a neutron star has a sort of crystalline structure which is determined by the nature of the degenerate neutrons and other constituents. As the spin rate decreases, the neutron star feels less stress and there can be an abrupt change in the crystalline structure. In effect, the neutron star shrinks, ever so slightly but very abruptly, into some new configuration. Since angular momentum is conserved, the star must spin faster, just like the figure skater who draws in his or her arms during a spin. These glitches - their size and frequency - allow us to determine something about the interior structure of neutron stars, just as seismology tells us about the interior of the Earth and the GONG project tells us about the interior of the sun.The Crab Nebula: An Ancient Supernova.In the year 1054 AD, a bright supernova was observed in the constellation Taurus. Although it was not recorded in European annals, it must have been seen, so its absence from the records emphasises the poor state of scientific endeavour in Europe at the time. But various Oriental records, and in particular those of the Chinese court, describe a star which became visible to the naked eye during the day. There are also rock paintings which suggest that indiginous Americans saw and recorded the event as well. The Crab nebula, shown in a photograph on page 565 of your textbook, is a classical supernova remnant, an expanding cloud of gas. In fact, photographs taken years apart reveal that the gas cloud is expanding, and if one extrapolates this behaviour backwards one can deduce that the cloud started its expansion about a thousand years ago. There is no doubt about it: this is what the bright supernova of 1054 AD produced.The Crab Nebula: The Connection Proven.The Crab Nebula is important in one other significant way: it contains a pulsar right in the centre. This is the definitive piece of evidence we need to confirm our belief that supernovae produce pulsars. The pulsar in the Crab Nebula has a period of about 30 milliseconds, which means that it flashes on and off about thirty times a second. (In fact, it is one of the pulsars from which we detect both of the beams, so we really see it go on and off sixty times a second.) This behaviour is shown on page 581, in a figure which demonstrates that the Crab Nebula can be seen to pulse in visible light (and, as it happens, in X-rays) as well as in the radio. Of course, our eyes cannot notice the rapid flickering of the faint central star which is the neutron star, but high-speed instruments and detectors can, as the figure demonstrates. 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.)
