Note: you REALLY NEED to read the book! Here are some pulsar sites. the first is Jocelyn Bell's recollection of the discovery of pulsars. the last contains the optical crab pulsar movie we showed in class Wednesday April 17. http://www.bigear.org/vol1no1/burnell.htm http://pulsar.princeton.edu/pulsar/index.shtml http://www.rog.nmm.ac.uk/leaflets/pulsars/pulsars.html http://pulsar.princeton.edu/pulsar/multimedia.shtml#sounds http://www.jb.man.ac.uk/~pulsar/Education/Sounds/sounds.html http://zebu.uoregon.edu/andy.html http://astrosun.tn.cornell.edu/courses/astro201/top_pulsars.htm http://www-astronomy.mps.ohio-state.edu/~ryden/ast162_5/notes21.html http://www.noao.edu/image_gallery/html/im0565.html We've sketched stellar evolution. All stars run out of fuel, and change their structure. Mass loss, at its peak when the star is physically largest and/or when the core is smallest and most luminous, plays an important role. We've mentioned that to some degree of approximation the core and the rest of the star can be considered as two separate objects. This is not entirely fair because for main sequence stars the mass of the rest of the star is what makes the core hot and is what contains the fusion. In later stages of stellar evolution we also have shell burning sources and matter joining the core, as well as mass loss. But it is the core that plays the important role in the final stages of evolution of stars. We can divide the stars into three types based on core mass: stars destined to become white dwarfs, stars destined to become neutron stars, and stars destined to become black holes (there are actually a couple of equally compelling classes, namely, stars destined to leave behind no remnants, and white dwarfs that end up exploding as supernovae). I. White dwarfs We can talk here about all stars that start out on the main sequence with masses less than 8 solar masses. Gravity and mass loss work so that the masses of the core are less than the Chandrasekhar mass of 1.4 solar masses, so these stars will end up as white dwarfs. The first question you might ask is "how do we know that this is true?" We've talked in class about being able to age-date star clusters by measuring the brightness and color of every star and then making an HR diagram of the cluster. Well, we can search for white dwarfs in star clusters of differing ages (masses of the most massive remaining main sequence stars). Because red-giant evolution is so fast relative to main-sequence evolution, the evolved stars we see in this clusters have, to a good approximation, the same mass as the most massive main sequence stars remaining in the cluster. So, if we see that a cluster with a main-sequence turnoff mass of 8 solar masses has white dwarfs in it, we know that there's been enough mass loss to turn an 8 solar mass star into a star with a core of less than 1.4 solar masses. We also have found many white dwarfs in binary star systems, so we've been able to use the laws of gravity to measure white dwarf masses, and the sizes of white dwarfs. There aren't any white dwarfs more massive than 1.4 solar masses; in fact, most white dwarfs cluster around 0.6 solar masses. Well, such 1.4 solar masses, or less, cores, will have burned hydrogen into helium, and will have turned helium into Carbon and Oxygen. So we predict that white dwarfs will have C-O cores held up by degeneracy pressure. White dwarfs are held up by degeneracy pressure, so if a white dwarf is left alone it will simply cool off and fade away, too faint to be straightforwardly detected. Later in these notes we'll talk about what happens when a white dwarf is able to accrete matter from another star. Theory and observation tell us that the more massive a white dwarf is, the smaller it is. This is because gravity does manage to squeeze electrons closer together as it squeezes harder (more mass). The electron degeneracy pressure resists mightily, but it doesn't resist infinitely well. So, in fact, the Chandrasekhar mass might be defined as the mass at which the radius of a white dwarf shrinks to ZERO. We defined it in class as that mass where the electrons are forced into the nuclei, making neutrons, and simultaneously losing the electron degeneracy which counteracted gravity. The typical white dwarf is about the size of the Earth. We don't really talk about a white dwarf TURNING INTO a neutron star by the addition of matter, but we just point out that a core more massive than 1.4 solar masses cannot use electron degeneracy to hold itself up against gravity. It collapses to a smaller object. more like the size of Tucson, that supports itself against gravity by neutron degeneracy pressure. We talked about planetary nebulae in previous sets of these notes. You can think of a star as making two interesting objects simultaneously: a white dwarf in the core, very hot and luminous; and a shell of gas from the snowplow effect of mass loss. The ultraviolet photons from the white dwarf are absorbed by the atoms in this shell and reradiated, thus allowing us to see this planetary nebula. Now, the planetary is still expanding, so it eventually merges with the interstellar medium. But even if it were not expanding it would eventually fade out of sight as the central white dwarf cooled off. II. White dwarf binaries and "novae" Every once in a while a star in the night sky suddenly brightens by a huge factor, perhaps as much as a million. If the star were too faint to be seen by the naked eye, and now has brightened to naked-eye visibility, it would have been called a NOVA (plural "novae") by ancient skywatchers. Literally it would have seemed to be a new star! But in fact, novae are part of the endpoints of stellar evolution, not "new". Binary stars come in many flavors. Some pairs of stars are so far apart that they do not affect the evolution of each other. Aside from perhaps seeing two stars in your sky, you wouldn't have a lot to fear if you were on a planet in this binary system. But some stars form close enough together that the evolution of one star affects the evolution of the other. If the pair of stars already contains a white dwarf, then high-energy effects, and perhaps even explosions, can happen. Let's imagine a hydrogen atom in the envelope of an atmosphere of a normal main sequence star or red giant. This normal star is orbiting with a white dwarf. Remember that gravity works such that you can consider all of the mass as being a point in the center of the star. As an example, consider the Earth, 4000 miles in radius. Your weight, which is the force of the Earth's gravity on you, is the mass of the Earth times the mass of you divided by the distance from you to the center of the earth squared (this is just Newton's Law of Gravity). So, thinking about this hydrogen atom, the farther it gets from the center of "its star" the less held on by gravity it is. Well, the white dwarf also has gravity. There must be a point where this atom feels the gravity of the white dwarf as much as it feels the gravity of its own star. This place is called the Roche surface. So, by stellar evolution, one star can fill its Roche surface and matter can stream onto the other star. Well, it's hard to hit a moving target from a moving rifle range, so the matter ends up making a disk around the white dwarf. Particles in the disk interact and matter eventually falls onto the surface of the white dwarf. This matter gets heated up and eventually fuses (it's hydrogen!). Because it's sitting on a degenerate object, which has lost control over fusion, the fusion of this new material happens quickly. So this is an explosion of some sort, and makes enormous amounts of energy, brightening the system enormously. But we didn't blow up the white dwarf! So matter continues to fall on the white dwarf, and decades or centuries later the explosion happens again! We have seen and studied many such objects. This model is confirmed by observation (and by many details we're not discussing here). We'll come back to a similar model for completely exploding stars later. Binary star evolution is exciting because of this interaction of one star with another. III. Pulsars and Neutron stars. YOU REALLY SHOULD READ JOCELYN BELL'S RECOLLECTIONS: http://www.bigear.org/vol1no1/burnell.htm In this section we'll describe the discovery of radio pulsars. We'll then ask if we can understand these objects... are they any objects we already know about or are they an entirely new type of object, AND HOW WOULD WE KNOW? We'll then talk about the until-then hypothetical object called a neutron star, and note that the theoretical and observational properties of neutron stars are the same. We'll eliminate white dwarfs as pulsars. First we have to talk about stars twinkling. If you go outside at night, you'll notice that on some nights the stars twinkle like crazy. Yuo might also notice that the planets aren't twinkling. Why is this? Think of the Earth's atmosphere as being a bunch of different layers of air, with blobs of air travelling through these layers. Each layer of air bends light a little bit differently, and each blob momentarily bends a small part of the light very differently. Or, imagine that you wear glasses but that a joker can somehow electronically change your prescription. He does that. Sometimes your glasses are stronger, sometimes they're weaker. You can easily imagine that an image will dance around in front of your eyes. The twinkling of starlight is the "dancing around" of starlight as it passes through the atmosphere. It does more than just dance around, it brightens and fades. (in fact it's easier to see the brightening and fading then to see the dancing). Well, twinkling works best for a point source of light. In an extended source, such as a planet (in other words, you can look through binoculars to see that a planet is NOT a point), some of the light from the planet is getting brighter while some is getting fainter while passing through the atmosphere. In other words, an extended source can be though of as a bunch of point sources. So the twinkling averages out and we see a steady source. So, in the late 1960s astronomers came up with a way to discover very distant radio sources (quasars) by the way the radio light twinkled as it passed through the interstellar medium. So in England an experiment was set up to find these distant, thus point source, fairly newly discovered sorts of objects. (we already knew quasars were far away) Jocelyn Bell was a grad student who was getting her doctorate by doing this experiment designed by her doctoral advisor. Like a good grad student she made many tests to ensure that the instrument was working right. She found the expected sorts of objects. But like any prepared scientist she noted a specific object in the data that behaved very differently. Its radio strngth (number of radio photons detected per second) seemed to change dramatically on timescales of a second or so. THIS MADE NO SENSE. So test #1 was to ensure that the instrument was really working properly and that there was no outside interference caused by cars or a factory or a police radio or something like that. She rapidly realized that it was moving in the sky daily just like a star. Well, celestial objects don't behave like this, right! Nothing pulsates or spins in one second. SO WAS IT A DETECTION OF A SIGNAL FROM AN EXTRATERRESTRIAL INTELLIGENCE? The discovery of a second and a third such object negated the "little green men" idea. So it was not bad equipment, not interference from man-made objects, it was definitely celestial, and it was not celestial but artificial. So, now an explanation of celestial origin is needed. Ideas about neutron stars had been around for tens of years, and some of the properties of such objects were predicted. Sure enough, neutron stars could fit the bill. So, the observation is that there are celestial radio sources that change their intensiy by large factors on timescales of 1/1000th to 1 or a few seconds. Apaprently a spinning neutron star can do this. But how? And how do we know a pulsar is a neutron star? IV. Neutron stars As always, before we can talk intelligently about an object, we have to lay out the physics. Above, we laid out the idea of twinkling and how it can only work for a point source. So we know pulsars are small enough (or far enough away) that they twinkle. But are they physically small, and how would we know? Well, eventually we'll say that we found binary star systems containing a pulsar, and sure enough they're tiny. Just right, in fact, to be a neutron star. But that comes later. So we have to discuss the idea that the brightening or fading of a celestial object is limited by its size, more specifically, by the communication time across that object. Ultimately we'll say that a pulsar has to be physically small because it changes its brightness so quickly. And when we realize that a pulsar is a rotating neutron star we'll rule out a rotating white dwarf because of the speed of the rotation. How does an object brighten? One thing it DOES NOT DO is for the entire object to agree that at a certain time every piece of the object will just get brighter. There has to be a communication time (often called the soundspeed, or the light crossing time, depending on the circumstances... but the idea is the same). So let's do the following thought experiment... We're in a dark football stadium. Everyone has an air horn. They're told to honk their horn for one second when they hear the sound from another horn. So down at the fifty yard line we have the ultimate honker, the person who'll start this process. Now you know that sound only travels at about 1000 feet per second. Even in a football stadium you've heard echos. So do you think that all 50,000 horns will sound simultaneously, or that the there will be a wave of honking as the sound gets to new people and they honk? Right, the honking won't happen all at once. In fact, by the time the outermost people honk, the innermost people will be partially done honking. So the sound intensifies gradually and falls off gradually. Now let's do the identical experiment with the identical number of people, only this time we'll make the "football stadium" the size of Tucson. Well, imaginging that Tucson is 10 miles in radius, that makes it about one sound minute in radius. So the outermost people won't know to honk till the innermost people were done honking for a minute! So this wave of honking will be less loud and can only go up and down in intensity on a longer timescale. So if an object is pulsating, it can only pulsate on a sound-crossing time, on a communicaiton time. So if something is pulsating really fast, it must be really small. What if it's not pulsating, but rotating? Well, if you spin a red giant really fast, it'll simply fall apart. It's like trying to hold on a really rapidly spinning merry go round. You can envision a merry go round spinning so fast that your muscles aren't strong enough to keep you conencted and you go flying off. We have to tell you one more set of facts before we can get back to neutron stars. If an object has any spin whatsoever, as you make it smaller it spins faster. You saw Jeremy demostrate this in class. You've seen figure skaters control their spin in this way. If an object has a magnetic field, as it collapses the field gets stronger. So a collapsed object should be rapidly spinning and should be incredibly strongly magnetized. It turns out that a rapidly spinning, highly magnetized neutron star can make pulses of light! Charged particles flow from the surface of the neutron star and spiral long the magnetic lines of force, giving off light. They give off most of their light along the north and south poles of the magnet. So you end up with twin beams of light, pulsed because of the spin. So if we happen to be in the line of sight of these beams of light, we see a pulsar. If we aren't correctly oriented, the pulsar is pretty much hidden from us, unless it's in a binary star system. Once we examine such objects in binaries, indeed it's shown that they're much smaller than white dwarfs. And in fact white dwarfs cannot spin faster than once per minute. So everything fits, pulsars are neutron stars. We've discovered and seen degenerate neutron matter. V. Black holes Jeremy is going to talk about black holes. Let me just say that there's an upper mass limit for neutron degeneracy to hold itself up against gravity, just as there is for electron degeneracy. VI. Supernovae We now want to talk about exploding entire stars. It turns out that there are two ways to do this. One way is through the gravitational collapse of massive stars, so we turn gravitational potential energy into the explosion. The other way is to blow up a white dwarf through explosive nuclear burning. ( A third way is to coalesce two white dwarfs). Along the way, perhaps we'll make a neutron star or a black hole, or perhaps we'll blow up the entire star leaving nothing behind. We'll continue this in the next set of notes. Ancient observers recorded what we now call supernovae as "novae", new stars. Once we realized that theses explosions were much much more powerful than ordinary novae, the term SUPERnovae was coined.